%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ALG162+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 16:39:14 EDT 2023

% Result   : Unsatisfiable 27.04s 4.38s
% Output   : Proof 160.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : ALG162+1 : TPTP v8.1.2. Released v2.7.0.
% 0.10/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n011.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon Aug 28 04:18:55 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.31/1.46  Prover 4: Preprocessing ...
% 4.31/1.46  Prover 1: Preprocessing ...
% 5.36/1.50  Prover 5: Preprocessing ...
% 5.36/1.50  Prover 6: Preprocessing ...
% 5.36/1.50  Prover 3: Preprocessing ...
% 5.36/1.50  Prover 2: Preprocessing ...
% 5.36/1.50  Prover 0: Preprocessing ...
% 8.93/2.01  Prover 3: Constructing countermodel ...
% 8.93/2.01  Prover 2: Constructing countermodel ...
% 8.93/2.01  Prover 0: Constructing countermodel ...
% 8.93/2.06  Prover 4: Constructing countermodel ...
% 9.74/2.07  Prover 6: Constructing countermodel ...
% 9.74/2.08  Prover 1: Constructing countermodel ...
% 11.90/2.37  Prover 5: Constructing countermodel ...
% 27.04/4.38  Prover 0: proved (3739ms)
% 27.04/4.38  
% 27.04/4.38  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.04/4.38  
% 27.04/4.38  Prover 2: stopped
% 27.04/4.38  Prover 3: stopped
% 27.04/4.38  Prover 6: stopped
% 27.04/4.38  Prover 5: stopped
% 27.04/4.38  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 27.04/4.38  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 27.04/4.38  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 27.04/4.38  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 27.04/4.38  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 29.75/4.71  Prover 13: Preprocessing ...
% 29.75/4.72  Prover 10: Preprocessing ...
% 29.75/4.72  Prover 7: Preprocessing ...
% 29.75/4.72  Prover 11: Preprocessing ...
% 29.75/4.73  Prover 8: Preprocessing ...
% 30.02/4.89  Prover 8: Constructing countermodel ...
% 31.70/4.98  Prover 7: Constructing countermodel ...
% 31.70/4.98  Prover 13: Constructing countermodel ...
% 32.19/5.04  Prover 10: Constructing countermodel ...
% 32.19/5.05  Prover 11: Constructing countermodel ...
% 67.78/9.69  Prover 13: stopped
% 67.78/9.70  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 68.96/9.81  Prover 16: Preprocessing ...
% 70.57/10.09  Prover 16: Constructing countermodel ...
% 111.90/15.49  Prover 16: stopped
% 111.90/15.50  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 113.34/15.58  Prover 19: Preprocessing ...
% 114.32/15.74  Prover 19: Constructing countermodel ...
% 116.69/15.99  Prover 1: stopped
% 141.53/19.26  Prover 19: stopped
% 142.74/19.42  Prover 7: Found proof (size 173220)
% 142.74/19.42  Prover 7: proved (14897ms)
% 142.74/19.43  Prover 8: stopped
% 142.74/19.43  Prover 11: stopped
% 142.74/19.43  Prover 4: stopped
% 142.74/19.43  Prover 10: stopped
% 142.74/19.43  
% 142.74/19.43  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 142.74/19.43  
% 145.21/20.19  % SZS output start Proof for theBenchmark
% 145.62/20.37  Assumptions after simplification:
% 145.62/20.37  ---------------------------------
% 145.62/20.37  
% 145.62/20.37    (ax1)
% 145.80/20.44    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 145.80/20.44    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 145.80/20.44      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 145.80/20.44      $i] :  ? [v14: $i] :  ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 145.80/20.44      op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 145.80/20.44      op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 145.80/20.44      op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 145.80/20.44      op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 145.80/20.44      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 145.80/20.44      $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 145.80/20.44        e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 145.80/20.44        v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 145.80/20.44        = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 145.80/20.44        v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 145.80/20.44        v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 145.80/20.44        v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 145.80/20.44      (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 145.80/20.44        = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 145.80/20.44        = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 145.80/20.44  
% 145.80/20.44    (ax10)
% 145.80/20.44    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 145.80/20.44    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e3) = v2 &
% 145.80/20.44          $i(v2)) | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1))))
% 145.80/20.44  
% 145.80/20.44    (ax11)
% 145.80/20.45    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 145.80/20.45    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e3) = v2 &
% 145.80/20.45          $i(v2)) | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1))))
% 145.80/20.45  
% 145.80/20.45    (ax12)
% 145.80/20.45    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 145.80/20.45    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e0) = v2 &
% 145.80/20.45          $i(v2)) | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1))))
% 145.80/20.45  
% 145.80/20.45    (ax13)
% 145.80/20.46    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 145.80/20.46    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e0) = v2 &
% 145.80/20.46          $i(v2)) | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1))))
% 145.80/20.46  
% 145.80/20.46    (ax14)
% 145.80/20.46    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 145.80/20.46    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e2) = v2 &
% 145.80/20.46          $i(v2)) | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1))))
% 145.80/20.46  
% 145.80/20.46    (ax15)
% 145.80/20.46    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 145.80/20.46    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e2) = v2 &
% 145.80/20.46          $i(v2)) | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1))))
% 145.80/20.46  
% 145.80/20.46    (ax16)
% 145.80/20.46    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 145.80/20.46    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e3) = v2 &
% 145.80/20.46          $i(v2)) | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1))))
% 145.80/20.46  
% 145.80/20.46    (ax17)
% 145.80/20.47    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 145.80/20.47    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e3) = v2 &
% 145.80/20.47          $i(v2)) | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1))))
% 145.80/20.47  
% 145.80/20.47    (ax18)
% 145.80/20.47    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 145.80/20.47    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e0) = v2 &
% 145.80/20.47          $i(v2)) | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1))))
% 145.80/20.47  
% 145.80/20.47    (ax19)
% 145.80/20.47    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 145.80/20.47    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e0) = v2 &
% 145.80/20.47          $i(v2)) | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1))))
% 145.80/20.47  
% 145.80/20.47    (ax2)
% 146.16/20.51    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 146.16/20.51    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 146.16/20.51      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 146.16/20.51      $i] :  ? [v14: $i] :  ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 =
% 146.16/20.51          e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3,
% 146.16/20.51            e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 146.16/20.51          e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15
% 146.16/20.51          = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 &
% 146.16/20.51          op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3,
% 146.16/20.51            e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2)
% 146.16/20.51        | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1
% 146.16/20.51          & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3,
% 146.16/20.51            e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) =
% 146.16/20.51          e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15
% 146.16/20.51          = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 146.16/20.51          op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3,
% 146.16/20.51            e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0)
% 146.16/20.51        | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3
% 146.16/20.51          & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2)
% 146.16/20.51          = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 146.16/20.51        (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 146.16/20.51          op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2)
% 146.16/20.51          = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) |
% 146.16/20.51        (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 &
% 146.16/20.51          op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2,
% 146.16/20.51            e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) =
% 146.16/20.51          e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 146.16/20.51        (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 146.16/20.51          op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1)
% 146.16/20.51          = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) |
% 146.16/20.51        (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 &
% 146.16/20.51          op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2,
% 146.16/20.51            e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3))
% 146.16/20.51      & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 146.16/20.51          op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3,
% 146.16/20.51            e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1)
% 146.16/20.51        | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0
% 146.16/20.51          & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1)
% 146.16/20.51          = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) |
% 146.16/20.51        (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 146.16/20.51          op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) =
% 146.16/20.51          e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8
% 146.16/20.51          = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 &
% 146.16/20.51          op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2)
% 146.16/20.51          = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) &
% 146.16/20.51      ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 146.16/20.51          op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0)
% 146.16/20.51          = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0
% 146.16/20.51          = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 &
% 146.16/20.51          op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) =
% 146.16/20.51          e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1
% 146.16/20.51          = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 146.16/20.51          op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) =
% 146.16/20.51          e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2
% 146.16/20.51          = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 &
% 146.16/20.51          op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3,
% 146.16/20.51                e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) =
% 146.16/20.51              e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) |
% 146.16/20.51            (v1 = e0 & op(e0, e1) = e0)))))
% 146.16/20.51  
% 146.16/20.52    (ax20)
% 146.16/20.52    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.52    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e1) = v2 &
% 146.16/20.52          $i(v2)) | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1))))
% 146.16/20.52  
% 146.16/20.52    (ax21)
% 146.16/20.52    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.52    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e1) = v2 &
% 146.16/20.52          $i(v2)) | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1))))
% 146.16/20.52  
% 146.16/20.52    (ax22)
% 146.16/20.52    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.52    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e3) = v2 &
% 146.16/20.52          $i(v2)) | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1))))
% 146.16/20.52  
% 146.16/20.52    (ax23)
% 146.16/20.52    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.52    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e3) = v2 &
% 146.16/20.52          $i(v2)) | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1))))
% 146.16/20.52  
% 146.16/20.52    (ax24)
% 146.16/20.52    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.52    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e0) = v2 &
% 146.16/20.52          $i(v2)) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1))))
% 146.16/20.52  
% 146.16/20.52    (ax25)
% 146.16/20.52    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.52    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e0) = v2 &
% 146.16/20.52          $i(v2)) | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1))))
% 146.16/20.52  
% 146.16/20.52    (ax26)
% 146.16/20.53    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.53    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e1) = v2 &
% 146.16/20.53          $i(v2)) | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1))))
% 146.16/20.53  
% 146.16/20.53    (ax27)
% 146.16/20.53    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.53    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e1) = v2 &
% 146.16/20.53          $i(v2)) | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1))))
% 146.16/20.53  
% 146.16/20.53    (ax28)
% 146.16/20.53    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.53    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e2) = v2 &
% 146.16/20.53          $i(v2)) | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1))))
% 146.16/20.53  
% 146.16/20.53    (ax29)
% 146.16/20.53    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.53    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e2) = v2 &
% 146.16/20.53          $i(v2)) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1))))
% 146.16/20.53  
% 146.16/20.53    (ax3)
% 146.16/20.53    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 146.16/20.53    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 146.16/20.53      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 146.16/20.53      $i] :  ? [v14: $i] :  ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~
% 146.16/20.54      (v15 = v12) &  ~ (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 =
% 146.16/20.54        v13) &  ~ (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) & 
% 146.16/20.54      ~ (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12 =
% 146.16/20.54        v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 = v9) &  ~
% 146.16/20.54      (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9) &  ~ (v10 = v8) &
% 146.16/20.54       ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~ (v9 = v5) &  ~ (v9 = v1) &
% 146.16/20.54       ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6) &  ~ (v7 = v5) &  ~ (v7 = v4) & 
% 146.16/20.54      ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6 = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~
% 146.16/20.54      (v5 = v1) &  ~ (v4 = v0) &  ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~
% 146.16/20.54      (v2 = v1) &  ~ (v2 = v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 146.16/20.54      v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 146.16/20.54      v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 146.16/20.54      & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 146.16/20.54      op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 146.16/20.54      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 146.16/20.54      $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 146.16/20.54  
% 146.16/20.54    (ax4)
% 146.16/20.54     ~ (e3 = e2) &  ~ (e3 = e1) &  ~ (e3 = e0) &  ~ (e2 = e1) &  ~ (e2 = e0) &  ~
% 146.16/20.54    (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 146.16/20.54  
% 146.16/20.54    (ax5)
% 146.16/20.56    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 146.16/20.56    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 146.16/20.56      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 146.16/20.56      $i] :  ? [v14: $i] :  ? [v15: $i] : (((v15 = e2 & v14 = e3 & v5 = e2 &  ~
% 146.16/20.56          (v3 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 146.16/20.56            e2) = v3 & $i(v3)) | (v15 = e2 & v14 = e3 & v3 = e3 &  ~ (v5 = e2) &
% 146.16/20.56          op(e3, e3) = v5 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 146.16/20.56          $i(v5)) | (v15 = e2 & v12 = e1 & v1 = e2 &  ~ (v3 = e3) & op(e2, e3) =
% 146.16/20.56          e2 & op(e2, e2) = v3 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(v3)) |
% 146.16/20.56        (v15 = e2 & v11 = e3 & v3 = e3 &  ~ (v5 = e1) & op(e3, e3) = v5 & op(e3,
% 146.16/20.56            e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(v5)) | (v15 = e2 &
% 146.16/20.56          v8 = e0 & v0 = e2 &  ~ (v3 = e3) & op(e2, e3) = e2 & op(e2, e2) = v3 &
% 146.16/20.56          op(e0, e2) = e0 & op(e0, e0) = e2 & $i(v3)) | (v15 = e2 & v6 = e3 & v3 =
% 146.16/20.56          e3 &  ~ (v5 = e0) & op(e3, e3) = v5 & op(e3, e0) = e3 & op(e2, e3) = e2
% 146.16/20.56          & op(e2, e2) = e3 & $i(v5)) | (v15 = e2 & v3 = e2 &  ~ (e3 = e2) &
% 146.16/20.56          op(e2, e3) = e2 & op(e2, e2) = e2) | (v14 = e3 & v13 = e1 & v1 = e3 &  ~
% 146.16/20.56          (v5 = e2) & op(e3, e3) = v5 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 146.16/20.56            e1) = e3 & $i(v5)) | (v14 = e3 & v10 = e2 & v5 = e2 &  ~ (v3 = e1) &
% 146.16/20.56          op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = v3 & op(e2, e1) = e2 &
% 146.16/20.56          $i(v3)) | (v14 = e3 & v9 = e0 & v0 = e3 &  ~ (v5 = e2) & op(e3, e3) = v5
% 146.16/20.56          & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(v5)) | (v14 =
% 146.16/20.56          e3 & v5 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) | (v14
% 146.16/20.56          = e3 & v5 = e2 & v4 = e2 &  ~ (v3 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 146.16/20.56          e3 & op(e2, e2) = v3 & op(e2, e0) = e2 & $i(v3)) | (v13 = e1 & v11 = e3
% 146.16/20.56          & v5 = e1 &  ~ (v1 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 146.16/20.56            e3) = e1 & op(e1, e1) = v1 & $i(v1)) | (v13 = e1 & v11 = e3 & v1 = e3
% 146.16/20.56          &  ~ (v5 = e1) & op(e3, e3) = v5 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 146.16/20.56          op(e1, e1) = e3 & $i(v5)) | (v13 = e1 & v10 = e2 & v3 = e1 &  ~ (v1 =
% 146.16/20.56            e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1)
% 146.16/20.56          = v1 & $i(v1)) | (v13 = e1 & v7 = e0 & v0 = e1 &  ~ (v1 = e3) & op(e1,
% 146.16/20.56            e3) = e1 & op(e1, e1) = v1 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 146.16/20.56          $i(v1)) | (v13 = e1 & v6 = e3 & v1 = e3 &  ~ (v5 = e0) & op(e3, e3) = v5
% 146.16/20.56          & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(v5)) | (v13 =
% 146.16/20.56          e1 & v1 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1) | (v12
% 146.16/20.56          = e1 & v11 = e3 & v5 = e1 &  ~ (v1 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 146.16/20.56          = e3 & op(e1, e2) = e1 & op(e1, e1) = v1 & $i(v1)) | (v12 = e1 & v10 =
% 146.16/20.56          e2 & v3 = e1 &  ~ (v1 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 146.16/20.56            e2) = e1 & op(e1, e1) = v1 & $i(v1)) | (v12 = e1 & v10 = e2 & v1 = e2
% 146.16/20.56          &  ~ (v3 = e1) & op(e2, e2) = v3 & op(e2, e1) = e2 & op(e1, e2) = e1 &
% 146.16/20.56          op(e1, e1) = e2 & $i(v3)) | (v12 = e1 & v7 = e0 & v0 = e1 &  ~ (v1 = e2)
% 146.16/20.56          & op(e1, e2) = e1 & op(e1, e1) = v1 & op(e0, e1) = e0 & op(e0, e0) = e1
% 146.16/20.56          & $i(v1)) | (v12 = e1 & v4 = e2 & v1 = e2 &  ~ (v3 = e0) & op(e2, e2) =
% 146.16/20.56          v3 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(v3)) |
% 146.16/20.56        (v12 = e1 & v1 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 146.16/20.56        (v11 = e3 & v9 = e0 & v0 = e3 &  ~ (v5 = e1) & op(e3, e3) = v5 & op(e3,
% 146.16/20.56            e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(v5)) | (v11 = e3 &
% 146.16/20.56          v5 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (v11 = e3
% 146.16/20.56          & v5 = e1 & v2 = e1 &  ~ (v1 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 146.16/20.56          op(e1, e1) = v1 & op(e1, e0) = e1 & $i(v1)) | (v10 = e2 & v8 = e0 & v0 =
% 146.16/20.56          e2 &  ~ (v3 = e1) & op(e2, e2) = v3 & op(e2, e1) = e2 & op(e0, e2) = e0
% 146.16/20.56          & op(e0, e0) = e2 & $i(v3)) | (v10 = e2 & v3 = e2 &  ~ (e2 = e1) &
% 146.16/20.56          op(e2, e2) = e2 & op(e2, e1) = e2) | (v10 = e2 & v3 = e1 & v2 = e1 &  ~
% 146.16/20.56          (v1 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = v1 & op(e1,
% 146.16/20.56            e0) = e1 & $i(v1)) | (v9 = e0 & v6 = e3 & v0 = e3 &  ~ (v5 = e0) &
% 146.16/20.56          op(e3, e3) = v5 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 146.16/20.56          $i(v5)) | (v8 = e0 & v4 = e2 & v0 = e2 &  ~ (v3 = e0) & op(e2, e2) = v3
% 146.16/20.56          & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(v3)) | (v6 =
% 146.16/20.56          e3 & v5 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (v4 =
% 146.16/20.56          e2 & v3 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) | (v2 =
% 146.16/20.56          e1 & v1 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 146.16/20.56        (op(e0, e0) = v0 & $i(v0) & ((v9 = e0 & v6 = e3 & v5 = e0 &  ~ (v0 = e3) &
% 146.16/20.56              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (v9 = e0 & v4
% 146.16/20.56              = e2 & v3 = e0 &  ~ (v0 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 146.16/20.56              op(e0, e3) = e0) | (v9 = e0 & v2 = e1 & v1 = e0 &  ~ (v0 = e3) &
% 146.16/20.56              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (v9 = e0 & v0
% 146.16/20.56              = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (v8 = e0 & v6 = e3 & v5 =
% 146.16/20.56              e0 &  ~ (v0 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 146.16/20.56              e0) | (v8 = e0 & v4 = e2 & v3 = e0 &  ~ (v0 = e2) & op(e2, e2) = e0
% 146.16/20.56              & op(e2, e0) = e2 & op(e0, e2) = e0) | (v8 = e0 & v2 = e1 & v1 = e0
% 146.16/20.56              &  ~ (v0 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 146.16/20.56              e0) | (v8 = e0 & v0 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (v7 =
% 146.16/20.56              e0 & v6 = e3 & v5 = e0 &  ~ (v0 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 146.16/20.56              = e3 & op(e0, e1) = e0) | (v7 = e0 & v4 = e2 & v3 = e0 &  ~ (v0 =
% 146.16/20.56                e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (v7 =
% 146.16/20.56              e0 & v2 = e1 & v1 = e0 &  ~ (v0 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 146.16/20.56              = e1 & op(e0, e1) = e0) | (v7 = e0 & v2 = e1 & v0 = e1 &  ~ (v1 =
% 146.16/20.56                e0) & op(e1, e1) = v1 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 146.16/20.56              $i(v1)) | (v7 = e0 & v0 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))) &
% 146.16/20.56      ((v5 = e3 & op(e3, e3) = e3 & ((v3 = e3 & op(e2, e2) = e3) | ( ~ (v15 = e2)
% 146.16/20.56              & op(e2, e3) = v15 & $i(v15))) & ((v1 = e3 & op(e1, e1) = e3) | ( ~
% 146.16/20.56              (v13 = e1) & op(e1, e3) = v13 & $i(v13))) & ((v0 = e3 & op(e0, e0) =
% 146.16/20.56              e3) | ( ~ (v9 = e0) & op(e0, e3) = v9 & $i(v9)))) | (v3 = e2 &
% 146.16/20.56          op(e2, e2) = e2 & ((v5 = e2 & op(e3, e3) = e2) | ( ~ (v14 = e3) & op(e3,
% 146.16/20.56                e2) = v14 & $i(v14))) & ((v1 = e2 & op(e1, e1) = e2) | ( ~ (v12 =
% 146.16/20.56                e1) & op(e1, e2) = v12 & $i(v12))) & ((v0 = e2 & op(e0, e0) = e2)
% 146.16/20.56            | ( ~ (v8 = e0) & op(e0, e2) = v8 & $i(v8)))) | (v1 = e1 & op(e1, e1)
% 146.16/20.56          = e1 & ((v5 = e1 & op(e3, e3) = e1) | ( ~ (v11 = e3) & op(e3, e1) = v11
% 146.16/20.56              & $i(v11))) & ((v3 = e1 & op(e2, e2) = e1) | ( ~ (v10 = e2) & op(e2,
% 146.16/20.56                e1) = v10 & $i(v10))) & ((v0 = e1 & op(e0, e0) = e1) | ( ~ (v7 =
% 146.16/20.56                e0) & op(e0, e1) = v7 & $i(v7)))) | (v0 = e0 & op(e0, e0) = e0 &
% 146.16/20.56          ((v5 = e0 & op(e3, e3) = e0) | ( ~ (v6 = e3) & op(e3, e0) = v6 &
% 146.16/20.56              $i(v6))) & ((v3 = e0 & op(e2, e2) = e0) | ( ~ (v4 = e2) & op(e2, e0)
% 146.16/20.56              = v4 & $i(v4))) & ((v1 = e0 & op(e1, e1) = e0) | ( ~ (v2 = e1) &
% 146.16/20.56              op(e1, e0) = v2 & $i(v2))))))
% 146.16/20.56  
% 146.16/20.56    (ax6)
% 146.16/20.57    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.57    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e1) = v2 &
% 146.16/20.57          $i(v2)) | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1))))
% 146.16/20.57  
% 146.16/20.57    (ax7)
% 146.16/20.57    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.57    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e1) = v2 &
% 146.16/20.57          $i(v2)) | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1))))
% 146.16/20.57  
% 146.16/20.57    (ax8)
% 146.16/20.57    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.57    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e2) = v2 &
% 146.16/20.57          $i(v2)) | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1))))
% 146.16/20.57  
% 146.16/20.57    (ax9)
% 146.16/20.57    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 146.16/20.57    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e2) = v2 &
% 146.16/20.57          $i(v2)) | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1))))
% 146.16/20.57  
% 146.16/20.57    (function-axioms)
% 146.16/20.57     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (op(v3,
% 146.16/20.57          v2) = v1) |  ~ (op(v3, v2) = v0))
% 146.16/20.57  
% 146.16/20.57  Those formulas are unsatisfiable:
% 146.16/20.57  ---------------------------------
% 146.16/20.57  
% 146.16/20.57  Begin of proof
% 146.16/20.57  | 
% 146.16/20.57  | ALPHA: (ax1) implies:
% 146.58/20.58  |   (1)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 146.58/20.58  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 146.58/20.58  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 146.58/20.58  |         ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 146.58/20.58  |          & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 146.58/20.58  |          = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 146.58/20.58  |            e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 146.58/20.58  |          op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 146.58/20.58  |          $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 146.58/20.58  |          $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 146.58/20.58  |            = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 146.58/20.58  |            = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 146.58/20.58  |            v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 146.58/20.58  |            v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 146.58/20.58  |            | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 146.58/20.58  |            = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 146.58/20.58  |            e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 146.58/20.58  |          (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 146.58/20.58  |            e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 146.58/20.58  |            | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 146.58/20.58  |            = e0))
% 146.58/20.58  | 
% 146.58/20.58  | ALPHA: (ax2) implies:
% 146.60/20.60  |   (2)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 146.60/20.60  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 146.60/20.60  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 146.60/20.60  |         ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & op(e3, e2)
% 146.60/20.60  |              = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, e0) =
% 146.60/20.60  |              e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 146.60/20.60  |              e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3))
% 146.60/20.60  |          & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11
% 146.60/20.60  |              = e2 & op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 =
% 146.60/20.60  |              e2 & op(e3, e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 &
% 146.60/20.60  |              op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 &
% 146.60/20.60  |              op(e3, e3) = e1) | (v14 = e1 & op(e3, e2) = e1) | (v11 = e1 &
% 146.60/20.60  |              op(e3, e1) = e1) | (v6 = e1 & op(e3, e0) = e1)) & ((v15 = e1 &
% 146.60/20.60  |              op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = e1) | (v9 = e1 &
% 146.60/20.60  |              op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 = e0 &
% 146.60/20.60  |              op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 146.60/20.60  |              op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 &
% 146.60/20.60  |              op(e3, e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 &
% 146.60/20.60  |              op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 &
% 146.60/20.60  |              op(e3, e2) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v8 = e3 &
% 146.60/20.60  |              op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v14 = e2 &
% 146.60/20.60  |              op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v8 = e2 &
% 146.60/20.60  |              op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 146.60/20.60  |              op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 &
% 146.60/20.60  |              op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 &
% 146.60/20.60  |              op(e3, e2) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 &
% 146.60/20.60  |              op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v13 = e3 &
% 146.60/20.60  |              op(e2, e3) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v10 = e3 &
% 146.60/20.60  |              op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = e3)) & ((v13 = e2 &
% 146.60/20.60  |              op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v10 = e2 &
% 146.60/20.60  |              op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 146.60/20.60  |              op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 &
% 146.60/20.60  |              op(e2, e1) = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 &
% 146.60/20.60  |              op(e2, e3) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 &
% 146.60/20.60  |              op(e2, e1) = e0) | (v5 = e0 & op(e2, e0) = e0)) & ((v11 = e3 &
% 146.60/20.60  |              op(e3, e1) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v7 = e3 &
% 146.60/20.60  |              op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v11 = e2 &
% 146.60/20.60  |              op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 146.60/20.60  |              op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 &
% 146.60/20.60  |              op(e3, e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 &
% 146.60/20.60  |              op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 &
% 146.60/20.60  |              op(e3, e1) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v7 = e0 &
% 146.60/20.60  |              op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v9 = e3 &
% 146.60/20.60  |              op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v7 = e3 &
% 146.60/20.60  |              op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 146.60/20.60  |              op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 &
% 146.60/20.60  |              op(e1, e1) = e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 &
% 146.60/20.60  |              op(e1, e3) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v7 = e1 &
% 146.60/20.60  |              op(e1, e1) = e1) | (v4 = e1 & op(e1, e0) = e1)) & ((v9 = e0 &
% 146.60/20.60  |              op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v7 = e0 &
% 146.60/20.60  |              op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v6 = e3 &
% 146.60/20.60  |              op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 146.60/20.60  |              op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 &
% 146.60/20.60  |              op(e3, e0) = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 &
% 146.60/20.60  |              op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v6 = e1 &
% 146.60/20.60  |              op(e3, e0) = e1) | (v5 = e1 & op(e2, e0) = e1) | (v4 = e1 &
% 146.60/20.60  |              op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v3 = e3 &
% 146.60/20.60  |              op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 &
% 146.60/20.60  |              op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 146.60/20.60  |              op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 &
% 146.60/20.60  |              op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 &
% 146.60/20.60  |              op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 &
% 146.60/20.60  |              op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 &
% 146.60/20.60  |              op(e0, e0) = e0) | (((v6 = e0 & op(e3, e0) = e0) | (v5 = e0 &
% 146.60/20.60  |                  op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v3 = e0 &
% 146.60/20.60  |                  op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 &
% 146.60/20.60  |                  op(e0, e1) = e0)))))
% 146.60/20.60  | 
% 146.60/20.60  | ALPHA: (ax3) implies:
% 146.69/20.60  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 146.69/20.60  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 146.69/20.60  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 146.69/20.60  |         ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~ (v15 = v12) &  ~
% 146.69/20.60  |          (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 = v13) &  ~
% 146.69/20.60  |          (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) &  ~
% 146.69/20.60  |          (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12
% 146.69/20.60  |            = v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 =
% 146.69/20.60  |            v9) &  ~ (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9)
% 146.69/20.60  |          &  ~ (v10 = v8) &  ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~
% 146.69/20.60  |          (v9 = v5) &  ~ (v9 = v1) &  ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6)
% 146.69/20.60  |          &  ~ (v7 = v5) &  ~ (v7 = v4) &  ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6
% 146.69/20.60  |            = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~ (v5 = v1) &  ~ (v4 = v0) &
% 146.69/20.60  |           ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~ (v2 = v1) &  ~ (v2 =
% 146.69/20.60  |            v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 146.69/20.60  |            e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 146.69/20.60  |          op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 146.69/20.60  |          v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 146.69/20.60  |            e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 146.69/20.60  |          $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 146.69/20.60  |          $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 146.69/20.60  | 
% 146.69/20.60  | ALPHA: (ax4) implies:
% 146.69/20.60  |   (4)   ~ (e1 = e0)
% 146.69/20.60  |   (5)   ~ (e2 = e0)
% 146.69/20.60  |   (6)   ~ (e2 = e1)
% 146.69/20.60  |   (7)   ~ (e3 = e0)
% 146.69/20.60  |   (8)   ~ (e3 = e1)
% 146.69/20.60  |   (9)   ~ (e3 = e2)
% 146.69/20.60  | 
% 146.69/20.60  | ALPHA: (ax5) implies:
% 146.77/20.62  |   (10)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 146.77/20.62  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] : 
% 146.77/20.62  |         ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14:
% 146.77/20.62  |           $i] :  ? [v15: $i] : (((v15 = e2 & v14 = e3 & v5 = e2 &  ~ (v3 = e3)
% 146.77/20.62  |               & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 146.77/20.62  |                 e2) = v3 & $i(v3)) | (v15 = e2 & v14 = e3 & v3 = e3 &  ~ (v5 =
% 146.77/20.62  |                 e2) & op(e3, e3) = v5 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 146.77/20.62  |               op(e2, e2) = e3 & $i(v5)) | (v15 = e2 & v12 = e1 & v1 = e2 &  ~
% 146.77/20.62  |               (v3 = e3) & op(e2, e3) = e2 & op(e2, e2) = v3 & op(e1, e2) = e1
% 146.77/20.62  |               & op(e1, e1) = e2 & $i(v3)) | (v15 = e2 & v11 = e3 & v3 = e3 & 
% 146.77/20.62  |               ~ (v5 = e1) & op(e3, e3) = v5 & op(e3, e1) = e3 & op(e2, e3) =
% 146.77/20.62  |               e2 & op(e2, e2) = e3 & $i(v5)) | (v15 = e2 & v8 = e0 & v0 = e2 &
% 146.77/20.62  |                ~ (v3 = e3) & op(e2, e3) = e2 & op(e2, e2) = v3 & op(e0, e2) =
% 146.77/20.62  |               e0 & op(e0, e0) = e2 & $i(v3)) | (v15 = e2 & v6 = e3 & v3 = e3 &
% 146.77/20.62  |                ~ (v5 = e0) & op(e3, e3) = v5 & op(e3, e0) = e3 & op(e2, e3) =
% 146.77/20.62  |               e2 & op(e2, e2) = e3 & $i(v5)) | (v15 = e2 & v3 = e2 &  ~ (e3 =
% 146.77/20.62  |                 e2) & op(e2, e3) = e2 & op(e2, e2) = e2) | (v14 = e3 & v13 =
% 146.77/20.62  |               e1 & v1 = e3 &  ~ (v5 = e2) & op(e3, e3) = v5 & op(e3, e2) = e3
% 146.77/20.62  |               & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(v5)) | (v14 = e3 & v10
% 146.77/20.62  |               = e2 & v5 = e2 &  ~ (v3 = e1) & op(e3, e3) = e2 & op(e3, e2) =
% 146.77/20.62  |               e3 & op(e2, e2) = v3 & op(e2, e1) = e2 & $i(v3)) | (v14 = e3 &
% 146.77/20.62  |               v9 = e0 & v0 = e3 &  ~ (v5 = e2) & op(e3, e3) = v5 & op(e3, e2)
% 146.77/20.62  |               = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(v5)) | (v14 = e3 &
% 146.77/20.62  |               v5 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 146.77/20.62  |             (v14 = e3 & v5 = e2 & v4 = e2 &  ~ (v3 = e0) & op(e3, e3) = e2 &
% 146.77/20.62  |               op(e3, e2) = e3 & op(e2, e2) = v3 & op(e2, e0) = e2 & $i(v3)) |
% 146.77/20.62  |             (v13 = e1 & v11 = e3 & v5 = e1 &  ~ (v1 = e3) & op(e3, e3) = e1 &
% 146.77/20.62  |               op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = v1 & $i(v1)) |
% 146.77/20.62  |             (v13 = e1 & v11 = e3 & v1 = e3 &  ~ (v5 = e1) & op(e3, e3) = v5 &
% 146.77/20.62  |               op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(v5)) |
% 146.77/20.62  |             (v13 = e1 & v10 = e2 & v3 = e1 &  ~ (v1 = e3) & op(e2, e2) = e1 &
% 146.77/20.62  |               op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) = v1 & $i(v1)) |
% 146.77/20.62  |             (v13 = e1 & v7 = e0 & v0 = e1 &  ~ (v1 = e3) & op(e1, e3) = e1 &
% 146.77/20.62  |               op(e1, e1) = v1 & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(v1)) |
% 146.77/20.62  |             (v13 = e1 & v6 = e3 & v1 = e3 &  ~ (v5 = e0) & op(e3, e3) = v5 &
% 146.77/20.62  |               op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(v5)) |
% 146.77/20.62  |             (v13 = e1 & v1 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1)
% 146.77/20.62  |               = e1) | (v12 = e1 & v11 = e3 & v5 = e1 &  ~ (v1 = e2) & op(e3,
% 146.77/20.62  |                 e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) = v1
% 146.77/20.62  |               & $i(v1)) | (v12 = e1 & v10 = e2 & v3 = e1 &  ~ (v1 = e2) &
% 146.77/20.62  |               op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 146.77/20.62  |               = v1 & $i(v1)) | (v12 = e1 & v10 = e2 & v1 = e2 &  ~ (v3 = e1) &
% 146.77/20.62  |               op(e2, e2) = v3 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 146.77/20.62  |               = e2 & $i(v3)) | (v12 = e1 & v7 = e0 & v0 = e1 &  ~ (v1 = e2) &
% 146.77/20.62  |               op(e1, e2) = e1 & op(e1, e1) = v1 & op(e0, e1) = e0 & op(e0, e0)
% 146.77/20.62  |               = e1 & $i(v1)) | (v12 = e1 & v4 = e2 & v1 = e2 &  ~ (v3 = e0) &
% 146.77/20.62  |               op(e2, e2) = v3 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 146.77/20.62  |               = e2 & $i(v3)) | (v12 = e1 & v1 = e1 &  ~ (e2 = e1) & op(e1, e2)
% 146.77/20.62  |               = e1 & op(e1, e1) = e1) | (v11 = e3 & v9 = e0 & v0 = e3 &  ~ (v5
% 146.77/20.62  |                 = e1) & op(e3, e3) = v5 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 146.77/20.62  |               op(e0, e0) = e3 & $i(v5)) | (v11 = e3 & v5 = e3 &  ~ (e3 = e1) &
% 146.77/20.62  |               op(e3, e3) = e3 & op(e3, e1) = e3) | (v11 = e3 & v5 = e1 & v2 =
% 146.77/20.62  |               e1 &  ~ (v1 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 146.77/20.62  |                 e1) = v1 & op(e1, e0) = e1 & $i(v1)) | (v10 = e2 & v8 = e0 &
% 146.77/20.62  |               v0 = e2 &  ~ (v3 = e1) & op(e2, e2) = v3 & op(e2, e1) = e2 &
% 146.77/20.62  |               op(e0, e2) = e0 & op(e0, e0) = e2 & $i(v3)) | (v10 = e2 & v3 =
% 146.77/20.62  |               e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) | (v10 =
% 146.77/20.62  |               e2 & v3 = e1 & v2 = e1 &  ~ (v1 = e0) & op(e2, e2) = e1 & op(e2,
% 146.77/20.62  |                 e1) = e2 & op(e1, e1) = v1 & op(e1, e0) = e1 & $i(v1)) | (v9 =
% 146.77/20.62  |               e0 & v6 = e3 & v0 = e3 &  ~ (v5 = e0) & op(e3, e3) = v5 & op(e3,
% 146.77/20.62  |                 e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(v5)) | (v8 =
% 146.77/20.62  |               e0 & v4 = e2 & v0 = e2 &  ~ (v3 = e0) & op(e2, e2) = v3 & op(e2,
% 146.77/20.62  |                 e0) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(v3)) | (v6 =
% 146.77/20.62  |               e3 & v5 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3)
% 146.77/20.62  |             | (v4 = e2 & v3 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0)
% 146.77/20.62  |               = e2) | (v2 = e1 & v1 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 146.77/20.62  |               op(e1, e0) = e1) | (op(e0, e0) = v0 & $i(v0) & ((v9 = e0 & v6 =
% 146.77/20.62  |                   e3 & v5 = e0 &  ~ (v0 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 146.77/20.62  |                   e3 & op(e0, e3) = e0) | (v9 = e0 & v4 = e2 & v3 = e0 &  ~
% 146.77/20.62  |                   (v0 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 146.77/20.62  |                   e0) | (v9 = e0 & v2 = e1 & v1 = e0 &  ~ (v0 = e3) & op(e1,
% 146.77/20.62  |                     e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (v9 = e0 &
% 146.77/20.62  |                   v0 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (v8 = e0 & v6 =
% 146.77/20.62  |                   e3 & v5 = e0 &  ~ (v0 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 146.77/20.62  |                   e3 & op(e0, e2) = e0) | (v8 = e0 & v4 = e2 & v3 = e0 &  ~
% 146.77/20.62  |                   (v0 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 146.77/20.62  |                   e0) | (v8 = e0 & v2 = e1 & v1 = e0 &  ~ (v0 = e2) & op(e1,
% 146.77/20.62  |                     e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (v8 = e0 &
% 146.77/20.62  |                   v0 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (v7 = e0 & v6 =
% 146.77/20.62  |                   e3 & v5 = e0 &  ~ (v0 = e1) & op(e3, e3) = e0 & op(e3, e0) =
% 146.77/20.62  |                   e3 & op(e0, e1) = e0) | (v7 = e0 & v4 = e2 & v3 = e0 &  ~
% 146.77/20.62  |                   (v0 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) =
% 146.77/20.62  |                   e0) | (v7 = e0 & v2 = e1 & v1 = e0 &  ~ (v0 = e1) & op(e1,
% 146.77/20.62  |                     e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (v7 = e0 &
% 146.77/20.62  |                   v2 = e1 & v0 = e1 &  ~ (v1 = e0) & op(e1, e1) = v1 & op(e1,
% 146.77/20.62  |                     e0) = e1 & op(e0, e1) = e0 & $i(v1)) | (v7 = e0 & v0 = e0
% 146.77/20.62  |                   &  ~ (e1 = e0) & op(e0, e1) = e0)))) & ((v5 = e3 & op(e3,
% 146.77/20.62  |                 e3) = e3 & ((v3 = e3 & op(e2, e2) = e3) | ( ~ (v15 = e2) &
% 146.77/20.62  |                   op(e2, e3) = v15 & $i(v15))) & ((v1 = e3 & op(e1, e1) = e3)
% 146.77/20.62  |                 | ( ~ (v13 = e1) & op(e1, e3) = v13 & $i(v13))) & ((v0 = e3 &
% 146.77/20.62  |                   op(e0, e0) = e3) | ( ~ (v9 = e0) & op(e0, e3) = v9 &
% 146.77/20.62  |                   $i(v9)))) | (v3 = e2 & op(e2, e2) = e2 & ((v5 = e2 & op(e3,
% 146.77/20.62  |                     e3) = e2) | ( ~ (v14 = e3) & op(e3, e2) = v14 & $i(v14)))
% 146.77/20.62  |               & ((v1 = e2 & op(e1, e1) = e2) | ( ~ (v12 = e1) & op(e1, e2) =
% 146.77/20.62  |                   v12 & $i(v12))) & ((v0 = e2 & op(e0, e0) = e2) | ( ~ (v8 =
% 146.77/20.62  |                     e0) & op(e0, e2) = v8 & $i(v8)))) | (v1 = e1 & op(e1, e1)
% 146.77/20.62  |               = e1 & ((v5 = e1 & op(e3, e3) = e1) | ( ~ (v11 = e3) & op(e3,
% 146.77/20.62  |                     e1) = v11 & $i(v11))) & ((v3 = e1 & op(e2, e2) = e1) | ( ~
% 146.77/20.62  |                   (v10 = e2) & op(e2, e1) = v10 & $i(v10))) & ((v0 = e1 &
% 146.77/20.62  |                   op(e0, e0) = e1) | ( ~ (v7 = e0) & op(e0, e1) = v7 &
% 146.77/20.62  |                   $i(v7)))) | (v0 = e0 & op(e0, e0) = e0 & ((v5 = e0 & op(e3,
% 146.77/20.62  |                     e3) = e0) | ( ~ (v6 = e3) & op(e3, e0) = v6 & $i(v6))) &
% 146.77/20.62  |               ((v3 = e0 & op(e2, e2) = e0) | ( ~ (v4 = e2) & op(e2, e0) = v4 &
% 146.77/20.62  |                   $i(v4))) & ((v1 = e0 & op(e1, e1) = e0) | ( ~ (v2 = e1) &
% 146.77/20.62  |                   op(e1, e0) = v2 & $i(v2))))))
% 146.77/20.62  | 
% 146.77/20.62  | ALPHA: (ax6) implies:
% 146.77/20.62  |   (11)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 146.77/20.62  |           ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e1) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.62  |                 = e0) & op(e2, e2) = v1 & $i(v1))))
% 146.77/20.62  | 
% 146.77/20.62  | ALPHA: (ax7) implies:
% 146.77/20.62  |   (12)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 146.77/20.62  |           ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e1) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.62  |                 = e0) & op(e3, e3) = v1 & $i(v1))))
% 146.77/20.62  | 
% 146.77/20.62  | ALPHA: (ax8) implies:
% 146.77/20.62  |   (13)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 146.77/20.62  |           ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e2) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.62  |                 = e0) & op(e1, e1) = v1 & $i(v1))))
% 146.77/20.62  | 
% 146.77/20.62  | ALPHA: (ax9) implies:
% 146.77/20.62  |   (14)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 146.77/20.62  |           ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e2) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.62  |                 = e0) & op(e3, e3) = v1 & $i(v1))))
% 146.77/20.62  | 
% 146.77/20.62  | ALPHA: (ax10) implies:
% 146.77/20.63  |   (15)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e3) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e0) & op(e1, e1) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax11) implies:
% 146.77/20.63  |   (16)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e3) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e0) & op(e2, e2) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax12) implies:
% 146.77/20.63  |   (17)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e0) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e1) & op(e2, e2) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax13) implies:
% 146.77/20.63  |   (18)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e0) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e1) & op(e3, e3) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax14) implies:
% 146.77/20.63  |   (19)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e2) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e1) & op(e0, e0) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax15) implies:
% 146.77/20.63  |   (20)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e2) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e1) & op(e3, e3) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax16) implies:
% 146.77/20.63  |   (21)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e3) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e1) & op(e0, e0) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax17) implies:
% 146.77/20.63  |   (22)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e3) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e1) & op(e2, e2) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax18) implies:
% 146.77/20.63  |   (23)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e0) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e2) & op(e1, e1) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax19) implies:
% 146.77/20.63  |   (24)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e0) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e2) & op(e3, e3) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax20) implies:
% 146.77/20.63  |   (25)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e1) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e2) & op(e0, e0) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax21) implies:
% 146.77/20.63  |   (26)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e1) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e2) & op(e3, e3) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax22) implies:
% 146.77/20.63  |   (27)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e3) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e2) & op(e0, e0) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax23) implies:
% 146.77/20.63  |   (28)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e3) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e2) & op(e1, e1) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax24) implies:
% 146.77/20.63  |   (29)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 146.77/20.63  |           ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e0) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.63  |                 = e3) & op(e1, e1) = v1 & $i(v1))))
% 146.77/20.63  | 
% 146.77/20.63  | ALPHA: (ax25) implies:
% 146.77/20.64  |   (30)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 146.77/20.64  |           ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e0) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.64  |                 = e3) & op(e2, e2) = v1 & $i(v1))))
% 146.77/20.64  | 
% 146.77/20.64  | ALPHA: (ax26) implies:
% 146.77/20.64  |   (31)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 146.77/20.64  |           ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e1) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.64  |                 = e3) & op(e0, e0) = v1 & $i(v1))))
% 146.77/20.64  | 
% 146.77/20.64  | ALPHA: (ax27) implies:
% 146.77/20.64  |   (32)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 146.77/20.64  |           ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e1) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.64  |                 = e3) & op(e2, e2) = v1 & $i(v1))))
% 146.77/20.64  | 
% 146.77/20.64  | ALPHA: (ax28) implies:
% 146.77/20.64  |   (33)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 146.77/20.64  |           ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e2) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.64  |                 = e3) & op(e0, e0) = v1 & $i(v1))))
% 146.77/20.64  | 
% 146.77/20.64  | ALPHA: (ax29) implies:
% 146.77/20.64  |   (34)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 146.77/20.64  |           ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e2) = v2 & $i(v2)) | ( ~ (v1
% 146.77/20.64  |                 = e3) & op(e1, e1) = v1 & $i(v1))))
% 146.77/20.64  | 
% 146.77/20.64  | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 146.77/20.64  |   (35)  op(e2, e2) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e3) | ( ~ (all_4_0
% 146.77/20.64  |               = e0) & op(e3, e2) = all_4_0 & $i(all_4_0)) | ( ~ (all_4_1 = e1)
% 146.77/20.64  |             & op(e3, e3) = all_4_1 & $i(all_4_1)))
% 146.77/20.64  | 
% 146.77/20.64  | ALPHA: (35) implies:
% 146.77/20.64  |   (36)  op(e2, e2) = all_4_2
% 146.77/20.64  |   (37)   ~ (all_4_2 = e3) | ( ~ (all_4_0 = e0) & op(e3, e2) = all_4_0 &
% 146.77/20.64  |           $i(all_4_0)) | ( ~ (all_4_1 = e1) & op(e3, e3) = all_4_1 &
% 146.77/20.64  |           $i(all_4_1))
% 146.77/20.64  | 
% 146.77/20.64  | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 146.77/20.64  |   (38)  op(e3, e3) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e0) | ( ~ (all_6_0
% 146.77/20.64  |               = e1) & op(e0, e3) = all_6_0 & $i(all_6_0)) | ( ~ (all_6_1 = e2)
% 146.77/20.64  |             & op(e0, e0) = all_6_1 & $i(all_6_1)))
% 146.77/20.64  | 
% 146.77/20.64  | ALPHA: (38) implies:
% 146.77/20.64  |   (39)  op(e3, e3) = all_6_2
% 146.77/20.64  |   (40)   ~ (all_6_2 = e0) | ( ~ (all_6_0 = e1) & op(e0, e3) = all_6_0 &
% 146.77/20.64  |           $i(all_6_0)) | ( ~ (all_6_1 = e2) & op(e0, e0) = all_6_1 &
% 146.77/20.64  |           $i(all_6_1))
% 146.77/20.64  | 
% 146.77/20.64  | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 146.77/20.64  |   (41)  op(e3, e3) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e0) | ( ~ (all_8_0
% 146.77/20.64  |               = e2) & op(e0, e3) = all_8_0 & $i(all_8_0)) | ( ~ (all_8_1 = e1)
% 146.77/20.64  |             & op(e0, e0) = all_8_1 & $i(all_8_1)))
% 146.77/20.64  | 
% 146.77/20.64  | ALPHA: (41) implies:
% 146.77/20.64  |   (42)  op(e3, e3) = all_8_2
% 146.77/20.64  |   (43)   ~ (all_8_2 = e0) | ( ~ (all_8_0 = e2) & op(e0, e3) = all_8_0 &
% 146.77/20.64  |           $i(all_8_0)) | ( ~ (all_8_1 = e1) & op(e0, e0) = all_8_1 &
% 146.77/20.64  |           $i(all_8_1))
% 146.77/20.64  | 
% 146.77/20.64  | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 146.77/20.64  |        gives:
% 146.77/20.64  |   (44)  op(e1, e1) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e2) | ( ~
% 146.77/20.64  |             (all_10_0 = e3) & op(e2, e1) = all_10_0 & $i(all_10_0)) | ( ~
% 146.77/20.64  |             (all_10_1 = e0) & op(e2, e2) = all_10_1 & $i(all_10_1)))
% 146.77/20.64  | 
% 146.77/20.64  | ALPHA: (44) implies:
% 146.77/20.64  |   (45)  op(e1, e1) = all_10_2
% 146.77/20.64  |   (46)   ~ (all_10_2 = e2) | ( ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 &
% 146.77/20.64  |           $i(all_10_0)) | ( ~ (all_10_1 = e0) & op(e2, e2) = all_10_1 &
% 146.77/20.64  |           $i(all_10_1))
% 146.77/20.64  | 
% 146.77/20.64  | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 146.77/20.64  |        gives:
% 146.77/20.64  |   (47)  op(e3, e3) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e2) | ( ~
% 146.77/20.64  |             (all_12_0 = e0) & op(e2, e3) = all_12_0 & $i(all_12_0)) | ( ~
% 146.77/20.64  |             (all_12_1 = e1) & op(e2, e2) = all_12_1 & $i(all_12_1)))
% 146.77/20.64  | 
% 146.77/20.64  | ALPHA: (47) implies:
% 146.77/20.64  |   (48)  op(e3, e3) = all_12_2
% 146.77/20.64  |   (49)   ~ (all_12_2 = e2) | ( ~ (all_12_0 = e0) & op(e2, e3) = all_12_0 &
% 146.77/20.64  |           $i(all_12_0)) | ( ~ (all_12_1 = e1) & op(e2, e2) = all_12_1 &
% 146.77/20.64  |           $i(all_12_1))
% 146.77/20.64  | 
% 146.77/20.64  | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 146.77/20.64  |        gives:
% 146.77/20.65  |   (50)  op(e0, e0) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e1) | ( ~
% 146.77/20.65  |             (all_14_0 = e2) & op(e1, e0) = all_14_0 & $i(all_14_0)) | ( ~
% 146.77/20.65  |             (all_14_1 = e3) & op(e1, e1) = all_14_1 & $i(all_14_1)))
% 146.77/20.65  | 
% 146.77/20.65  | ALPHA: (50) implies:
% 146.77/20.65  |   (51)  op(e0, e0) = all_14_2
% 146.77/20.65  |   (52)   ~ (all_14_2 = e1) | ( ~ (all_14_0 = e2) & op(e1, e0) = all_14_0 &
% 146.77/20.65  |           $i(all_14_0)) | ( ~ (all_14_1 = e3) & op(e1, e1) = all_14_1 &
% 146.77/20.65  |           $i(all_14_1))
% 146.77/20.65  | 
% 146.77/20.65  | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2
% 146.77/20.65  |        gives:
% 146.77/20.65  |   (53)  op(e0, e0) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e1) | ( ~
% 146.77/20.65  |             (all_16_0 = e3) & op(e1, e0) = all_16_0 & $i(all_16_0)) | ( ~
% 146.77/20.65  |             (all_16_1 = e2) & op(e1, e1) = all_16_1 & $i(all_16_1)))
% 146.77/20.65  | 
% 146.77/20.65  | ALPHA: (53) implies:
% 146.77/20.65  |   (54)  op(e0, e0) = all_16_2
% 146.77/20.65  |   (55)   ~ (all_16_2 = e1) | ( ~ (all_16_0 = e3) & op(e1, e0) = all_16_0 &
% 146.77/20.65  |           $i(all_16_0)) | ( ~ (all_16_1 = e2) & op(e1, e1) = all_16_1 &
% 146.77/20.65  |           $i(all_16_1))
% 146.77/20.65  | 
% 146.77/20.65  | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2
% 146.77/20.65  |        gives:
% 146.77/20.65  |   (56)  op(e0, e0) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e3) | ( ~
% 146.77/20.65  |             (all_18_0 = e1) & op(e3, e0) = all_18_0 & $i(all_18_0)) | ( ~
% 146.77/20.65  |             (all_18_1 = e2) & op(e3, e3) = all_18_1 & $i(all_18_1)))
% 146.77/20.65  | 
% 146.77/20.65  | ALPHA: (56) implies:
% 146.77/20.65  |   (57)  op(e0, e0) = all_18_2
% 146.77/20.65  |   (58)   ~ (all_18_2 = e3) | ( ~ (all_18_0 = e1) & op(e3, e0) = all_18_0 &
% 146.77/20.65  |           $i(all_18_0)) | ( ~ (all_18_1 = e2) & op(e3, e3) = all_18_1 &
% 146.77/20.65  |           $i(all_18_1))
% 146.77/20.65  | 
% 146.77/20.65  | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2
% 146.77/20.65  |        gives:
% 146.77/20.65  |   (59)  op(e1, e1) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e3) | ( ~
% 146.77/20.65  |             (all_20_0 = e0) & op(e3, e1) = all_20_0 & $i(all_20_0)) | ( ~
% 146.77/20.65  |             (all_20_1 = e2) & op(e3, e3) = all_20_1 & $i(all_20_1)))
% 146.77/20.65  | 
% 146.77/20.65  | ALPHA: (59) implies:
% 146.77/20.65  |   (60)  op(e1, e1) = all_20_2
% 146.77/20.65  |   (61)   ~ (all_20_2 = e3) | ( ~ (all_20_0 = e0) & op(e3, e1) = all_20_0 &
% 146.77/20.65  |           $i(all_20_0)) | ( ~ (all_20_1 = e2) & op(e3, e3) = all_20_1 &
% 146.77/20.65  |           $i(all_20_1))
% 146.77/20.65  | 
% 146.77/20.65  | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2
% 146.77/20.65  |        gives:
% 146.77/20.65  |   (62)  op(e1, e1) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e0) | ( ~
% 146.77/20.65  |             (all_22_0 = e2) & op(e0, e1) = all_22_0 & $i(all_22_0)) | ( ~
% 146.77/20.65  |             (all_22_1 = e3) & op(e0, e0) = all_22_1 & $i(all_22_1)))
% 146.77/20.65  | 
% 146.77/20.65  | ALPHA: (62) implies:
% 146.77/20.65  |   (63)  op(e1, e1) = all_22_2
% 146.77/20.65  |   (64)   ~ (all_22_2 = e0) | ( ~ (all_22_0 = e2) & op(e0, e1) = all_22_0 &
% 146.77/20.65  |           $i(all_22_0)) | ( ~ (all_22_1 = e3) & op(e0, e0) = all_22_1 &
% 146.77/20.65  |           $i(all_22_1))
% 146.77/20.65  | 
% 146.77/20.65  | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2
% 146.77/20.65  |        gives:
% 146.77/20.65  |   (65)  op(e2, e2) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e1) | ( ~
% 146.77/20.65  |             (all_24_0 = e3) & op(e1, e2) = all_24_0 & $i(all_24_0)) | ( ~
% 146.77/20.65  |             (all_24_1 = e0) & op(e1, e1) = all_24_1 & $i(all_24_1)))
% 146.77/20.65  | 
% 146.77/20.65  | ALPHA: (65) implies:
% 146.77/20.65  |   (66)  op(e2, e2) = all_24_2
% 146.77/20.65  |   (67)   ~ (all_24_2 = e1) | ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 &
% 146.77/20.65  |           $i(all_24_0)) | ( ~ (all_24_1 = e0) & op(e1, e1) = all_24_1 &
% 146.77/20.65  |           $i(all_24_1))
% 146.77/20.65  | 
% 146.77/20.65  | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2
% 146.77/20.65  |        gives:
% 146.77/20.66  |   (68)  op(e3, e3) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e1) | ( ~
% 146.77/20.66  |             (all_26_0 = e0) & op(e1, e3) = all_26_0 & $i(all_26_0)) | ( ~
% 146.77/20.66  |             (all_26_1 = e2) & op(e1, e1) = all_26_1 & $i(all_26_1)))
% 146.77/20.66  | 
% 146.77/20.66  | ALPHA: (68) implies:
% 146.77/20.66  |   (69)  op(e3, e3) = all_26_2
% 146.77/20.66  |   (70)   ~ (all_26_2 = e1) | ( ~ (all_26_0 = e0) & op(e1, e3) = all_26_0 &
% 146.77/20.66  |           $i(all_26_0)) | ( ~ (all_26_1 = e2) & op(e1, e1) = all_26_1 &
% 146.77/20.66  |           $i(all_26_1))
% 146.77/20.66  | 
% 146.77/20.66  | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2
% 146.77/20.66  |        gives:
% 146.77/20.66  |   (71)  op(e0, e0) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e2) | ( ~
% 146.77/20.66  |             (all_28_0 = e1) & op(e2, e0) = all_28_0 & $i(all_28_0)) | ( ~
% 146.77/20.66  |             (all_28_1 = e3) & op(e2, e2) = all_28_1 & $i(all_28_1)))
% 146.77/20.66  | 
% 146.77/20.66  | ALPHA: (71) implies:
% 146.77/20.66  |   (72)  op(e0, e0) = all_28_2
% 146.77/20.66  |   (73)   ~ (all_28_2 = e2) | ( ~ (all_28_0 = e1) & op(e2, e0) = all_28_0 &
% 146.77/20.66  |           $i(all_28_0)) | ( ~ (all_28_1 = e3) & op(e2, e2) = all_28_1 &
% 146.77/20.66  |           $i(all_28_1))
% 146.77/20.66  | 
% 146.77/20.66  | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2
% 146.77/20.66  |        gives:
% 146.77/20.66  |   (74)  op(e1, e1) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e3) | ( ~
% 146.77/20.66  |             (all_30_0 = e2) & op(e3, e1) = all_30_0 & $i(all_30_0)) | ( ~
% 146.77/20.66  |             (all_30_1 = e0) & op(e3, e3) = all_30_1 & $i(all_30_1)))
% 146.77/20.66  | 
% 146.77/20.66  | ALPHA: (74) implies:
% 146.77/20.66  |   (75)  op(e1, e1) = all_30_2
% 146.77/20.66  |   (76)   ~ (all_30_2 = e3) | ( ~ (all_30_0 = e2) & op(e3, e1) = all_30_0 &
% 146.77/20.66  |           $i(all_30_0)) | ( ~ (all_30_1 = e0) & op(e3, e3) = all_30_1 &
% 146.77/20.66  |           $i(all_30_1))
% 146.77/20.66  | 
% 146.77/20.66  | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2
% 146.77/20.66  |        gives:
% 146.77/20.66  |   (77)  op(e2, e2) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e0) | ( ~
% 146.77/20.66  |             (all_32_0 = e3) & op(e0, e2) = all_32_0 & $i(all_32_0)) | ( ~
% 146.77/20.66  |             (all_32_1 = e1) & op(e0, e0) = all_32_1 & $i(all_32_1)))
% 146.77/20.66  | 
% 146.77/20.66  | ALPHA: (77) implies:
% 146.77/20.66  |   (78)  op(e2, e2) = all_32_2
% 146.77/20.66  |   (79)   ~ (all_32_2 = e0) | ( ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 &
% 146.77/20.66  |           $i(all_32_0)) | ( ~ (all_32_1 = e1) & op(e0, e0) = all_32_1 &
% 146.77/20.66  |           $i(all_32_1))
% 146.77/20.66  | 
% 146.77/20.66  | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2
% 146.77/20.66  |        gives:
% 146.77/20.66  |   (80)  op(e1, e1) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e2) | ( ~
% 146.77/20.66  |             (all_34_0 = e0) & op(e2, e1) = all_34_0 & $i(all_34_0)) | ( ~
% 146.77/20.66  |             (all_34_1 = e3) & op(e2, e2) = all_34_1 & $i(all_34_1)))
% 146.77/20.66  | 
% 146.77/20.66  | ALPHA: (80) implies:
% 146.77/20.66  |   (81)  op(e1, e1) = all_34_2
% 146.77/20.66  |   (82)   ~ (all_34_2 = e2) | ( ~ (all_34_0 = e0) & op(e2, e1) = all_34_0 &
% 146.77/20.66  |           $i(all_34_0)) | ( ~ (all_34_1 = e3) & op(e2, e2) = all_34_1 &
% 146.77/20.66  |           $i(all_34_1))
% 146.77/20.66  | 
% 146.77/20.66  | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2
% 146.77/20.66  |        gives:
% 146.77/20.66  |   (83)  op(e2, e2) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e0) | ( ~
% 146.77/20.66  |             (all_36_0 = e1) & op(e0, e2) = all_36_0 & $i(all_36_0)) | ( ~
% 146.77/20.66  |             (all_36_1 = e3) & op(e0, e0) = all_36_1 & $i(all_36_1)))
% 146.77/20.66  | 
% 146.77/20.66  | ALPHA: (83) implies:
% 146.77/20.66  |   (84)  op(e2, e2) = all_36_2
% 146.77/20.66  |   (85)   ~ (all_36_2 = e0) | ( ~ (all_36_0 = e1) & op(e0, e2) = all_36_0 &
% 146.77/20.66  |           $i(all_36_0)) | ( ~ (all_36_1 = e3) & op(e0, e0) = all_36_1 &
% 146.77/20.66  |           $i(all_36_1))
% 146.77/20.66  | 
% 146.77/20.66  | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2
% 146.77/20.66  |        gives:
% 146.77/20.67  |   (86)  op(e1, e1) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e0) | ( ~
% 146.77/20.67  |             (all_38_0 = e3) & op(e0, e1) = all_38_0 & $i(all_38_0)) | ( ~
% 146.77/20.67  |             (all_38_1 = e2) & op(e0, e0) = all_38_1 & $i(all_38_1)))
% 146.77/20.67  | 
% 146.77/20.67  | ALPHA: (86) implies:
% 146.77/20.67  |   (87)  op(e1, e1) = all_38_2
% 146.77/20.67  |   (88)   ~ (all_38_2 = e0) | ( ~ (all_38_0 = e3) & op(e0, e1) = all_38_0 &
% 146.77/20.67  |           $i(all_38_0)) | ( ~ (all_38_1 = e2) & op(e0, e0) = all_38_1 &
% 146.77/20.67  |           $i(all_38_1))
% 146.77/20.67  | 
% 146.77/20.67  | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2
% 146.77/20.67  |        gives:
% 146.77/20.67  |   (89)  op(e2, e2) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e3) | ( ~
% 146.77/20.67  |             (all_40_0 = e1) & op(e3, e2) = all_40_0 & $i(all_40_0)) | ( ~
% 146.77/20.67  |             (all_40_1 = e0) & op(e3, e3) = all_40_1 & $i(all_40_1)))
% 146.77/20.67  | 
% 146.77/20.67  | ALPHA: (89) implies:
% 146.77/20.67  |   (90)  op(e2, e2) = all_40_2
% 146.77/20.67  |   (91)   ~ (all_40_2 = e3) | ( ~ (all_40_0 = e1) & op(e3, e2) = all_40_0 &
% 146.77/20.67  |           $i(all_40_0)) | ( ~ (all_40_1 = e0) & op(e3, e3) = all_40_1 &
% 146.77/20.67  |           $i(all_40_1))
% 146.77/20.67  | 
% 146.77/20.67  | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2
% 146.77/20.67  |        gives:
% 146.77/20.67  |   (92)  op(e3, e3) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e1) | ( ~
% 146.77/20.67  |             (all_42_0 = e2) & op(e1, e3) = all_42_0 & $i(all_42_0)) | ( ~
% 146.77/20.67  |             (all_42_1 = e0) & op(e1, e1) = all_42_1 & $i(all_42_1)))
% 146.77/20.67  | 
% 146.77/20.67  | ALPHA: (92) implies:
% 146.77/20.67  |   (93)  op(e3, e3) = all_42_2
% 146.77/20.67  |   (94)   ~ (all_42_2 = e1) | ( ~ (all_42_0 = e2) & op(e1, e3) = all_42_0 &
% 146.77/20.67  |           $i(all_42_0)) | ( ~ (all_42_1 = e0) & op(e1, e1) = all_42_1 &
% 146.77/20.67  |           $i(all_42_1))
% 146.77/20.67  | 
% 146.77/20.67  | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2
% 146.77/20.67  |        gives:
% 146.77/20.67  |   (95)  op(e2, e2) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e1) | ( ~
% 146.77/20.67  |             (all_44_0 = e0) & op(e1, e2) = all_44_0 & $i(all_44_0)) | ( ~
% 146.77/20.67  |             (all_44_1 = e3) & op(e1, e1) = all_44_1 & $i(all_44_1)))
% 146.77/20.67  | 
% 146.77/20.67  | ALPHA: (95) implies:
% 146.77/20.67  |   (96)  op(e2, e2) = all_44_2
% 146.77/20.67  |   (97)   ~ (all_44_2 = e1) | ( ~ (all_44_0 = e0) & op(e1, e2) = all_44_0 &
% 146.77/20.67  |           $i(all_44_0)) | ( ~ (all_44_1 = e3) & op(e1, e1) = all_44_1 &
% 146.77/20.67  |           $i(all_44_1))
% 146.77/20.67  | 
% 146.77/20.67  | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 146.77/20.67  |        gives:
% 146.77/20.67  |   (98)  op(e3, e3) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e2) | ( ~
% 146.77/20.67  |             (all_46_0 = e1) & op(e2, e3) = all_46_0 & $i(all_46_0)) | ( ~
% 146.77/20.67  |             (all_46_1 = e0) & op(e2, e2) = all_46_1 & $i(all_46_1)))
% 146.77/20.67  | 
% 146.77/20.67  | ALPHA: (98) implies:
% 146.77/20.67  |   (99)  op(e3, e3) = all_46_2
% 146.77/20.67  |   (100)   ~ (all_46_2 = e2) | ( ~ (all_46_0 = e1) & op(e2, e3) = all_46_0 &
% 146.77/20.67  |            $i(all_46_0)) | ( ~ (all_46_1 = e0) & op(e2, e2) = all_46_1 &
% 146.77/20.67  |            $i(all_46_1))
% 146.77/20.67  | 
% 146.77/20.67  | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2
% 146.77/20.67  |        gives:
% 146.77/20.67  |   (101)  op(e0, e0) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e3) | ( ~
% 146.77/20.67  |              (all_48_0 = e2) & op(e3, e0) = all_48_0 & $i(all_48_0)) | ( ~
% 146.77/20.67  |              (all_48_1 = e1) & op(e3, e3) = all_48_1 & $i(all_48_1)))
% 146.77/20.67  | 
% 146.77/20.67  | ALPHA: (101) implies:
% 146.77/20.67  |   (102)  op(e0, e0) = all_48_2
% 146.77/20.67  |   (103)   ~ (all_48_2 = e3) | ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 &
% 146.77/20.67  |            $i(all_48_0)) | ( ~ (all_48_1 = e1) & op(e3, e3) = all_48_1 &
% 146.77/20.67  |            $i(all_48_1))
% 146.77/20.67  | 
% 146.77/20.67  | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2
% 146.77/20.67  |        gives:
% 146.77/20.67  |   (104)  op(e0, e0) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e2) | ( ~
% 146.77/20.67  |              (all_50_0 = e3) & op(e2, e0) = all_50_0 & $i(all_50_0)) | ( ~
% 146.77/20.67  |              (all_50_1 = e1) & op(e2, e2) = all_50_1 & $i(all_50_1)))
% 146.77/20.67  | 
% 146.77/20.67  | ALPHA: (104) implies:
% 146.77/20.67  |   (105)  op(e0, e0) = all_50_2
% 146.77/20.67  |   (106)   ~ (all_50_2 = e2) | ( ~ (all_50_0 = e3) & op(e2, e0) = all_50_0 &
% 146.77/20.67  |            $i(all_50_0)) | ( ~ (all_50_1 = e1) & op(e2, e2) = all_50_1 &
% 146.77/20.67  |            $i(all_50_1))
% 146.77/20.67  | 
% 146.77/20.67  | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2,
% 146.77/20.67  |        all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 146.77/20.67  |        all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives:
% 146.77/20.67  |   (107)   ~ (all_52_0 = all_52_1) &  ~ (all_52_0 = all_52_2) &  ~ (all_52_0 =
% 146.77/20.67  |            all_52_3) &  ~ (all_52_0 = all_52_4) &  ~ (all_52_0 = all_52_8) & 
% 146.77/20.67  |          ~ (all_52_0 = all_52_12) &  ~ (all_52_1 = all_52_2) &  ~ (all_52_1 =
% 146.77/20.67  |            all_52_3) &  ~ (all_52_1 = all_52_5) &  ~ (all_52_1 = all_52_9) & 
% 146.77/20.67  |          ~ (all_52_1 = all_52_13) &  ~ (all_52_2 = all_52_3) &  ~ (all_52_2 =
% 146.77/20.67  |            all_52_6) &  ~ (all_52_2 = all_52_10) &  ~ (all_52_2 = all_52_14) &
% 146.77/20.67  |           ~ (all_52_3 = all_52_7) &  ~ (all_52_3 = all_52_11) &  ~ (all_52_3 =
% 146.77/20.67  |            all_52_15) &  ~ (all_52_4 = all_52_5) &  ~ (all_52_4 = all_52_6) & 
% 146.77/20.67  |          ~ (all_52_4 = all_52_7) &  ~ (all_52_4 = all_52_8) &  ~ (all_52_4 =
% 146.77/20.67  |            all_52_12) &  ~ (all_52_5 = all_52_6) &  ~ (all_52_5 = all_52_7) & 
% 146.77/20.67  |          ~ (all_52_5 = all_52_9) &  ~ (all_52_5 = all_52_13) &  ~ (all_52_6 =
% 146.77/20.67  |            all_52_7) &  ~ (all_52_6 = all_52_10) &  ~ (all_52_6 = all_52_14) &
% 146.77/20.67  |           ~ (all_52_7 = all_52_11) &  ~ (all_52_7 = all_52_15) &  ~ (all_52_8
% 146.77/20.67  |            = all_52_9) &  ~ (all_52_8 = all_52_10) &  ~ (all_52_8 = all_52_11)
% 146.77/20.67  |          &  ~ (all_52_8 = all_52_12) &  ~ (all_52_9 = all_52_10) &  ~
% 146.77/20.67  |          (all_52_9 = all_52_11) &  ~ (all_52_9 = all_52_13) &  ~ (all_52_10 =
% 146.77/20.67  |            all_52_11) &  ~ (all_52_10 = all_52_14) &  ~ (all_52_11 =
% 146.77/20.67  |            all_52_15) &  ~ (all_52_12 = all_52_13) &  ~ (all_52_12 =
% 146.77/20.67  |            all_52_14) &  ~ (all_52_12 = all_52_15) &  ~ (all_52_13 =
% 146.77/20.67  |            all_52_14) &  ~ (all_52_13 = all_52_15) &  ~ (all_52_14 =
% 146.77/20.67  |            all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3,
% 146.77/20.67  |            e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 &
% 146.77/20.67  |          op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) =
% 146.77/20.67  |          all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1,
% 146.77/20.67  |            e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 &
% 146.77/20.67  |          op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) =
% 146.77/20.67  |          all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3)
% 146.77/20.67  |          & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) &
% 146.77/20.67  |          $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) &
% 146.77/20.67  |          $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15)
% 146.77/20.67  | 
% 146.77/20.67  | ALPHA: (107) implies:
% 146.77/20.68  |   (108)   ~ (all_52_14 = all_52_15)
% 146.77/20.68  |   (109)   ~ (all_52_13 = all_52_15)
% 146.77/20.68  |   (110)   ~ (all_52_13 = all_52_14)
% 146.77/20.68  |   (111)   ~ (all_52_12 = all_52_15)
% 146.77/20.68  |   (112)   ~ (all_52_12 = all_52_14)
% 146.77/20.68  |   (113)   ~ (all_52_12 = all_52_13)
% 146.77/20.68  |   (114)   ~ (all_52_11 = all_52_15)
% 146.77/20.68  |   (115)   ~ (all_52_10 = all_52_14)
% 146.77/20.68  |   (116)   ~ (all_52_10 = all_52_11)
% 146.77/20.68  |   (117)   ~ (all_52_9 = all_52_13)
% 146.77/20.68  |   (118)   ~ (all_52_9 = all_52_11)
% 146.77/20.68  |   (119)   ~ (all_52_9 = all_52_10)
% 146.77/20.68  |   (120)   ~ (all_52_8 = all_52_12)
% 146.77/20.68  |   (121)   ~ (all_52_8 = all_52_11)
% 146.77/20.68  |   (122)   ~ (all_52_8 = all_52_10)
% 146.77/20.68  |   (123)   ~ (all_52_8 = all_52_9)
% 146.77/20.68  |   (124)   ~ (all_52_7 = all_52_15)
% 146.77/20.68  |   (125)   ~ (all_52_7 = all_52_11)
% 146.77/20.68  |   (126)   ~ (all_52_6 = all_52_14)
% 146.77/20.68  |   (127)   ~ (all_52_6 = all_52_10)
% 146.77/20.68  |   (128)   ~ (all_52_6 = all_52_7)
% 146.77/20.68  |   (129)   ~ (all_52_5 = all_52_13)
% 146.77/20.68  |   (130)   ~ (all_52_5 = all_52_9)
% 146.77/20.68  |   (131)   ~ (all_52_5 = all_52_7)
% 146.77/20.68  |   (132)   ~ (all_52_5 = all_52_6)
% 146.77/20.68  |   (133)   ~ (all_52_4 = all_52_12)
% 146.77/20.68  |   (134)   ~ (all_52_4 = all_52_8)
% 146.77/20.68  |   (135)   ~ (all_52_4 = all_52_7)
% 146.77/20.68  |   (136)   ~ (all_52_4 = all_52_6)
% 146.77/20.68  |   (137)   ~ (all_52_4 = all_52_5)
% 146.77/20.68  |   (138)   ~ (all_52_3 = all_52_15)
% 146.77/20.68  |   (139)   ~ (all_52_3 = all_52_11)
% 146.77/20.68  |   (140)   ~ (all_52_3 = all_52_7)
% 146.77/20.68  |   (141)   ~ (all_52_2 = all_52_14)
% 146.77/20.68  |   (142)   ~ (all_52_2 = all_52_10)
% 146.77/20.68  |   (143)   ~ (all_52_2 = all_52_6)
% 146.77/20.68  |   (144)   ~ (all_52_2 = all_52_3)
% 146.77/20.68  |   (145)   ~ (all_52_1 = all_52_13)
% 146.77/20.68  |   (146)   ~ (all_52_1 = all_52_9)
% 146.77/20.68  |   (147)   ~ (all_52_1 = all_52_5)
% 146.77/20.68  |   (148)   ~ (all_52_1 = all_52_3)
% 146.77/20.68  |   (149)   ~ (all_52_1 = all_52_2)
% 146.77/20.68  |   (150)   ~ (all_52_0 = all_52_12)
% 146.77/20.68  |   (151)   ~ (all_52_0 = all_52_8)
% 146.77/20.68  |   (152)   ~ (all_52_0 = all_52_4)
% 146.77/20.68  |   (153)   ~ (all_52_0 = all_52_3)
% 146.77/20.68  |   (154)   ~ (all_52_0 = all_52_2)
% 146.77/20.68  |   (155)   ~ (all_52_0 = all_52_1)
% 146.77/20.68  |   (156)  op(e0, e0) = all_52_15
% 146.77/20.68  |   (157)  op(e0, e1) = all_52_11
% 146.77/20.68  |   (158)  op(e0, e2) = all_52_7
% 146.77/20.68  |   (159)  op(e0, e3) = all_52_3
% 146.77/20.68  |   (160)  op(e1, e0) = all_52_14
% 146.77/20.68  |   (161)  op(e1, e1) = all_52_10
% 146.77/20.68  |   (162)  op(e1, e2) = all_52_6
% 146.77/20.68  |   (163)  op(e1, e3) = all_52_2
% 146.77/20.68  |   (164)  op(e2, e0) = all_52_13
% 146.77/20.68  |   (165)  op(e2, e1) = all_52_9
% 146.77/20.68  |   (166)  op(e2, e2) = all_52_5
% 146.77/20.68  |   (167)  op(e2, e3) = all_52_1
% 146.77/20.68  |   (168)  op(e3, e0) = all_52_12
% 146.77/20.68  |   (169)  op(e3, e1) = all_52_8
% 146.77/20.68  |   (170)  op(e3, e2) = all_52_4
% 146.77/20.68  |   (171)  op(e3, e3) = all_52_0
% 146.77/20.68  | 
% 146.77/20.68  | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2,
% 146.77/20.68  |        all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 146.77/20.68  |        all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 146.77/20.68  |   (172)  op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2
% 146.77/20.68  |          & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) =
% 146.77/20.68  |          all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3)
% 146.77/20.68  |          = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1,
% 146.77/20.68  |            e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 &
% 146.77/20.68  |          op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) &
% 146.77/20.68  |          $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) &
% 146.77/20.68  |          $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) &
% 146.77/20.68  |          $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) &
% 146.77/20.68  |          $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 |
% 146.77/20.68  |            all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 |
% 146.77/20.68  |            all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 |
% 146.77/20.68  |            all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 |
% 146.77/20.68  |            all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 |
% 146.77/20.68  |            all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 |
% 146.77/20.68  |            all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 |
% 146.77/20.68  |            all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 |
% 146.77/20.68  |            all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 |
% 146.77/20.68  |            all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 |
% 146.77/20.68  |            all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 |
% 146.77/20.68  |            all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3
% 146.77/20.68  |            | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 =
% 146.77/20.68  |            e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13
% 146.77/20.68  |            = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) &
% 146.77/20.68  |          (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) &
% 146.77/20.68  |          (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0)
% 146.77/20.68  | 
% 146.77/20.68  | ALPHA: (172) implies:
% 146.77/20.68  |   (173)  op(e0, e0) = all_54_15
% 146.77/20.68  |   (174)  op(e0, e1) = all_54_14
% 146.77/20.68  |   (175)  op(e0, e2) = all_54_13
% 146.77/20.68  |   (176)  op(e0, e3) = all_54_12
% 146.77/20.68  |   (177)  op(e1, e0) = all_54_11
% 146.77/20.68  |   (178)  op(e1, e1) = all_54_10
% 146.77/20.68  |   (179)  op(e1, e2) = all_54_9
% 146.77/20.68  |   (180)  op(e1, e3) = all_54_8
% 146.77/20.68  |   (181)  op(e2, e0) = all_54_7
% 146.77/20.68  |   (182)  op(e2, e1) = all_54_6
% 146.77/20.68  |   (183)  op(e2, e2) = all_54_5
% 146.77/20.69  |   (184)  op(e2, e3) = all_54_4
% 146.77/20.69  |   (185)  op(e3, e0) = all_54_3
% 146.77/20.69  |   (186)  op(e3, e1) = all_54_2
% 146.77/20.69  |   (187)  op(e3, e2) = all_54_1
% 146.77/20.69  |   (188)  op(e3, e3) = all_54_0
% 146.77/20.69  |   (189)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 146.77/20.69  |   (190)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 146.77/20.69  |   (191)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 146.77/20.69  |   (192)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 146.77/20.69  |   (193)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 146.77/20.69  |   (194)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 146.77/20.69  |   (195)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 146.77/20.69  |   (196)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 146.77/20.69  |   (197)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 146.77/20.69  |   (198)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 146.77/20.69  |   (199)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 146.77/20.69  |   (200)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 146.77/20.69  |   (201)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 146.77/20.69  |   (202)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 146.77/20.69  |   (203)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 146.77/20.69  |   (204)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 146.77/20.69  | 
% 146.77/20.69  | DELTA: instantiating (2) with fresh symbols all_56_0, all_56_1, all_56_2,
% 146.77/20.69  |        all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 146.77/20.69  |        all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives:
% 146.77/20.69  |   (205)  ((all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 146.77/20.69  |              e3) | (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3,
% 146.77/20.69  |                e0) = e3)) & ((all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 =
% 146.77/20.69  |              e3 & op(e2, e3) = e3) | (all_56_6 = e3 & op(e1, e3) = e3) |
% 146.77/20.69  |            (all_56_12 = e3 & op(e0, e3) = e3)) & ((all_56_0 = e2 & op(e3, e3)
% 146.77/20.69  |              = e2) | (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_4 = e2 &
% 146.77/20.69  |              op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)) &
% 146.77/20.69  |          ((all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 146.77/20.69  |              e2) | (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 146.77/20.69  |              op(e0, e3) = e2)) & ((all_56_0 = e1 & op(e3, e3) = e1) |
% 146.77/20.69  |            (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_4 = e1 & op(e3, e1) =
% 146.77/20.69  |              e1) | (all_56_9 = e1 & op(e3, e0) = e1)) & ((all_56_0 = e1 &
% 146.77/20.69  |              op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_6
% 146.77/20.69  |              = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)) &
% 146.77/20.69  |          ((all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 146.77/20.69  |              e0) | (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3,
% 146.77/20.69  |                e0) = e0)) & ((all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 =
% 146.77/20.69  |              e0 & op(e2, e3) = e0) | (all_56_6 = e0 & op(e1, e3) = e0) |
% 146.77/20.69  |            (all_56_12 = e0 & op(e0, e3) = e0)) & ((all_56_1 = e3 & op(e3, e2)
% 146.77/20.69  |              = e3) | (all_56_3 = e3 & op(e2, e2) = e3) | (all_56_7 = e3 &
% 146.77/20.69  |              op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)) &
% 146.77/20.69  |          ((all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 146.77/20.69  |              e2) | (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 &
% 146.77/20.69  |              op(e0, e2) = e2)) & ((all_56_1 = e1 & op(e3, e2) = e1) |
% 146.77/20.69  |            (all_56_3 = e1 & op(e2, e2) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 146.77/20.69  |              e1) | (all_56_13 = e1 & op(e0, e2) = e1)) & ((all_56_1 = e0 &
% 146.77/20.69  |              op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) | (all_56_7
% 146.77/20.70  |              = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)) &
% 146.77/20.70  |          ((all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 146.77/20.70  |              e3) | (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 &
% 146.77/20.70  |              op(e2, e0) = e3)) & ((all_56_2 = e2 & op(e2, e3) = e2) |
% 146.77/20.70  |            (all_56_3 = e2 & op(e2, e2) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 146.77/20.70  |              e2) | (all_56_10 = e2 & op(e2, e0) = e2)) & ((all_56_2 = e1 &
% 146.77/20.70  |              op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) | (all_56_5
% 146.77/20.70  |              = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)) &
% 146.77/20.70  |          ((all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 146.77/20.70  |              e0) | (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 &
% 146.77/20.70  |              op(e2, e0) = e0)) & ((all_56_4 = e3 & op(e3, e1) = e3) |
% 146.77/20.70  |            (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_8 = e3 & op(e1, e1) =
% 146.77/20.70  |              e3) | (all_56_14 = e3 & op(e0, e1) = e3)) & ((all_56_4 = e2 &
% 146.77/20.70  |              op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_8
% 146.77/20.70  |              = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)) &
% 146.77/20.70  |          ((all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) =
% 146.77/20.70  |              e1) | (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 &
% 146.77/20.70  |              op(e0, e1) = e1)) & ((all_56_4 = e0 & op(e3, e1) = e0) |
% 146.77/20.70  |            (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_8 = e0 & op(e1, e1) =
% 146.77/20.70  |              e0) | (all_56_14 = e0 & op(e0, e1) = e0)) & ((all_56_6 = e3 &
% 146.77/20.70  |              op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_8
% 146.77/20.70  |              = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)) &
% 146.77/20.70  |          ((all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 146.77/20.70  |              e2) | (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 &
% 146.77/20.70  |              op(e1, e0) = e2)) & ((all_56_6 = e1 & op(e1, e3) = e1) |
% 146.77/20.70  |            (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_8 = e1 & op(e1, e1) =
% 146.77/20.70  |              e1) | (all_56_11 = e1 & op(e1, e0) = e1)) & ((all_56_6 = e0 &
% 146.77/20.70  |              op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_8
% 146.77/20.70  |              = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 146.77/20.70  |          ((all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 146.77/20.70  |              e3) | (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 &
% 146.77/20.70  |              op(e0, e0) = e3)) & ((all_56_9 = e2 & op(e3, e0) = e2) |
% 146.77/20.70  |            (all_56_10 = e2 & op(e2, e0) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 146.77/20.70  |              e2) | (all_56_15 = e2 & op(e0, e0) = e2)) & ((all_56_9 = e1 &
% 146.77/20.70  |              op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 146.77/20.70  |            (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 146.77/20.70  |              e1)) & ((all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 &
% 146.77/20.70  |              op(e0, e2) = e3) | (all_56_14 = e3 & op(e0, e1) = e3) |
% 146.77/20.70  |            (all_56_15 = e3 & op(e0, e0) = e3)) & ((all_56_12 = e2 & op(e0, e3)
% 146.77/20.70  |              = e2) | (all_56_13 = e2 & op(e0, e2) = e2) | (all_56_14 = e2 &
% 146.77/20.70  |              op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)) &
% 146.77/20.70  |          ((all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 146.77/20.70  |              e1) | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 &
% 146.77/20.70  |              op(e0, e0) = e1)) & ((all_56_15 = e0 & op(e0, e0) = e0) |
% 146.77/20.70  |            (((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0)
% 146.77/20.70  |                  = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 =
% 146.77/20.70  |                  e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 146.77/20.70  |                (all_56_14 = e0 & op(e0, e1) = e0))))
% 146.77/20.70  | 
% 146.77/20.70  | ALPHA: (205) implies:
% 146.77/20.70  |   (206)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) =
% 146.77/20.70  |                e0) | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 146.77/20.70  |                op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) |
% 146.77/20.70  |              (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1)
% 146.77/20.70  |                = e0)))
% 146.77/20.70  |   (207)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 146.77/20.70  |            e1) | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0,
% 146.77/20.70  |              e0) = e1)
% 146.77/20.70  |   (208)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 146.77/20.70  |            e2) | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0,
% 146.77/20.70  |              e0) = e2)
% 146.77/20.70  |   (209)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 146.77/20.70  |            e3) | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0,
% 146.77/20.70  |              e0) = e3)
% 146.77/20.70  |   (210)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 146.77/20.70  |            e1) | (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0,
% 146.77/20.70  |              e0) = e1)
% 146.77/20.70  |   (211)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 146.77/20.70  |            e2) | (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0,
% 146.77/20.70  |              e0) = e2)
% 146.77/20.70  |   (212)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 146.77/20.70  |            e3) | (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0,
% 146.77/20.70  |              e0) = e3)
% 146.77/20.70  |   (213)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0)
% 146.77/20.70  |          | (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 146.77/20.70  |            e0)
% 146.77/20.70  |   (214)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1)
% 146.77/20.70  |          | (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 146.77/20.70  |            e1)
% 146.77/20.70  |   (215)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2)
% 146.77/20.70  |          | (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 146.77/20.70  |            e2)
% 146.77/20.70  |   (216)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3)
% 146.77/20.70  |          | (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) =
% 146.77/20.70  |            e3)
% 146.77/20.70  |   (217)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0)
% 146.77/20.70  |          | (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 146.77/20.70  |            e0)
% 146.77/20.70  |   (218)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1)
% 146.77/20.70  |          | (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) =
% 146.77/20.70  |            e1)
% 146.77/20.70  |   (219)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2)
% 146.77/20.70  |          | (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 146.77/20.70  |            e2)
% 146.77/20.70  |   (220)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3)
% 146.77/20.70  |          | (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 146.77/20.70  |            e3)
% 146.77/20.70  |   (221)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 146.77/20.70  |          | (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 146.77/20.70  |            e0)
% 146.77/20.70  |   (222)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 146.77/20.70  |          | (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 146.77/20.70  |            e1)
% 146.77/20.70  |   (223)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 146.77/20.70  |          | (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 146.77/20.70  |            e2)
% 146.77/20.70  |   (224)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 146.77/20.70  |          | (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 146.77/20.70  |            e3)
% 146.77/20.70  |   (225)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 146.77/20.70  |          | (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 146.77/20.70  |            e0)
% 146.77/20.70  |   (226)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 146.77/20.70  |          | (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 146.77/20.70  |            e1)
% 146.77/20.70  |   (227)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 146.77/20.70  |          | (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 146.77/20.70  |            e2)
% 146.77/20.70  |   (228)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 146.77/20.70  |          | (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 146.77/20.70  |            e3)
% 146.77/20.71  |   (229)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 146.77/20.71  |          | (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 146.77/20.71  |            e0)
% 146.77/20.71  |   (230)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 146.77/20.71  |          | (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 146.77/20.71  |            e0)
% 146.77/20.71  |   (231)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 146.77/20.71  |          | (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 146.77/20.71  |            e1)
% 146.77/20.71  |   (232)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1)
% 146.77/20.71  |          | (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 146.77/20.71  |            e1)
% 146.77/20.71  |   (233)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 146.77/20.71  |          | (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 146.77/20.71  |            e2)
% 146.77/20.71  |   (234)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2)
% 146.77/20.71  |          | (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 146.77/20.71  |            e2)
% 146.77/20.71  |   (235)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 146.77/20.71  |          | (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 146.77/20.71  |            e3)
% 146.77/20.71  |   (236)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 146.77/20.71  |          | (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 146.77/20.71  |            e3)
% 146.77/20.71  | 
% 146.77/20.71  | DELTA: instantiating (10) with fresh symbols all_57_0, all_57_1, all_57_2,
% 146.77/20.71  |        all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9,
% 146.77/20.71  |        all_57_10, all_57_11, all_57_12, all_57_13, all_57_14, all_57_15 gives:
% 146.77/20.71  |   (237)  ((all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 =
% 146.77/20.71  |                e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 146.77/20.71  |              op(e2, e2) = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 146.77/20.71  |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 146.77/20.71  |              = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3
% 146.77/20.71  |              & $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 & all_57_14 =
% 146.77/20.71  |              e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 146.77/20.71  |              all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 146.77/20.71  |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 146.77/20.71  |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) =
% 146.77/20.71  |              e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 146.77/20.71  |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.77/20.71  |              op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 146.77/20.71  |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 146.77/20.71  |              &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 146.77/20.71  |              & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0
% 146.77/20.71  |              = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2,
% 146.77/20.71  |                e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 146.77/20.71  |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.77/20.71  |              op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 146.77/20.71  |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 146.77/20.71  |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 146.77/20.71  |              op(e2, e1) = e2 & $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0
% 146.77/20.71  |              & all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.77/20.71  |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 146.77/20.71  |              $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 146.77/20.71  |              op(e3, e3) = e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 =
% 146.77/20.71  |              e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 &
% 146.77/20.71  |              op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.77/20.71  |              $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 146.77/20.71  |              &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 146.77/20.71  |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 146.77/20.71  |            (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 146.77/20.71  |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) =
% 146.77/20.71  |              e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 146.77/20.71  |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 &
% 146.77/20.71  |              op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.77/20.71  |              $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1
% 146.77/20.71  |              &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 146.77/20.71  |              & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2
% 146.77/20.71  |              = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) &
% 146.77/20.71  |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 146.77/20.71  |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 146.77/20.71  |              e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1) |
% 146.77/20.71  |            (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 146.77/20.71  |                e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 &
% 146.77/20.71  |              op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 146.77/20.72  |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 146.77/20.72  |              = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 146.77/20.72  |              & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 =
% 146.77/20.72  |              e2 &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 146.77/20.72  |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 146.77/20.72  |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 =
% 146.77/20.72  |                e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) =
% 146.77/20.72  |              e0 & op(e0, e0) = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 146.77/20.72  |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 146.77/20.72  |                e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1,
% 146.77/20.72  |                e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 & 
% 146.77/20.72  |              ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) | (all_57_4 = e3
% 146.77/20.72  |              & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 146.77/20.72  |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 146.77/20.72  |                e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 & 
% 146.77/20.72  |              ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3
% 146.77/20.72  |              & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 146.77/20.72  |                e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 146.77/20.72  |                e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 &
% 146.77/20.72  |              all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.77/20.72  |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 146.77/20.72  |              $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 146.77/20.72  |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 =
% 146.77/20.72  |              e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 &
% 146.77/20.72  |              op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.77/20.72  |              $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3
% 146.77/20.72  |              &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 146.77/20.72  |              & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7
% 146.77/20.72  |              = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 146.77/20.72  |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 &
% 146.77/20.72  |              op(e0, e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 =
% 146.77/20.72  |              e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) |
% 146.77/20.72  |            (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 &
% 146.77/20.72  |              op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 =
% 146.77/20.72  |                e0) & op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 146.77/20.72  |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 146.77/20.72  |                  all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 146.77/20.72  |                  op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 146.77/20.72  |                  all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 146.77/20.72  |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 146.77/20.72  |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 146.77/20.72  |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 146.77/20.72  |                    e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 146.77/20.72  |                  & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 146.77/20.72  |                  all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 146.77/20.72  |                  op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 146.77/20.72  |                  all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 146.77/20.72  |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) |
% 146.77/20.72  |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 146.77/20.72  |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 146.77/20.72  |                    e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 146.77/20.72  |                  & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 146.77/20.72  |                  all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 146.77/20.72  |                  op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 146.77/20.72  |                  all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 146.77/20.72  |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 146.77/20.72  |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 146.77/20.72  |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 146.77/20.72  |                    e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 146.77/20.72  |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1,
% 146.77/20.72  |                    e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 146.77/20.72  |                  e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))) &
% 146.77/20.72  |          ((all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 146.77/20.72  |                  e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 146.77/20.72  |                  $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 146.77/20.72  |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 146.77/20.72  |              ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 146.77/20.72  |                  op(e0, e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 &
% 146.77/20.72  |              op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 146.77/20.72  |                  (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 146.77/20.72  |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 146.77/20.72  |                  op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 &
% 146.77/20.72  |                  op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 146.77/20.72  |                  all_57_7 & $i(all_57_7)))) | (all_57_14 = e1 & op(e1, e1) =
% 146.77/20.72  |              e1 & ((all_57_10 = e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 146.77/20.72  |                  op(e3, e1) = all_57_4 & $i(all_57_4))) & ((all_57_12 = e1 &
% 146.77/20.72  |                  op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 146.77/20.72  |                  all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) =
% 146.77/20.72  |                  e1) | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 &
% 146.77/20.72  |                  $i(all_57_8)))) | (all_57_15 = e0 & op(e0, e0) = e0 &
% 146.77/20.72  |              ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 146.77/20.72  |                  op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 = e0 &
% 146.77/20.72  |                  op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 146.77/20.72  |                  all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 146.77/20.72  |                  e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 146.77/20.72  |                  $i(all_57_13)))))
% 146.77/20.72  | 
% 146.77/20.72  | ALPHA: (237) implies:
% 146.77/20.72  |   (238)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 146.77/20.72  |                e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 146.77/20.72  |                $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 146.77/20.72  |                (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 146.77/20.72  |            ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 146.77/20.72  |                  e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 146.77/20.72  |              e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 146.77/20.72  |                  e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 146.77/20.72  |                e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 146.77/20.72  |                all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 146.77/20.72  |              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 146.77/20.72  |          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 146.77/20.72  |                e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 146.77/20.72  |                $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 146.77/20.72  |                (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 146.77/20.72  |            ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 146.77/20.72  |                  e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 146.77/20.72  |              e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 146.77/20.72  |                  e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 =
% 146.77/20.72  |                e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 146.77/20.72  |                all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 146.77/20.72  |                e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 146.77/20.72  |                $i(all_57_13))))
% 146.77/20.72  |   (239)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 146.77/20.72  |            & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 146.77/20.72  |            = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 146.77/20.72  |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.77/20.72  |            op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 146.77/20.72  |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 146.77/20.72  |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 146.77/20.72  |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 146.77/20.72  |            & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 146.77/20.72  |            = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 146.77/20.72  |            $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 146.77/20.72  |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 146.77/20.72  |            op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 146.77/20.72  |            & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 146.77/20.72  |            = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 146.77/20.72  |            $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 146.77/20.72  |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1
% 146.77/20.72  |            & all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.77/20.72  |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 146.77/20.72  |            $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 146.77/20.72  |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 146.77/20.72  |            = all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) | (all_57_1 = e3 &
% 146.77/20.72  |            all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.77/20.72  |            all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 146.77/20.72  |            $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 146.77/20.72  |            op(e3, e3) = e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 =
% 146.77/20.72  |            e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 &
% 146.77/20.72  |            op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.77/20.72  |            $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 146.77/20.72  |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 146.77/20.73  |            = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 146.77/20.73  |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.77/20.73  |            all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 146.77/20.73  |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 146.77/20.73  |            ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 146.77/20.73  |            = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 146.77/20.73  |            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 146.77/20.73  |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 146.77/20.73  |            $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 146.77/20.73  |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.77/20.73  |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 146.77/20.73  |            & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 146.77/20.73  |            e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 146.77/20.73  |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 146.77/20.73  |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 146.77/20.73  |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 146.77/20.73  |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.77/20.73  |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 146.77/20.73  |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 146.77/20.73  |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1
% 146.77/20.73  |            & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2)
% 146.77/20.73  |            = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 146.77/20.73  |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 146.77/20.73  |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.77/20.73  |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1
% 146.77/20.73  |            & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 146.77/20.73  |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 146.77/20.73  |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 146.77/20.73  |            op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3
% 146.77/20.73  |            & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) =
% 146.77/20.73  |            e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 146.77/20.73  |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 146.77/20.73  |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 &
% 146.77/20.73  |            all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.77/20.73  |            all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 146.77/20.73  |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 146.77/20.73  |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 =
% 146.77/20.73  |            e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 &
% 146.77/20.73  |            op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.77/20.73  |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 146.77/20.73  |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.77/20.73  |            op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0
% 146.77/20.73  |            & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 146.77/20.73  |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 146.77/20.73  |            = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 =
% 146.77/20.73  |              e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 146.77/20.73  |            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2)
% 146.77/20.73  |          | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 146.77/20.73  |            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.77/20.73  |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 146.77/20.73  |                  e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 146.77/20.73  |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 146.77/20.73  |                  = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0)
% 146.77/20.73  |              | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 146.77/20.73  |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 146.77/20.73  |                  e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 146.77/20.73  |                op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 146.77/20.73  |                e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 146.77/20.73  |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12
% 146.77/20.73  |                = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2
% 146.77/20.73  |                & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 146.77/20.73  |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 146.77/20.73  |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 = e0
% 146.77/20.73  |                &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 146.77/20.73  |                e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 146.77/20.73  |                op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 146.77/20.73  |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 146.77/20.73  |                op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13
% 146.77/20.73  |                = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 146.77/20.73  |                op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13
% 146.77/20.73  |                = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 146.77/20.73  |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14))
% 146.77/20.73  |              | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 146.77/20.73  |                e0)))
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_18_2, all_28_2, e0, e0,
% 146.77/20.73  |              simplifying with (57), (72) gives:
% 146.77/20.73  |   (240)  all_28_2 = all_18_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_16_2, all_28_2, e0, e0,
% 146.77/20.73  |              simplifying with (54), (72) gives:
% 146.77/20.73  |   (241)  all_28_2 = all_16_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_18_2, all_48_2, e0, e0,
% 146.77/20.73  |              simplifying with (57), (102) gives:
% 146.77/20.73  |   (242)  all_48_2 = all_18_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_50_2, all_52_15, e0, e0,
% 146.77/20.73  |              simplifying with (105), (156) gives:
% 146.77/20.73  |   (243)  all_52_15 = all_50_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_48_2, all_52_15, e0, e0,
% 146.77/20.73  |              simplifying with (102), (156) gives:
% 146.77/20.73  |   (244)  all_52_15 = all_48_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_15, all_54_15, e0,
% 146.77/20.73  |              e0, simplifying with (156), (173) gives:
% 146.77/20.73  |   (245)  all_54_15 = all_52_15
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_14_2, all_54_15, e0, e0,
% 146.77/20.73  |              simplifying with (51), (173) gives:
% 146.77/20.73  |   (246)  all_54_15 = all_14_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_14, e1,
% 146.77/20.73  |              e0, simplifying with (157), (174) gives:
% 146.77/20.73  |   (247)  all_54_14 = all_52_11
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_7, all_54_13, e2, e0,
% 146.77/20.73  |              simplifying with (158), (175) gives:
% 146.77/20.73  |   (248)  all_54_13 = all_52_7
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_3, all_54_12, e3, e0,
% 146.77/20.73  |              simplifying with (159), (176) gives:
% 146.77/20.73  |   (249)  all_54_12 = all_52_3
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_14, all_54_11, e0,
% 146.77/20.73  |              e1, simplifying with (160), (177) gives:
% 146.77/20.73  |   (250)  all_54_11 = all_52_14
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_10_2, all_22_2, e1, e1,
% 146.77/20.73  |              simplifying with (45), (63) gives:
% 146.77/20.73  |   (251)  all_22_2 = all_10_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_38_2, all_52_10, e1, e1,
% 146.77/20.73  |              simplifying with (87), (161) gives:
% 146.77/20.73  |   (252)  all_52_10 = all_38_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_30_2, all_52_10, e1, e1,
% 146.77/20.73  |              simplifying with (75), (161) gives:
% 146.77/20.73  |   (253)  all_52_10 = all_30_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_22_2, all_52_10, e1, e1,
% 146.77/20.73  |              simplifying with (63), (161) gives:
% 146.77/20.73  |   (254)  all_52_10 = all_22_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_10, all_54_10, e1,
% 146.77/20.73  |              e1, simplifying with (161), (178) gives:
% 146.77/20.73  |   (255)  all_54_10 = all_52_10
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_34_2, all_54_10, e1, e1,
% 146.77/20.73  |              simplifying with (81), (178) gives:
% 146.77/20.73  |   (256)  all_54_10 = all_34_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_20_2, all_54_10, e1, e1,
% 146.77/20.73  |              simplifying with (60), (178) gives:
% 146.77/20.73  |   (257)  all_54_10 = all_20_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_6, all_54_9, e2, e1,
% 146.77/20.73  |              simplifying with (162), (179) gives:
% 146.77/20.73  |   (258)  all_54_9 = all_52_6
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_2, all_54_8, e3, e1,
% 146.77/20.73  |              simplifying with (163), (180) gives:
% 146.77/20.73  |   (259)  all_54_8 = all_52_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_13, all_54_7, e0, e2,
% 146.77/20.73  |              simplifying with (164), (181) gives:
% 146.77/20.73  |   (260)  all_54_7 = all_52_13
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_9, all_54_6, e1, e2,
% 146.77/20.73  |              simplifying with (165), (182) gives:
% 146.77/20.73  |   (261)  all_54_6 = all_52_9
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_24_2, all_32_2, e2, e2,
% 146.77/20.73  |              simplifying with (66), (78) gives:
% 146.77/20.73  |   (262)  all_32_2 = all_24_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_32_2, all_36_2, e2, e2,
% 146.77/20.73  |              simplifying with (78), (84) gives:
% 146.77/20.73  |   (263)  all_36_2 = all_32_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_36_2, all_40_2, e2, e2,
% 146.77/20.73  |              simplifying with (84), (90) gives:
% 146.77/20.73  |   (264)  all_40_2 = all_36_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_44_2, all_52_5, e2, e2,
% 146.77/20.73  |              simplifying with (96), (166) gives:
% 146.77/20.73  |   (265)  all_52_5 = all_44_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_40_2, all_52_5, e2, e2,
% 146.77/20.73  |              simplifying with (90), (166) gives:
% 146.77/20.73  |   (266)  all_52_5 = all_40_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_5, all_54_5, e2, e2,
% 146.77/20.73  |              simplifying with (166), (183) gives:
% 146.77/20.73  |   (267)  all_54_5 = all_52_5
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_4_2, all_54_5, e2, e2,
% 146.77/20.73  |              simplifying with (36), (183) gives:
% 146.77/20.73  |   (268)  all_54_5 = all_4_2
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_1, all_54_4, e3, e2,
% 146.77/20.73  |              simplifying with (167), (184) gives:
% 146.77/20.73  |   (269)  all_54_4 = all_52_1
% 146.77/20.73  | 
% 146.77/20.73  | GROUND_INST: instantiating (function-axioms) with all_52_12, all_54_3, e0, e3,
% 146.77/20.73  |              simplifying with (168), (185) gives:
% 146.77/20.73  |   (270)  all_54_3 = all_52_12
% 146.77/20.73  | 
% 146.77/20.74  | GROUND_INST: instantiating (function-axioms) with all_52_8, all_54_2, e1, e3,
% 146.77/20.74  |              simplifying with (169), (186) gives:
% 146.77/20.74  |   (271)  all_54_2 = all_52_8
% 146.77/20.74  | 
% 146.77/20.74  | GROUND_INST: instantiating (function-axioms) with all_52_4, all_54_1, e2, e3,
% 146.77/20.74  |              simplifying with (170), (187) gives:
% 146.77/20.74  |   (272)  all_54_1 = all_52_4
% 146.77/20.74  | 
% 146.77/20.74  | GROUND_INST: instantiating (function-axioms) with all_26_2, all_42_2, e3, e3,
% 146.77/20.74  |              simplifying with (69), (93) gives:
% 146.77/20.74  |   (273)  all_42_2 = all_26_2
% 146.77/20.74  | 
% 146.77/20.74  | GROUND_INST: instantiating (function-axioms) with all_12_2, all_42_2, e3, e3,
% 146.77/20.74  |              simplifying with (48), (93) gives:
% 146.77/20.74  |   (274)  all_42_2 = all_12_2
% 146.77/20.74  | 
% 146.77/20.74  | GROUND_INST: instantiating (function-axioms) with all_42_2, all_46_2, e3, e3,
% 146.77/20.74  |              simplifying with (93), (99) gives:
% 146.77/20.74  |   (275)  all_46_2 = all_42_2
% 146.77/20.74  | 
% 146.77/20.74  | GROUND_INST: instantiating (function-axioms) with all_12_2, all_52_0, e3, e3,
% 146.77/20.74  |              simplifying with (48), (171) gives:
% 146.77/20.74  |   (276)  all_52_0 = all_12_2
% 146.77/20.74  | 
% 146.77/20.74  | GROUND_INST: instantiating (function-axioms) with all_8_2, all_52_0, e3, e3,
% 146.77/20.74  |              simplifying with (42), (171) gives:
% 146.77/20.74  |   (277)  all_52_0 = all_8_2
% 146.77/20.74  | 
% 146.77/20.74  | GROUND_INST: instantiating (function-axioms) with all_46_2, all_54_0, e3, e3,
% 146.77/20.74  |              simplifying with (99), (188) gives:
% 146.77/20.74  |   (278)  all_54_0 = all_46_2
% 146.77/20.74  | 
% 146.77/20.74  | GROUND_INST: instantiating (function-axioms) with all_6_2, all_54_0, e3, e3,
% 146.77/20.74  |              simplifying with (39), (188) gives:
% 146.77/20.74  |   (279)  all_54_0 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (278), (279) imply:
% 146.77/20.74  |   (280)  all_46_2 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (280) implies:
% 146.77/20.74  |   (281)  all_46_2 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (267), (268) imply:
% 146.77/20.74  |   (282)  all_52_5 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (282) implies:
% 146.77/20.74  |   (283)  all_52_5 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (256), (257) imply:
% 146.77/20.74  |   (284)  all_34_2 = all_20_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (255), (256) imply:
% 146.77/20.74  |   (285)  all_52_10 = all_34_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (285) implies:
% 146.77/20.74  |   (286)  all_52_10 = all_34_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (245), (246) imply:
% 146.77/20.74  |   (287)  all_52_15 = all_14_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (287) implies:
% 146.77/20.74  |   (288)  all_52_15 = all_14_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (276), (277) imply:
% 146.77/20.74  |   (289)  all_12_2 = all_8_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (289) implies:
% 146.77/20.74  |   (290)  all_12_2 = all_8_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (265), (266) imply:
% 146.77/20.74  |   (291)  all_44_2 = all_40_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (265), (283) imply:
% 146.77/20.74  |   (292)  all_44_2 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (252), (253) imply:
% 146.77/20.74  |   (293)  all_38_2 = all_30_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (252), (254) imply:
% 146.77/20.74  |   (294)  all_38_2 = all_22_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (252), (286) imply:
% 146.77/20.74  |   (295)  all_38_2 = all_34_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (243), (244) imply:
% 146.77/20.74  |   (296)  all_50_2 = all_48_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (243), (288) imply:
% 146.77/20.74  |   (297)  all_50_2 = all_14_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (296), (297) imply:
% 146.77/20.74  |   (298)  all_48_2 = all_14_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (298) implies:
% 146.77/20.74  |   (299)  all_48_2 = all_14_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (242), (299) imply:
% 146.77/20.74  |   (300)  all_18_2 = all_14_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (300) implies:
% 146.77/20.74  |   (301)  all_18_2 = all_14_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (275), (281) imply:
% 146.77/20.74  |   (302)  all_42_2 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (302) implies:
% 146.77/20.74  |   (303)  all_42_2 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (291), (292) imply:
% 146.77/20.74  |   (304)  all_40_2 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (304) implies:
% 146.77/20.74  |   (305)  all_40_2 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (273), (274) imply:
% 146.77/20.74  |   (306)  all_26_2 = all_12_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (273), (303) imply:
% 146.77/20.74  |   (307)  all_26_2 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (264), (305) imply:
% 146.77/20.74  |   (308)  all_36_2 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (308) implies:
% 146.77/20.74  |   (309)  all_36_2 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (293), (294) imply:
% 146.77/20.74  |   (310)  all_30_2 = all_22_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (293), (295) imply:
% 146.77/20.74  |   (311)  all_34_2 = all_30_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (311) implies:
% 146.77/20.74  |   (312)  all_34_2 = all_30_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (263), (309) imply:
% 146.77/20.74  |   (313)  all_32_2 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (313) implies:
% 146.77/20.74  |   (314)  all_32_2 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (284), (312) imply:
% 146.77/20.74  |   (315)  all_30_2 = all_20_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (315) implies:
% 146.77/20.74  |   (316)  all_30_2 = all_20_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (262), (314) imply:
% 146.77/20.74  |   (317)  all_24_2 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (317) implies:
% 146.77/20.74  |   (318)  all_24_2 = all_4_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (310), (316) imply:
% 146.77/20.74  |   (319)  all_22_2 = all_20_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (319) implies:
% 146.77/20.74  |   (320)  all_22_2 = all_20_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (240), (241) imply:
% 146.77/20.74  |   (321)  all_18_2 = all_16_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (321) implies:
% 146.77/20.74  |   (322)  all_18_2 = all_16_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (306), (307) imply:
% 146.77/20.74  |   (323)  all_12_2 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (323) implies:
% 146.77/20.74  |   (324)  all_12_2 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (251), (320) imply:
% 146.77/20.74  |   (325)  all_20_2 = all_10_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (301), (322) imply:
% 146.77/20.74  |   (326)  all_16_2 = all_14_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (326) implies:
% 146.77/20.74  |   (327)  all_16_2 = all_14_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (290), (324) imply:
% 146.77/20.74  |   (328)  all_8_2 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (328) implies:
% 146.77/20.74  |   (329)  all_8_2 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (241), (327) imply:
% 146.77/20.74  |   (330)  all_28_2 = all_14_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (316), (325) imply:
% 146.77/20.74  |   (331)  all_30_2 = all_10_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (284), (325) imply:
% 146.77/20.74  |   (332)  all_34_2 = all_10_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (293), (331) imply:
% 146.77/20.74  |   (333)  all_38_2 = all_10_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (252), (333) imply:
% 146.77/20.74  |   (334)  all_52_10 = all_10_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (277), (329) imply:
% 146.77/20.74  |   (335)  all_52_0 = all_6_2
% 146.77/20.74  | 
% 146.77/20.74  | COMBINE_EQS: (256), (332) imply:
% 146.77/20.74  |   (336)  all_54_10 = all_10_2
% 146.77/20.74  | 
% 146.77/20.74  | REDUCE: (155), (335) imply:
% 146.77/20.74  |   (337)   ~ (all_52_1 = all_6_2)
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (337) implies:
% 146.77/20.74  |   (338)   ~ (all_52_1 = all_6_2)
% 146.77/20.74  | 
% 146.77/20.74  | REDUCE: (154), (335) imply:
% 146.77/20.74  |   (339)   ~ (all_52_2 = all_6_2)
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (339) implies:
% 146.77/20.74  |   (340)   ~ (all_52_2 = all_6_2)
% 146.77/20.74  | 
% 146.77/20.74  | REDUCE: (153), (335) imply:
% 146.77/20.74  |   (341)   ~ (all_52_3 = all_6_2)
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (341) implies:
% 146.77/20.74  |   (342)   ~ (all_52_3 = all_6_2)
% 146.77/20.74  | 
% 146.77/20.74  | REDUCE: (152), (335) imply:
% 146.77/20.74  |   (343)   ~ (all_52_4 = all_6_2)
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (343) implies:
% 146.77/20.74  |   (344)   ~ (all_52_4 = all_6_2)
% 146.77/20.74  | 
% 146.77/20.74  | REDUCE: (151), (335) imply:
% 146.77/20.74  |   (345)   ~ (all_52_8 = all_6_2)
% 146.77/20.74  | 
% 146.77/20.74  | SIMP: (345) implies:
% 146.77/20.74  |   (346)   ~ (all_52_8 = all_6_2)
% 146.77/20.74  | 
% 146.77/20.74  | REDUCE: (150), (335) imply:
% 146.77/20.75  |   (347)   ~ (all_52_12 = all_6_2)
% 146.77/20.75  | 
% 146.77/20.75  | SIMP: (347) implies:
% 146.77/20.75  |   (348)   ~ (all_52_12 = all_6_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (147), (283) imply:
% 146.77/20.75  |   (349)   ~ (all_52_1 = all_4_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (142), (334) imply:
% 146.77/20.75  |   (350)   ~ (all_52_2 = all_10_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (138), (288) imply:
% 146.77/20.75  |   (351)   ~ (all_52_3 = all_14_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (137), (283) imply:
% 146.77/20.75  |   (352)   ~ (all_52_4 = all_4_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (132), (283) imply:
% 146.77/20.75  |   (353)   ~ (all_52_6 = all_4_2)
% 146.77/20.75  | 
% 146.77/20.75  | SIMP: (353) implies:
% 146.77/20.75  |   (354)   ~ (all_52_6 = all_4_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (131), (283) imply:
% 146.77/20.75  |   (355)   ~ (all_52_7 = all_4_2)
% 146.77/20.75  | 
% 146.77/20.75  | SIMP: (355) implies:
% 146.77/20.75  |   (356)   ~ (all_52_7 = all_4_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (130), (283) imply:
% 146.77/20.75  |   (357)   ~ (all_52_9 = all_4_2)
% 146.77/20.75  | 
% 146.77/20.75  | SIMP: (357) implies:
% 146.77/20.75  |   (358)   ~ (all_52_9 = all_4_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (129), (283) imply:
% 146.77/20.75  |   (359)   ~ (all_52_13 = all_4_2)
% 146.77/20.75  | 
% 146.77/20.75  | SIMP: (359) implies:
% 146.77/20.75  |   (360)   ~ (all_52_13 = all_4_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (127), (334) imply:
% 146.77/20.75  |   (361)   ~ (all_52_6 = all_10_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (124), (288) imply:
% 146.77/20.75  |   (362)   ~ (all_52_7 = all_14_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (122), (334) imply:
% 146.77/20.75  |   (363)   ~ (all_52_8 = all_10_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (119), (334) imply:
% 146.77/20.75  |   (364)   ~ (all_52_9 = all_10_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (116), (334) imply:
% 146.77/20.75  |   (365)   ~ (all_52_11 = all_10_2)
% 146.77/20.75  | 
% 146.77/20.75  | SIMP: (365) implies:
% 146.77/20.75  |   (366)   ~ (all_52_11 = all_10_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (115), (334) imply:
% 146.77/20.75  |   (367)   ~ (all_52_14 = all_10_2)
% 146.77/20.75  | 
% 146.77/20.75  | SIMP: (367) implies:
% 146.77/20.75  |   (368)   ~ (all_52_14 = all_10_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (114), (288) imply:
% 146.77/20.75  |   (369)   ~ (all_52_11 = all_14_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (111), (288) imply:
% 146.77/20.75  |   (370)   ~ (all_52_12 = all_14_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (109), (288) imply:
% 146.77/20.75  |   (371)   ~ (all_52_13 = all_14_2)
% 146.77/20.75  | 
% 146.77/20.75  | REDUCE: (108), (288) imply:
% 146.77/20.75  |   (372)   ~ (all_52_14 = all_14_2)
% 146.77/20.75  | 
% 146.77/20.75  | BETA: splitting (37) gives:
% 146.77/20.75  | 
% 146.77/20.75  | Case 1:
% 146.77/20.75  | | 
% 146.77/20.75  | |   (373)   ~ (all_4_2 = e3)
% 146.77/20.75  | | 
% 146.77/20.75  | | BETA: splitting (40) gives:
% 146.77/20.75  | | 
% 146.77/20.75  | | Case 1:
% 146.77/20.75  | | | 
% 146.77/20.75  | | |   (374)   ~ (all_6_2 = e0)
% 146.77/20.75  | | | 
% 146.77/20.75  | | | BETA: splitting (46) gives:
% 146.77/20.75  | | | 
% 146.77/20.75  | | | Case 1:
% 146.77/20.75  | | | | 
% 146.77/20.75  | | | |   (375)   ~ (all_10_2 = e2)
% 146.77/20.75  | | | | 
% 146.77/20.75  | | | | BETA: splitting (49) gives:
% 146.77/20.75  | | | | 
% 146.77/20.75  | | | | Case 1:
% 146.77/20.75  | | | | | 
% 146.77/20.75  | | | | |   (376)   ~ (all_12_2 = e2)
% 146.77/20.75  | | | | | 
% 146.77/20.75  | | | | | REDUCE: (324), (376) imply:
% 146.77/20.75  | | | | |   (377)   ~ (all_6_2 = e2)
% 146.77/20.75  | | | | | 
% 146.77/20.75  | | | | | BETA: splitting (52) gives:
% 146.77/20.75  | | | | | 
% 146.77/20.75  | | | | | Case 1:
% 146.77/20.75  | | | | | | 
% 146.77/20.75  | | | | | |   (378)   ~ (all_14_2 = e1)
% 146.77/20.75  | | | | | | 
% 146.77/20.75  | | | | | | BETA: splitting (58) gives:
% 146.77/20.75  | | | | | | 
% 146.77/20.75  | | | | | | Case 1:
% 146.77/20.75  | | | | | | | 
% 146.77/20.75  | | | | | | |   (379)   ~ (all_18_2 = e3)
% 146.77/20.75  | | | | | | | 
% 146.77/20.75  | | | | | | | REDUCE: (301), (379) imply:
% 146.77/20.75  | | | | | | |   (380)   ~ (all_14_2 = e3)
% 146.77/20.75  | | | | | | | 
% 146.77/20.75  | | | | | | | BETA: splitting (61) gives:
% 146.77/20.75  | | | | | | | 
% 146.77/20.75  | | | | | | | Case 1:
% 146.77/20.75  | | | | | | | | 
% 146.77/20.75  | | | | | | | |   (381)   ~ (all_20_2 = e3)
% 146.77/20.75  | | | | | | | | 
% 146.77/20.75  | | | | | | | | REDUCE: (325), (381) imply:
% 146.77/20.75  | | | | | | | |   (382)   ~ (all_10_2 = e3)
% 146.77/20.75  | | | | | | | | 
% 146.77/20.75  | | | | | | | | BETA: splitting (64) gives:
% 146.77/20.75  | | | | | | | | 
% 146.77/20.75  | | | | | | | | Case 1:
% 146.77/20.75  | | | | | | | | | 
% 146.77/20.75  | | | | | | | | |   (383)   ~ (all_22_2 = e0)
% 146.77/20.75  | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | REDUCE: (251), (383) imply:
% 146.77/20.75  | | | | | | | | |   (384)   ~ (all_10_2 = e0)
% 146.77/20.75  | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | BETA: splitting (194) gives:
% 146.77/20.75  | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | Case 1:
% 146.77/20.75  | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | |   (385)  all_54_10 = e3
% 146.77/20.75  | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | COMBINE_EQS: (336), (385) imply:
% 146.77/20.75  | | | | | | | | | |   (386)  all_10_2 = e3
% 146.77/20.75  | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | REDUCE: (382), (386) imply:
% 146.77/20.75  | | | | | | | | | |   (387)  $false
% 146.77/20.75  | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | CLOSE: (387) is inconsistent.
% 146.77/20.75  | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | Case 2:
% 146.77/20.75  | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | |   (388)   ~ (all_54_10 = e3)
% 146.77/20.75  | | | | | | | | | |   (389)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 146.77/20.75  | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | BETA: splitting (389) gives:
% 146.77/20.75  | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | Case 1:
% 146.77/20.75  | | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | |   (390)  all_54_10 = e2
% 146.77/20.75  | | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | | COMBINE_EQS: (336), (390) imply:
% 146.77/20.75  | | | | | | | | | | |   (391)  all_10_2 = e2
% 146.77/20.75  | | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | | REDUCE: (375), (391) imply:
% 146.77/20.75  | | | | | | | | | | |   (392)  $false
% 146.77/20.75  | | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | | CLOSE: (392) is inconsistent.
% 146.77/20.75  | | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | Case 2:
% 146.77/20.75  | | | | | | | | | | | 
% 146.77/20.75  | | | | | | | | | | |   (393)   ~ (all_54_10 = e2)
% 146.77/20.76  | | | | | | | | | | |   (394)  all_54_10 = e1 | all_54_10 = e0
% 146.77/20.76  | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | BETA: splitting (394) gives:
% 146.77/20.76  | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | |   (395)  all_54_10 = e1
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | COMBINE_EQS: (336), (395) imply:
% 146.77/20.76  | | | | | | | | | | | |   (396)  all_10_2 = e1
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | REDUCE: (350), (396) imply:
% 146.77/20.76  | | | | | | | | | | | |   (397)   ~ (all_52_2 = e1)
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | REDUCE: (361), (396) imply:
% 146.77/20.76  | | | | | | | | | | | |   (398)   ~ (all_52_6 = e1)
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | REDUCE: (366), (396) imply:
% 146.77/20.76  | | | | | | | | | | | |   (399)   ~ (all_52_11 = e1)
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | REDUCE: (368), (396) imply:
% 146.77/20.76  | | | | | | | | | | | |   (400)   ~ (all_52_14 = e1)
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | REDUCE: (382), (396) imply:
% 146.77/20.76  | | | | | | | | | | | |   (401)   ~ (e3 = e1)
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | REDUCE: (375), (396) imply:
% 146.77/20.76  | | | | | | | | | | | |   (402)   ~ (e2 = e1)
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | REDUCE: (45), (396) imply:
% 146.77/20.76  | | | | | | | | | | | |   (403)  op(e1, e1) = e1
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | BETA: splitting (67) gives:
% 146.77/20.76  | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | |   (404)   ~ (all_24_2 = e1)
% 146.77/20.76  | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | REDUCE: (318), (404) imply:
% 146.77/20.76  | | | | | | | | | | | | |   (405)   ~ (all_4_2 = e1)
% 146.77/20.76  | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | BETA: splitting (70) gives:
% 146.77/20.76  | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | |   (406)   ~ (all_26_2 = e1)
% 146.77/20.76  | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | REDUCE: (307), (406) imply:
% 146.77/20.76  | | | | | | | | | | | | | |   (407)   ~ (all_6_2 = e1)
% 146.77/20.76  | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 146.77/20.76  | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | |   (408)  all_54_0 = e3
% 146.77/20.76  | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | COMBINE_EQS: (279), (408) imply:
% 146.77/20.76  | | | | | | | | | | | | | | |   (409)  all_6_2 = e3
% 146.77/20.76  | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | REDUCE: (338), (409) imply:
% 146.77/20.76  | | | | | | | | | | | | | | |   (410)   ~ (all_52_1 = e3)
% 146.77/20.76  | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | REDUCE: (344), (409) imply:
% 146.77/20.76  | | | | | | | | | | | | | | |   (411)   ~ (all_52_4 = e3)
% 146.77/20.76  | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | REDUCE: (346), (409) imply:
% 146.77/20.76  | | | | | | | | | | | | | | |   (412)   ~ (all_52_8 = e3)
% 146.77/20.76  | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | REDUCE: (348), (409) imply:
% 146.77/20.76  | | | | | | | | | | | | | | |   (413)   ~ (all_52_12 = e3)
% 146.77/20.76  | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | REDUCE: (39), (409) imply:
% 146.77/20.76  | | | | | | | | | | | | | | |   (414)  op(e3, e3) = e3
% 146.77/20.76  | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 146.77/20.76  | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | |   (415)   ~ (all_28_2 = e2)
% 146.77/20.76  | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | REDUCE: (330), (415) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | |   (416)   ~ (all_14_2 = e2)
% 146.77/20.76  | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 146.77/20.76  | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | |   (417)  all_54_15 = e3
% 146.77/20.76  | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (380), (417) are inconsistent by sub-proof
% 146.77/20.76  | | | | | | | | | | | | | | | | |            #1010.
% 146.77/20.76  | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | Case 2:
% 146.77/20.76  | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | |   (418)   ~ (all_54_15 = e3)
% 146.77/20.76  | | | | | | | | | | | | | | | | |   (419)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 146.77/20.76  | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | BETA: splitting (419) gives:
% 146.77/20.76  | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | |   (420)  all_54_15 = e2
% 146.77/20.76  | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (416), (420) are inconsistent by sub-proof
% 146.77/20.76  | | | | | | | | | | | | | | | | | |            #1009.
% 146.77/20.76  | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | Case 2:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | |   (421)   ~ (all_54_15 = e2)
% 146.77/20.76  | | | | | | | | | | | | | | | | | |   (422)  all_54_15 = e1 | all_54_15 = e0
% 146.77/20.76  | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | BETA: splitting (422) gives:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |   (423)  all_54_15 = e1
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (378), (423) are inconsistent by sub-proof
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |            #1008.
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | Case 2:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |   (424)  all_54_15 = e0
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (424) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |   (425)  all_14_2 = e0
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | SIMP: (425) implies:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |   (426)  all_14_2 = e0
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | REDUCE: (351), (426) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |   (427)   ~ (all_52_3 = e0)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | REDUCE: (362), (426) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |   (428)   ~ (all_52_7 = e0)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | REDUCE: (369), (426) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |   (429)   ~ (all_52_11 = e0)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | REDUCE: (380), (426) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |   (430)   ~ (e3 = e0)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | REDUCE: (416), (426) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |   (431)   ~ (e2 = e0)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | REDUCE: (378), (426) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | |   (432)   ~ (e1 = e0)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | |   (433)  all_56_15 = e0 & op(e0, e0) = e0
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | ALPHA: (433) implies:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | |   (434)  all_56_15 = e0
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | |   (435)  op(e0, e0) = e0
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | |   (436)   ~ (all_32_2 = e0)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (436) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | |   (437)   ~ (all_4_2 = e0)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | |   (438)  all_54_5 = e3
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (438) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | |   (439)  all_4_2 = e3
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (439) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | |   (440)  $false
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (440) is inconsistent.
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | |   (441)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (441) gives:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | |   (442)  all_54_5 = e2
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (442) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | |   (443)  all_4_2 = e2
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (443) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | |   (444)   ~ (all_52_1 = e2)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (443) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | |   (445)   ~ (all_52_9 = e2)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (443) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | |   (446)   ~ (all_52_13 = e2)
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (443) imply:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | |   (447)  op(e2, e2) = e2
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.77/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (448)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (448) gives:
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.77/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (449)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (167), (403), (444), (445), (449),
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            #1000.
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (450)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (450) gives:
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (451)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (451) gives:
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (452)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (411), (435), (452), (function-axioms)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #997.
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (453)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (414), (446), (453), (function-axioms)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #994.
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (454)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (454) gives:
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (403), (447), (455), (function-axioms)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #992.
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (163), (397), (403), (435), (456),
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #988.
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |   (457)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0 & op(e0, e0) = e3 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) |
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e2) = e0) |
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) |
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | |                = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives:
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (458)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.31/20.82  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives:
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (459) gives:
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (414), (447), (460), (function-axioms)
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #987.
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (403), (435), (461),
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #985.
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14))
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives:
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (463)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1)
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (398), (403), (463), (function-axioms)
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #983.
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (464)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (169), (412), (414), (435), (464),
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #980.
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (465)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (465) gives:
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (466)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives:
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2)
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (165), (435), (445), (467), (function-axioms)
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #978.
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (435), (447), (468), (function-axioms)
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #977.
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (469)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0)))
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (469) gives:
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (470)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3)
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (413), (435), (470), (function-axioms)
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #975.
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (471)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (471) gives:
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (472)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (472) implies:
% 147.31/20.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (473)  op(e2, e0) = e2
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (446), (473), (function-axioms) are
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (474)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (474) gives:
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (475) implies:
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)  op(e1, e0) = e1
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (476), (function-axioms) are
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.31/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (477)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0))
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (477) implies:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (157), (158), (159), (164), (360),
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (414), (427), (428), (429), (447), (478),
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #963.
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | |   (479)  all_54_5 = e1 | all_54_5 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (405), (437), (479) are inconsistent by
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | |   (480)  all_32_2 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (480) imply:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | |   (481)  all_4_2 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (481) imply:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | |   (482)   ~ (all_52_6 = e0)
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (481) imply:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | |   (483)  op(e2, e2) = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | |   (484)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (484) gives:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | |   (485)  all_56_6 = e0 & op(e1, e3) = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_56_6 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | |   (487)  op(e1, e3) = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | |   (488)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (488) gives:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  all_56_1 = e0 & op(e3, e2) = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (489) implies:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_56_1 = e0
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (491)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (483), (490), (491), (function-axioms) are
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #959.
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (492)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (492) gives:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (493)  all_56_7 = e1 & op(e1, e2) = e1
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (493) implies:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (494)  op(e1, e2) = e1
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (398), (494), (function-axioms) are
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #984.
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (495)  all_56_13 = e1 & op(e0, e2) = e1
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (495) implies:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)  all_56_13 = e1
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (414), (483), (490), (496),
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #935.
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (497)  all_56_3 = e0 & op(e2, e2) = e0
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (497) implies:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (498)  all_56_3 = e0
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (499) gives:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (500) gives:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (501) gives:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (414), (483), (502), (function-axioms)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #934.
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (403), (483), (503), (function-axioms)
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #933.
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_12))
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (504) gives:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (413), (435), (505), (function-axioms)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #932.
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (167), (199), (200), (268), (269),
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (349), (373), (403), (405), (410), (414), (506),
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #923.
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (507) gives:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (508) gives:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (509)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (411), (435), (509), (function-axioms)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #997.
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (510)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (414), (510), (function-axioms) are
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (511)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (511) gives:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (512)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (403), (483), (512), (function-axioms)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #921.
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (513)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (163), (397), (403), (435), (513),
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #988.
% 147.87/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0 & op(e0, e0) = e3 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) |
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e2) = e0) |
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) |
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (514) gives:
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (515) gives:
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (516)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (516) gives:
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (517)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (414), (483), (517), (function-axioms)
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #920.
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (518)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (403), (435), (518),
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #985.
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (519)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14))
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (519) gives:
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (520)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1)
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (398), (403), (520), (function-axioms)
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #983.
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (521)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (169), (412), (414), (435), (521),
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #980.
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (522)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (522) gives:
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (523)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (435), (483), (523),
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #918.
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (524)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0)))
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (524) gives:
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (525)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3)
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (413), (435), (525), (function-axioms)
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #975.
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (526)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives:
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (527)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (527) implies:
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (528)  op(e2, e2) = e2
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (483), (528), (function-axioms) are
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (529)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (529) gives:
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (530)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (530) implies:
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (531)  op(e1, e0) = e1
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (531), (function-axioms) are
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (532)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0))
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (532) implies:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (533)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (533) gives:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (534)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (534) gives:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (535)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (535) gives:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (536)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = e3 & op(e0, e3) = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (536) implies:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (537)  op(e0, e3) = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (427), (537), (function-axioms) are
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (538)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (538) gives:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (539)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = e2 & op(e0, e3) = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (539) implies:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (540)  op(e0, e3) = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (427), (540), (function-axioms) are
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (541)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = e1 & op(e0, e3) = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (541) implies:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (542)  op(e1, e1) = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (214), (215),
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (225), (226), (227), (228), (230), (232),
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (400), (414), (483), (486), (487), (498),
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (542), (function-axioms) are inconsistent by
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #901.
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (543)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (159), (414), (427), (428), (543),
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #899.
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (544)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (544) gives:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (545)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (545) gives:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (546)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = e1 & op(e0, e2) = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (546) implies:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (547)  op(e1, e1) = e0
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (214), (215),
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (225), (226), (227), (228), (230), (232),
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (400), (414), (483), (486), (487), (498),
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (547), (function-axioms) are inconsistent by
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #901.
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (548)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (414), (428), (548), (function-axioms)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #968.
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (549)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (549) gives:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (550)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (550) gives:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (551)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = e2 & op(e0, e1) = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (551) implies:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (552)  op(e0, e1) = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (429), (552), (function-axioms) are
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (553)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = e1 & op(e0, e1) = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (553) implies:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (554)  op(e1, e1) = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (214), (215),
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (225), (226), (227), (228), (230), (232),
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (400), (414), (483), (486), (487), (498),
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (554), (function-axioms) are inconsistent by
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #901.
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (555)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (429), (555), (function-axioms) are
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | |   (556)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (428), (482), (556),
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | |            #897.
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | |   (557)  all_56_7 = e0 & op(e1, e2) = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (482), (557), (function-axioms) are
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #898.
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | |   (558)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (558) gives:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | |   (559)  all_56_8 = e0 & op(e1, e1) = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (559) implies:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | |   (560)  op(e1, e1) = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (403), (560), (function-axioms) are
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | |   (561)  all_56_11 = e0 & op(e1, e0) = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (561) implies:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | |   (562)  all_56_11 = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (210), (211), (212),
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | |            (434), (435), (562), (function-axioms) are
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #883.
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | |   (563)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | |   (564)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (427), (428), (429), (564),
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | |            #881.
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | End of split
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | Case 2:
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | |   (565)  all_28_2 = e2
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (565) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | |   (566)  all_14_2 = e2
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | SIMP: (566) implies:
% 147.87/20.93  | | | | | | | | | | | | | | | |   (567)  all_14_2 = e2
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | REDUCE: (351), (567) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | |   (568)   ~ (all_52_3 = e2)
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | REDUCE: (370), (567) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | |   (569)   ~ (all_52_12 = e2)
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | REDUCE: (371), (567) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | |   (570)   ~ (all_52_13 = e2)
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | REDUCE: (372), (567) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | |   (571)   ~ (all_52_14 = e2)
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | REDUCE: (380), (567) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | |   (572)   ~ (e3 = e2)
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | REDUCE: (51), (567) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | |   (573)  op(e0, e0) = e2
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 147.87/20.93  | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.93  | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | |   (574)   ~ (all_32_2 = e0)
% 147.87/20.93  | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | REDUCE: (314), (574) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | | |   (575)   ~ (all_4_2 = e0)
% 147.87/20.93  | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 147.87/20.93  | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | |   (576)  all_54_5 = e3
% 147.87/20.93  | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (576) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | | | |   (577)  all_4_2 = e3
% 147.87/20.93  | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | REDUCE: (373), (577) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | | | |   (578)  $false
% 147.87/20.93  | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | CLOSE: (578) is inconsistent.
% 147.87/20.93  | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | |   (579)   ~ (all_54_5 = e3)
% 147.87/20.93  | | | | | | | | | | | | | | | | | |   (580)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 147.87/20.93  | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | BETA: splitting (580) gives:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | |   (581)  all_54_5 = e2
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (581) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | |   (582)  all_4_2 = e2
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | REDUCE: (349), (582) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | |   (583)   ~ (all_52_1 = e2)
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | REDUCE: (358), (582) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | |   (584)   ~ (all_52_9 = e2)
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (582) imply:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | |   (585)  op(e2, e2) = e2
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | 
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.93  | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |   (586)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |          (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | |            e1)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives:
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |   (587)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (167), (403), (583), (584), (587),
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            #1000.
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |   (588)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | |            e1)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (588) gives:
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |   (589)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (589) gives:
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |   (590)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (160), (164), (168), (170), (211),
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            (360), (411), (569), (571), (585), (590),
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            #876.
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |   (591)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (414), (570), (591), (function-axioms)
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #994.
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.87/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |   (592)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | |            e1)
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (592) gives:
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.22/20.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (593)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (403), (585), (593), (function-axioms)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #992.
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (594)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (163), (397), (403), (573), (594),
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            #874.
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | End of split
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |   (595)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0 & op(e0, e0) = e3 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |            & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) |
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e2) = e0) |
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) |
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | |                = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | BETA: splitting (595) gives:
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |   (596)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (596) gives:
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |   (597)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (597) gives:
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (598)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (414), (585), (598), (function-axioms)
% 148.22/20.95  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #987.
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |   (599)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (403), (573), (599), (function-axioms) are
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |   (600)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14))
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (600) gives:
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |   (601)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1)
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (398), (403), (601), (function-axioms)
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #983.
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |   (602)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (160), (164), (168), (169), (211),
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            (360), (412), (414), (569), (571), (585), (602),
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | |            #872.
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |   (603)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | |                e0)))
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (603) gives:
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |   (604)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (160), (164), (165), (168), (211),
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            (360), (569), (571), (584), (585), (604),
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | |            #870.
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.22/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |   (605)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0)))
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (605) gives:
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |   (606)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3)
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (413), (570), (606),
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |            #869.
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |   (607)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (607) gives:
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | |   (608)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (608) implies:
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | |   (609)  op(e2, e0) = e2
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (570), (609), (function-axioms) are
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.22/20.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |   (610)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (610) gives:
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (611)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (611) implies:
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (612)  op(e1, e0) = e1
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (612), (function-axioms) are
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (613)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |              e0))
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (613) implies:
% 148.22/20.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (614)  op(e0, e0) = all_57_15
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (615)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (159), (160), (164), (167),
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (400), (403), (414), (568), (570), (573),
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            (583), (614), (615), (function-axioms) are
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #857.
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | End of split
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | End of split
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | Case 2:
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | |   (616)  all_54_5 = e1 | all_54_5 = e0
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (405), (575), (616) are inconsistent by
% 148.37/20.99  | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | End of split
% 148.37/20.99  | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | End of split
% 148.37/20.99  | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | Case 2:
% 148.37/20.99  | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | |   (617)  all_32_2 = e0
% 148.37/20.99  | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (617) imply:
% 148.37/20.99  | | | | | | | | | | | | | | | | |   (618)  all_4_2 = e0
% 148.37/20.99  | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | REDUCE: (356), (618) imply:
% 148.37/20.99  | | | | | | | | | | | | | | | | |   (619)   ~ (all_52_7 = e0)
% 148.37/20.99  | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | REDUCE: (373), (618) imply:
% 148.37/20.99  | | | | | | | | | | | | | | | | |   (620)   ~ (e3 = e0)
% 148.37/20.99  | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | REDUCE: (405), (618) imply:
% 148.37/20.99  | | | | | | | | | | | | | | | | |   (621)   ~ (e1 = e0)
% 148.37/20.99  | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | REDUCE: (36), (618) imply:
% 148.37/20.99  | | | | | | | | | | | | | | | | |   (622)  op(e2, e2) = e0
% 148.37/20.99  | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 148.37/20.99  | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | Case 1:
% 148.37/20.99  | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | |   (623)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.37/20.99  | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 148.37/20.99  | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 148.37/20.99  | | | | | | | | | | | | | | | | | |          (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 148.37/20.99  | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 148.37/20.99  | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/20.99  | | | | | | | | | | | | | | | | | |            e1)
% 148.37/20.99  | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | BETA: splitting (623) gives:
% 148.37/20.99  | | | | | | | | | | | | | | | | | | 
% 148.37/20.99  | | | | | | | | | | | | | | | | | | Case 1:
% 148.37/20.99  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |   (624)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | BETA: splitting (624) gives:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |   (625)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | BETA: splitting (625) gives:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |   (626)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (414), (622), (626), (function-axioms)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #934.
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |   (627)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (403), (622), (627), (function-axioms)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #933.
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | End of split
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |   (628)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | |            & $i(all_57_12))
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | BETA: splitting (628) gives:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |   (629)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (629) gives:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | |   (630)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | |          = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_12)
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (630) implies:
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | |   (631)  op(e0, e2) = e0
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (619), (631), (function-axioms) are
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 148.37/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | |   (632)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | |          op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (632) implies:
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | |   (633)  op(e3, e0) = e3
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (413), (633), (function-axioms) are
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |   (634)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (167), (199), (200), (268), (269),
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            (349), (373), (403), (405), (410), (414), (634),
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            #923.
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | End of split
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | End of split
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | Case 2:
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |   (635)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | |            e1)
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (635) gives:
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |   (636)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | BETA: splitting (636) gives:
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |   (637)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |              e2) = e3)
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (411), (573), (637), (function-axioms)
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #856.
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |   (638)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (414), (570), (638), (function-axioms)
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #994.
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | End of split
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.37/21.01  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |   (639)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | |            e1)
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | BETA: splitting (639) gives:
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |   (640)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (403), (622), (640), (function-axioms)
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #921.
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |   (641)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            e1)
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (163), (397), (403), (573), (641),
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | |            #874.
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | End of split
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | End of split
% 148.37/21.02  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | | End of split
% 148.37/21.02  | | | | | | | | | | | | | | | | | | 
% 148.37/21.02  | | | | | | | | | | | | | | | | | Case 2:
% 148.37/21.02  | | | | | | | | | | | | | | | | | | 
% 148.37/21.03  | | | | | | | | | | | | | | | | | |   (642)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.37/21.03  | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 148.37/21.03  | | | | | | | | | | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0 & op(e0, e0) = e3 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 148.37/21.03  | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 148.37/21.03  | | | | | | | | | | | | | | | | | |            & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) |
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e2) = e0) |
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) |
% 148.37/21.03  | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 148.37/21.03  | | | | | | | | | | | | | | | | | |                = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 148.37/21.03  | | | | | | | | | | | | | | | | | | 
% 148.37/21.03  | | | | | | | | | | | | | | | | | | BETA: splitting (642) gives:
% 148.37/21.03  | | | | | | | | | | | | | | | | | | 
% 148.37/21.03  | | | | | | | | | | | | | | | | | | Case 1:
% 148.37/21.03  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |   (643)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 148.37/21.03  | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.37/21.04  | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 148.37/21.04  | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 148.37/21.04  | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 148.37/21.04  | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 148.37/21.04  | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 148.37/21.04  | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 148.37/21.04  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.37/21.04  | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.37/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (643) gives:
% 148.37/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.37/21.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.37/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |   (644)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (644) gives:
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |   (645)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (414), (622), (645), (function-axioms)
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #920.
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |   (646)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (403), (573), (646), (function-axioms) are
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | End of split
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |   (647)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14))
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (647) gives:
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |   (648)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |              e1) = e1)
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (398), (403), (648), (function-axioms)
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #983.
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |   (649)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (169), (412), (414), (573), (649),
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | |            #855.
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | End of split
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | End of split
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.60/21.04  | | | | | | | | | | | | | | | | | | Case 2:
% 148.60/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |   (650)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | |                e0)))
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (650) gives:
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |   (651)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | BETA: splitting (651) gives:
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | |   (652)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | |              e1) = e2)
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (652) gives:
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | |   (653)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | |          e2 & $i(all_57_12)
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (653) implies:
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | |   (654)  op(e0, e2) = e0
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (619), (654), (function-axioms) are
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | |   (655)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e1) = e2
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (655) implies:
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | |   (656)  op(e2, e2) = e2
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (622), (656), (function-axioms) are
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 148.60/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |   (657)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (573), (622), (657), (function-axioms)
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #854.
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |   (658)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0)))
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | BETA: splitting (658) gives:
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |   (659)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |              e0) = e3)
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (413), (570), (659),
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | |            #869.
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |   (660)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | |                e0)))
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (660) gives:
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |   (661)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (661) implies:
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |   (662)  op(e2, e2) = e2
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (622), (662), (function-axioms) are
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |   (663)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (663) gives:
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |   (664)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (664) implies:
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |   (665)  op(e1, e0) = e1
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (665), (function-axioms) are
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |   (666)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |              e0))
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (666) implies:
% 148.65/21.06  | | | | | | | | | | | | | | | | | | | | | | |   (667)  op(e0, e0) = all_57_15
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |   (668)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (573), (667)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |   (669)  all_57_15 = e2
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (160), (164), (400), (403), (414),
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            (570), (668), (669), (function-axioms) are
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #859.
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | End of split
% 148.65/21.07  | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | End of split
% 148.65/21.07  | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | End of split
% 148.65/21.07  | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | Case 2:
% 148.65/21.07  | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | |   (670)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 148.65/21.07  | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (407), (670) are inconsistent
% 148.65/21.07  | | | | | | | | | | | | | | |            by sub-proof #853.
% 148.65/21.07  | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | End of split
% 148.65/21.07  | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | Case 2:
% 148.65/21.07  | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | |   (671)  all_26_2 = e1
% 148.65/21.07  | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | COMBINE_EQS: (307), (671) imply:
% 148.65/21.07  | | | | | | | | | | | | | |   (672)  all_6_2 = e1
% 148.65/21.07  | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | SIMP: (672) implies:
% 148.65/21.07  | | | | | | | | | | | | | |   (673)  all_6_2 = e1
% 148.65/21.07  | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | REDUCE: (342), (673) imply:
% 148.65/21.07  | | | | | | | | | | | | | |   (674)   ~ (all_52_3 = e1)
% 148.65/21.07  | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | REDUCE: (348), (673) imply:
% 148.65/21.07  | | | | | | | | | | | | | |   (675)   ~ (all_52_12 = e1)
% 148.65/21.07  | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | REDUCE: (39), (673) imply:
% 148.65/21.07  | | | | | | | | | | | | | |   (676)  op(e3, e3) = e1
% 148.65/21.07  | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 148.65/21.07  | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | |   (677)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 148.65/21.07  | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 148.65/21.07  | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | BETA: splitting (677) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | |   (678)  all_56_12 = e1 & op(e0, e3) = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (674), (678), (function-axioms) are
% 148.65/21.07  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #852.
% 148.65/21.07  | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | Case 2:
% 148.65/21.07  | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | |   (679)  all_56_13 = e1 & op(e0, e2) = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | ALPHA: (679) implies:
% 148.65/21.07  | | | | | | | | | | | | | | | |   (680)  op(e0, e2) = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | |   (681)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 148.65/21.07  | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 148.65/21.07  | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | BETA: splitting (681) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | |   (682)  all_56_9 = e1 & op(e3, e0) = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (675), (682), (function-axioms) are
% 148.65/21.07  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #851.
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | |   (683)  all_56_10 = e1 & op(e2, e0) = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | ALPHA: (683) implies:
% 148.65/21.07  | | | | | | | | | | | | | | | | | |   (684)  all_56_10 = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | | |   (685)  op(e2, e0) = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e1,
% 148.65/21.07  | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (680) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | |   (686)  all_52_7 = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 148.65/21.07  | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (164), (685) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | |   (687)  all_52_13 = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | REDUCE: (110), (687) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | |   (688)   ~ (all_52_14 = e1)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | REDUCE: (371), (687) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | |   (689)   ~ (all_14_2 = e1)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | REDUCE: (360), (687) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | |   (690)   ~ (all_4_2 = e1)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | |   (691)   ~ (all_28_2 = e2)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | REDUCE: (330), (691) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | |   (692)   ~ (all_14_2 = e2)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | |   (693)  all_54_15 = e3
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (693) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | |   (694)  all_14_2 = e3
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (694) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | |   (695)  $false
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | CLOSE: (695) is inconsistent.
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | |   (696)   ~ (all_54_15 = e3)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | |   (697)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (697) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | |   (698)  all_54_15 = e2
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (698) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | |   (699)  all_14_2 = e2
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | REDUCE: (692), (699) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | |   (700)  $false
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | CLOSE: (700) is inconsistent.
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | |   (701)   ~ (all_54_15 = e2)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | |   (702)  all_54_15 = e1 | all_54_15 = e0
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (702) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (703)  all_54_15 = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (703) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (704)  all_14_2 = e1
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (704) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (705)  $false
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (705) is inconsistent.
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (706)  all_54_15 = e0
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (706) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (707)  all_14_2 = e0
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (707) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (708)   ~ (all_52_3 = e0)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (707) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (709)   ~ (all_52_11 = e0)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (707) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (710)   ~ (e3 = e0)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (692), (707) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (711)   ~ (e2 = e0)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (707) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (712)   ~ (e1 = e0)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (707) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | |   (713)  op(e0, e0) = e0
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |   (714)   ~ (all_32_2 = e0)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (714) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | |   (715)   ~ (all_4_2 = e0)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | |   (716)  all_54_5 = e3
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (373), (716) are inconsistent by sub-proof
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | |            #930.
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | |   (717)   ~ (all_54_5 = e3)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | |   (718)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (718) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (719)  all_54_5 = e2
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (719) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (720)  all_4_2 = e2
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (720) implies:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (721)  all_4_2 = e2
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (721) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (722)   ~ (all_52_1 = e2)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (721) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (723)   ~ (all_52_9 = e2)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (721) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (724)   ~ (e3 = e2)
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (721) imply:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (725)  op(e2, e2) = e2
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (726)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (726) gives:
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (727)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (167), (403), (722), (723), (727),
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1000.
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (728)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (728) gives:
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (729)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (729) gives:
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (730)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3)
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (676), (713), (730), (function-axioms)
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #850.
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (731)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (163), (164), (360), (397), (725), (731),
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #849.
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (732)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (732) gives:
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (733)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (403), (684), (723), (733),
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #841.
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (734)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (163), (397), (403), (713), (734),
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #988.
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.65/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (735)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0 & op(e0, e0) = e3 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) |
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e2) = e0) |
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) |
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (735) gives:
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (736)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (736) gives:
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.65/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (737)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (737) gives:
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (738)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (165), (221),
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (398), (684), (723), (738),
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #840.
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (739)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (403), (713), (739),
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #985.
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (740)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14))
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (160), (162), (398), (400), (403),
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (676), (713), (740), (function-axioms) are
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #838.
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (741)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (741) gives:
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (742)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (684), (713), (723), (742),
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #837.
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (743)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0)))
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (743) gives:
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (744)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3)
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (676), (713), (744), (function-axioms)
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #836.
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (745)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (745) gives:
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (746)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (746) implies:
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (747)  op(e2, e0) = e2
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (725), (747),
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (748)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (748) gives:
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (749)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (749) implies:
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (750)  op(e1, e0) = e1
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (750), (function-axioms) are
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (751)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0))
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (751) implies:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (752)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (753)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (754)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (754) gives:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (755)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = e3 & op(e0, e3) = e0
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (755) implies:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (756)  op(e0, e3) = e0
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (708), (756), (function-axioms) are
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (757)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (164), (360), (403), (725), (757),
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #835.
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (758)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (759)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e0, e3) = e0
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (759) implies:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (760)  op(e0, e3) = e0
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (708), (760), (function-axioms) are
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (761)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (164), (360), (676), (725), (761),
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #833.
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (762)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (762) gives:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (763)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (403), (676), (680), (763), (function-axioms)
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #830.
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (764)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (764) gives:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (765)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (164), (360), (403), (725), (765),
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #829.
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (766)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (709), (766), (function-axioms) are
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (767)  all_54_5 = e1 | all_54_5 = e0
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (405), (715), (767) are inconsistent by
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | |   (768)  all_32_2 = e0
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (768) imply:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | |   (769)  all_4_2 = e0
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (769) imply:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | |   (770)  op(e2, e2) = e0
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |   (771)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (771) gives:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (772)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (772) gives:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (773)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (774)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (676), (770), (774), (function-axioms)
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #827.
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (775)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (403), (770), (775), (function-axioms)
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #933.
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (776)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_12))
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives:
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (777)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (713), (770), (777), (function-axioms)
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #826.
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.94/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (778)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (403), (676), (770), (778),
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #824.
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (779)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (779) gives:
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (780)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (780) gives:
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (781)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (676), (713), (781), (function-axioms)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #850.
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (782)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (397), (676), (782), (function-axioms)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #823.
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (783)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives:
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (784)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (403), (770), (784), (function-axioms)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #921.
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (785)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 149.16/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (163), (397), (403), (713), (785),
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #988.
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |   (786)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0 & op(e0, e0) = e3 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) |
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e2) = e0) |
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) |
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (786) gives:
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (787)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (787) gives:
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (788)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (788) gives:
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (789)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (398), (770), (789), (function-axioms)
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #822.
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (790)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (403), (713), (790),
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #985.
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (791)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14))
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (160), (162), (398), (400), (403),
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (676), (713), (791), (function-axioms) are
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #838.
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (792)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (792) gives:
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (793)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (713), (770), (793),
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            #918.
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (794)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0)))
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (794) gives:
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (795)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3)
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (676), (713), (795), (function-axioms)
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #836.
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (796)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (796) gives:
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (797)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (797) implies:
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (798)  op(e2, e2) = e2
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (770), (798), (function-axioms) are
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (799)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (799) gives:
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (800)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (800) implies:
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (801)  op(e1, e0) = e1
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (801), (function-axioms) are
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (802)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0))
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (802) implies:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (803)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (159), (403), (676), (680), (708),
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (709), (803), (function-axioms) are inconsistent
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #819.
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | |   (804)  all_28_2 = e2
% 149.16/21.21  | | | | | | | | | | | | | | | | | | |   (805)  ( ~ (all_28_0 = e1) & op(e2, e0) = all_28_0 &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | |            $i(all_28_0)) | ( ~ (all_28_1 = e3) & op(e2, e2)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | |            = all_28_1 & $i(all_28_1))
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (804) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | |   (806)  all_14_2 = e2
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | SIMP: (806) implies:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | |   (807)  all_14_2 = e2
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | REDUCE: (370), (807) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | |   (808)   ~ (all_52_12 = e2)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | REDUCE: (372), (807) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | |   (809)   ~ (all_52_14 = e2)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | REDUCE: (380), (807) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | |   (810)   ~ (e3 = e2)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | REDUCE: (51), (807) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | |   (811)  op(e0, e0) = e2
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | BETA: splitting (805) gives:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |   (812)   ~ (all_28_0 = e1) & op(e2, e0) = all_28_0 &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |          $i(all_28_0)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | ALPHA: (812) implies:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |   (813)   ~ (all_28_0 = e1)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |   (814)  op(e2, e0) = all_28_0
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_28_0,
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (685), (814) gives:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |   (815)  all_28_0 = e1
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (813), (815) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |   (816)  $false
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | CLOSE: (816) is inconsistent.
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |   (817)   ~ (all_28_1 = e3) & op(e2, e2) = all_28_1 &
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |          $i(all_28_1)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | ALPHA: (817) implies:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |   (818)   ~ (all_28_1 = e3)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |   (819)  op(e2, e2) = all_28_1
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |              all_28_1, e2, e2, simplifying with (36), (819)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |              gives:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | |   (820)  all_28_1 = all_4_2
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | |   (821)   ~ (all_32_2 = e0)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (821) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | |   (822)   ~ (all_4_2 = e0)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | |   (823)  all_54_5 = e3
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (373), (823) are inconsistent by sub-proof
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | |            #930.
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | |   (824)   ~ (all_54_5 = e3)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | |   (825)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (825) gives:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | |   (826)  all_54_5 = e2
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (826) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | |   (827)  all_4_2 = e2
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (827) implies:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | |   (828)  all_4_2 = e2
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (828) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | |   (829)   ~ (all_52_1 = e2)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (828) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | |   (830)   ~ (all_52_6 = e2)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (828) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | |   (831)   ~ (all_52_9 = e2)
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (828) imply:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | |   (832)  op(e2, e2) = e2
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |   (833)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (833) gives:
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (834)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (167), (403), (829), (831), (834),
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            #1000.
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (835)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (835) gives:
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (836)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (160), (163), (164), (168), (211),
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            (360), (397), (676), (808), (809), (832), (836),
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            #818.
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (837)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (837) gives:
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (838)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (403), (684), (831), (838),
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #841.
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (839)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (163), (397), (403), (811), (839),
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #874.
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.16/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |   (840)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0 & op(e0, e0) = e3 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) |
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e2) = e0) |
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) |
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (840) gives:
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.16/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (841)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.53/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.53/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.53/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (841) gives:
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (842)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (842) gives:
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (843)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (165), (221),
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (398), (684), (831), (843),
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #840.
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (844)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (403), (811), (844), (function-axioms) are
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (845)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14))
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (845) gives:
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (846)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1)
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (398), (403), (846), (function-axioms)
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #983.
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (847)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (847) gives:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (848)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (848) implies:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (849)  op(e0, e0) = e3
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (160), (164), (168), (211), (360),
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (808), (809), (832), (849), (function-axioms) are
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #877.
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (850)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14))
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (676), (850), (function-axioms) are
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #839.
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (851)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (851) gives:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (852)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (852) gives:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (853)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2)
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (831), (853), (function-axioms) are
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #871.
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (854)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (854) gives:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (855)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_14)
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (855) implies:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (856)  op(e2, e2) = e1
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (684), (831), (856), (function-axioms) are
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #842.
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (857)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (857) implies:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (858)  op(e0, e0) = e3
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (160), (164), (168), (211), (360),
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (808), (809), (832), (858), (function-axioms) are
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #877.
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (859)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0)))
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (859) gives:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (860)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3)
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (164), (360), (676), (832), (860),
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #817.
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (861)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (861) gives:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (862)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (862) implies:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (863)  op(e2, e0) = e2
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (832), (863),
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (864)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (864) gives:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (865)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (865) implies:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (866)  op(e1, e0) = e1
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (866), (function-axioms) are
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (867)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0))
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (867) implies:
% 149.53/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (868)  op(e0, e0) = all_57_15
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (869)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (870)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (870) gives:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (811), (868)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (871)  all_57_15 = e2
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (869) gives:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (872)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (872) gives:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (873)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (873) gives:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (874)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = e3 & op(e0, e3) = e0
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (874) implies:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (875)  op(e3, e3) = e0
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (676), (875), (function-axioms) are
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (876)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (164), (360), (403), (832), (876),
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #835.
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (877)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (877) gives:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (878)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e0, e3) = e0
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (871), (878) are inconsistent by sub-proof
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #865.
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (879)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (164), (360), (676), (832), (879),
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #833.
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (880)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (880) gives:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.53/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (881)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (403), (676), (680), (881), (function-axioms)
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #830.
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (882)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (882) gives:
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (883)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (164), (360), (403), (832), (883),
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #829.
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (884)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (400), (871), (884), (function-axioms)
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #860.
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (885)  all_56_7 = e2 & op(e1, e2) = e2
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (830), (885), (function-axioms) are
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (886)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (403), (809), (886), (function-axioms)
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #815.
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | |   (887)  all_54_5 = e1 | all_54_5 = e0
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (405), (822), (887) are inconsistent by
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | |   (888)  all_32_2 = e0
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (888) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | |   (889)  all_4_2 = e0
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | SIMP: (889) implies:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | |   (890)  all_4_2 = e0
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (890) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | |   (891)   ~ (e3 = e0)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (890) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | |   (892)   ~ (e1 = e0)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (890) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | |   (893)  op(e2, e2) = e0
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |   (894)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                  e3) = all_57_6 & $i(all_57_6)))) |
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_7 & $i(all_57_7))))
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (676), (893), (894), (function-axioms)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #814.
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |   (895)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_8 & $i(all_57_8)))) |
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13))))
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (895) gives:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |   (896)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & $i(all_57_8)))
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (896) implies:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |   (897)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (163),
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |            (239), (397), (398), (400), (403), (676), (680),
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |            (685), (811), (893), (897), (function-axioms) are
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #806.
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |   (898)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_57_13 & $i(all_57_13)))
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (898) implies:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |   (899)  op(e0, e0) = e0
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (811), (899), (function-axioms) are
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.29  | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | End of split
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (900)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 149.68/21.29  | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (160), (378), (400), (900),
% 149.68/21.29  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.68/21.29  | | | | | | | | | | | | | | | | |            #804.
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | End of split
% 149.68/21.29  | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | End of split
% 149.68/21.29  | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | Case 2:
% 149.68/21.29  | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | |   (901)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 149.68/21.29  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 149.68/21.29  | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | REF_CLOSE: (51), (157), (378), (399), (901),
% 149.68/21.29  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.68/21.29  | | | | | | | | | | | | | | |            #802.
% 149.68/21.29  | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | End of split
% 149.68/21.29  | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | End of split
% 149.68/21.29  | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | Case 2:
% 149.68/21.29  | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | |   (902)  all_24_2 = e1
% 149.68/21.29  | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | COMBINE_EQS: (318), (902) imply:
% 149.68/21.29  | | | | | | | | | | | | |   (903)  all_4_2 = e1
% 149.68/21.29  | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | SIMP: (903) implies:
% 149.68/21.29  | | | | | | | | | | | | |   (904)  all_4_2 = e1
% 149.68/21.29  | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | REDUCE: (356), (904) imply:
% 149.68/21.29  | | | | | | | | | | | | |   (905)   ~ (all_52_7 = e1)
% 149.68/21.29  | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | REDUCE: (360), (904) imply:
% 149.68/21.29  | | | | | | | | | | | | |   (906)   ~ (all_52_13 = e1)
% 149.68/21.29  | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | REDUCE: (36), (904) imply:
% 149.68/21.29  | | | | | | | | | | | | |   (907)  op(e2, e2) = e1
% 149.68/21.29  | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | BETA: splitting (207) gives:
% 149.68/21.29  | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | Case 1:
% 149.68/21.29  | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | |   (908)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 149.68/21.29  | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 149.68/21.29  | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | BETA: splitting (908) gives:
% 149.68/21.29  | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | Case 1:
% 149.68/21.29  | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | |   (909)  all_56_12 = e1 & op(e0, e3) = e1
% 149.68/21.29  | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | ALPHA: (909) implies:
% 149.68/21.29  | | | | | | | | | | | | | | |   (910)  all_56_12 = e1
% 149.68/21.29  | | | | | | | | | | | | | | |   (911)  op(e0, e3) = e1
% 149.68/21.29  | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 149.68/21.29  | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | Case 1:
% 149.68/21.29  | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | |   (912)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 149.68/21.29  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 149.68/21.29  | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | BETA: splitting (912) gives:
% 149.68/21.29  | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (913)  all_56_9 = e1 & op(e3, e0) = e1
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | ALPHA: (913) implies:
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (914)  all_56_9 = e1
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (915)  op(e3, e0) = e1
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 149.68/21.29  | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (911) gives:
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (916)  all_52_3 = e1
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 149.68/21.29  | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (168), (915) gives:
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (917)  all_52_12 = e1
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | REDUCE: (148), (916) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (918)   ~ (all_52_1 = e1)
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | REDUCE: (140), (916) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (919)   ~ (all_52_7 = e1)
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | REDUCE: (139), (916) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (920)   ~ (all_52_11 = e1)
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | REDUCE: (112), (917) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (921)   ~ (all_52_14 = e1)
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | REDUCE: (370), (917) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (922)   ~ (all_14_2 = e1)
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | REDUCE: (348), (917) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (923)   ~ (all_6_2 = e1)
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | SIMP: (923) implies:
% 149.68/21.29  | | | | | | | | | | | | | | | | |   (924)   ~ (all_6_2 = e1)
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 149.68/21.29  | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | |   (925)  all_54_0 = e3
% 149.68/21.29  | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (925) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | | |   (926)  all_6_2 = e3
% 149.68/21.29  | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | REDUCE: (338), (926) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | | |   (927)   ~ (all_52_1 = e3)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | REDUCE: (344), (926) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | | |   (928)   ~ (all_52_4 = e3)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | REDUCE: (346), (926) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | | |   (929)   ~ (all_52_8 = e3)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | REDUCE: (39), (926) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | | |   (930)  op(e3, e3) = e3
% 149.68/21.29  | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | |   (931)   ~ (all_28_2 = e2)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | REDUCE: (330), (931) imply:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | |   (932)   ~ (all_14_2 = e2)
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.29  | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |   (933)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |          (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | |            e1)
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | BETA: splitting (933) gives:
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |   (934)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (934) gives:
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.30  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |   (935)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (935) gives:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |   (936)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (907), (930), (936), (function-axioms)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #801.
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |   (937)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (403), (907), (937), (function-axioms)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #800.
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |   (938)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_12))
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (938) gives:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |   (939)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (939) gives:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (940)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |          = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_12)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (940) implies:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (941)  op(e0, e0) = e2
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (189), (246), (378), (380), (932), (941),
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            #797.
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (942)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (942) implies:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (943)  op(e3, e0) = e3
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (915), (943), (function-axioms) are
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #796.
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |   (944)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (403), (907), (944), (function-axioms)
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #793.
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.31  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |   (945)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | |            e1)
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (945) gives:
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |   (946)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (946) gives:
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |   (947)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3)
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (928), (947), (function-axioms) are
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #792.
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |   (948)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (930), (948), (function-axioms) are
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |   (949)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | |            e1)
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (949) gives:
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |   (950)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (397), (403), (950), (function-axioms)
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #791.
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | |   (951)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | |            e1)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (951) gives:
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |   (952)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |          = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_14)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (952) implies:
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |   (953)  op(e0, e0) = e1
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (189), (246), (378), (380), (932), (953),
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |            #789.
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |   (954)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (397), (403), (954), (function-axioms)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #989.
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | End of split
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |   (955)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0 & op(e0, e0) = e3 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |            & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) |
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e2) = e0) |
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) |
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |              (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | |                = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | BETA: splitting (955) gives:
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.68/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |   (956)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (956) gives:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |   (957)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (957) gives:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (958)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (398), (930), (958), (function-axioms)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #788.
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (959)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (959) gives:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (960)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |          e2 & $i(all_57_12)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (960) implies:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (961)  op(e1, e1) = e2
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (403), (961), (function-axioms) are
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (962)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |          = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_14)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (962) implies:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (963)  op(e0, e0) = e1
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (189), (246), (378), (380), (932), (963),
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | |            #789.
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |   (964)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | |            & $i(all_57_14))
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (964) gives:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (965)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (398), (403), (965), (function-axioms)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #983.
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (966)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (929), (930), (966), (function-axioms)
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #787.
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |   (967)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | |                e0)))
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (967) gives:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |   (968)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (968) gives:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |   (969)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2)
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (969) gives:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (970)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          e2 & $i(all_57_12)
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (970) implies:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (971)  op(e0, e0) = e2
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (189), (246), (378), (380), (932), (971),
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |            #797.
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (972)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e1) = e2
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (972) implies:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (973)  op(e2, e2) = e2
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (907), (973), (function-axioms) are
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |   (974)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (974) gives:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (975)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_14)
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (975) implies:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (976)  op(e1, e0) = e1
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (976), (function-axioms) are
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (977)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (977) implies:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (978)  op(e3, e0) = e3
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (915), (978), (function-axioms) are
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #796.
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |   (979)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0)))
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (979) gives:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |   (980)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3)
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (980) gives:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (981)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          e2 & $i(all_57_12)
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (981) implies:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (982)  op(e0, e0) = e2
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (189), (246), (378), (380), (932), (982),
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |            #797.
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (983)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e0) = e3
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (983) implies:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (984)  op(e3, e0) = e3
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (915), (984), (function-axioms) are
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #796.
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |   (985)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (985) gives:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |   (986)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (986) implies:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |   (987)  op(e2, e2) = e2
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (907), (987), (function-axioms) are
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |   (988)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | |                e0)))
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (988) gives:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (989)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (989) implies:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (990)  op(e1, e0) = e1
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (990), (function-axioms) are
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (991)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e0))
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (991) implies:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (992)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (993)  all_54_15 = e3
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (993) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (994)  all_14_2 = e3
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (994) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (995)  $false
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (995) is inconsistent.
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (996)   ~ (all_54_15 = e3)
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (997)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (997) gives:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (998)  all_54_15 = e2
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (998) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (999)  all_14_2 = e2
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (932), (999) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1000)  $false
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1000) is inconsistent.
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1001)  all_54_15 = e1 | all_54_15 = e0
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1001) gives:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1002)  all_54_15 = e1
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1002) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1003)  all_14_2 = e1
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (1003) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1004)  $false
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1004) is inconsistent.
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1005)  all_54_15 = e0
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1005) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1006)  all_14_2 = e0
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1006) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1007)   ~ (all_52_7 = e0)
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (1006) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1008)   ~ (all_52_11 = e0)
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (1006) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1009)   ~ (e3 = e0)
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (1006) imply:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1010)   ~ (e1 = e0)
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (992) gives:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1011)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1011) gives:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1012)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1012) gives:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1013)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1013) implies:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1014)  op(e0, e3) = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (911), (1014), (function-axioms) are
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1015)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1015) gives:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1016)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e3) = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1016) implies:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1017)  op(e2, e2) = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (907), (1017), (function-axioms) are
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1018)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e3) = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1018) implies:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1019)  op(e1, e1) = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (403), (1019), (function-axioms) are
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1020)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (907), (911), (930), (1020),
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #785.
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1021)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1021) gives:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1022)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (158), (403), (930), (1007), (1022),
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #784.
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1023)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1023) gives:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1024)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1024) gives:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1025)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e1) = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1025) implies:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1026)  op(e2, e2) = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (907), (1026), (function-axioms) are
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1027)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e1) = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1027) implies:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1028)  op(e1, e1) = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (403), (1028), (function-axioms) are
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1029)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1008), (1029), (function-axioms) are
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | |   (1030)  all_28_2 = e2
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (1030) imply:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | |   (1031)  all_14_2 = e2
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (1031) imply:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | |   (1032)  all_50_2 = e2
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1031) imply:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | |   (1033)   ~ (all_52_7 = e2)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | REDUCE: (369), (1031) imply:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | |   (1034)   ~ (all_52_11 = e2)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | REDUCE: (371), (1031) imply:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | |   (1035)   ~ (all_52_13 = e2)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | REDUCE: (380), (1031) imply:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | |   (1036)   ~ (e3 = e2)
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | REDUCE: (51), (1031) imply:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | |   (1037)  op(e0, e0) = e2
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |   (1038)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | |             e1)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1038) gives:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |   (1039)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1039) gives:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |   (1040)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1040) gives:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (1041)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (907), (930), (1041), (function-axioms)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #801.
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (1042)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1042) gives:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1043)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1043) implies:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1044)  op(e1, e1) = e2
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1045)  op(e2, e3) = e2
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (238), (907), (1037), (1044),
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |            (1045), (function-axioms) are inconsistent by
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #779.
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1046)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1046) implies:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1047)  op(e2, e2) = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (907), (1047), (function-axioms) are
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |   (1048)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1048) gives:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (1049)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1049) gives:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1050)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1050) implies:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1051)   ~ (all_57_12 = e3)
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1052)  op(e0, e2) = e0
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1053)  op(e2, e2) = all_57_12
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1054)  op(e2, e3) = e2
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (1055)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (907), (1054), (1055), (function-axioms)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #781.
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (1056)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1056) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1057)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1057) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1058)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1059)  (all_57_10 = e1 & op(e3, e3) = e1) | ( ~ (all_57_4
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1059) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1060)  all_57_10 = e1 & op(e3, e3) = e1
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1060) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1061)  op(e3, e3) = e1
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (930), (1061), (function-axioms) are
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1062)   ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1062) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1063)  op(e3, e1) = all_57_4
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1058) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1064)  all_57_15 = e1 & op(e0, e0) = e1
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1064) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1065)  op(e0, e0) = e1
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1037), (1065), (function-axioms) are
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1066)   ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_8)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1066) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1067)  op(e0, e1) = all_57_8
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_8, e1, e0, simplifying with (157), (1067)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1068)  all_57_8 = all_52_11
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (1052) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1069)  all_52_7 = e0
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (907), (1053)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1070)  all_57_12 = e1
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (1054) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1071)  all_52_1 = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4, e1, e3, simplifying with (169), (1063)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1072)  all_57_4 = all_52_8
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1071) imply:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1073)   ~ (all_52_2 = e2)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1073) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1074)   ~ (all_52_2 = e2)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1071) imply:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1075)   ~ (all_52_9 = e2)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1075) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1076)   ~ (all_52_9 = e2)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (1069) imply:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1077)   ~ (all_52_11 = e0)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1077) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1078)   ~ (all_52_11 = e0)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1033), (1069) imply:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1079)   ~ (e2 = e0)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (905), (1069) imply:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1080)   ~ (e1 = e0)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1081)  all_56_15 = e0 & op(e0, e0) = e0
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1081) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1082)  op(e0, e0) = e0
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1037), (1082), (function-axioms) are
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1083)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1083) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1084)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1085)  all_54_14 = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1085) imply:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1086)  all_52_11 = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1086) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1087)  all_52_11 = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1087) imply:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1088)   ~ (all_52_9 = e3)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1089)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (907), (930), (1089), (function-axioms) are
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #764.
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1090)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1090) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1091)  all_56_5 = e3 & op(e2, e1) = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1091) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1092)  op(e2, e1) = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1088), (1092), (function-axioms) are
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #763.
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1093)  all_56_10 = e3 & op(e2, e0) = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1093) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1094)  all_56_10 = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1095)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (907), (930), (1095), (function-axioms) are
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #762.
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1096)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1096) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1097)  all_56_7 = e3 & op(e1, e2) = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1097) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1098)  all_56_7 = e3
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1099)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1099) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1100)  all_56_4 = e2 & op(e3, e1) = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1100) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1101)  all_56_4 = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1102)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1102) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1103)  all_56_6 = e2 & op(e1, e3) = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1074), (1103), (function-axioms) are
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1104)  all_56_7 = e2 & op(e1, e2) = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1104) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1105)  all_56_7 = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1098), (1105) imply:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1106)  e3 = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1106) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1107)  e3 = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1094), (1107) imply:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1108)  all_56_10 = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (210), (212),
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (930), (1037), (1101), (1108),
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #752.
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1109)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1109) gives:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1110)  all_56_8 = e2 & op(e1, e1) = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1110) implies:
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1111)  op(e1, e1) = e2
% 149.90/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (51), (73), (157), (158),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (162), (163), (165), (168), (169), (170),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (189), (204), (233), (238), (239), (246), (279),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (330), (344), (346), (348), (351), (362), (369),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (377), (378), (380), (398), (907), (924),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1074), (1076), (1111), (function-axioms) are
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #741.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1112)  all_56_11 = e2 & op(e1, e0) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1112) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1113)  all_56_11 = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (914), (1084), (1094), (1113) are
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #738.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1114)  all_56_5 = e2 & op(e2, e1) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1114) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1115)  op(e2, e1) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1076), (1115), (function-axioms) are
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1116)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1116) gives:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1117)  all_56_8 = e2 & op(e1, e1) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1117) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1118)  op(e1, e1) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (51), (73), (157), (158),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (162), (163), (165), (168), (169), (170),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (189), (204), (233), (238), (239), (246), (279),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (330), (344), (346), (348), (351), (362), (369),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (377), (378), (380), (398), (907), (924),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1074), (1076), (1118), (function-axioms) are
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #741.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1119)  all_56_14 = e2 & op(e0, e1) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (207), (209),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (231), (233), (930), (1037), (1119),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #721.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1120)  all_56_13 = e3 & op(e0, e2) = e3
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1120) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1121)  op(e0, e2) = e3
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1052), (1121), (function-axioms) are
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #726.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1122)   ~ (all_54_14 = e3)
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (247), (1122) imply:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1123)   ~ (all_52_11 = e3)
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1124)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1124) gives:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1125)  all_56_0 = e2 & op(e3, e3) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1125) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1126)  op(e3, e3) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (930), (1126), (function-axioms) are
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1127)  all_56_2 = e2 & op(e2, e3) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1127) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1128)  all_56_2 = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1129)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1129) gives:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1130)  all_56_12 = e3 & op(e0, e3) = e3
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1130) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1131)  all_56_12 = e3
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (229), (231), (930),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1128), (1131), (function-axioms) are inconsistent
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #734.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1132)  all_56_13 = e3 & op(e0, e2) = e3
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1132) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1133)  op(e0, e2) = e3
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1052), (1133), (function-axioms) are
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #726.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1134)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (1037), (1123), (1134),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #719.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1135)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (910), (1074), (1135),
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #717.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1136)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1136) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1137)  op(e0, e0) = e0
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1037), (1137), (function-axioms) are
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |   (1138)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1138) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |   (1139)  op(e2, e2) = e3
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (907), (1139), (function-axioms) are
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | |   (1140)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1140) gives:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |   (1141)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1141) implies:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |   (1142)  op(e2, e2) = e2
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (907), (1142), (function-axioms) are
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |   (1143)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.90/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (403), (930), (1143), (function-axioms)
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #924.
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |   (1144)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | |             e1)
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1144) gives:
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |   (1145)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1145) gives:
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (1146)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (928), (1037), (1146),
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |            #856.
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (1147)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (930), (1035), (1147),
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |            #994.
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |   (1148)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | |             e1)
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1148) gives:
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (1149)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (397), (403), (1149),
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | |            #791.
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |   (1150)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (163), (397), (403), (1037), (1150),
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | |            #874.
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |   (1151)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1151) gives:
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | |   (1152)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.90/21.42  | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1152) gives:
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |   (1153)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1153) gives:
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (1154)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (398), (930), (1154),
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |            #788.
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (1155)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (403), (1037), (1155), (function-axioms) are
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |   (1156)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1156) gives:
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (1157)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (398), (403), (1157),
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (1158)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 149.90/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (169), (929), (930), (1037), (1158),
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | |            #855.
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |   (1159)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1159) gives:
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |   (1160)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (400), (907), (1037), (1160),
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | |            #716.
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.44  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |   (1161)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1161) gives:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |   (1162)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (915), (1035), (1162),
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |            #715.
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |   (1163)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1163) gives:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |   (1164)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1164) implies:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |   (1165)  op(e2, e2) = e2
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (907), (1165), (function-axioms) are
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |   (1166)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1166) gives:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (1167)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1167) implies:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (1168)  op(e1, e0) = e1
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (400), (1168), (function-axioms) are
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.90/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (1169)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1169) implies:
% 149.90/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (1170)  op(e0, e0) = all_57_15
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (1171)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1172)   ~ (all_50_2 = e2)
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1032), (1172) imply:
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1173)  $false
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1173) is inconsistent.
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1174)  ( ~ (all_50_0 = e3) & op(e2, e0) = all_50_0 &
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_50_0)) | ( ~ (all_50_1 = e1) & op(e2, e2)
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (160), (164), (400), (403), (907),
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            (930), (1035), (1037), (1170), (1171), (1174),
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            #714.
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.46  | | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.46  | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.46  | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | |   (1175)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 150.12/21.46  | | | | | | | | | | | | | | | | | | 
% 150.12/21.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (924), (1175) are
% 150.12/21.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 150.12/21.47  | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | End of split
% 150.12/21.47  | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | |   (1176)  all_56_10 = e1 & op(e2, e0) = e1
% 150.12/21.47  | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (906), (1176), (function-axioms) are
% 150.12/21.47  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 150.12/21.47  | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | End of split
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | |   (1177)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 150.12/21.47  | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | REF_CLOSE: (51), (160), (378), (400), (1177),
% 150.12/21.47  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.47  | | | | | | | | | | | | | | | |            #804.
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | End of split
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | |   (1178)  all_56_13 = e1 & op(e0, e2) = e1
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | REF_CLOSE: (158), (905), (1178), (function-axioms) are
% 150.12/21.47  | | | | | | | | | | | | | | |            inconsistent by sub-proof #712.
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | End of split
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | |   (1179)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 150.12/21.47  | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | REF_CLOSE: (51), (157), (378), (399), (1179),
% 150.12/21.47  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.47  | | | | | | | | | | | | | |            #802.
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | End of split
% 150.12/21.47  | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | End of split
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | |   (1180)  all_54_10 = e0
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | COMBINE_EQS: (336), (1180) imply:
% 150.12/21.47  | | | | | | | | | | | |   (1181)  all_10_2 = e0
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | REDUCE: (384), (1181) imply:
% 150.12/21.47  | | | | | | | | | | | |   (1182)  $false
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | CLOSE: (1182) is inconsistent.
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | End of split
% 150.12/21.47  | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | End of split
% 150.12/21.47  | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | End of split
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | |   (1183)  all_22_2 = e0
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | COMBINE_EQS: (251), (1183) imply:
% 150.12/21.47  | | | | | | | | |   (1184)  all_10_2 = e0
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | SIMP: (1184) implies:
% 150.12/21.47  | | | | | | | | |   (1185)  all_10_2 = e0
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | COMBINE_EQS: (333), (1185) imply:
% 150.12/21.47  | | | | | | | | |   (1186)  all_38_2 = e0
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | REDUCE: (350), (1185) imply:
% 150.12/21.47  | | | | | | | | |   (1187)   ~ (all_52_2 = e0)
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | REDUCE: (361), (1185) imply:
% 150.12/21.47  | | | | | | | | |   (1188)   ~ (all_52_6 = e0)
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | REDUCE: (363), (1185) imply:
% 150.12/21.47  | | | | | | | | |   (1189)   ~ (all_52_8 = e0)
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | REDUCE: (366), (1185) imply:
% 150.12/21.47  | | | | | | | | |   (1190)   ~ (all_52_11 = e0)
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | REDUCE: (382), (1185) imply:
% 150.12/21.47  | | | | | | | | |   (1191)   ~ (e3 = e0)
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | REDUCE: (375), (1185) imply:
% 150.12/21.47  | | | | | | | | |   (1192)   ~ (e2 = e0)
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | REDUCE: (45), (1185) imply:
% 150.12/21.47  | | | | | | | | |   (1193)  op(e1, e1) = e0
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | BETA: splitting (67) gives:
% 150.12/21.47  | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | |   (1194)   ~ (all_24_2 = e1)
% 150.12/21.47  | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | REDUCE: (318), (1194) imply:
% 150.12/21.47  | | | | | | | | | |   (1195)   ~ (all_4_2 = e1)
% 150.12/21.47  | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | BETA: splitting (70) gives:
% 150.12/21.47  | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | |   (1196)   ~ (all_26_2 = e1)
% 150.12/21.47  | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | REDUCE: (307), (1196) imply:
% 150.12/21.47  | | | | | | | | | | |   (1197)   ~ (all_6_2 = e1)
% 150.12/21.47  | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | BETA: splitting (204) gives:
% 150.12/21.47  | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | |   (1198)  all_54_0 = e3
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | COMBINE_EQS: (279), (1198) imply:
% 150.12/21.47  | | | | | | | | | | | |   (1199)  all_6_2 = e3
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | REDUCE: (340), (1199) imply:
% 150.12/21.47  | | | | | | | | | | | |   (1200)   ~ (all_52_2 = e3)
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | REDUCE: (342), (1199) imply:
% 150.12/21.47  | | | | | | | | | | | |   (1201)   ~ (all_52_3 = e3)
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | REDUCE: (344), (1199) imply:
% 150.12/21.47  | | | | | | | | | | | |   (1202)   ~ (all_52_4 = e3)
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | REDUCE: (346), (1199) imply:
% 150.12/21.47  | | | | | | | | | | | |   (1203)   ~ (all_52_8 = e3)
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | REDUCE: (348), (1199) imply:
% 150.12/21.47  | | | | | | | | | | | |   (1204)   ~ (all_52_12 = e3)
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | REDUCE: (39), (1199) imply:
% 150.12/21.47  | | | | | | | | | | | |   (1205)  op(e3, e3) = e3
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | BETA: splitting (73) gives:
% 150.12/21.47  | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | |   (1206)   ~ (all_28_2 = e2)
% 150.12/21.47  | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | REDUCE: (330), (1206) imply:
% 150.12/21.47  | | | | | | | | | | | | |   (1207)   ~ (all_14_2 = e2)
% 150.12/21.47  | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | BETA: splitting (189) gives:
% 150.12/21.47  | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | |   (1208)  all_54_15 = e3
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | COMBINE_EQS: (246), (1208) imply:
% 150.12/21.47  | | | | | | | | | | | | | |   (1209)  all_14_2 = e3
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | REDUCE: (380), (1209) imply:
% 150.12/21.47  | | | | | | | | | | | | | |   (1210)  $false
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | CLOSE: (1210) is inconsistent.
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | |   (1211)   ~ (all_54_15 = e3)
% 150.12/21.47  | | | | | | | | | | | | | |   (1212)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | BETA: splitting (1212) gives:
% 150.12/21.47  | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | |   (1213)  all_54_15 = e2
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1213) imply:
% 150.12/21.47  | | | | | | | | | | | | | | |   (1214)  all_14_2 = e2
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | REDUCE: (1207), (1214) imply:
% 150.12/21.47  | | | | | | | | | | | | | | |   (1215)  $false
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | CLOSE: (1215) is inconsistent.
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | |   (1216)  all_54_15 = e1 | all_54_15 = e0
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | BETA: splitting (1216) gives:
% 150.12/21.47  | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | |   (1217)  all_54_15 = e1
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1217) imply:
% 150.12/21.47  | | | | | | | | | | | | | | | |   (1218)  all_14_2 = e1
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | REDUCE: (378), (1218) imply:
% 150.12/21.47  | | | | | | | | | | | | | | | |   (1219)  $false
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | CLOSE: (1219) is inconsistent.
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | |   (1220)  all_54_15 = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1220) imply:
% 150.12/21.47  | | | | | | | | | | | | | | | |   (1221)  all_14_2 = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | REDUCE: (351), (1221) imply:
% 150.12/21.47  | | | | | | | | | | | | | | | |   (1222)   ~ (all_52_3 = e0)
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | REDUCE: (370), (1221) imply:
% 150.12/21.47  | | | | | | | | | | | | | | | |   (1223)   ~ (all_52_12 = e0)
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | REDUCE: (378), (1221) imply:
% 150.12/21.47  | | | | | | | | | | | | | | | |   (1224)   ~ (e1 = e0)
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | REDUCE: (51), (1221) imply:
% 150.12/21.47  | | | | | | | | | | | | | | | |   (1225)  op(e0, e0) = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 150.12/21.47  | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | |   (1226)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 150.12/21.47  | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | BETA: splitting (1226) gives:
% 150.12/21.47  | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | |   (1227)  all_56_0 = e0 & op(e3, e3) = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | ALPHA: (1227) implies:
% 150.12/21.47  | | | | | | | | | | | | | | | | | |   (1228)  op(e3, e3) = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1205), (1228), (function-axioms) are
% 150.12/21.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 150.12/21.47  | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | |   (1229)  all_56_2 = e0 & op(e2, e3) = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | ALPHA: (1229) implies:
% 150.12/21.47  | | | | | | | | | | | | | | | | | |   (1230)  op(e2, e3) = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 150.12/21.47  | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | |   (1231)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (1231) gives:
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | |   (1232)  all_56_0 = e0 & op(e3, e3) = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | | ALPHA: (1232) implies:
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | |   (1233)  op(e3, e3) = e0
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1205), (1233), (function-axioms) are
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.47  | | | | | | | | | | | | | | | | | | | |   (1234)  all_56_1 = e0 & op(e3, e2) = e0
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | ALPHA: (1234) implies:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | |   (1235)  op(e3, e2) = e0
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (1230) gives:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | |   (1236)  all_52_1 = e0
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (1235) gives:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | |   (1237)  all_52_4 = e0
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (1236) imply:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | |   (1238)   ~ (all_52_3 = e0)
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1237) imply:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | |   (1239)   ~ (all_52_7 = e0)
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | SIMP: (1239) implies:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | |   (1240)   ~ (all_52_7 = e0)
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (1237) imply:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | |   (1241)   ~ (all_4_2 = e0)
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | SIMP: (1241) implies:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | |   (1242)   ~ (all_4_2 = e0)
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | |   (1243)  all_54_5 = e3
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (1243) imply:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | |   (1244)  all_4_2 = e3
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1244) imply:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | |   (1245)  $false
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | CLOSE: (1245) is inconsistent.
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | |   (1246)   ~ (all_54_5 = e3)
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | |   (1247)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1247) gives:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | |   (1248)  all_54_5 = e2
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (1248) imply:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | |   (1249)  all_4_2 = e2
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (1249) imply:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | |   (1250)   ~ (all_52_9 = e2)
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1249) imply:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | |   (1251)   ~ (e3 = e2)
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1249) imply:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | |   (1252)  op(e2, e2) = e2
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |   (1253)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.12/21.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1253) gives:
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |   (1254)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1254) gives:
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (1255)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1255) gives:
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1256)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.12/21.49  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (373), (1205), (1256),
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            #710.
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1257)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1257) gives:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1258)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1258) implies:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1259)  op(e1, e1) = e2
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1193), (1259), (function-axioms) are
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1260)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1260) implies:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1261)  op(e2, e2) = e3
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1261), (function-axioms) are
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #711.
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (1262)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1262) gives:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1263)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (1204), (1225), (1263),
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            #932.
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1264)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (165), (1193), (1230), (1250), (1264),
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            #707.
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (1265)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1265) gives:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (1266)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1266) gives:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1267)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (1202), (1225), (1267),
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            #997.
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1268)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (164), (360), (1205), (1252), (1268),
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            #706.
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (1269)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1269) gives:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1270)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (1193), (1252), (1270),
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            #705.
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1271)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (51), (246), (378), (1193), (1216),
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (1271), (function-axioms) are inconsistent by
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #703.
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |   (1272)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1272) gives:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |   (1273)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1273) gives:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (1274)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1274) gives:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1275)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (1205), (1252), (1275),
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            #987.
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1276)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (51), (246), (378), (1193), (1216), (1276),
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            #702.
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (1277)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1277) gives:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1278)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1193), (1278), (function-axioms) are
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1279)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (169), (1203), (1205), (1225), (1279),
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            #980.
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |   (1280)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1280) gives:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (1281)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1281) gives:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1282)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (165), (1225), (1250), (1282),
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            #978.
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1283)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (1225), (1252), (1283),
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            #977.
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (1284)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1284) gives:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1285)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (1204), (1225), (1285),
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            #975.
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1286)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1286) gives:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1287)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1287) implies:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1288)  op(e2, e0) = e2
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (1252), (1288),
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1289)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1289) gives:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1290)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1290) implies:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1291)  op(e1, e1) = e1
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (1291), (function-axioms) are
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1292)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1292) implies:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1293)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (157), (158), (159), (164), (360),
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1190), (1205), (1222), (1240), (1252), (1293),
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #963.
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | |   (1294)  all_54_5 = e1 | all_54_5 = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (1195), (1242), (1294) are inconsistent by
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | |   (1295)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (1295) gives:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | |   (1296)  all_56_4 = e0 & op(e3, e1) = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1189), (1296), (function-axioms) are
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #700.
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | |   (1297)  all_56_9 = e0 & op(e3, e0) = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (1297) implies:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | |   (1298)  op(e3, e0) = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (1298) gives:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | |   (1299)  all_52_12 = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | REDUCE: (1223), (1299) imply:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | |   (1300)  $false
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | CLOSE: (1300) is inconsistent.
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | |   (1301)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 150.12/21.52  | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (1187), (1222), (1301),
% 150.12/21.52  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.12/21.52  | | | | | | | | | | | | | | | | |            #698.
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | End of split
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | Case 2:
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | |   (1302)  all_28_2 = e2
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | COMBINE_EQS: (330), (1302) imply:
% 150.12/21.52  | | | | | | | | | | | | |   (1303)  all_14_2 = e2
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | SIMP: (1303) implies:
% 150.12/21.52  | | | | | | | | | | | | |   (1304)  all_14_2 = e2
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | REDUCE: (351), (1304) imply:
% 150.12/21.52  | | | | | | | | | | | | |   (1305)   ~ (all_52_3 = e2)
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | REDUCE: (369), (1304) imply:
% 150.12/21.52  | | | | | | | | | | | | |   (1306)   ~ (all_52_11 = e2)
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | REDUCE: (371), (1304) imply:
% 150.12/21.52  | | | | | | | | | | | | |   (1307)   ~ (all_52_13 = e2)
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | REDUCE: (380), (1304) imply:
% 150.12/21.52  | | | | | | | | | | | | |   (1308)   ~ (e3 = e2)
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | REDUCE: (51), (1304) imply:
% 150.12/21.52  | | | | | | | | | | | | |   (1309)  op(e0, e0) = e2
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | BETA: splitting (88) gives:
% 150.12/21.52  | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | Case 1:
% 150.12/21.52  | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | |   (1310)   ~ (all_38_2 = e0)
% 150.12/21.52  | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | REDUCE: (1186), (1310) imply:
% 150.12/21.52  | | | | | | | | | | | | | |   (1311)  $false
% 150.12/21.52  | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | CLOSE: (1311) is inconsistent.
% 150.12/21.52  | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | Case 2:
% 150.12/21.52  | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | |   (1312)  ( ~ (all_38_0 = e3) & op(e0, e1) = all_38_0 &
% 150.12/21.52  | | | | | | | | | | | | | |             $i(all_38_0)) | ( ~ (all_38_1 = e2) & op(e0, e0)
% 150.12/21.52  | | | | | | | | | | | | | |             = all_38_1 & $i(all_38_1))
% 150.12/21.52  | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | BETA: splitting (1312) gives:
% 150.12/21.52  | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | Case 1:
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | |   (1313)   ~ (all_38_0 = e3) & op(e0, e1) = all_38_0 &
% 150.12/21.52  | | | | | | | | | | | | | | |           $i(all_38_0)
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | ALPHA: (1313) implies:
% 150.12/21.52  | | | | | | | | | | | | | | |   (1314)   ~ (all_38_0 = e3)
% 150.12/21.52  | | | | | | | | | | | | | | |   (1315)  op(e0, e1) = all_38_0
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 150.12/21.52  | | | | | | | | | | | | | | |              all_38_0, e1, e0, simplifying with (157), (1315)
% 150.12/21.52  | | | | | | | | | | | | | | |              gives:
% 150.12/21.52  | | | | | | | | | | | | | | |   (1316)  all_52_11 = all_38_0
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1316) imply:
% 150.12/21.52  | | | | | | | | | | | | | | |   (1317)  all_54_14 = all_38_0
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | REDUCE: (139), (1316) imply:
% 150.12/21.52  | | | | | | | | | | | | | | |   (1318)   ~ (all_52_3 = all_38_0)
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | REDUCE: (125), (1316) imply:
% 150.12/21.52  | | | | | | | | | | | | | | |   (1319)   ~ (all_52_7 = all_38_0)
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | REDUCE: (121), (1316) imply:
% 150.12/21.52  | | | | | | | | | | | | | | |   (1320)   ~ (all_52_8 = all_38_0)
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | REDUCE: (1306), (1316) imply:
% 150.12/21.52  | | | | | | | | | | | | | | |   (1321)   ~ (all_38_0 = e2)
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | REDUCE: (1190), (1316) imply:
% 150.12/21.52  | | | | | | | | | | | | | | |   (1322)   ~ (all_38_0 = e0)
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 150.12/21.52  | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | Case 1:
% 150.12/21.52  | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | |   (1323)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 150.12/21.52  | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 150.12/21.52  | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | BETA: splitting (1323) gives:
% 150.12/21.52  | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | |   (1324)  all_56_4 = e3 & op(e3, e1) = e3
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | ALPHA: (1324) implies:
% 150.12/21.52  | | | | | | | | | | | | | | | | |   (1325)  op(e3, e1) = e3
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1203), (1325), (function-axioms) are
% 150.12/21.52  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | |   (1326)  all_56_5 = e3 & op(e2, e1) = e3
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | ALPHA: (1326) implies:
% 150.12/21.52  | | | | | | | | | | | | | | | | |   (1327)  all_56_5 = e3
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 150.12/21.52  | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | |   (1328)  all_54_14 = e3
% 150.12/21.52  | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1317), (1328) imply:
% 150.12/21.52  | | | | | | | | | | | | | | | | | |   (1329)  all_38_0 = e3
% 150.12/21.52  | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | REDUCE: (1314), (1329) imply:
% 150.12/21.52  | | | | | | | | | | | | | | | | | |   (1330)  $false
% 150.12/21.52  | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | CLOSE: (1330) is inconsistent.
% 150.12/21.52  | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | Case 2:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | |   (1331)   ~ (all_54_14 = e3)
% 150.12/21.52  | | | | | | | | | | | | | | | | | |   (1332)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 150.12/21.52  | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | 
% 150.12/21.52  | | | | | | | | | | | | | | | | | | Case 1:
% 150.12/21.52  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | |   (1333)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 150.61/21.52  | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (1333) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | |   (1334)  all_56_4 = e2 & op(e3, e1) = e2
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (1334) implies:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | |   (1335)  op(e3, e1) = e2
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1332) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | |   (1336)  all_54_14 = e2
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1317), (1336) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | |   (1337)  all_38_0 = e2
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | SIMP: (1337) implies:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | |   (1338)  all_38_0 = e2
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | REDUCE: (1321), (1338) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | |   (1339)  $false
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | CLOSE: (1339) is inconsistent.
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | |   (1340)   ~ (all_54_14 = e2)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | |   (1341)  all_54_14 = e1 | all_54_14 = e0
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1341) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | |   (1342)  all_54_14 = e1
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1317), (1342) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | |   (1343)  all_38_0 = e1
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1343) implies:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | |   (1344)  all_38_0 = e1
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1318), (1344) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | |   (1345)   ~ (all_52_3 = e1)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1319), (1344) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | |   (1346)   ~ (all_52_7 = e1)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1320), (1344) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | |   (1347)   ~ (all_52_8 = e1)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1314), (1344) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | |   (1348)   ~ (e3 = e1)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1321), (1344) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | |   (1349)   ~ (e2 = e1)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | |   (1350)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1350) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (1351)  all_56_12 = e1 & op(e0, e3) = e1
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1345), (1351), (function-axioms) are
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #852.
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (1352)  all_56_13 = e1 & op(e0, e2) = e1
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1346), (1352), (function-axioms) are
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #712.
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | |   (1353)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1353) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (1354)  all_56_14 = e1 & op(e0, e1) = e1
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1354) implies:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (1355)  all_56_14 = e1
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (1356)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1356) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1357)  all_56_12 = e3 & op(e0, e3) = e3
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1357) implies:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1358)  all_56_12 = e3
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            (1205), (1358), (function-axioms) are inconsistent
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1359)  all_56_13 = e3 & op(e0, e2) = e3
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1359) implies:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1360)  all_56_13 = e3
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1361)  all_54_2 = e3
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (1361) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1362)  all_52_8 = e3
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1203), (1362) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1363)  $false
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1363) is inconsistent.
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1364)   ~ (all_54_2 = e3)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1365)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1365) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1366)  all_54_2 = e2
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (1366) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1367)  all_52_8 = e2
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (1367) imply:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1368)   ~ (all_52_9 = e2)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1368) implies:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1369)   ~ (all_52_9 = e2)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1370)  all_54_12 = e3
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (1201), (1370) are inconsistent by
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #697.
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1371)   ~ (all_54_12 = e3)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1372)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1372) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1373)  all_54_12 = e2
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (1305), (1373) are inconsistent by
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #696.
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1374)   ~ (all_54_12 = e2)
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1375)  all_54_12 = e1 | all_54_12 = e0
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1375) gives:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1376)  all_54_12 = e1
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (1345), (1376) are inconsistent by
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #695.
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1377)  all_54_12 = e0
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (1377) imply:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1378)  all_52_3 = e0
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1378) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1379)  all_52_3 = e0
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1379) imply:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1380)   ~ (all_52_7 = e0)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1380) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1381)   ~ (all_52_7 = e0)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1345), (1379) imply:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1382)   ~ (e1 = e0)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1379) imply:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1383)  op(e0, e3) = e0
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1384)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1384) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1385)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1385) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1386)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1387)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1386) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1388)  all_57_15 = e3 & op(e0, e0) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1388) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1389)  op(e0, e0) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1309), (1389), (function-axioms) are
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1390)   ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_6)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1390) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1391)   ~ (all_57_6 = e0)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1392)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1392) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1393)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1393) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1394)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1394) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1395)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1395) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1396)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1396) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1397)  op(e2, e3) = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1387), (1397), (function-axioms) are
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #694.
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1398)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1398) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1399)  op(e2, e3) = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1387), (1399), (function-axioms) are
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #694.
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1400)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1400) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1401)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1401) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1402)  op(e2, e3) = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1387), (1402), (function-axioms) are
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #694.
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1403)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1403) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1404)  op(e2, e3) = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1387), (1404), (function-axioms) are
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #694.
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1405)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1405) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1406)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1406) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1407)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1407) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1408)  op(e2, e3) = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1387), (1408), (function-axioms) are
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #694.
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1409)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1409) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1410)  op(e2, e3) = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1387), (1410), (function-axioms) are
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #694.
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1411)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1411) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1412)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1412) implies:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1413)  op(e2, e3) = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1387), (1413), (function-axioms) are
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #694.
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1414)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (1193), (1369), (1414),
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #708.
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1415)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1415) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1416)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1416) gives:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1417)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (1202), (1309), (1417),
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #856.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1418)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (1205), (1307), (1418),
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #994.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1419)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1419) gives:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1420)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1420) gives:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1421)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1421) implies:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1422)  op(e1, e1) = e3
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1193), (1422), (function-axioms) are
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1423)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1423) implies:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1424)  op(e2, e2) = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (1195), (1424),
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #690.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1425)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1425) gives:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1426)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1426) implies:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1427)  op(e0, e0) = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (159), (208), (1355), (1360),
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1383), (1427), (function-axioms) are inconsistent
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #685.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1428)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (1193), (1428), (function-axioms) are
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #704.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1429)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1429) gives:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1430)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1430) gives:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1431)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1431) gives:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1432)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1432) gives:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1433)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1433) implies:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1434)  op(e3, e3) = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1205), (1434), (function-axioms) are
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1435)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1435) implies:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1436)  op(e2, e2) = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (1195), (1436),
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #690.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1437)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1437) gives:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1438)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1438) implies:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1439)  op(e1, e1) = e2
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1193), (1439), (function-axioms) are
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1440)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1440) implies:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1441)  op(e0, e0) = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (159), (208), (1355), (1360),
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1383), (1441), (function-axioms) are inconsistent
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #685.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1442)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1442) gives:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1443)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1193), (1443), (function-axioms) are
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1444)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (169), (1203), (1205), (1309), (1444),
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #855.
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1445)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.61/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1445) gives:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1446)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1446) gives:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1447)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1369), (1447), (function-axioms) are
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #871.
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1448)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1448) gives:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1449)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1449) implies:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1450)  op(e2, e2) = e1
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (1195), (1450),
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #690.
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1451)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1451) implies:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1452)  op(e0, e0) = e3
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1309), (1452), (function-axioms) are
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1453)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1453) gives:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1454)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1204), (1307), (1454),
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #869.
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1455)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1455) gives:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1456)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1456) implies:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1457)  op(e2, e0) = e2
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1458)  op(e2, e2) = e2
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (1457), (1458),
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1459)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1459) gives:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1460)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1460) implies:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1461)  op(e1, e1) = e1
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (1461), (function-axioms) are
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1462)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1462) implies:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1463)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1463) gives:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1464)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1464) gives:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1465)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1465) gives:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1466)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1466) implies:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1467)  all_57_6 = e0
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1468)   ~ (all_57_15 = e3)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1386), (1467), (1468) are inconsistent by
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #684.
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1469)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1469) gives:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1470)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e3) = e0
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1470) implies:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1471)  op(e2, e0) = e2
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1307), (1471), (function-axioms) are
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1472)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e3) = e0
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1472) implies:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1473)  all_57_6 = e0
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1474)   ~ (all_57_15 = e3)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1386), (1473), (1474) are inconsistent by
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #684.
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1475)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (164), (1205), (1307), (1391), (1475),
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #683.
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1476)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1476) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1477)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (1205), (1381), (1477),
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #967.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1478)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1478) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1479)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (164), (1190), (1307), (1479),
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #682.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1480)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1190), (1480), (function-axioms) are
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1481)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1481) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1482)  op(e2, e2) = e2
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1483)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1484)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1484) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1485)  all_56_6 = e3 & op(e1, e3) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1200), (1485), (function-axioms) are
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #681.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1486)  all_56_7 = e3 & op(e1, e2) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1486) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1487)  all_56_7 = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1488)  op(e1, e2) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (199), (225),
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (268), (373), (1195), (1360),
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1487), (1488), (function-axioms) are inconsistent
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #678.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1489)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1489) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1490)  all_56_8 = e3 & op(e1, e1) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1490) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1491)  op(e1, e1) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1193), (1491), (function-axioms) are
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1492)  all_56_11 = e3 & op(e1, e0) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1483) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1493)  all_57_14 = e2 & op(e1, e1) = e2
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1493) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1494)  op(e1, e1) = e2
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1193), (1494), (function-axioms) are
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1495)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1495) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1496)   ~ (all_57_3 = e1)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1497)  op(e1, e2) = all_57_3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1492) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1498)  op(e1, e0) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (160), (1498) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1499)  all_52_14 = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_3, e2, e1, simplifying with (162), (1497)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1500)  all_57_3 = all_52_6
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e2,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (1482) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1501)  all_4_2 = e2
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1496), (1500) imply:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1502)   ~ (all_52_6 = e1)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (1501) imply:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1503)   ~ (all_52_6 = e2)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (160), (195), (258), (1188), (1498),
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1502), (1503), (function-axioms) are inconsistent
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #672.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1504)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1193), (1309), (1504),
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #671.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1505)   ~ (all_54_2 = e2)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (271), (1505) imply:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1506)   ~ (all_52_8 = e2)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1335), (1506), (function-axioms) are
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (1507)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1507) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1508)  all_56_14 = e3 & op(e0, e1) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1508) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1509)  all_56_14 = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1355), (1509) are inconsistent by sub-proof
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            #669.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1510)  all_56_15 = e3 & op(e0, e0) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1510) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1511)  op(e0, e0) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1309), (1511), (function-axioms) are
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | |   (1512)  all_56_15 = e1 & op(e0, e0) = e1
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1512) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | |   (1513)  op(e0, e0) = e1
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1309), (1513), (function-axioms) are
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | |   (1514)  all_54_14 = e0
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1317), (1514) imply:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | |   (1515)  all_38_0 = e0
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1515) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | |   (1516)  all_38_0 = e0
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1322), (1516) imply:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | |   (1517)  $false
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1517) is inconsistent.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | |   (1518)  all_56_5 = e2 & op(e2, e1) = e2
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1327), (1518) are inconsistent by sub-proof
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | |            #668.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | |   (1519)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 150.61/21.56  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (1519) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | |   (1520)  all_56_8 = e2 & op(e1, e1) = e2
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (1520) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | |   (1521)  op(e1, e1) = e2
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1193), (1521), (function-axioms) are
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | |   (1522)  all_56_14 = e2 & op(e0, e1) = e2
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (207), (209),
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | |            (229), (231), (233), (1205), (1309), (1522),
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | |            #721.
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | |   (1523)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 150.61/21.56  | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 150.61/21.56  | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | BETA: splitting (1523) gives:
% 150.61/21.56  | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | |   (1524)  all_56_8 = e3 & op(e1, e1) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | ALPHA: (1524) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | |   (1525)  op(e1, e1) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1193), (1525), (function-axioms) are
% 150.61/21.56  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 150.61/21.56  | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | |   (1526)  all_56_14 = e3 & op(e0, e1) = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | ALPHA: (1526) implies:
% 150.61/21.56  | | | | | | | | | | | | | | | | |   (1527)  all_56_14 = e3
% 150.61/21.56  | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (159), (190), (207), (1309), (1314),
% 150.61/21.56  | | | | | | | | | | | | | | | | |            (1317), (1318), (1319), (1321), (1322), (1527),
% 150.61/21.56  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.61/21.56  | | | | | | | | | | | | | | | | |            #665.
% 150.61/21.56  | | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | |   (1528)   ~ (all_38_1 = e2) & op(e0, e0) = all_38_1 &
% 150.61/21.56  | | | | | | | | | | | | | | |           $i(all_38_1)
% 150.61/21.56  | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | ALPHA: (1528) implies:
% 150.61/21.56  | | | | | | | | | | | | | | |   (1529)   ~ (all_38_1 = e2)
% 150.61/21.56  | | | | | | | | | | | | | | |   (1530)  op(e0, e0) = all_38_1
% 150.61/21.56  | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_38_1,
% 150.61/21.56  | | | | | | | | | | | | | | |              e0, e0, simplifying with (1309), (1530) gives:
% 150.61/21.56  | | | | | | | | | | | | | | |   (1531)  all_38_1 = e2
% 150.61/21.56  | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | REDUCE: (1529), (1531) imply:
% 150.61/21.56  | | | | | | | | | | | | | | |   (1532)  $false
% 150.61/21.56  | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | | CLOSE: (1532) is inconsistent.
% 150.61/21.56  | | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | |   (1533)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (1197), (1533) are
% 150.61/21.56  | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | End of split
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | |   (1534)  all_26_2 = e1
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | COMBINE_EQS: (307), (1534) imply:
% 150.61/21.56  | | | | | | | | | | |   (1535)  all_6_2 = e1
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | COMBINE_EQS: (303), (1535) imply:
% 150.61/21.56  | | | | | | | | | | |   (1536)  all_42_2 = e1
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | REDUCE: (338), (1535) imply:
% 150.61/21.56  | | | | | | | | | | |   (1537)   ~ (all_52_1 = e1)
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | REDUCE: (340), (1535) imply:
% 150.61/21.56  | | | | | | | | | | |   (1538)   ~ (all_52_2 = e1)
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | REDUCE: (342), (1535) imply:
% 150.61/21.56  | | | | | | | | | | |   (1539)   ~ (all_52_3 = e1)
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | REDUCE: (348), (1535) imply:
% 150.61/21.56  | | | | | | | | | | |   (1540)   ~ (all_52_12 = e1)
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | REDUCE: (377), (1535) imply:
% 150.61/21.56  | | | | | | | | | | |   (1541)   ~ (e2 = e1)
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | REDUCE: (39), (1535) imply:
% 150.61/21.56  | | | | | | | | | | |   (1542)  op(e3, e3) = e1
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | BETA: splitting (94) gives:
% 150.61/21.56  | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | |   (1543)   ~ (all_42_2 = e1)
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | REDUCE: (1536), (1543) imply:
% 150.61/21.56  | | | | | | | | | | | |   (1544)  $false
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | CLOSE: (1544) is inconsistent.
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | Case 2:
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | |   (1545)  ( ~ (all_42_0 = e2) & op(e1, e3) = all_42_0 &
% 150.61/21.56  | | | | | | | | | | | |             $i(all_42_0)) | ( ~ (all_42_1 = e0) & op(e1, e1)
% 150.61/21.56  | | | | | | | | | | | |             = all_42_1 & $i(all_42_1))
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | BETA: splitting (1545) gives:
% 150.61/21.56  | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | |   (1546)   ~ (all_42_0 = e2) & op(e1, e3) = all_42_0 &
% 150.61/21.56  | | | | | | | | | | | | |           $i(all_42_0)
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | ALPHA: (1546) implies:
% 150.61/21.56  | | | | | | | | | | | | |   (1547)   ~ (all_42_0 = e2)
% 150.61/21.56  | | | | | | | | | | | | |   (1548)  op(e1, e3) = all_42_0
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 150.61/21.56  | | | | | | | | | | | | |              all_42_0, e3, e1, simplifying with (163), (1548)
% 150.61/21.56  | | | | | | | | | | | | |              gives:
% 150.61/21.56  | | | | | | | | | | | | |   (1549)  all_52_2 = all_42_0
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | COMBINE_EQS: (259), (1549) imply:
% 150.61/21.56  | | | | | | | | | | | | |   (1550)  all_54_8 = all_42_0
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | REDUCE: (149), (1549) imply:
% 150.61/21.56  | | | | | | | | | | | | |   (1551)   ~ (all_52_1 = all_42_0)
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | REDUCE: (144), (1549) imply:
% 150.61/21.56  | | | | | | | | | | | | |   (1552)   ~ (all_52_3 = all_42_0)
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | SIMP: (1552) implies:
% 150.61/21.56  | | | | | | | | | | | | |   (1553)   ~ (all_52_3 = all_42_0)
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | REDUCE: (143), (1549) imply:
% 150.61/21.56  | | | | | | | | | | | | |   (1554)   ~ (all_52_6 = all_42_0)
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | SIMP: (1554) implies:
% 150.61/21.56  | | | | | | | | | | | | |   (1555)   ~ (all_52_6 = all_42_0)
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | REDUCE: (141), (1549) imply:
% 150.61/21.56  | | | | | | | | | | | | |   (1556)   ~ (all_52_14 = all_42_0)
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | SIMP: (1556) implies:
% 150.61/21.56  | | | | | | | | | | | | |   (1557)   ~ (all_52_14 = all_42_0)
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | REDUCE: (1538), (1549) imply:
% 150.61/21.56  | | | | | | | | | | | | |   (1558)   ~ (all_42_0 = e1)
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | REDUCE: (1187), (1549) imply:
% 150.61/21.56  | | | | | | | | | | | | |   (1559)   ~ (all_42_0 = e0)
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | BETA: splitting (196) gives:
% 150.61/21.56  | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | Case 1:
% 150.61/21.56  | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | |   (1560)  all_54_8 = e3
% 150.61/21.56  | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | COMBINE_EQS: (1550), (1560) imply:
% 150.61/21.56  | | | | | | | | | | | | | |   (1561)  all_42_0 = e3
% 150.61/21.56  | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | REDUCE: (1551), (1561) imply:
% 150.61/21.56  | | | | | | | | | | | | | |   (1562)   ~ (all_52_1 = e3)
% 150.61/21.56  | | | | | | | | | | | | | | 
% 150.61/21.56  | | | | | | | | | | | | | | REDUCE: (1553), (1561) imply:
% 150.61/21.57  | | | | | | | | | | | | | |   (1563)   ~ (all_52_3 = e3)
% 150.61/21.57  | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | REDUCE: (1555), (1561) imply:
% 150.61/21.57  | | | | | | | | | | | | | |   (1564)   ~ (all_52_6 = e3)
% 150.61/21.57  | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | REDUCE: (1557), (1561) imply:
% 150.61/21.57  | | | | | | | | | | | | | |   (1565)   ~ (all_52_14 = e3)
% 150.61/21.57  | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | REDUCE: (1548), (1561) imply:
% 150.61/21.57  | | | | | | | | | | | | | |   (1566)  op(e1, e3) = e3
% 150.61/21.57  | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 150.61/21.57  | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | |   (1567)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 150.61/21.57  | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 150.61/21.57  | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | BETA: splitting (1567) gives:
% 150.61/21.57  | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | |   (1568)  all_56_6 = e3 & op(e1, e3) = e3
% 150.61/21.57  | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | ALPHA: (1568) implies:
% 150.61/21.57  | | | | | | | | | | | | | | | |   (1569)  all_56_6 = e3
% 150.61/21.57  | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 150.61/21.57  | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | |   (1570)   ~ (all_28_2 = e2)
% 150.61/21.57  | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | REDUCE: (330), (1570) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | |   (1571)   ~ (all_14_2 = e2)
% 150.61/21.57  | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 150.61/21.57  | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | |   (1572)  all_54_15 = e3
% 150.61/21.57  | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1572) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | |   (1573)  all_14_2 = e3
% 150.61/21.57  | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | REDUCE: (380), (1573) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | |   (1574)  $false
% 150.61/21.57  | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | CLOSE: (1574) is inconsistent.
% 150.61/21.57  | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | |   (1575)   ~ (all_54_15 = e3)
% 150.61/21.57  | | | | | | | | | | | | | | | | | |   (1576)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 150.61/21.57  | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | BETA: splitting (1576) gives:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | |   (1577)  all_54_15 = e2
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1577) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | |   (1578)  all_14_2 = e2
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | REDUCE: (1571), (1578) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | |   (1579)  $false
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | CLOSE: (1579) is inconsistent.
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | |   (1580)   ~ (all_54_15 = e2)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | |   (1581)  all_54_15 = e1 | all_54_15 = e0
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (1581) gives:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1582)  all_54_15 = e1
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1582) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1583)  all_14_2 = e1
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (1583) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1584)  $false
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | CLOSE: (1584) is inconsistent.
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1585)  all_54_15 = e0
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1585) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1586)  all_14_2 = e0
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (1586) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1587)   ~ (all_52_3 = e0)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1586) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1588)   ~ (all_52_7 = e0)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (1586) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1589)   ~ (all_52_12 = e0)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (1586) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1590)   ~ (all_52_14 = e0)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (1586) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1591)   ~ (e1 = e0)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (1586) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | |   (1592)  op(e0, e0) = e0
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | |   (1593)  all_54_12 = e3
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (1563), (1593) are inconsistent by
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | |            sub-proof #697.
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | |   (1594)   ~ (all_54_12 = e3)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | |   (1595)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1595) gives:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | |   (1596)  all_54_12 = e2
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (1596) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | |   (1597)  all_52_3 = e2
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1597) implies:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | |   (1598)  all_52_3 = e2
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (1598) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | |   (1599)   ~ (all_52_1 = e2)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1563), (1598) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | |   (1600)   ~ (e3 = e2)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1598) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | |   (1601)  op(e0, e3) = e2
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | |   (1602)  all_54_4 = e3
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1602) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | |   (1603)  all_52_1 = e3
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1562), (1603) imply:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | |   (1604)  $false
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1604) is inconsistent.
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | |   (1605)   ~ (all_54_4 = e3)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | |   (1606)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | |   (1607)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1607) gives:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (1608)  all_56_0 = e0 & op(e3, e3) = e0
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1608) implies:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (1609)  op(e3, e3) = e0
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1542), (1609), (function-axioms) are
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.61/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (1610)  all_56_1 = e0 & op(e3, e2) = e0
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1610) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (1611)  all_56_1 = e0
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1612)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1612) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1613)  all_56_1 = e3 & op(e3, e2) = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1611), (1613) are inconsistent by sub-proof
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #664.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1614)  all_56_3 = e3 & op(e2, e2) = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1614) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1615)  op(e2, e2) = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1615), (function-axioms) are
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #711.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1616)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1616) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1617)  all_56_7 = e3 & op(e1, e2) = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1617) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1618)  all_56_7 = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1619)  op(e1, e2) = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1620)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (1538), (1619), (1620),
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #663.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1621)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1621) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1622)  all_56_8 = e1 & op(e1, e1) = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1622) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1623)  op(e1, e1) = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (1623), (function-axioms) are
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1624)  all_56_11 = e1 & op(e1, e0) = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1624) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1625)  all_56_11 = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (213), (215), (1566),
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1569), (1618), (1625), (function-axioms) are
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #657.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1626)  all_56_13 = e3 & op(e0, e2) = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1626) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1627)  op(e0, e2) = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1606) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1628)  all_54_4 = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1628) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1629)  all_52_1 = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1599), (1629) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1630)  $false
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1630) is inconsistent.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1631)  all_54_4 = e1 | all_54_4 = e0
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1631) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1632)  all_54_4 = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1632) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1633)  all_52_1 = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1537), (1633) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1634)  $false
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1634) is inconsistent.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1635)  all_54_4 = e0
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1635) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1636)  all_52_1 = e0
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (1636) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1637)   ~ (all_4_2 = e0)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1637) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1638)   ~ (all_4_2 = e0)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1639)  all_54_5 = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (1639) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1640)  all_4_2 = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1640) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1641)  $false
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1641) is inconsistent.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1642)   ~ (all_54_5 = e3)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1643)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1643) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1644)  all_54_5 = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (1644) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1645)  all_4_2 = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (1645) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1646)   ~ (all_52_6 = e2)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (1645) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1647)   ~ (all_52_9 = e2)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1645) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1648)  op(e2, e2) = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1649)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1649) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1650)  all_56_6 = e2 & op(e1, e3) = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1569), (1650) are inconsistent by sub-proof
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #662.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1651)  all_56_7 = e2 & op(e1, e2) = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1646), (1651), (function-axioms) are
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1652)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1652) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1653)  all_56_8 = e2 & op(e1, e1) = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1653) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1654)  op(e1, e1) = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1193), (1654), (function-axioms) are
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1655)  all_56_11 = e2 & op(e1, e0) = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1655) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1656)  all_56_11 = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1657)  all_54_9 = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1564), (1657) are inconsistent by
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #656.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1658)   ~ (all_54_9 = e3)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1659)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1660)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1660) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1661)  all_56_9 = e1 & op(e3, e0) = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1540), (1661), (function-axioms) are
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #851.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1662)  all_56_10 = e1 & op(e2, e0) = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1662) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1663)  all_56_10 = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1659) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1664)  all_54_9 = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1646), (1664) are inconsistent by
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #676.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1665)  all_54_9 = e1 | all_54_9 = e0
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1665) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1666)  all_54_9 = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1666) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1667)  all_52_6 = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1667) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1668)  all_52_6 = e1
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (1668) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1669)   ~ (all_52_14 = e1)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1669) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1670)   ~ (all_52_14 = e1)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1564), (1668) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1671)   ~ (e3 = e1)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1672)  all_54_11 = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (1565), (1672) are inconsistent by
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #655.
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1673)   ~ (all_54_11 = e3)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1674)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1675)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1675) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1676)  all_56_9 = e3 & op(e3, e0) = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1676) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1677)  all_56_9 = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1678)  op(e3, e0) = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1674) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1679)  all_54_11 = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (1679) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1680)  all_52_14 = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1680) implies:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1681)  all_52_14 = e2
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (1681) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1682)   ~ (all_52_12 = e2)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1683)  all_54_3 = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (1683) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1684)  all_52_12 = e3
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (1684) imply:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1685)   ~ (all_52_8 = e3)
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1686)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1686) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1687)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1687) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1688)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (200), (268), (269), (349),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (1195), (1562), (1648), (1688),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #654.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1689)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1689) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1690)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (200), (268), (269), (349),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (1195), (1562), (1648), (1690),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #653.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1691)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1691) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1692)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1692) implies:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1693)  op(e2, e3) = e2
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (200), (268), (269), (349),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (1195), (1562), (1648), (1693),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #925.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1694)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1694) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1695)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1695) implies:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1696)  op(e1, e1) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (51), (79), (157), (158),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (163), (164), (165), (167), (169),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (189), (199), (238), (239), (246), (268), (314),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (349), (351), (356), (358), (360), (362), (369),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (378), (380), (1195), (1538), (1542),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1571), (1685), (1696), (function-axioms) are
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #636.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1697)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1697) implies:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1698)  op(e2, e1) = e2
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1647), (1698), (function-axioms) are
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1699)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1699) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1700)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1700) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1701)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1701) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1702)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1702) implies:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1703)  op(e0, e0) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1592), (1703), (function-axioms) are
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1704)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1704) implies:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1705)  op(e3, e3) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1677), (1705), (function-axioms) are inconsistent
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #632.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1706)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (163), (164), (360), (1538), (1648), (1706),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #849.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1707)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1707) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1708)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1708) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1709)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1709) implies:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1710)  op(e1, e1) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (51), (79), (157), (158),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (163), (164), (165), (167), (169),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (189), (199), (238), (239), (246), (268), (314),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (349), (351), (356), (358), (360), (362), (369),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (378), (380), (1195), (1538), (1542),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1571), (1685), (1710), (function-axioms) are
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #636.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1711)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1711) implies:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1712)  op(e2, e2) = e1
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (1647), (1663), (1712), (function-axioms)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #842.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1713)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1713) gives:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1714)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1714) implies:
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1715)  op(e0, e0) = e1
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (51), (160), (163), (214), (238),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1193), (1538), (1542), (1670), (1715),
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #628.
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1716)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1716) gives:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1717)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1717) implies:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1718)  op(e1, e1) = e3
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (51), (79), (157), (158),
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (163), (164), (165), (167), (169),
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (189), (199), (238), (239), (246), (268), (314),
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (349), (351), (356), (358), (360), (362), (369),
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (378), (380), (1195), (1538), (1542),
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1571), (1685), (1718), (function-axioms) are
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #636.
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1719)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1719) implies:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1720)  op(e1, e1) = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (1720), (function-axioms) are
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1721)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1721) gives:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1722)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1722) gives:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1723)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1723) gives:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1724)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1724) gives:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1725)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1725) implies:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1726)  op(e3, e1) = e3
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1685), (1726), (function-axioms) are
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1727)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1727) implies:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1728)  op(e2, e2) = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (1647), (1663), (1728), (function-axioms)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #842.
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1729)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1729) gives:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1730)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1730) implies:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1731)  op(e1, e1) = e2
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1193), (1731), (function-axioms) are
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1732)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1732) implies:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1733)  op(e0, e0) = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (51), (160), (163), (214), (238),
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1193), (1538), (1542), (1670), (1733),
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #628.
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1734)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1734) gives:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1735)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1193), (1735), (function-axioms) are
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1736)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1736) gives:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1737)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1737) implies:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1738)  op(e0, e0) = e3
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1592), (1738), (function-axioms) are
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1739)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1739) gives:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1740)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1740) implies:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1741)  op(e3, e3) = e3
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1677), (1741), (function-axioms) are inconsistent
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #632.
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1742)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1742) implies:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1743)  op(e1, e0) = e1
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (1670), (1743), (function-axioms) are
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1744)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 150.79/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1744) gives:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1745)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (1592), (1647), (1663), (1745),
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #837.
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1746)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1746) gives:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1747)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1747) gives:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1748)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1748) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1749)  op(e0, e0) = e2
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1592), (1749), (function-axioms) are
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1750)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1750) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1751)  op(e3, e3) = e3
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1677), (1751), (function-axioms) are inconsistent
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #632.
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1752)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1752) gives:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1753)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1753) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1754)  op(e2, e0) = e2
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (1648), (1754),
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1755)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1755) gives:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1756)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1756) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1757)  op(e1, e1) = e1
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (1757), (function-axioms) are
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1758)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1758) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1759)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1760)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1760) gives:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1761)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1761) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1762)  op(e3, e3) = e3
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (157), (158), (159), (164), (360),
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1190), (1587), (1588), (1648), (1759), (1762),
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #963.
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1763)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1763) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1764)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (160), (163), (214), (1193), (1538),
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1670), (1764), (function-axioms) are inconsistent
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #630.
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1765)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1765) gives:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1766)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1766) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1767)  op(e1, e1) = e1
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (1767), (function-axioms) are
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1768)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1768) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1769)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1770)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11))
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1770) gives:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1771)  all_57_12 = e0 & op(e2, e2) = e0
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1771) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1772)  op(e2, e2) = e0
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1648), (1772), (function-axioms) are
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1773)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1773) implies:
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1774)   ~ (all_57_11 = e2)
% 150.79/21.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1775)  op(e2, e0) = all_57_11
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (157), (159), (160), (164), (1190),
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1542), (1601), (1627), (1759), (1769), (1774),
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1775), (function-axioms) are inconsistent by
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #625.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1776)   ~ (all_54_3 = e3)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (1776) imply:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1777)   ~ (all_52_12 = e3)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1678), (1777), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1778)  all_54_11 = e1 | all_54_11 = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (1590), (1670), (1778) are inconsistent by
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #623.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1779)  all_56_10 = e3 & op(e2, e0) = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1779) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1780)  all_56_10 = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1663), (1780) are inconsistent by sub-proof
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #887.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1781)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (1565), (1592), (1781),
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #622.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1782)  all_54_9 = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1188), (1782) are inconsistent by
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #674.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1783)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1783) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1784)  all_56_11 = e1 & op(e1, e0) = e1
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1784) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1785)  all_56_11 = e1
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1656), (1785) are inconsistent by sub-proof
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #621.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1786)  all_56_15 = e1 & op(e0, e0) = e1
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1786) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1787)  op(e0, e0) = e1
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (378), (1581), (1787),
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #790.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1788)  all_54_5 = e1 | all_54_5 = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (1195), (1638), (1788) are inconsistent by
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1789)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1789) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (1790)  all_56_4 = e0 & op(e3, e1) = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1189), (1790), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #700.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (1791)  all_56_9 = e0 & op(e3, e0) = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1589), (1791), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #620.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | |   (1792)  all_54_12 = e1 | all_54_12 = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (1539), (1587), (1792) are inconsistent by
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #619.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | |   (1793)  all_28_2 = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (1793) imply:
% 150.79/21.61  | | | | | | | | | | | | | | | | |   (1794)  all_14_2 = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | SIMP: (1794) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | |   (1795)  all_14_2 = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | REDUCE: (351), (1795) imply:
% 150.79/21.61  | | | | | | | | | | | | | | | | |   (1796)   ~ (all_52_3 = e2)
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | REDUCE: (380), (1795) imply:
% 150.79/21.61  | | | | | | | | | | | | | | | | |   (1797)   ~ (e3 = e2)
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | REDUCE: (51), (1795) imply:
% 150.79/21.61  | | | | | | | | | | | | | | | | |   (1798)  op(e0, e0) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | |   (1799)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | BETA: splitting (1799) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |   (1800)  all_56_0 = e2 & op(e3, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | ALPHA: (1800) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |   (1801)  op(e3, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1542), (1801), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |   (1802)  all_56_2 = e2 & op(e2, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | ALPHA: (1802) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |   (1803)  op(e2, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |   (1804)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1804) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |   (1805)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1805) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |   (1806)  op(e3, e3) = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1542), (1806), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |   (1807)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1807) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |   (1808)  op(e2, e2) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (200), (268), (269), (349),
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |            (373), (1195), (1562), (1803), (1808),
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |            #925.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |   (1809)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1193), (1798), (1809),
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |            #671.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | |   (1810)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | BETA: splitting (1810) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |   (1811)  all_56_6 = e2 & op(e1, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1569), (1811) are inconsistent by sub-proof
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |            #662.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |   (1812)  all_56_12 = e2 & op(e0, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1796), (1812), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | |   (1813)  all_56_7 = e3 & op(e1, e2) = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | ALPHA: (1813) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | |   (1814)  all_56_7 = e3
% 150.79/21.61  | | | | | | | | | | | | | | | |   (1815)  op(e1, e2) = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | |   (1816)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 150.79/21.61  | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (1538), (1815), (1816),
% 150.79/21.61  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.61  | | | | | | | | | | | | | | | | |            #663.
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | |   (1817)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 150.79/21.61  | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | BETA: splitting (1817) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | |   (1818)  all_56_8 = e1 & op(e1, e1) = e1
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | ALPHA: (1818) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | |   (1819)  op(e1, e1) = e1
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (1819), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | |   (1820)  all_56_11 = e1 & op(e1, e0) = e1
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | ALPHA: (1820) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | |   (1821)  all_56_11 = e1
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |   (1822)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | BETA: splitting (1822) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |   (1823)  all_56_0 = e3 & op(e3, e3) = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | ALPHA: (1823) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |   (1824)  op(e3, e3) = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1542), (1824), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |   (1825)  all_56_2 = e3 & op(e2, e3) = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | ALPHA: (1825) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |   (1826)  all_56_2 = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |   (1827)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (1542), (1826), (1827),
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |            #618.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |   (1828)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1828) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | |   (1829)  all_56_6 = e0 & op(e1, e3) = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1829) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | |   (1830)  op(e1, e3) = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1566), (1830), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #913.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | |   (1831)  all_56_12 = e0 & op(e0, e3) = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1831) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | |   (1832)  op(e0, e3) = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | |   (1833)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1833) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1834)  all_56_0 = e2 & op(e3, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1834) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1835)  op(e3, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1542), (1835), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1836)  all_56_2 = e2 & op(e2, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1826), (1836) are inconsistent by sub-proof
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |            #778.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | |   (1837)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1837) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1838)  all_56_6 = e2 & op(e1, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1838) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1839)  op(e1, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1566), (1839), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #617.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1840)  all_56_12 = e2 & op(e0, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1840) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1841)  op(e0, e3) = e2
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (1832), (1841), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #689.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |   (1842)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 150.79/21.61  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | BETA: splitting (1842) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |   (1843)  all_56_6 = e3 & op(e1, e3) = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | ALPHA: (1843) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |   (1844)  all_56_6 = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (213), (215), (1566),
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |            (1814), (1821), (1844), (function-axioms) are
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #657.
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |   (1845)  all_56_12 = e3 & op(e0, e3) = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | ALPHA: (1845) implies:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | |   (1846)  all_56_12 = e3
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |   (1847)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1847) gives:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | |   (1848)  all_56_0 = e0 & op(e3, e3) = e0
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1848) implies:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | |   (1849)  op(e3, e3) = e0
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1542), (1849), (function-axioms) are
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | |   (1850)  all_56_2 = e0 & op(e2, e3) = e0
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1850) implies:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | |   (1851)  op(e2, e3) = e0
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (1852)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1852) gives:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |   (1853)  all_56_0 = e2 & op(e3, e3) = e2
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1853) implies:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |   (1854)  op(e3, e3) = e2
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1542), (1854), (function-axioms) are
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |   (1855)  all_56_2 = e2 & op(e2, e3) = e2
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1855) implies:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |   (1856)  op(e2, e3) = e2
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1851), (1856), (function-axioms) are
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #709.
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (1857)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1857) gives:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |   (1858)  all_56_6 = e2 & op(e1, e3) = e2
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1858) implies:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |   (1859)  op(e1, e3) = e2
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1566), (1859), (function-axioms) are
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #617.
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |   (1860)  all_56_12 = e2 & op(e0, e3) = e2
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1860) implies:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |   (1861)  all_56_12 = e2
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1846), (1861) are inconsistent by sub-proof
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | |            #616.
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | |   (1862)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1566), (1846), (1862), (function-axioms) are
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #615.
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | |   (1863)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 150.79/21.62  | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (1193), (1565), (1863),
% 150.79/21.62  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.62  | | | | | | | | | | | | | | |            #614.
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | |   (1864)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 150.79/21.62  | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | BETA: splitting (1864) gives:
% 150.79/21.62  | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | |   (1865)  all_54_8 = e2
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | COMBINE_EQS: (1550), (1865) imply:
% 150.79/21.62  | | | | | | | | | | | | | | |   (1866)  all_42_0 = e2
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | REDUCE: (1547), (1866) imply:
% 150.79/21.62  | | | | | | | | | | | | | | |   (1867)  $false
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | CLOSE: (1867) is inconsistent.
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | |   (1868)  all_54_8 = e1 | all_54_8 = e0
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | REF_CLOSE: (259), (1187), (1538), (1868) are inconsistent by
% 150.79/21.62  | | | | | | | | | | | | | | |            sub-proof #612.
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | |   (1869)   ~ (all_42_1 = e0) & op(e1, e1) = all_42_1 &
% 150.79/21.62  | | | | | | | | | | | | |           $i(all_42_1)
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | REF_CLOSE: (1193), (1869), (function-axioms) are inconsistent
% 150.79/21.62  | | | | | | | | | | | | |            by sub-proof #611.
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | End of split
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | |   (1870)  all_24_2 = e1
% 150.79/21.62  | | | | | | | | | |   (1871)  ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 &
% 150.79/21.62  | | | | | | | | | |             $i(all_24_0)) | ( ~ (all_24_1 = e0) & op(e1, e1)
% 150.79/21.62  | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | COMBINE_EQS: (318), (1870) imply:
% 150.79/21.62  | | | | | | | | | |   (1872)  all_4_2 = e1
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | REDUCE: (352), (1872) imply:
% 150.79/21.62  | | | | | | | | | |   (1873)   ~ (all_52_4 = e1)
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | REDUCE: (354), (1872) imply:
% 150.79/21.62  | | | | | | | | | |   (1874)   ~ (all_52_6 = e1)
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | REDUCE: (356), (1872) imply:
% 150.79/21.62  | | | | | | | | | |   (1875)   ~ (all_52_7 = e1)
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | REDUCE: (360), (1872) imply:
% 150.79/21.62  | | | | | | | | | |   (1876)   ~ (all_52_13 = e1)
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | REDUCE: (373), (1872) imply:
% 150.79/21.62  | | | | | | | | | |   (1877)   ~ (e3 = e1)
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | REDUCE: (36), (1872) imply:
% 150.79/21.62  | | | | | | | | | |   (1878)  op(e2, e2) = e1
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | BETA: splitting (1871) gives:
% 150.79/21.62  | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | |   (1879)   ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 &
% 150.79/21.62  | | | | | | | | | | |           $i(all_24_0)
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | ALPHA: (1879) implies:
% 150.79/21.62  | | | | | | | | | | |   (1880)   ~ (all_24_0 = e3)
% 150.79/21.62  | | | | | | | | | | |   (1881)  op(e1, e2) = all_24_0
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 150.79/21.62  | | | | | | | | | | |              all_24_0, e2, e1, simplifying with (162), (1881)
% 150.79/21.62  | | | | | | | | | | |              gives:
% 150.79/21.62  | | | | | | | | | | |   (1882)  all_52_6 = all_24_0
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | COMBINE_EQS: (258), (1882) imply:
% 150.79/21.62  | | | | | | | | | | |   (1883)  all_54_9 = all_24_0
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | REDUCE: (143), (1882) imply:
% 150.79/21.62  | | | | | | | | | | |   (1884)   ~ (all_52_2 = all_24_0)
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | REDUCE: (136), (1882) imply:
% 150.79/21.62  | | | | | | | | | | |   (1885)   ~ (all_52_4 = all_24_0)
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | REDUCE: (128), (1882) imply:
% 150.79/21.62  | | | | | | | | | | |   (1886)   ~ (all_52_7 = all_24_0)
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | SIMP: (1886) implies:
% 150.79/21.62  | | | | | | | | | | |   (1887)   ~ (all_52_7 = all_24_0)
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | REDUCE: (126), (1882) imply:
% 150.79/21.62  | | | | | | | | | | |   (1888)   ~ (all_52_14 = all_24_0)
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | SIMP: (1888) implies:
% 150.79/21.62  | | | | | | | | | | |   (1889)   ~ (all_52_14 = all_24_0)
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | REDUCE: (1874), (1882) imply:
% 150.79/21.62  | | | | | | | | | | |   (1890)   ~ (all_24_0 = e1)
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | REDUCE: (1188), (1882) imply:
% 150.79/21.62  | | | | | | | | | | |   (1891)   ~ (all_24_0 = e0)
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | BETA: splitting (195) gives:
% 150.79/21.62  | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | |   (1892)  all_54_9 = e3
% 150.79/21.62  | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | COMBINE_EQS: (1883), (1892) imply:
% 150.79/21.62  | | | | | | | | | | | |   (1893)  all_24_0 = e3
% 150.79/21.62  | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | REDUCE: (1880), (1893) imply:
% 150.79/21.62  | | | | | | | | | | | |   (1894)  $false
% 150.79/21.62  | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | CLOSE: (1894) is inconsistent.
% 150.79/21.62  | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | |   (1895)   ~ (all_54_9 = e3)
% 150.79/21.62  | | | | | | | | | | | |   (1896)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 150.79/21.62  | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | BETA: splitting (1896) gives:
% 150.79/21.62  | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | |   (1897)  all_54_9 = e2
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | COMBINE_EQS: (1883), (1897) imply:
% 150.79/21.62  | | | | | | | | | | | | |   (1898)  all_24_0 = e2
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | REDUCE: (1884), (1898) imply:
% 150.79/21.62  | | | | | | | | | | | | |   (1899)   ~ (all_52_2 = e2)
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | REDUCE: (1885), (1898) imply:
% 150.79/21.62  | | | | | | | | | | | | |   (1900)   ~ (all_52_4 = e2)
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | REDUCE: (1887), (1898) imply:
% 150.79/21.62  | | | | | | | | | | | | |   (1901)   ~ (all_52_7 = e2)
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | REDUCE: (1889), (1898) imply:
% 150.79/21.62  | | | | | | | | | | | | |   (1902)   ~ (all_52_14 = e2)
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | REDUCE: (1880), (1898) imply:
% 150.79/21.62  | | | | | | | | | | | | |   (1903)   ~ (e3 = e2)
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | BETA: splitting (215) gives:
% 150.79/21.62  | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | |   (1904)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 150.79/21.62  | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 150.79/21.62  | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | BETA: splitting (1904) gives:
% 150.79/21.62  | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | |   (1905)  all_56_6 = e2 & op(e1, e3) = e2
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | REF_CLOSE: (163), (1899), (1905), (function-axioms) are
% 150.79/21.62  | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | |   (1906)  all_56_7 = e2 & op(e1, e2) = e2
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | ALPHA: (1906) implies:
% 150.79/21.62  | | | | | | | | | | | | | | |   (1907)  all_56_7 = e2
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 150.79/21.62  | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | |   (1908)   ~ (all_26_2 = e1)
% 150.79/21.62  | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | REDUCE: (307), (1908) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | |   (1909)   ~ (all_6_2 = e1)
% 150.79/21.62  | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 150.79/21.62  | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | |   (1910)  all_54_0 = e3
% 150.79/21.62  | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (1910) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | | |   (1911)  all_6_2 = e3
% 150.79/21.62  | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | REDUCE: (340), (1911) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | | |   (1912)   ~ (all_52_2 = e3)
% 150.79/21.62  | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | REDUCE: (344), (1911) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | | |   (1913)   ~ (all_52_4 = e3)
% 150.79/21.62  | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | REDUCE: (346), (1911) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | | |   (1914)   ~ (all_52_8 = e3)
% 150.79/21.62  | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | REDUCE: (348), (1911) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | | |   (1915)   ~ (all_52_12 = e3)
% 150.79/21.62  | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | REDUCE: (39), (1911) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | | |   (1916)  op(e3, e3) = e3
% 150.79/21.62  | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 150.79/21.62  | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | |   (1917)  all_54_8 = e3
% 150.79/21.62  | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (1917) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | | | |   (1918)  all_52_2 = e3
% 150.79/21.62  | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | REDUCE: (1912), (1918) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | | | |   (1919)  $false
% 150.79/21.62  | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | CLOSE: (1919) is inconsistent.
% 150.79/21.62  | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | |   (1920)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 150.79/21.62  | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | |   (1921)  all_54_1 = e3
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (1921) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | |   (1922)  all_52_4 = e3
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | REDUCE: (1913), (1922) imply:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | |   (1923)  $false
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | CLOSE: (1923) is inconsistent.
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | |   (1924)   ~ (all_54_1 = e3)
% 150.79/21.62  | | | | | | | | | | | | | | | | | | |   (1925)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | |   (1926)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | |            (1878), (1916), (1926), (function-axioms) are
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #762.
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | |   (1927)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1927) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | |   (1928)  all_56_7 = e3 & op(e1, e2) = e3
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1928) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | |   (1929)  op(e1, e2) = e3
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1880), (1881), (1929), (function-axioms) are
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #610.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | |   (1930)  all_56_13 = e3 & op(e0, e2) = e3
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1930) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | |   (1931)  all_56_13 = e3
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | |   (1932)  op(e0, e2) = e3
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1925) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | |   (1933)  all_54_1 = e2
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (1900), (1933) are inconsistent by
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #609.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | |   (1934)   ~ (all_54_1 = e2)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | |   (1935)  all_54_1 = e1 | all_54_1 = e0
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1920) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | |   (1936)  all_54_8 = e2
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (1899), (1936) are inconsistent by
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #608.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | |   (1937)   ~ (all_54_8 = e2)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | |   (1938)  all_54_8 = e1 | all_54_8 = e0
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1938) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | |   (1939)  all_54_8 = e1
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (1939) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | |   (1940)  all_52_2 = e1
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1940) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | |   (1941)  all_52_2 = e1
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (1941) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | |   (1942)   ~ (all_52_3 = e1)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1942) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | |   (1943)   ~ (all_52_3 = e1)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (1941) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | |   (1944)   ~ (all_52_14 = e1)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1944) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | |   (1945)   ~ (all_52_14 = e1)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1899), (1941) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | |   (1946)   ~ (e2 = e1)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (1947)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1947) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1948)  all_56_1 = e0 & op(e3, e2) = e0
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1948) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1949)  all_56_1 = e0
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1950)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1950) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1951)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1951) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1952)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (160), (162), (163), (214), (1193),
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1874), (1945), (1952), (function-axioms) are
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #605.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1953)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1953) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1954)  op(e2, e2) = e2
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1878), (1954), (function-axioms) are
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1955)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1955) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1956)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1956) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1957)  op(e1, e1) = e1
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (1957), (function-axioms) are
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1958)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1958) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1959)  op(e0, e0) = e0
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1960)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11))
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1961)  (all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1960) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1962)  all_57_12 = e0 & op(e2, e2) = e0
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1962) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1963)  op(e2, e2) = e0
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (158), (226), (1875), (1907), (1949),
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1963), (function-axioms) are inconsistent by
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #603.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1964)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1964) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1965)   ~ (all_57_11 = e2)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1966)  op(e2, e0) = all_57_11
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1935) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1967)  all_54_1 = e1
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (1967) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1968)  all_52_4 = e1
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1873), (1968) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1969)  $false
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1969) is inconsistent.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1970)  all_54_1 = e0
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (1970) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1971)  all_52_4 = e0
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1971) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1972)   ~ (all_52_7 = e0)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1972) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1973)   ~ (all_52_7 = e0)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1971) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1974)   ~ (all_52_8 = e0)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1873), (1971) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1975)   ~ (e1 = e0)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1976)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1976) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1977)  all_56_12 = e1 & op(e0, e3) = e1
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1943), (1977), (function-axioms) are
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #852.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1978)  all_56_13 = e1 & op(e0, e2) = e1
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1875), (1978), (function-axioms) are
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #712.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1979)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1979) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1980)  all_56_14 = e1 & op(e0, e1) = e1
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1980) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1981)  all_56_14 = e1
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1982)  all_54_13 = e3
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1982) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1983)  all_52_7 = e3
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1983) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1984)  all_52_7 = e3
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1984) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1985)   ~ (all_52_3 = e3)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (1984) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1986)   ~ (all_52_11 = e3)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1986) implies:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1987)   ~ (all_52_11 = e3)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1984) imply:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1988)   ~ (all_14_2 = e3)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1989)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1878), (1916), (1989), (function-axioms) are
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #764.
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1990)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 150.79/21.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1990) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1991)  all_56_5 = e3 & op(e2, e1) = e3
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1991) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1992)  all_56_5 = e3
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1993)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1993) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1994)  all_56_9 = e1 & op(e3, e0) = e1
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1994) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1995)  op(e3, e0) = e1
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1961) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1996)  all_57_10 = e0 & op(e3, e3) = e0
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1996) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1997)  op(e3, e3) = e0
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1916), (1997), (function-axioms) are
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1998)   ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_9)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1998) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1999)  op(e3, e0) = all_57_9
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2000)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2000) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2001)  all_56_4 = e2 & op(e3, e1) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2001) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2002)  op(e3, e1) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e0,
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (51), (1959) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2003)  all_14_2 = e0
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11, e0, e2, simplifying with (164), (1966)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2004)  all_57_11 = all_52_13
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9, e0, e3, simplifying with (168), (1999)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2005)  all_57_9 = all_52_12
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_57_9,
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (1995), (1999) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2006)  all_57_9 = e1
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (2002) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2007)  all_52_8 = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2005), (2006) imply:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2008)  all_52_12 = e1
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (2003) imply:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2009)   ~ (all_52_3 = e0)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2010)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2010) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2011)  all_56_12 = e2 & op(e0, e3) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2011) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2012)  all_56_12 = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2013)  all_56_15 = e0 & op(e0, e0) = e0
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2013) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2014)  all_56_15 = e0
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (207), (209),
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (229), (231), (233), (1878), (1916),
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1931), (1965), (1966), (1992), (2012), (2014),
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #595.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2015)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2015) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2016)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (1190), (1973), (2009),
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2016), (function-axioms) are inconsistent by
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #881.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2017)  all_56_13 = e2 & op(e0, e2) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1901), (2017), (function-axioms) are
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #594.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2018)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2018) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2019)  all_56_14 = e2 & op(e0, e1) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1981), (2019) are inconsistent by sub-proof
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #686.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2020)  all_56_15 = e2 & op(e0, e0) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2020) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2021)  op(e0, e0) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1959), (2021), (function-axioms) are
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2022)  all_56_5 = e2 & op(e2, e1) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2022) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2023)  all_56_5 = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1992), (2023) are inconsistent by sub-proof
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #593.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2024)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2024) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2025)  all_56_8 = e2 & op(e1, e1) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2025) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2026)  op(e1, e1) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1193), (2026), (function-axioms) are
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2027)  all_56_14 = e2 & op(e0, e1) = e2
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1981), (2027) are inconsistent by sub-proof
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #686.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2028)  all_56_10 = e1 & op(e2, e0) = e1
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1876), (2028), (function-axioms) are
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2029)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2029) gives:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2030)  all_56_11 = e1 & op(e1, e0) = e1
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2030) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2031)  op(e1, e0) = e1
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (1945), (2031), (function-axioms) are
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2032)  all_56_15 = e1 & op(e0, e0) = e1
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2032) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2033)  op(e0, e0) = e1
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (51), (160), (162), (163), (214),
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (1193), (1874), (1878), (1945), (2033),
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #592.
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2034)  all_56_10 = e3 & op(e2, e0) = e3
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2034) implies:
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2035)  all_56_10 = e3
% 150.79/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2036)  op(e2, e0) = e3
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2037)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2037) gives:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2038)  all_56_4 = e3 & op(e3, e1) = e3
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2038) implies:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2039)  op(e3, e1) = e3
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1914), (2039), (function-axioms) are
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2040)  all_56_5 = e3 & op(e2, e1) = e3
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2040) implies:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2041)  all_56_5 = e3
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2042)  all_56_15 = e0 & op(e0, e0) = e0
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2042) implies:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2043)  all_56_15 = e0
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2044)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (158), (221), (226),
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1875), (1907), (1916), (1949), (2035), (2041),
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2044), (function-axioms) are inconsistent by
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #590.
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2045)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2045) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2046)  all_56_6 = e2 & op(e1, e3) = e2
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1899), (2046), (function-axioms) are
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2047)  all_56_12 = e2 & op(e0, e3) = e2
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2047) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2048)  all_56_12 = e2
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (207), (209),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (229), (231), (233), (1878), (1916),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1931), (1965), (1966), (2041), (2043), (2048),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #595.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2049)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2049) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2050)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2050) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2051)  all_56_12 = e0 & op(e0, e3) = e0
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2051) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2052)  op(e0, e3) = e0
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2053)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (158), (221), (226),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1875), (1907), (1916), (1949), (2035), (2041),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2053), (function-axioms) are inconsistent by
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #590.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2054)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (163), (1899), (2052), (2054),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #589.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2055)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (1190), (1973), (2055),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #882.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2056)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2056) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2057)  all_56_8 = e3 & op(e1, e1) = e3
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2057) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2058)  op(e1, e1) = e3
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (51), (79), (106),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (110), (112), (113), (117), (118), (120), (121),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (139), (145), (146), (148), (149), (157),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (163), (164), (165), (167), (168),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (189), (190), (192), (193), (198),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (200), (201), (202), (206), (207), (210),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (213), (214), (215), (217), (218),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (238),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (246), (247), (249), (250), (261), (268),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (271), (297), (314), (349), (351),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (358), (360), (369), (370), (371), (372), (373),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (378), (1189), (1876), (1878), (1902), (1913),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1914), (1916), (1931), (1932), (1985), (1987),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2035), (2036), (2058), (function-axioms) are
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #506.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2059)  all_56_14 = e3 & op(e0, e1) = e3
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2059) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2060)  op(e0, e1) = e3
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1987), (2060), (function-axioms) are
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #720.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2061)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (1875), (1901), (1973), (2061) are
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2062)  all_56_15 = e1 & op(e0, e0) = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2062) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2063)  op(e0, e0) = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (51), (160), (162), (163), (214),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (1193), (1874), (1878), (1945), (2063),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #592.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2064)  all_56_3 = e0 & op(e2, e2) = e0
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2064) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2065)  op(e2, e2) = e0
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1878), (2065), (function-axioms) are
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (2066)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (1188), (1932), (2066),
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | |            #501.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | |   (2067)  all_54_8 = e0
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (1187), (2067) are inconsistent by
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #613.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | |   (2068)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (1909), (2068) are
% 151.11/21.65  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | End of split
% 151.11/21.65  | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | |   (2069)  all_26_2 = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (2069) imply:
% 151.11/21.65  | | | | | | | | | | | | | | | |   (2070)  all_6_2 = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | SIMP: (2070) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | |   (2071)  all_6_2 = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | COMBINE_EQS: (303), (2071) imply:
% 151.11/21.65  | | | | | | | | | | | | | | | |   (2072)  all_42_2 = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | REDUCE: (340), (2071) imply:
% 151.11/21.65  | | | | | | | | | | | | | | | |   (2073)   ~ (all_52_2 = e1)
% 151.11/21.65  | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | REDUCE: (377), (2071) imply:
% 151.11/21.65  | | | | | | | | | | | | | | | |   (2074)   ~ (e2 = e1)
% 151.11/21.65  | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | REDUCE: (39), (2071) imply:
% 151.11/21.65  | | | | | | | | | | | | | | | |   (2075)  op(e3, e3) = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | |   (2076)   ~ (all_42_2 = e1)
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | REDUCE: (2072), (2076) imply:
% 151.11/21.65  | | | | | | | | | | | | | | | | |   (2077)  $false
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | CLOSE: (2077) is inconsistent.
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | |   (2078)  ( ~ (all_42_0 = e2) & op(e1, e3) = all_42_0 &
% 151.11/21.65  | | | | | | | | | | | | | | | | |             $i(all_42_0)) | ( ~ (all_42_1 = e0) & op(e1, e1)
% 151.11/21.65  | | | | | | | | | | | | | | | | |             = all_42_1 & $i(all_42_1))
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | |   (2079)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (1874), (2073), (2079),
% 151.11/21.65  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.11/21.65  | | | | | | | | | | | | | | | | | |            #500.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | |   (2080)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 151.11/21.65  | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | BETA: splitting (2080) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | |   (2081)  all_56_8 = e1 & op(e1, e1) = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | ALPHA: (2081) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | |   (2082)  op(e1, e1) = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (2082), (function-axioms) are
% 151.11/21.65  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | |   (2083)  all_56_11 = e1 & op(e1, e0) = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | ALPHA: (2083) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | |   (2084)  all_56_11 = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | | |   (2085)  op(e1, e0) = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | |   (2086)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2086) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | |   (2087)  all_56_0 = e1 & op(e3, e3) = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2087) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | |   (2088)  all_56_0 = e1
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | |   (2089)  all_54_8 = e3
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (2089) imply:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | |   (2090)  all_52_2 = e3
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | SIMP: (2090) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | |   (2091)  all_52_2 = e3
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (2091) imply:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | |   (2092)   ~ (all_52_14 = e3)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | SIMP: (2092) implies:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | |   (2093)   ~ (all_52_14 = e3)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | |   (2094)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2094) gives:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.65  | | | | | | | | | | | | | | | | | | | | | | | |   (2095)  all_56_6 = e3 & op(e1, e3) = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2095) implies:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | |   (2096)  all_56_6 = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | |   (2097)  op(e1, e3) = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (2098)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (1878), (2075), (2098),
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |            #499.
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (2099)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2099) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2100)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2100) implies:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2101)  op(e1, e1) = e1
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (2101), (function-axioms) are
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2102)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2102) implies:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2103)  all_57_15 = e0
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2104)  op(e0, e0) = e0
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2105)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13))
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2106)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11))
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2106) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2107)  all_57_12 = e0 & op(e2, e2) = e0
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2107) implies:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2108)  op(e2, e2) = e0
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1878), (2108), (function-axioms) are
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2109)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2109) implies:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2110)   ~ (all_57_11 = e2)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2111)  op(e2, e0) = all_57_11
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2078) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2112)   ~ (all_42_0 = e2) & op(e1, e3) = all_42_0 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_42_0)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2112) implies:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2113)   ~ (all_42_0 = e2)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2114)  op(e1, e3) = all_42_0
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2115)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2115) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2116)  all_56_12 = e1 & op(e0, e3) = e1
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2116) implies:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2117)  all_56_12 = e1
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (1899), (2075), (2117), (function-axioms)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #495.
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2118)  all_56_13 = e1 & op(e0, e2) = e1
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1875), (2118), (function-axioms) are
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #712.
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2119)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2119) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2120)  all_56_14 = e1 & op(e0, e1) = e1
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2120) implies:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2121)  all_56_14 = e1
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2122)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2122) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2123)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2123) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2124)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2124) gives:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2125)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (1878), (2075), (2125),
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #494.
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2126)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2126) gives:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2127)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2127) implies:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2128)  op(e1, e1) = e2
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1193), (2128), (function-axioms) are
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2129)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2129) implies:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2130)  op(e2, e2) = e3
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1878), (2130), (function-axioms) are
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2131)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2131) gives:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2132)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2132) gives:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2133)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2133) implies:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2134)  op(e0, e0) = e2
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2104), (2134), (function-axioms) are
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2135)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2135) implies:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2136)  op(e2, e2) = e3
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1878), (2136), (function-axioms) are
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2137)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2137) gives:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2138)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2138) implies:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2139)  op(e2, e2) = e2
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1878), (2139), (function-axioms) are
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2140)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2140) gives:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2141)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2141) implies:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2142)  op(e1, e1) = e3
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (2085), (2105), (2142),
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #493.
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2143)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2143) implies:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2144)  op(e3, e3) = e2
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2075), (2144), (function-axioms) are
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2145)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2145) gives:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2146)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2146) gives:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2147)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (2075), (2104), (2147),
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #850.
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2148)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 151.11/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2148) gives:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2149)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2149) implies:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2150)  op(e2, e0) = e2
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2110), (2111), (2150), (function-axioms)
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #627.
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2151)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2151) implies:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2152)  op(e1, e3) = e1
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2073), (2152), (function-axioms) are
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2153)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2153) gives:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2154)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2154) gives:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2155)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2155) implies:
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2156)  op(e1, e1) = e3
% 151.24/21.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (2085), (2105), (2156),
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #493.
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2157)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2157) implies:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2158)  op(e1, e3) = e1
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2073), (2158), (function-axioms) are
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2159)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2159) gives:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2160)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2160) implies:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2161)  op(e0, e0) = e1
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (2104), (2161), (function-axioms) are
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2162)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2162) gives:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2163)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2163) implies:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2164)  op(e1, e1) = e3
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (2085), (2105), (2164),
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #493.
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2165)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e1
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2165) implies:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2166)  op(e1, e1) = e1
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (2166), (function-axioms) are
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2167)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2167) gives:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2168)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2168) gives:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2169)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2169) gives:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2170)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1874), (2170), (function-axioms) are
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #492.
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2171)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (51), (1193), (2104), (2171),
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #491.
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2172)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2172) gives:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2173)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1193), (2173), (function-axioms) are
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2174)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2174) gives:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2175)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2175) implies:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2176)  op(e0, e0) = e3
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2104), (2176), (function-axioms) are
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2177)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2177) gives:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2178)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2178) implies:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2179)  op(e3, e3) = e3
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2075), (2179), (function-axioms) are
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2180)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2180) implies:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2181)   ~ (all_57_14 = e0)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2085), (2105), (2181), (function-axioms)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #626.
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2182)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2182) gives:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2183)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2183) gives:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2184)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1878), (2104), (2184), (function-axioms) are
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #576.
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2185)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2185) gives:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2186)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2186) implies:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2187)   ~ (all_57_14 = e0)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2085), (2105), (2187), (function-axioms)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #626.
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2188)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2188) implies:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2189)  op(e0, e0) = e3
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2104), (2189), (function-axioms) are
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2190)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2190) gives:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2191)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (2075), (2104), (2191),
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #836.
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2192)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.24/21.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2192) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2193)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2193) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2194)  op(e2, e2) = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1878), (2194), (function-axioms) are
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2195)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2195) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2196)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2196) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2197)  op(e1, e1) = e1
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1193), (2197), (function-axioms) are
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2198)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2198) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2199)  op(e0, e0) = all_57_15
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2200)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2201)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2201) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2202)  all_56_12 = e3 & op(e0, e3) = e3
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2202) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2203)  all_56_12 = e3
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2204)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2204) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2205)  all_56_0 = e0 & op(e3, e3) = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2205) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2206)  op(e3, e3) = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2075), (2206), (function-axioms) are
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2207)  all_56_2 = e0 & op(e2, e3) = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2207) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2208)  all_56_2 = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2209)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2209) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2210)  all_56_0 = e2 & op(e3, e3) = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2088), (2210) are inconsistent by sub-proof
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #490.
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2211)  all_56_2 = e2 & op(e2, e3) = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2211) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2212)  all_56_2 = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2208), (2212) are inconsistent by sub-proof
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #602.
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2213)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2213) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2214)  all_56_6 = e2 & op(e1, e3) = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1899), (2214), (function-axioms) are
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2215)  all_56_12 = e2 & op(e0, e3) = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2203), (2215) are inconsistent by sub-proof
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #730.
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2216)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2097), (2203), (2216), (function-axioms) are
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #615.
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2217)  all_56_13 = e3 & op(e0, e2) = e3
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2217) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2218)  op(e0, e2) = e3
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2219)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2219) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2220)  all_56_1 = e0 & op(e3, e2) = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2220) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2221)  op(e3, e2) = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2105) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e0,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (51), (2104) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2222)  all_14_2 = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (2218) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2223)  all_52_7 = e3
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_42_0,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (2097), (2114) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2224)  all_42_0 = e3
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11, e0, e2, simplifying with (164), (2111)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2225)  all_57_11 = all_52_13
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (2221) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2226)  all_52_4 = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (2222) imply:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2227)   ~ (all_52_3 = e0)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (2222) imply:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2228)   ~ (e1 = e0)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2229)  all_56_15 = e0 & op(e0, e0) = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2229) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2230)  all_56_15 = e0
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2231)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2231) gives:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2232)  all_56_0 = e2 & op(e3, e3) = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2232) implies:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2233)  op(e3, e3) = e2
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2075), (2233), (function-axioms) are
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2234)  all_56_2 = e2 & op(e2, e3) = e2
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2234) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2235)  all_56_2 = e2
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (210), (211),
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (229), (2084), (2088), (2096), (2104),
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2227), (2230), (2235), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #488.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2236)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2236) gives:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2237)  all_56_6 = e2 & op(e1, e3) = e2
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1899), (2237), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2238)  all_56_12 = e2 & op(e0, e3) = e2
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2238) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2239)  op(e0, e3) = e2
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (157), (159), (160), (164), (1190),
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2075), (2105), (2110), (2111), (2200), (2218),
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2239), (function-axioms) are inconsistent by
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #625.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2240)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2240) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2241)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2241) gives:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2242)  all_56_12 = e0 & op(e0, e3) = e0
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2242) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2243)  op(e0, e3) = e0
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2227), (2243), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2244)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2244) gives:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2245)  all_56_13 = e0 & op(e0, e2) = e0
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2245) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2246)  op(e0, e2) = e0
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2218), (2246), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #726.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2247)  all_56_14 = e0 & op(e0, e1) = e0
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2247) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2248)  op(e0, e1) = e0
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1190), (2248), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2249)   ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2249) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2250)   ~ (all_57_13 = e1)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2251)  op(e1, e0) = all_57_13
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2085), (2250), (2251), (function-axioms)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #637.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2252)  all_56_3 = e0 & op(e2, e2) = e0
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2252) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2253)  op(e2, e2) = e0
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1878), (2253), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2254)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (1188), (2218), (2254),
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #501.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2255)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2255) gives:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2256)  all_56_14 = e3 & op(e0, e1) = e3
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2256) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2257)  all_56_14 = e3
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2121), (2257) are inconsistent by sub-proof
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #669.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2258)  all_56_15 = e3 & op(e0, e0) = e3
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2258) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2259)  op(e0, e0) = e3
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2104), (2259), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2260)  all_56_15 = e1 & op(e0, e0) = e1
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2260) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2261)  op(e0, e0) = e1
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (2104), (2261), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2262)   ~ (all_42_1 = e0) & op(e1, e1) = all_42_1 &
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_42_1)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1193), (2262), (function-axioms) are inconsistent
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #611.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | |   (2263)  all_56_7 = e3 & op(e1, e2) = e3
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2263) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | |   (2264)  op(e1, e2) = e3
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1880), (1881), (2264), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #610.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | |   (2265)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2265) gives:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | |   (2266)  all_56_8 = e3 & op(e1, e1) = e3
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2266) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | |   (2267)  op(e1, e1) = e3
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (160), (238), (1878), (2075),
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | |            (2085), (2267), (function-axioms) are inconsistent
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #487.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | |   (2268)  all_56_11 = e3 & op(e1, e0) = e3
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2268) implies:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | |   (2269)  op(e1, e0) = e3
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2093), (2269), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #677.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | |   (2270)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2270) gives:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | |   (2271)  all_54_8 = e2
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (1899), (2271) are inconsistent by
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #608.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | |   (2272)  all_54_8 = e1 | all_54_8 = e0
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (1187), (2073), (2272) are inconsistent by
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #612.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | |   (2273)  all_56_2 = e1 & op(e2, e3) = e1
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (163), (229),
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | |            (233), (235), (1899), (2075), (2273),
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | |            #480.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | |   (2274)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | |            (235), (1899), (2073), (2075), (2274),
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | |            #479.
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | |   (2275)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 151.24/21.71  | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 151.24/21.71  | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | BETA: splitting (2275) gives:
% 151.24/21.71  | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | Case 1:
% 151.24/21.71  | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | |   (2276)  all_56_8 = e2 & op(e1, e1) = e2
% 151.24/21.71  | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | ALPHA: (2276) implies:
% 151.24/21.71  | | | | | | | | | | | | | | |   (2277)  op(e1, e1) = e2
% 151.24/21.71  | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | REF_CLOSE: (5), (1193), (2277), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 151.24/21.71  | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | |   (2278)  all_56_11 = e2 & op(e1, e0) = e2
% 151.24/21.71  | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | | REF_CLOSE: (160), (1902), (2278), (function-axioms) are
% 151.24/21.71  | | | | | | | | | | | | | | |            inconsistent by sub-proof #879.
% 151.24/21.71  | | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | |   (2279)  all_54_9 = e1 | all_54_9 = e0
% 151.24/21.71  | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | | REF_CLOSE: (258), (1188), (1874), (2279) are inconsistent by
% 151.24/21.71  | | | | | | | | | | | | |            sub-proof #478.
% 151.24/21.71  | | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | |   (2280)   ~ (all_24_1 = e0) & op(e1, e1) = all_24_1 &
% 151.24/21.71  | | | | | | | | | | |           $i(all_24_1)
% 151.24/21.71  | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | REF_CLOSE: (1193), (2280), (function-axioms) are inconsistent
% 151.24/21.71  | | | | | | | | | | |            by sub-proof #477.
% 151.24/21.71  | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | | 
% 151.24/21.71  | | | | | | | | End of split
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | Case 2:
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | |   (2281)  all_20_2 = e3
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | | COMBINE_EQS: (325), (2281) imply:
% 151.24/21.71  | | | | | | | |   (2282)  all_10_2 = e3
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | | SIMP: (2282) implies:
% 151.24/21.71  | | | | | | | |   (2283)  all_10_2 = e3
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | | REDUCE: (361), (2283) imply:
% 151.24/21.71  | | | | | | | |   (2284)   ~ (all_52_6 = e3)
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | | REDUCE: (363), (2283) imply:
% 151.24/21.71  | | | | | | | |   (2285)   ~ (all_52_8 = e3)
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | | REDUCE: (364), (2283) imply:
% 151.24/21.71  | | | | | | | |   (2286)   ~ (all_52_9 = e3)
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | | REDUCE: (366), (2283) imply:
% 151.24/21.71  | | | | | | | |   (2287)   ~ (all_52_11 = e3)
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | | REDUCE: (368), (2283) imply:
% 151.24/21.71  | | | | | | | |   (2288)   ~ (all_52_14 = e3)
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | | REDUCE: (45), (2283) imply:
% 151.24/21.71  | | | | | | | |   (2289)  op(e1, e1) = e3
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | | BETA: splitting (67) gives:
% 151.24/21.71  | | | | | | | | 
% 151.24/21.71  | | | | | | | | Case 1:
% 151.24/21.71  | | | | | | | | | 
% 151.24/21.71  | | | | | | | | |   (2290)   ~ (all_24_2 = e1)
% 151.24/21.71  | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | REDUCE: (318), (2290) imply:
% 151.24/21.71  | | | | | | | | |   (2291)   ~ (all_4_2 = e1)
% 151.24/21.71  | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | BETA: splitting (70) gives:
% 151.24/21.71  | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | Case 1:
% 151.24/21.71  | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | |   (2292)   ~ (all_26_2 = e1)
% 151.24/21.71  | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | REDUCE: (307), (2292) imply:
% 151.24/21.71  | | | | | | | | | |   (2293)   ~ (all_6_2 = e1)
% 151.24/21.71  | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | BETA: splitting (204) gives:
% 151.24/21.71  | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | Case 1:
% 151.24/21.71  | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | |   (2294)  all_54_0 = e3
% 151.24/21.71  | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | COMBINE_EQS: (279), (2294) imply:
% 151.24/21.71  | | | | | | | | | | |   (2295)  all_6_2 = e3
% 151.24/21.71  | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | REDUCE: (338), (2295) imply:
% 151.24/21.71  | | | | | | | | | | |   (2296)   ~ (all_52_1 = e3)
% 151.24/21.71  | | | | | | | | | | | 
% 151.24/21.71  | | | | | | | | | | | REDUCE: (342), (2295) imply:
% 151.24/21.71  | | | | | | | | | | |   (2297)   ~ (all_52_3 = e3)
% 151.24/21.71  | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | REDUCE: (344), (2295) imply:
% 151.24/21.72  | | | | | | | | | | |   (2298)   ~ (all_52_4 = e3)
% 151.24/21.72  | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | REDUCE: (348), (2295) imply:
% 151.24/21.72  | | | | | | | | | | |   (2299)   ~ (all_52_12 = e3)
% 151.24/21.72  | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | REDUCE: (39), (2295) imply:
% 151.24/21.72  | | | | | | | | | | |   (2300)  op(e3, e3) = e3
% 151.24/21.72  | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | BETA: splitting (228) gives:
% 151.24/21.72  | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | |   (2301)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 151.24/21.72  | | | | | | | | | | | |             & op(e2, e2) = e3)
% 151.24/21.72  | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (230), (232),
% 151.24/21.72  | | | | | | | | | | | |            (234), (373), (2300), (2301), (function-axioms)
% 151.24/21.72  | | | | | | | | | | | |            are inconsistent by sub-proof #476.
% 151.24/21.72  | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | Case 2:
% 151.24/21.72  | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | |   (2302)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 151.24/21.72  | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 151.24/21.72  | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | BETA: splitting (2302) gives:
% 151.24/21.72  | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | |   (2303)  all_56_7 = e3 & op(e1, e2) = e3
% 151.24/21.72  | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | ALPHA: (2303) implies:
% 151.24/21.72  | | | | | | | | | | | | |   (2304)  all_56_7 = e3
% 151.24/21.72  | | | | | | | | | | | | |   (2305)  op(e1, e2) = e3
% 151.24/21.72  | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (157), (165),
% 151.24/21.72  | | | | | | | | | | | | |            (199), (206), (209), (210), (211), (224), (225),
% 151.24/21.72  | | | | | | | | | | | | |            (226), (227), (229), (231), (233), (268), (373),
% 151.24/21.72  | | | | | | | | | | | | |            (2286), (2287), (2291), (2300), (2304), (2305),
% 151.24/21.72  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.24/21.72  | | | | | | | | | | | | |            #464.
% 151.24/21.72  | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | Case 2:
% 151.24/21.72  | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | |   (2306)  all_56_13 = e3 & op(e0, e2) = e3
% 151.24/21.72  | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | ALPHA: (2306) implies:
% 151.24/21.72  | | | | | | | | | | | | |   (2307)  all_56_13 = e3
% 151.24/21.72  | | | | | | | | | | | | |   (2308)  op(e0, e2) = e3
% 151.24/21.72  | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | BETA: splitting (224) gives:
% 151.24/21.72  | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | |   (2309)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 151.24/21.72  | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 151.24/21.72  | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (229), (231),
% 151.24/21.72  | | | | | | | | | | | | | |            (233), (373), (2300), (2309), (function-axioms)
% 151.24/21.72  | | | | | | | | | | | | | |            are inconsistent by sub-proof #475.
% 151.24/21.72  | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | Case 2:
% 151.24/21.72  | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | |   (2310)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 151.24/21.72  | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 151.24/21.72  | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | BETA: splitting (2310) gives:
% 151.24/21.72  | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | |   (2311)  all_56_5 = e3 & op(e2, e1) = e3
% 151.24/21.72  | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | ALPHA: (2311) implies:
% 151.24/21.72  | | | | | | | | | | | | | | |   (2312)  op(e2, e1) = e3
% 151.24/21.72  | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | REF_CLOSE: (165), (2286), (2312), (function-axioms) are
% 151.24/21.72  | | | | | | | | | | | | | | |            inconsistent by sub-proof #763.
% 151.24/21.72  | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | Case 2:
% 151.24/21.72  | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | |   (2313)  all_56_10 = e3 & op(e2, e0) = e3
% 151.24/21.72  | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | ALPHA: (2313) implies:
% 151.24/21.72  | | | | | | | | | | | | | | |   (2314)  all_56_10 = e3
% 151.24/21.72  | | | | | | | | | | | | | | |   (2315)  op(e2, e0) = e3
% 151.24/21.72  | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 151.24/21.72  | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | |   (2316)   ~ (all_28_2 = e2)
% 151.24/21.72  | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | REDUCE: (330), (2316) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | |   (2317)   ~ (all_14_2 = e2)
% 151.24/21.72  | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 151.24/21.72  | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | |   (2318)  all_54_15 = e3
% 151.24/21.72  | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (380), (2318) are inconsistent by sub-proof
% 151.24/21.72  | | | | | | | | | | | | | | | | |            #1010.
% 151.24/21.72  | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.72  | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | |   (2319)   ~ (all_54_15 = e3)
% 151.24/21.72  | | | | | | | | | | | | | | | | |   (2320)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 151.24/21.72  | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | BETA: splitting (2320) gives:
% 151.24/21.72  | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | |   (2321)  all_54_15 = e2
% 151.24/21.72  | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2317), (2321) are inconsistent by
% 151.24/21.72  | | | | | | | | | | | | | | | | | |            sub-proof #1009.
% 151.24/21.72  | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | |   (2322)   ~ (all_54_15 = e2)
% 151.24/21.72  | | | | | | | | | | | | | | | | | |   (2323)  all_54_15 = e1 | all_54_15 = e0
% 151.24/21.72  | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | BETA: splitting (2323) gives:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |   (2324)  all_54_15 = e1
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (378), (2324) are inconsistent by sub-proof
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |            #1008.
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |   (2325)  all_54_15 = e0
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (2325) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |   (2326)  all_14_2 = e0
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | SIMP: (2326) implies:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |   (2327)  all_14_2 = e0
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | REDUCE: (351), (2327) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |   (2328)   ~ (all_52_3 = e0)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | REDUCE: (369), (2327) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |   (2329)   ~ (all_52_11 = e0)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | REDUCE: (380), (2327) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |   (2330)   ~ (e3 = e0)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | REDUCE: (2317), (2327) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |   (2331)   ~ (e2 = e0)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | REDUCE: (378), (2327) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |   (2332)   ~ (e1 = e0)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | REDUCE: (51), (2327) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | |   (2333)  op(e0, e0) = e0
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | |   (2334)   ~ (all_32_2 = e0)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (2334) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | |   (2335)   ~ (all_4_2 = e0)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | |   (2336)  all_54_5 = e3
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (373), (2336) are inconsistent by sub-proof
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | |            #930.
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | |   (2337)   ~ (all_54_5 = e3)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | |   (2338)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2338) gives:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | |   (2339)  all_54_5 = e2
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2339) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | |   (2340)  all_4_2 = e2
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | SIMP: (2340) implies:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | |   (2341)  all_4_2 = e2
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (2341) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | |   (2342)   ~ (all_52_1 = e2)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (2341) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | |   (2343)   ~ (all_52_9 = e2)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (2341) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | |   (2344)   ~ (e3 = e2)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2341) imply:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | |   (2345)  op(e2, e2) = e2
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |   (2346)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2346) gives:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (2347)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2347) gives:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.24/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (2348)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2342), (2348), (function-axioms) are
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.24/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (2349)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (167), (170), (2298), (2342), (2343),
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |            (2349), (function-axioms) are inconsistent by
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #566.
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |   (2350)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2350) gives:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (2351)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2351) gives:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2352)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (2298), (2333), (2352),
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            #997.
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2353)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (2300), (2315), (2353),
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            #579.
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (2354)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2354) gives:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2355)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (2285), (2345), (2355),
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            #565.
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2356)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (168), (2289), (2299), (2333), (2356),
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            #463.
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |   (2357)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2357) gives:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |   (2358)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2358) gives:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (2359)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2359) gives:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2360)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2300), (2345), (2360),
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            #987.
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2361)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (51), (2289), (2333), (2361),
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            #645.
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (2362)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2362) gives:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2363)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (2289), (2363), (function-axioms) are
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #644.
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2364)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (169), (2285), (2300), (2333), (2364),
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            #980.
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |   (2365)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2365) gives:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (2366)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2366) gives:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2367)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (165), (2333), (2343), (2367),
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            #978.
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2368)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (2333), (2345), (2368),
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            #977.
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (2369)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2369) gives:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2370)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (2299), (2333), (2370),
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            #975.
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2371)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2371) gives:
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2372)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2372) implies:
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2373)  op(e2, e0) = e2
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2315), (2373), (function-axioms) are
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #580.
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2374)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2374) gives:
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2375)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2375) implies:
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2376)  op(e1, e1) = e1
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2289), (2376), (function-axioms) are
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2377)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.47/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2377) implies:
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2378)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (157), (159), (2289), (2300), (2308),
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2315), (2328), (2329), (2378), (function-axioms)
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #570.
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | |   (2379)  all_54_5 = e1 | all_54_5 = e0
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (2291), (2335), (2379) are inconsistent by
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | |   (2380)  all_32_2 = e0
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (2380) imply:
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | |   (2381)  all_4_2 = e0
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2381) imply:
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | |   (2382)  op(e2, e2) = e0
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |   (2383)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2383) gives:
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | |   (2384)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.56/21.75  | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2384) gives:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |   (2385)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2385) gives:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2386)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (2300), (2382), (2386),
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            #934.
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2387)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (2289), (2382), (2387),
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            #638.
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |   (2388)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2388) gives:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2389)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (2299), (2333), (2389),
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            #932.
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2390)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2390) gives:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (2391)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2391) implies:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (2392)  op(e2, e2) = e2
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2382), (2392), (function-axioms) are
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (2393)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2298), (2300), (2393),
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | |            #538.
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |   (2394)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2394) gives:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |   (2395)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2395) gives:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2396)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (2298), (2333), (2396),
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            #997.
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2397)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (2300), (2315), (2397),
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            #579.
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |   (2398)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2398) gives:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2399)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (169), (2285), (2382), (2399),
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            #537.
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2400)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (168), (2289), (2299), (2333), (2400),
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | |            #463.
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.76  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |   (2401)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2401) gives:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |   (2402)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2402) gives:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (2403)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2403) gives:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |   (2404)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (2300), (2382), (2404),
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |            #920.
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |   (2405)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (51), (2289), (2333), (2405),
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |            #645.
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (2406)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2406) gives:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |   (2407)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (2289), (2407), (function-axioms) are
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #644.
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |   (2408)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (169), (2285), (2300), (2333), (2408),
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | |            #980.
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |   (2409)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2409) gives:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (2410)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (2333), (2382), (2410),
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | |            #918.
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |   (2411)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2411) gives:
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (2412)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (2299), (2333), (2412),
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |            #975.
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (2413)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2413) gives:
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (2414)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2414) implies:
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (2415)  op(e2, e2) = e2
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2382), (2415), (function-axioms) are
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (2416)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (157), (159), (2289), (2300),
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |            (2308), (2315), (2328), (2329), (2416),
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |            #569.
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | Case 2:
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | |   (2417)  all_28_2 = e2
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (2417) imply:
% 151.56/21.78  | | | | | | | | | | | | | | | |   (2418)  all_14_2 = e2
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | SIMP: (2418) implies:
% 151.56/21.78  | | | | | | | | | | | | | | | |   (2419)  all_14_2 = e2
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (2419) imply:
% 151.56/21.78  | | | | | | | | | | | | | | | |   (2420)  all_50_2 = e2
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | REDUCE: (351), (2419) imply:
% 151.56/21.78  | | | | | | | | | | | | | | | |   (2421)   ~ (all_52_3 = e2)
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | REDUCE: (370), (2419) imply:
% 151.56/21.78  | | | | | | | | | | | | | | | |   (2422)   ~ (all_52_12 = e2)
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | REDUCE: (372), (2419) imply:
% 151.56/21.78  | | | | | | | | | | | | | | | |   (2423)   ~ (all_52_14 = e2)
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | REDUCE: (380), (2419) imply:
% 151.56/21.78  | | | | | | | | | | | | | | | |   (2424)   ~ (e3 = e2)
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | REDUCE: (51), (2419) imply:
% 151.56/21.78  | | | | | | | | | | | | | | | |   (2425)  op(e0, e0) = e2
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.78  | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | |   (2426)   ~ (all_50_2 = e2)
% 151.56/21.78  | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | REDUCE: (2420), (2426) imply:
% 151.56/21.78  | | | | | | | | | | | | | | | | |   (2427)  $false
% 151.56/21.78  | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | CLOSE: (2427) is inconsistent.
% 151.56/21.78  | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.78  | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | |   (2428)  ( ~ (all_50_0 = e3) & op(e2, e0) = all_50_0 &
% 151.56/21.78  | | | | | | | | | | | | | | | | |             $i(all_50_0)) | ( ~ (all_50_1 = e1) & op(e2, e2)
% 151.56/21.78  | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 151.56/21.78  | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (79), (123),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (139), (146), (148), (149), (157), (159), (160),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (192), (198), (199), (200), (206), (207), (210),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (211), (212), (213), (214), (215), (217), (218),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (238),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (239), (249), (261), (268), (269), (314), (349),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (358), (360), (373), (2285), (2286), (2289),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (2296), (2297), (2298), (2299), (2300), (2307),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (2308), (2314), (2315), (2421), (2422), (2423),
% 151.56/21.78  | | | | | | | | | | | | | | | | |            (2425), (2428), (function-axioms) are inconsistent
% 151.56/21.78  | | | | | | | | | | | | | | | | |            by sub-proof #507.
% 151.56/21.78  | | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | Case 2:
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | |   (2429)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (2293), (2429) are
% 151.56/21.78  | | | | | | | | | | |            inconsistent by sub-proof #853.
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | End of split
% 151.56/21.78  | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | Case 2:
% 151.56/21.78  | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | |   (2430)  all_26_2 = e1
% 151.56/21.78  | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | COMBINE_EQS: (307), (2430) imply:
% 151.56/21.78  | | | | | | | | | |   (2431)  all_6_2 = e1
% 151.56/21.78  | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | REDUCE: (340), (2431) imply:
% 151.56/21.78  | | | | | | | | | |   (2432)   ~ (all_52_2 = e1)
% 151.56/21.78  | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | REDUCE: (377), (2431) imply:
% 151.56/21.78  | | | | | | | | | |   (2433)   ~ (e2 = e1)
% 151.56/21.78  | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | REDUCE: (39), (2431) imply:
% 151.56/21.78  | | | | | | | | | |   (2434)  op(e3, e3) = e1
% 151.56/21.78  | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | BETA: splitting (73) gives:
% 151.56/21.78  | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | Case 1:
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | |   (2435)   ~ (all_28_2 = e2)
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | REDUCE: (330), (2435) imply:
% 151.56/21.78  | | | | | | | | | | |   (2436)   ~ (all_14_2 = e2)
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (51), (79), (157), (158),
% 151.56/21.78  | | | | | | | | | | |            (159), (160), (163), (164), (165), (167), (169),
% 151.56/21.78  | | | | | | | | | | |            (189), (199), (238), (239), (246), (268), (314),
% 151.56/21.78  | | | | | | | | | | |            (349), (351), (356), (358), (360), (362), (369),
% 151.56/21.78  | | | | | | | | | | |            (373), (378), (380), (2285), (2289), (2291),
% 151.56/21.78  | | | | | | | | | | |            (2432), (2434), (2436), (function-axioms) are
% 151.56/21.78  | | | | | | | | | | |            inconsistent by sub-proof #636.
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | Case 2:
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | |   (2437)  all_28_2 = e2
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | COMBINE_EQS: (330), (2437) imply:
% 151.56/21.78  | | | | | | | | | | |   (2438)  all_14_2 = e2
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | SIMP: (2438) implies:
% 151.56/21.78  | | | | | | | | | | |   (2439)  all_14_2 = e2
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | REDUCE: (370), (2439) imply:
% 151.56/21.78  | | | | | | | | | | |   (2440)   ~ (all_52_12 = e2)
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | REDUCE: (372), (2439) imply:
% 151.56/21.78  | | | | | | | | | | |   (2441)   ~ (all_52_14 = e2)
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | REDUCE: (380), (2439) imply:
% 151.56/21.78  | | | | | | | | | | |   (2442)   ~ (e3 = e2)
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | REDUCE: (51), (2439) imply:
% 151.56/21.78  | | | | | | | | | | |   (2443)  op(e0, e0) = e2
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | BETA: splitting (238) gives:
% 151.56/21.78  | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | Case 1:
% 151.56/21.78  | | | | | | | | | | | | 
% 151.56/21.78  | | | | | | | | | | | |   (2444)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 151.56/21.78  | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 151.56/21.78  | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 151.56/21.78  | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 151.56/21.78  | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 151.56/21.78  | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 151.56/21.78  | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 151.56/21.78  | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 151.56/21.78  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 151.56/21.78  | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 151.56/21.78  | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 151.56/21.78  | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 151.56/21.78  | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 151.56/21.79  | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 151.56/21.79  | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 151.56/21.79  | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 151.56/21.79  | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | BETA: splitting (2444) gives:
% 151.56/21.79  | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | Case 1:
% 151.56/21.79  | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | |   (2445)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 151.56/21.79  | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 151.56/21.79  | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 151.56/21.79  | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 151.56/21.79  | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 151.56/21.79  | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 151.56/21.79  | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 151.56/21.79  | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 151.56/21.79  | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | ALPHA: (2445) implies:
% 151.56/21.79  | | | | | | | | | | | | |   (2446)  op(e3, e3) = e3
% 151.56/21.79  | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | REF_CLOSE: (8), (2434), (2446), (function-axioms) are
% 151.56/21.79  | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 151.56/21.79  | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | Case 2:
% 151.56/21.79  | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | |   (2447)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 151.56/21.79  | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 151.56/21.79  | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 151.56/21.79  | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 151.56/21.79  | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 151.56/21.79  | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 151.56/21.79  | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 151.56/21.79  | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 151.56/21.79  | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | ALPHA: (2447) implies:
% 151.56/21.79  | | | | | | | | | | | | |   (2448)  op(e2, e2) = e2
% 151.56/21.79  | | | | | | | | | | | | |   (2449)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 151.56/21.79  | | | | | | | | | | | | |               = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))
% 151.56/21.79  | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | BETA: splitting (2449) gives:
% 151.56/21.79  | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | Case 1:
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | |   (2450)  all_57_14 = e2 & op(e1, e1) = e2
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | ALPHA: (2450) implies:
% 151.56/21.79  | | | | | | | | | | | | | |   (2451)  op(e1, e1) = e2
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | REF_CLOSE: (9), (2289), (2451), (function-axioms) are
% 151.56/21.79  | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | Case 2:
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | |   (2452)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 151.56/21.79  | | | | | | | | | | | | | |           $i(all_57_3)
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | ALPHA: (2452) implies:
% 151.56/21.79  | | | | | | | | | | | | | |   (2453)   ~ (all_57_3 = e1)
% 151.56/21.79  | | | | | | | | | | | | | |   (2454)  op(e1, e2) = all_57_3
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 151.56/21.79  | | | | | | | | | | | | | |              all_57_3, e2, e1, simplifying with (162), (2454)
% 151.56/21.79  | | | | | | | | | | | | | |              gives:
% 151.56/21.79  | | | | | | | | | | | | | |   (2455)  all_57_3 = all_52_6
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e2,
% 151.56/21.79  | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (2448) gives:
% 151.56/21.79  | | | | | | | | | | | | | |   (2456)  all_4_2 = e2
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | REDUCE: (2453), (2455) imply:
% 151.56/21.79  | | | | | | | | | | | | | |   (2457)   ~ (all_52_6 = e1)
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | REDUCE: (349), (2456) imply:
% 151.56/21.79  | | | | | | | | | | | | | |   (2458)   ~ (all_52_1 = e2)
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | REDUCE: (354), (2456) imply:
% 151.56/21.79  | | | | | | | | | | | | | |   (2459)   ~ (all_52_6 = e2)
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | REDUCE: (358), (2456) imply:
% 151.56/21.79  | | | | | | | | | | | | | |   (2460)   ~ (all_52_9 = e2)
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 151.56/21.79  | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | Case 1:
% 151.56/21.79  | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | |   (2461)  all_54_9 = e3
% 151.56/21.79  | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | REF_CLOSE: (258), (2284), (2461) are inconsistent by
% 151.56/21.79  | | | | | | | | | | | | | | |            sub-proof #656.
% 151.56/21.79  | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | Case 2:
% 151.56/21.79  | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | |   (2462)   ~ (all_54_9 = e3)
% 151.56/21.79  | | | | | | | | | | | | | | |   (2463)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 151.56/21.79  | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 151.56/21.79  | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | Case 1:
% 151.56/21.79  | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | |   (2464)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.56/21.79  | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.79  | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.56/21.79  | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.56/21.79  | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.56/21.79  | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.56/21.79  | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.56/21.79  | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.79  | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.56/21.79  | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.79  | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 151.56/21.79  | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 151.56/21.79  | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 151.56/21.79  | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 151.56/21.79  | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 151.56/21.79  | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.56/21.79  | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.56/21.79  | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.56/21.79  | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.56/21.79  | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.56/21.79  | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.79  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 151.56/21.79  | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.56/21.79  | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.79  | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.56/21.79  | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.79  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.56/21.79  | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.79  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.79  | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.56/21.79  | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 151.56/21.79  | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 151.56/21.79  | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.56/21.79  | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.79  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.56/21.79  | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.79  | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.79  | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.56/21.79  | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.79  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.56/21.79  | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | |             e1)
% 151.56/21.79  | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | BETA: splitting (2464) gives:
% 151.56/21.79  | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.79  | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | |   (2465)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.79  | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.56/21.79  | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.56/21.79  | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.56/21.79  | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.79  | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.56/21.79  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 151.56/21.79  | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 151.56/21.79  | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 151.56/21.79  | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 151.56/21.79  | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.56/21.79  | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.56/21.79  | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.56/21.79  | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.79  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.56/21.79  | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (165), (167), (2432), (2458), (2460),
% 151.56/21.79  | | | | | | | | | | | | | | | | |            (2465), (function-axioms) are inconsistent by
% 151.56/21.79  | | | | | | | | | | | | | | | | |            sub-proof #652.
% 151.56/21.79  | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.79  | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | |   (2466)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.79  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.56/21.79  | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.79  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.56/21.79  | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.56/21.79  | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 151.56/21.79  | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.56/21.79  | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.79  | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.79  | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.56/21.79  | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.79  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.56/21.79  | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | | |             e1)
% 151.56/21.79  | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | BETA: splitting (2466) gives:
% 151.56/21.79  | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.79  | | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | |   (2467)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.56/21.79  | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.56/21.79  | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 151.56/21.79  | | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (160), (163), (164), (168), (211),
% 151.56/21.79  | | | | | | | | | | | | | | | | | |            (360), (2432), (2434), (2440), (2441), (2448),
% 151.56/21.79  | | | | | | | | | | | | | | | | | |            (2467), (function-axioms) are inconsistent by
% 151.56/21.79  | | | | | | | | | | | | | | | | | |            sub-proof #818.
% 151.56/21.79  | | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.79  | | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | |   (2468)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.56/21.79  | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.56/21.79  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.79  | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | | | |             e1)
% 151.56/21.79  | | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | | BETA: splitting (2468) gives:
% 151.56/21.79  | | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.79  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |   (2469)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 151.56/21.79  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (2432), (2448), (2469),
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |            #650.
% 151.56/21.79  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.79  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |   (2470)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.79  | | | | | | | | | | | | | | | | | | |             e1)
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | BETA: splitting (2470) gives:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |   (2471)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | ALPHA: (2471) implies:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |   (2472)  op(e0, e0) = e1
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2443), (2472), (function-axioms) are
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |   (2473)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2289), (2432), (2473), (function-axioms)
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #649.
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.80  | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | End of split
% 151.56/21.80  | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | End of split
% 151.56/21.80  | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | Case 2:
% 151.56/21.80  | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | |   (2474)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.80  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.56/21.80  | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.56/21.80  | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.56/21.80  | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.56/21.80  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.56/21.80  | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.80  | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.80  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.56/21.80  | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.80  | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 151.56/21.80  | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.56/21.80  | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 151.56/21.80  | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 151.56/21.80  | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.56/21.80  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 151.56/21.80  | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 151.56/21.80  | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 151.56/21.80  | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 151.56/21.80  | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.56/21.80  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 151.56/21.80  | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 151.56/21.80  | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 151.56/21.80  | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 151.56/21.80  | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 151.56/21.80  | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 151.56/21.80  | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.56/21.80  | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 151.56/21.80  | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 151.56/21.80  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 151.56/21.80  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 151.56/21.80  | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 151.56/21.80  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 151.56/21.80  | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 151.56/21.80  | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 151.56/21.80  | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 151.56/21.80  | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 151.56/21.80  | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 151.56/21.80  | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 151.56/21.80  | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 151.56/21.80  | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 151.56/21.80  | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.56/21.80  | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 151.56/21.80  | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 151.56/21.80  | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.56/21.80  | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 151.56/21.80  | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 151.56/21.80  | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.56/21.80  | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 151.56/21.80  | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 151.56/21.80  | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 151.56/21.80  | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 151.56/21.80  | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 151.56/21.80  | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 151.56/21.80  | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 151.56/21.80  | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 151.56/21.80  | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 151.56/21.80  | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 151.56/21.80  | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 151.56/21.80  | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 151.56/21.80  | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 151.56/21.80  | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.56/21.80  | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 151.56/21.80  | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 151.56/21.80  | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.80  | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 151.56/21.80  | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 151.56/21.80  | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.80  | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 151.56/21.80  | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 151.56/21.80  | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 151.56/21.80  | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.56/21.80  | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 151.56/21.80  | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 151.56/21.80  | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 151.56/21.80  | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | BETA: splitting (2474) gives:
% 151.56/21.80  | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.80  | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | |   (2475)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.80  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.56/21.80  | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.56/21.80  | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.56/21.80  | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.80  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.56/21.80  | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.56/21.80  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.56/21.80  | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.80  | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.80  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.56/21.80  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.80  | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 151.56/21.80  | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.56/21.80  | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.56/21.80  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 151.56/21.80  | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 151.56/21.80  | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.56/21.80  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 151.56/21.80  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 151.56/21.80  | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 151.56/21.80  | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 151.56/21.80  | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 151.56/21.80  | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.56/21.80  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.56/21.80  | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | BETA: splitting (2475) gives:
% 151.56/21.80  | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | |   (2476)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.56/21.80  | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.56/21.80  | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.56/21.80  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.56/21.80  | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.56/21.80  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 151.56/21.80  | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | BETA: splitting (2476) gives:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |   (2477)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (2285), (2448), (2477),
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |            #647.
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |   (2478)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (2289), (2443), (2478),
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |            #563.
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.80  | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | |   (2479)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 151.56/21.80  | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 151.56/21.80  | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 151.56/21.80  | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.56/21.80  | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 151.56/21.80  | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | BETA: splitting (2479) gives:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |   (2480)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (2289), (2480), (function-axioms) are
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #644.
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |   (2481)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 151.56/21.80  | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | BETA: splitting (2481) gives:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |   (2482)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | ALPHA: (2482) implies:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |   (2483)  op(e0, e0) = e3
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (160), (164), (168), (211), (360),
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |            (2440), (2441), (2448), (2483), (function-axioms)
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #877.
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |   (2484)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2285), (2434), (2484), (function-axioms)
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #643.
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.80  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.80  | | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | | End of split
% 151.56/21.80  | | | | | | | | | | | | | | | | | 
% 151.56/21.80  | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.80  | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | |   (2485)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.56/21.81  | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.56/21.81  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.56/21.81  | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 151.56/21.81  | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 151.56/21.81  | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 151.56/21.81  | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 151.56/21.81  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 151.56/21.81  | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 151.56/21.81  | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.56/21.81  | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.81  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 151.56/21.81  | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 151.56/21.81  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.56/21.81  | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.56/21.81  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 151.56/21.81  | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 151.56/21.81  | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 151.56/21.81  | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 151.56/21.81  | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.56/21.81  | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 151.56/21.81  | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.81  | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.56/21.81  | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.56/21.81  | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | |                 e0)))
% 151.56/21.81  | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | BETA: splitting (2485) gives:
% 151.56/21.81  | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | |   (2486)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 151.56/21.81  | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 151.56/21.81  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 151.56/21.81  | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (160), (164), (165), (168), (211),
% 151.56/21.81  | | | | | | | | | | | | | | | | | |            (360), (2440), (2441), (2448), (2460), (2486),
% 151.56/21.81  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.81  | | | | | | | | | | | | | | | | | |            #870.
% 151.56/21.81  | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | |   (2487)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 151.56/21.81  | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 151.56/21.81  | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 151.56/21.81  | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | BETA: splitting (2487) gives:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |   (2488)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (164), (360), (2434), (2448), (2488),
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |            #817.
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |   (2489)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | BETA: splitting (2489) gives:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |   (2490)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | ALPHA: (2490) implies:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |   (2491)  op(e2, e0) = e2
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (2448), (2491),
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |            #972.
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |   (2492)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | |                 e0)))
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2492) gives:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |   (2493)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2493) implies:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |   (2494)  op(e1, e1) = e1
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2289), (2494), (function-axioms) are
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |   (2495)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |               e0))
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2495) implies:
% 151.56/21.81  | | | | | | | | | | | | | | | | | | | | |   (2496)  op(e0, e0) = all_57_15
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |   (2497)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2463) gives:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | |   (2498)  all_54_9 = e2
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (2459), (2498) are inconsistent by
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #676.
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | |   (2499)   ~ (all_54_9 = e2)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | |   (2500)  all_54_9 = e1 | all_54_9 = e0
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2500) gives:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | |   (2501)  all_54_9 = e1
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (2457), (2501) are inconsistent by
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #675.
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | |   (2502)  all_54_9 = e0
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (2502) imply:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | |   (2503)  all_52_6 = e0
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2503) implies:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | |   (2504)  all_52_6 = e0
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (2504) imply:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | |   (2505)   ~ (all_52_7 = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2505) implies:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | |   (2506)   ~ (all_52_7 = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2284), (2504) imply:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | |   (2507)   ~ (e3 = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2459), (2504) imply:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | |   (2508)   ~ (e2 = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2457), (2504) imply:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | |   (2509)   ~ (e1 = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2497) gives:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |   (2510)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2510) gives:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (2511)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2511) gives:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2512)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2512) implies:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2513)  op(e3, e3) = e0
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2434), (2513), (function-axioms) are
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2514)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (164), (360), (2289), (2448), (2514),
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            #462.
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (2515)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2515) gives:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2516)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2516) implies:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2517)  all_57_15 = e0
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2496), (2517) imply:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2518)  op(e0, e0) = e0
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2443), (2518), (function-axioms) are
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2519)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (164), (360), (2434), (2448), (2519),
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            #833.
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.56/21.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |   (2520)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2520) gives:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (2521)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (158), (2289), (2434), (2506), (2521),
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |            #640.
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (2522)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2522) gives:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2523)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (164), (360), (2289), (2448), (2523),
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            #461.
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2524)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2524) gives:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2525)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 & 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2525) implies:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2526)  all_57_15 = e1
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2496), (2526) imply:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2527)  op(e0, e0) = e1
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2443), (2527), (function-axioms) are
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2528)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = e0
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2528) implies:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2529)  all_57_15 = e0
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2496), (2529) imply:
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2530)  op(e0, e0) = e0
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2443), (2530), (function-axioms) are
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | Case 2:
% 151.85/21.82  | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | |   (2531)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 151.85/21.82  | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 151.85/21.82  | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 151.85/21.82  | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 151.85/21.82  | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 151.85/21.82  | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 151.85/21.82  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 151.85/21.82  | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 151.85/21.82  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 151.85/21.82  | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 151.85/21.82  | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 151.85/21.82  | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 151.85/21.82  | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 151.85/21.82  | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 151.85/21.82  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 151.85/21.82  | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 151.85/21.82  | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | | REF_CLOSE: (5), (8), (2289), (2443), (2531),
% 151.85/21.82  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.82  | | | | | | | | | | | |            #508.
% 151.85/21.82  | | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | End of split
% 151.85/21.82  | | | | | | | | | 
% 151.85/21.82  | | | | | | | | Case 2:
% 151.85/21.82  | | | | | | | | | 
% 151.85/21.82  | | | | | | | | |   (2532)  all_24_2 = e1
% 151.85/21.82  | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | COMBINE_EQS: (318), (2532) imply:
% 151.85/21.82  | | | | | | | | |   (2533)  all_4_2 = e1
% 151.85/21.82  | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | COMBINE_EQS: (292), (2533) imply:
% 151.85/21.82  | | | | | | | | |   (2534)  all_44_2 = e1
% 151.85/21.82  | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | REDUCE: (352), (2533) imply:
% 151.85/21.82  | | | | | | | | |   (2535)   ~ (all_52_4 = e1)
% 151.85/21.82  | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | REDUCE: (354), (2533) imply:
% 151.85/21.82  | | | | | | | | |   (2536)   ~ (all_52_6 = e1)
% 151.85/21.82  | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | REDUCE: (360), (2533) imply:
% 151.85/21.82  | | | | | | | | |   (2537)   ~ (all_52_13 = e1)
% 151.85/21.82  | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | REDUCE: (373), (2533) imply:
% 151.85/21.82  | | | | | | | | |   (2538)   ~ (e3 = e1)
% 151.85/21.82  | | | | | | | | | 
% 151.85/21.82  | | | | | | | | | REDUCE: (36), (2533) imply:
% 151.85/21.83  | | | | | | | | |   (2539)  op(e2, e2) = e1
% 151.85/21.83  | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | BETA: splitting (97) gives:
% 151.85/21.83  | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | |   (2540)   ~ (all_44_2 = e1)
% 151.85/21.83  | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | REDUCE: (2534), (2540) imply:
% 151.85/21.83  | | | | | | | | | |   (2541)  $false
% 151.85/21.83  | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | CLOSE: (2541) is inconsistent.
% 151.85/21.83  | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | |   (2542)  ( ~ (all_44_0 = e0) & op(e1, e2) = all_44_0 &
% 151.85/21.83  | | | | | | | | | |             $i(all_44_0)) | ( ~ (all_44_1 = e3) & op(e1, e1)
% 151.85/21.83  | | | | | | | | | |             = all_44_1 & $i(all_44_1))
% 151.85/21.83  | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | BETA: splitting (2542) gives:
% 151.85/21.83  | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | |   (2543)   ~ (all_44_0 = e0) & op(e1, e2) = all_44_0 &
% 151.85/21.83  | | | | | | | | | | |           $i(all_44_0)
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | ALPHA: (2543) implies:
% 151.85/21.83  | | | | | | | | | | |   (2544)   ~ (all_44_0 = e0)
% 151.85/21.83  | | | | | | | | | | |   (2545)  op(e1, e2) = all_44_0
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 151.85/21.83  | | | | | | | | | | |              all_44_0, e2, e1, simplifying with (162), (2545)
% 151.85/21.83  | | | | | | | | | | |              gives:
% 151.85/21.83  | | | | | | | | | | |   (2546)  all_52_6 = all_44_0
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | COMBINE_EQS: (258), (2546) imply:
% 151.85/21.83  | | | | | | | | | | |   (2547)  all_54_9 = all_44_0
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | REDUCE: (136), (2546) imply:
% 151.85/21.83  | | | | | | | | | | |   (2548)   ~ (all_52_4 = all_44_0)
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | REDUCE: (126), (2546) imply:
% 151.85/21.83  | | | | | | | | | | |   (2549)   ~ (all_52_14 = all_44_0)
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | SIMP: (2549) implies:
% 151.85/21.83  | | | | | | | | | | |   (2550)   ~ (all_52_14 = all_44_0)
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | REDUCE: (2284), (2546) imply:
% 151.85/21.83  | | | | | | | | | | |   (2551)   ~ (all_44_0 = e3)
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | REDUCE: (2536), (2546) imply:
% 151.85/21.83  | | | | | | | | | | |   (2552)   ~ (all_44_0 = e1)
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | BETA: splitting (195) gives:
% 151.85/21.83  | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | |   (2553)  all_54_9 = e3
% 151.85/21.83  | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | COMBINE_EQS: (2547), (2553) imply:
% 151.85/21.83  | | | | | | | | | | | |   (2554)  all_44_0 = e3
% 151.85/21.83  | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | REDUCE: (2551), (2554) imply:
% 151.85/21.83  | | | | | | | | | | | |   (2555)  $false
% 151.85/21.83  | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | CLOSE: (2555) is inconsistent.
% 151.85/21.83  | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | |   (2556)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 151.85/21.83  | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | BETA: splitting (2556) gives:
% 151.85/21.83  | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | |   (2557)  all_54_9 = e2
% 151.85/21.83  | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | COMBINE_EQS: (2547), (2557) imply:
% 151.85/21.83  | | | | | | | | | | | | |   (2558)  all_44_0 = e2
% 151.85/21.83  | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | REDUCE: (2548), (2558) imply:
% 151.85/21.83  | | | | | | | | | | | | |   (2559)   ~ (all_52_4 = e2)
% 151.85/21.83  | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | REDUCE: (2550), (2558) imply:
% 151.85/21.83  | | | | | | | | | | | | |   (2560)   ~ (all_52_14 = e2)
% 151.85/21.83  | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | BETA: splitting (70) gives:
% 151.85/21.83  | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | |   (2561)   ~ (all_26_2 = e1)
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | REDUCE: (307), (2561) imply:
% 151.85/21.83  | | | | | | | | | | | | | |   (2562)   ~ (all_6_2 = e1)
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | |   (2563)  all_54_0 = e3
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | COMBINE_EQS: (279), (2563) imply:
% 151.85/21.83  | | | | | | | | | | | | | | |   (2564)  all_6_2 = e3
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | REDUCE: (342), (2564) imply:
% 151.85/21.83  | | | | | | | | | | | | | | |   (2565)   ~ (all_52_3 = e3)
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | REDUCE: (344), (2564) imply:
% 151.85/21.83  | | | | | | | | | | | | | | |   (2566)   ~ (all_52_4 = e3)
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | REDUCE: (39), (2564) imply:
% 151.85/21.83  | | | | | | | | | | | | | | |   (2567)  op(e3, e3) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | |   (2568)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 151.85/21.83  | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 151.85/21.83  | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | BETA: splitting (2568) gives:
% 151.85/21.83  | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | |   (2569)  all_56_12 = e3 & op(e0, e3) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | ALPHA: (2569) implies:
% 151.85/21.83  | | | | | | | | | | | | | | | | |   (2570)  all_56_12 = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 151.85/21.83  | | | | | | | | | | | | | | | | |            (2567), (2570), (function-axioms) are inconsistent
% 151.85/21.83  | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | |   (2571)  all_56_13 = e3 & op(e0, e2) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | ALPHA: (2571) implies:
% 151.85/21.83  | | | | | | | | | | | | | | | | |   (2572)  all_56_13 = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | |   (2573)  op(e0, e2) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | |   (2574)  all_54_1 = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (2574) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | |   (2575)  all_52_4 = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | REDUCE: (2566), (2575) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | |   (2576)  $false
% 151.85/21.83  | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | CLOSE: (2576) is inconsistent.
% 151.85/21.83  | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | |   (2577)   ~ (all_54_1 = e3)
% 151.85/21.83  | | | | | | | | | | | | | | | | | |   (2578)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 151.85/21.83  | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | BETA: splitting (2578) gives:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | |   (2579)  all_54_1 = e2
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (2579) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | |   (2580)  all_52_4 = e2
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | REDUCE: (2559), (2580) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | |   (2581)  $false
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | CLOSE: (2581) is inconsistent.
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | |   (2582)   ~ (all_54_1 = e2)
% 151.85/21.83  | | | | | | | | | | | | | | | | | | |   (2583)  all_54_1 = e1 | all_54_1 = e0
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | BETA: splitting (2583) gives:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | |   (2584)  all_54_1 = e1
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (2584) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | |   (2585)  all_52_4 = e1
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | REDUCE: (2535), (2585) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | |   (2586)  $false
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | CLOSE: (2586) is inconsistent.
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | |   (2587)  all_54_1 = e0
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (2587) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | |   (2588)  all_52_4 = e0
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (2588) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | |   (2589)   ~ (all_52_8 = e0)
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | SIMP: (2589) implies:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | |   (2590)   ~ (all_52_8 = e0)
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | REDUCE: (2566), (2588) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | |   (2591)   ~ (e3 = e0)
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | REDUCE: (2559), (2588) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | |   (2592)   ~ (e2 = e0)
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | REDUCE: (2535), (2588) imply:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | |   (2593)   ~ (e1 = e0)
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | |   (2594)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2594) gives:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |   (2595)  all_56_9 = e3 & op(e3, e0) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2595) implies:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |   (2596)  all_56_9 = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (2567), (2596), (function-axioms) are inconsistent
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #632.
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |   (2597)  all_56_10 = e3 & op(e2, e0) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2597) implies:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |   (2598)  all_56_10 = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |   (2599)  op(e2, e0) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (51), (79), (106),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (110), (112), (113), (117), (118), (120), (121),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (123), (139), (145), (146), (148), (149), (157),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (163), (164), (165), (167), (168),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (189), (190), (192), (193), (198),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (199), (200), (201), (202), (206), (207), (210),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (213), (214), (215), (217), (218),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (238),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (239), (246), (247), (249), (250), (261), (268),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (271), (297), (314), (349), (351),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (358), (360), (369), (370), (371), (372), (373),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (378), (2285), (2287), (2289), (2537), (2539),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (2560), (2565), (2566), (2567), (2572), (2573),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (2590), (2598), (2599), (function-axioms) are
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #506.
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | |   (2600)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2600) gives:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |   (2601)  all_56_11 = e3 & op(e1, e0) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2601) implies:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |   (2602)  op(e1, e0) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2288), (2602), (function-axioms) are
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #677.
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |   (2603)  all_56_15 = e3 & op(e0, e0) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2603) implies:
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |   (2604)  op(e0, e0) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (206), (210),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (211), (224), (229), (231), (233), (2286), (2539),
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            (2567), (2604), (function-axioms) are inconsistent
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #460.
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.83  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.83  | | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | End of split
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | End of split
% 151.85/21.83  | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | |   (2605)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 151.85/21.83  | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 151.85/21.83  | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | BETA: splitting (2605) gives:
% 151.85/21.83  | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | |   (2606)  all_56_14 = e3 & op(e0, e1) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | ALPHA: (2606) implies:
% 151.85/21.83  | | | | | | | | | | | | | | | | |   (2607)  op(e0, e1) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2287), (2607), (function-axioms) are
% 151.85/21.83  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #720.
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | |   (2608)  all_56_15 = e3 & op(e0, e0) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | ALPHA: (2608) implies:
% 151.85/21.83  | | | | | | | | | | | | | | | | |   (2609)  op(e0, e0) = e3
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (206), (210),
% 151.85/21.83  | | | | | | | | | | | | | | | | |            (211), (224), (229), (231), (233), (2286), (2539),
% 151.85/21.83  | | | | | | | | | | | | | | | | |            (2567), (2609), (function-axioms) are inconsistent
% 151.85/21.83  | | | | | | | | | | | | | | | | |            by sub-proof #460.
% 151.85/21.83  | | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | | End of split
% 151.85/21.83  | | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | End of split
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | |   (2610)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (2562), (2610) are
% 151.85/21.83  | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 151.85/21.83  | | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | End of split
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | Case 2:
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | |   (2611)  all_26_2 = e1
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | COMBINE_EQS: (307), (2611) imply:
% 151.85/21.83  | | | | | | | | | | | | | |   (2612)  all_6_2 = e1
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | SIMP: (2612) implies:
% 151.85/21.83  | | | | | | | | | | | | | |   (2613)  all_6_2 = e1
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | REDUCE: (340), (2613) imply:
% 151.85/21.83  | | | | | | | | | | | | | |   (2614)   ~ (all_52_2 = e1)
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | REDUCE: (377), (2613) imply:
% 151.85/21.83  | | | | | | | | | | | | | |   (2615)   ~ (e2 = e1)
% 151.85/21.83  | | | | | | | | | | | | | | 
% 151.85/21.83  | | | | | | | | | | | | | | REDUCE: (39), (2613) imply:
% 151.85/21.83  | | | | | | | | | | | | | |   (2616)  op(e3, e3) = e1
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | |   (2617)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 151.85/21.84  | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (2536), (2614), (2617),
% 151.85/21.84  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.84  | | | | | | | | | | | | | | |            #500.
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | Case 2:
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | |   (2618)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 151.85/21.84  | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | BETA: splitting (2618) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | |   (2619)  all_56_8 = e1 & op(e1, e1) = e1
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | ALPHA: (2619) implies:
% 151.85/21.84  | | | | | | | | | | | | | | | |   (2620)  op(e1, e1) = e1
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2289), (2620), (function-axioms) are
% 151.85/21.84  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | Case 2:
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | |   (2621)  all_56_11 = e1 & op(e1, e0) = e1
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | ALPHA: (2621) implies:
% 151.85/21.84  | | | | | | | | | | | | | | | |   (2622)  op(e1, e0) = e1
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (160), (238), (2289), (2539),
% 151.85/21.84  | | | | | | | | | | | | | | | |            (2616), (2622), (function-axioms) are inconsistent
% 151.85/21.84  | | | | | | | | | | | | | | | |            by sub-proof #487.
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | End of split
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | End of split
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | End of split
% 151.85/21.84  | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | Case 2:
% 151.85/21.84  | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | |   (2623)  all_54_9 = e1 | all_54_9 = e0
% 151.85/21.84  | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | BETA: splitting (2623) gives:
% 151.85/21.84  | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | |   (2624)  all_54_9 = e1
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | COMBINE_EQS: (2547), (2624) imply:
% 151.85/21.84  | | | | | | | | | | | | | |   (2625)  all_44_0 = e1
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | REDUCE: (2552), (2625) imply:
% 151.85/21.84  | | | | | | | | | | | | | |   (2626)  $false
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | CLOSE: (2626) is inconsistent.
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | Case 2:
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | |   (2627)  all_54_9 = e0
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | COMBINE_EQS: (2547), (2627) imply:
% 151.85/21.84  | | | | | | | | | | | | | |   (2628)  all_44_0 = e0
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | REDUCE: (2544), (2628) imply:
% 151.85/21.84  | | | | | | | | | | | | | |   (2629)  $false
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | CLOSE: (2629) is inconsistent.
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | End of split
% 151.85/21.84  | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | End of split
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | End of split
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | Case 2:
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | |   (2630)   ~ (all_44_1 = e3) & op(e1, e1) = all_44_1 &
% 151.85/21.84  | | | | | | | | | | |           $i(all_44_1)
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | ALPHA: (2630) implies:
% 151.85/21.84  | | | | | | | | | | |   (2631)   ~ (all_44_1 = e3)
% 151.85/21.84  | | | | | | | | | | |   (2632)  op(e1, e1) = all_44_1
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 151.85/21.84  | | | | | | | | | | |              e1, e1, simplifying with (2289), (2632) gives:
% 151.85/21.84  | | | | | | | | | | |   (2633)  all_44_1 = e3
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | REDUCE: (2631), (2633) imply:
% 151.85/21.84  | | | | | | | | | | |   (2634)  $false
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | CLOSE: (2634) is inconsistent.
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | End of split
% 151.85/21.84  | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | End of split
% 151.85/21.84  | | | | | | | | | 
% 151.85/21.84  | | | | | | | | End of split
% 151.85/21.84  | | | | | | | | 
% 151.85/21.84  | | | | | | | End of split
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | Case 2:
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | |   (2635)  all_18_2 = e3
% 151.85/21.84  | | | | | | |   (2636)  ( ~ (all_18_0 = e1) & op(e3, e0) = all_18_0 &
% 151.85/21.84  | | | | | | |             $i(all_18_0)) | ( ~ (all_18_1 = e2) & op(e3, e3) =
% 151.85/21.84  | | | | | | |             all_18_1 & $i(all_18_1))
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | COMBINE_EQS: (301), (2635) imply:
% 151.85/21.84  | | | | | | |   (2637)  all_14_2 = e3
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | COMBINE_EQS: (299), (2637) imply:
% 151.85/21.84  | | | | | | |   (2638)  all_48_2 = e3
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | REDUCE: (351), (2637) imply:
% 151.85/21.84  | | | | | | |   (2639)   ~ (all_52_3 = e3)
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | REDUCE: (362), (2637) imply:
% 151.85/21.84  | | | | | | |   (2640)   ~ (all_52_7 = e3)
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | REDUCE: (369), (2637) imply:
% 151.85/21.84  | | | | | | |   (2641)   ~ (all_52_11 = e3)
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | REDUCE: (370), (2637) imply:
% 151.85/21.84  | | | | | | |   (2642)   ~ (all_52_12 = e3)
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | REDUCE: (371), (2637) imply:
% 151.85/21.84  | | | | | | |   (2643)   ~ (all_52_13 = e3)
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | REDUCE: (372), (2637) imply:
% 151.85/21.84  | | | | | | |   (2644)   ~ (all_52_14 = e3)
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | REDUCE: (51), (2637) imply:
% 151.85/21.84  | | | | | | |   (2645)  op(e0, e0) = e3
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | BETA: splitting (64) gives:
% 151.85/21.84  | | | | | | | 
% 151.85/21.84  | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | 
% 151.85/21.84  | | | | | | | |   (2646)   ~ (all_22_2 = e0)
% 151.85/21.84  | | | | | | | | 
% 151.85/21.84  | | | | | | | | REDUCE: (251), (2646) imply:
% 151.85/21.84  | | | | | | | |   (2647)   ~ (all_10_2 = e0)
% 151.85/21.84  | | | | | | | | 
% 151.85/21.84  | | | | | | | | BETA: splitting (61) gives:
% 151.85/21.84  | | | | | | | | 
% 151.85/21.84  | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | 
% 151.85/21.84  | | | | | | | | |   (2648)   ~ (all_20_2 = e3)
% 151.85/21.84  | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | REDUCE: (325), (2648) imply:
% 151.85/21.84  | | | | | | | | |   (2649)   ~ (all_10_2 = e3)
% 151.85/21.84  | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | BETA: splitting (194) gives:
% 151.85/21.84  | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | |   (2650)  all_54_10 = e3
% 151.85/21.84  | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | COMBINE_EQS: (336), (2650) imply:
% 151.85/21.84  | | | | | | | | | |   (2651)  all_10_2 = e3
% 151.85/21.84  | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | REDUCE: (2649), (2651) imply:
% 151.85/21.84  | | | | | | | | | |   (2652)  $false
% 151.85/21.84  | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | CLOSE: (2652) is inconsistent.
% 151.85/21.84  | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | Case 2:
% 151.85/21.84  | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | |   (2653)   ~ (all_54_10 = e3)
% 151.85/21.84  | | | | | | | | | |   (2654)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 151.85/21.84  | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | BETA: splitting (2654) gives:
% 151.85/21.84  | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | |   (2655)  all_54_10 = e2
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | COMBINE_EQS: (336), (2655) imply:
% 151.85/21.84  | | | | | | | | | | |   (2656)  all_10_2 = e2
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | REDUCE: (375), (2656) imply:
% 151.85/21.84  | | | | | | | | | | |   (2657)  $false
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | CLOSE: (2657) is inconsistent.
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | Case 2:
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | |   (2658)   ~ (all_54_10 = e2)
% 151.85/21.84  | | | | | | | | | | |   (2659)  all_54_10 = e1 | all_54_10 = e0
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | BETA: splitting (2659) gives:
% 151.85/21.84  | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | |   (2660)  all_54_10 = e1
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | COMBINE_EQS: (336), (2660) imply:
% 151.85/21.84  | | | | | | | | | | | |   (2661)  all_10_2 = e1
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | REDUCE: (350), (2661) imply:
% 151.85/21.84  | | | | | | | | | | | |   (2662)   ~ (all_52_2 = e1)
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | REDUCE: (361), (2661) imply:
% 151.85/21.84  | | | | | | | | | | | |   (2663)   ~ (all_52_6 = e1)
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | REDUCE: (364), (2661) imply:
% 151.85/21.84  | | | | | | | | | | | |   (2664)   ~ (all_52_9 = e1)
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | REDUCE: (366), (2661) imply:
% 151.85/21.84  | | | | | | | | | | | |   (2665)   ~ (all_52_11 = e1)
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | REDUCE: (368), (2661) imply:
% 151.85/21.84  | | | | | | | | | | | |   (2666)   ~ (all_52_14 = e1)
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | REDUCE: (2649), (2661) imply:
% 151.85/21.84  | | | | | | | | | | | |   (2667)   ~ (e3 = e1)
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | REDUCE: (375), (2661) imply:
% 151.85/21.84  | | | | | | | | | | | |   (2668)   ~ (e2 = e1)
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | REDUCE: (45), (2661) imply:
% 151.85/21.84  | | | | | | | | | | | |   (2669)  op(e1, e1) = e1
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | BETA: splitting (67) gives:
% 151.85/21.84  | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | |   (2670)   ~ (all_24_2 = e1)
% 151.85/21.84  | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | REDUCE: (318), (2670) imply:
% 151.85/21.84  | | | | | | | | | | | | |   (2671)   ~ (all_4_2 = e1)
% 151.85/21.84  | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | BETA: splitting (70) gives:
% 151.85/21.84  | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | |   (2672)   ~ (all_26_2 = e1)
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | REDUCE: (307), (2672) imply:
% 151.85/21.84  | | | | | | | | | | | | | |   (2673)   ~ (all_6_2 = e1)
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 151.85/21.84  | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | |   (2674)  all_54_0 = e3
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | COMBINE_EQS: (279), (2674) imply:
% 151.85/21.84  | | | | | | | | | | | | | | |   (2675)  all_6_2 = e3
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | SIMP: (2675) implies:
% 151.85/21.84  | | | | | | | | | | | | | | |   (2676)  all_6_2 = e3
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | REDUCE: (39), (2676) imply:
% 151.85/21.84  | | | | | | | | | | | | | | |   (2677)  op(e3, e3) = e3
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | |   (2678)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 151.85/21.84  | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (229), (231),
% 151.85/21.84  | | | | | | | | | | | | | | | |            (233), (373), (2677), (2678), (function-axioms)
% 151.85/21.84  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #475.
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | Case 2:
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | |   (2679)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 151.85/21.84  | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | BETA: splitting (2679) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | |   (2680)  all_56_5 = e3 & op(e2, e1) = e3
% 151.85/21.84  | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | ALPHA: (2680) implies:
% 151.85/21.84  | | | | | | | | | | | | | | | | |   (2681)  all_56_5 = e3
% 151.85/21.84  | | | | | | | | | | | | | | | | |   (2682)  op(e2, e1) = e3
% 151.85/21.84  | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | |   (2683)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 151.85/21.84  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (230), (232),
% 151.85/21.84  | | | | | | | | | | | | | | | | | |            (234), (373), (2677), (2683), (function-axioms)
% 151.85/21.84  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #476.
% 151.85/21.84  | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | |   (2684)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 151.85/21.84  | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | BETA: splitting (2684) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2685)  all_56_7 = e3 & op(e1, e2) = e3
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | ALPHA: (2685) implies:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2686)  all_56_7 = e3
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2687)  op(e1, e2) = e3
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (2687) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2688)  all_52_6 = e3
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (2682) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2689)  all_52_9 = e3
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2689) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2690)   ~ (all_52_1 = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | REDUCE: (136), (2688) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2691)   ~ (all_52_4 = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | REDUCE: (123), (2689) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2692)   ~ (all_52_8 = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2689) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2693)   ~ (all_52_11 = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | REDUCE: (117), (2689) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2694)   ~ (all_52_13 = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | REDUCE: (358), (2689) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | |   (2695)   ~ (all_4_2 = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | |   (2696)   ~ (all_32_2 = e0)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (2696) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | |   (2697)   ~ (all_4_2 = e0)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | |   (2698)  all_54_5 = e3
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (373), (2698) are inconsistent by sub-proof
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | |            #930.
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | |   (2699)   ~ (all_54_5 = e3)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | |   (2700)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2700) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | |   (2701)  all_54_5 = e2
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2701) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | |   (2702)  all_4_2 = e2
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | SIMP: (2702) implies:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | |   (2703)  all_4_2 = e2
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (2703) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | |   (2704)   ~ (all_52_13 = e2)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (2703) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | |   (2705)   ~ (e3 = e2)
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2703) imply:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | |   (2706)  op(e2, e2) = e2
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |   (2707)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2707) gives:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |   (2708)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2708) gives:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (2709)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (200), (268), (269), (349),
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (2671), (2690), (2706), (2709),
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |            #654.
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (2710)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2710) gives:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2711)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (200), (268), (269), (349),
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (2671), (2690), (2706), (2711),
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            #653.
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2712)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2712) gives:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2713)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2713) implies:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2714)  op(e2, e3) = e2
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (200), (268), (269), (349),
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (2671), (2690), (2706), (2714),
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #925.
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2715)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2715) gives:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2716)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2716) implies:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2717)  op(e1, e1) = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (2666), (2686), (2687), (2717),
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #457.
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2718)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2718) implies:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2719)  op(e2, e1) = e2
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2682), (2719), (function-axioms) are
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #456.
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |   (2720)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2720) gives:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (2721)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2721) gives:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2722)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (2691), (2722), (function-axioms) are
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #792.
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2723)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 151.85/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (2677), (2704), (2723),
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            #994.
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (2724)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2724) gives:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2725)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2725) gives:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2726)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2726) implies:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2727)  op(e1, e1) = e3
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (2666), (2686), (2687), (2727),
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #457.
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2728)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2728) implies:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2729)  op(e2, e2) = e1
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2706), (2729), (function-axioms) are
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2730)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (163), (213),
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (2645), (2662), (2666), (2686),
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2687), (2730), (function-axioms) are inconsistent
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #454.
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |   (2731)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2731) gives:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |   (2732)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2732) gives:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (2733)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2733) gives:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2734)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2677), (2706), (2734),
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            #987.
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2735)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2645), (2669), (2735),
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            #453.
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (2736)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2736) gives:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.85/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2737)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (2663), (2669), (2737),
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2738)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (2677), (2692), (2738),
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            #787.
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.85/21.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |   (2739)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2739) gives:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (2740)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2740) gives:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2741)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2741) gives:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2742)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2742) implies:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2743)  op(e0, e0) = e2
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2645), (2743), (function-axioms) are
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2744)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2744) implies:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2745)  op(e2, e1) = e2
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e2, e1,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (2682), (2745) gives:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2746)  e3 = e2
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2746) imply:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2747)  $false
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2747) is inconsistent.
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2748)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (2642), (2706), (2748),
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            #452.
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (2749)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2749) gives:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2750)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2642), (2645), (2750),
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            #451.
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2751)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2751) gives:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2752)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2752) implies:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2753)  op(e2, e0) = e2
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2704), (2753), (function-axioms) are
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2754)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2754) gives:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2755)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2755) implies:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2756)  op(e1, e0) = e1
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2666), (2756), (function-axioms) are
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2757)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2757) implies:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2758)  op(e0, e0) = all_57_15
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2759)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (2645), (2758)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2760)  all_57_15 = e3
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2759) gives:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2761)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2761) gives:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2762)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (164), (2669), (2677), (2704), (2762),
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #866.
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2763)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2763) gives:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2764)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2760), (2764) are inconsistent by sub-proof #450.
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2765)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (164), (2677), (2704), (2765),
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #864.
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2766)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2766) gives:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2767)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2767) gives:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2768)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2768) implies:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2769)  op(e1, e1) = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2669), (2769), (function-axioms) are
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2770)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2677), (2760), (2770), (function-axioms) are
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #448.
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2771)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2771) gives:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2772)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (2669), (2704), (2772),
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #862.
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2773)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (2666), (2760), (2773),
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #446.
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | |   (2774)  all_54_5 = e1 | all_54_5 = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (2671), (2697), (2774) are inconsistent by
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | |   (2775)  all_32_2 = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (2775) imply:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | |   (2776)  all_4_2 = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (2776) imply:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | |   (2777)   ~ (all_52_7 = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (2776) imply:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | |   (2778)   ~ (all_52_13 = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (2776) imply:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | |   (2779)   ~ (e3 = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | REDUCE: (2671), (2776) imply:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | |   (2780)   ~ (e1 = e0)
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2776) imply:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | |   (2781)  op(e2, e2) = e0
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.88  | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |   (2782)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2782) gives:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |   (2783)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2783) gives:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |   (2784)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2784) gives:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |   (2785)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (2677), (2781), (2785),
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |            #934.
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |   (2786)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (2669), (2781), (2786),
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |            #933.
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |   (2787)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2787) gives:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |   (2788)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2642), (2645), (2788),
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |            #445.
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |   (2789)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2789) gives:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (2790)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2790) implies:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (2791)  op(e2, e2) = e2
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2781), (2791), (function-axioms) are
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (2792)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2792) gives:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2793)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2793) implies:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2794)  op(e1, e1) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (2666), (2686), (2687), (2794),
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            #457.
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2795)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2795) implies:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2796)  op(e3, e3) = e2
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2677), (2796), (function-axioms) are
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |   (2797)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2797) gives:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |   (2798)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2798) gives:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |   (2799)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (2691), (2799), (function-axioms) are
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #792.
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |   (2800)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 152.03/21.89  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (2677), (2800), (function-axioms) are
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |   (2801)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2801) gives:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |   (2802)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            (215), (2666), (2686), (2687), (2781), (2802),
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            #444.
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |   (2803)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (163), (213),
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (2645), (2662), (2666), (2686),
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            (2687), (2803), (function-axioms) are inconsistent
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #454.
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |   (2804)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2804) gives:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |   (2805)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2805) gives:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |   (2806)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2806) gives:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |   (2807)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (2677), (2781), (2807),
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            #920.
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |   (2808)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2645), (2669), (2808),
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            #453.
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |   (2809)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2809) gives:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |   (2810)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (2663), (2669), (2810),
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |   (2811)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (2677), (2692), (2811),
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            #787.
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |   (2812)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2812) gives:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |   (2813)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (168), (2642), (2645), (2781),
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |            (2813), (function-axioms) are inconsistent by
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #442.
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |   (2814)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2814) gives:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |   (2815)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2642), (2645), (2815),
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |            #451.
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |   (2816)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2816) gives:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (2817)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2817) implies:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (2818)  op(e2, e2) = e2
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2781), (2818), (function-axioms) are
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (2819)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2819) gives:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2820)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2820) implies:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2821)  op(e1, e0) = e1
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2666), (2821), (function-axioms) are
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2822)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2822) implies:
% 152.03/21.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2823)  op(e0, e0) = all_57_15
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2824)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (2645), (2823)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2825)  all_57_15 = e3
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2824) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2826)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2826) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2827)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2827) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2828)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2828) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2829)  op(e3, e3) = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2677), (2829), (function-axioms) are
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2830)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2830) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2831)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e3) = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2831) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2832)   ~ (all_57_15 = e3)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2825), (2832) imply:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2833)  $false
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2833) is inconsistent.
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2834)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e3) = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2834) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2835)  op(e1, e1) = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2669), (2835), (function-axioms) are
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2836)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (222), (223),
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (229), (231), (233), (2677), (2681),
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2777), (2781), (2825), (2836), (function-axioms)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #438.
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2837)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2837) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2838)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (158), (2669), (2677), (2777), (2838),
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #784.
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2839)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2839) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2840)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2840) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2841)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e1) = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2841) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2842)  all_57_8 = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2843)   ~ (all_57_15 = e1)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2844)  op(e0, e1) = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2845)  op(e2, e0) = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2846)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2846) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2847)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2847) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2848)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2848) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2849)  all_57_12 = e3 & op(e2, e2) = e3
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2849) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2850)  op(e2, e2) = e3
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2781), (2850), (function-axioms) are
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2851)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2851) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2852)  op(e2, e3) = all_57_0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (2844) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2853)  all_52_11 = e0
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (2845) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2854)  all_52_13 = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0, e3, e2, simplifying with (167), (2852)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2855)  all_57_0 = all_52_1
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (2854) imply:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2856)   ~ (all_52_1 = e2)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2853) imply:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2857)   ~ (all_52_3 = e0)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (2854) imply:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2858)   ~ (all_52_12 = e2)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (2854) imply:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2859)   ~ (all_52_14 = e2)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2859) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2860)   ~ (all_52_14 = e2)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2643), (2854) imply:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2861)   ~ (e3 = e2)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2862)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2862) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2863)  all_56_12 = e1 & op(e0, e3) = e1
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2863) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2864)  op(e0, e3) = e1
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2865)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2865) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2866)  all_56_6 = e2 & op(e1, e3) = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2866) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2867)  all_56_6 = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2868)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2868) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2869)  all_56_2 = e2 & op(e2, e3) = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2869) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2870)  op(e2, e3) = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2856), (2870), (function-axioms) are
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2871)  all_56_3 = e2 & op(e2, e2) = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2871) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2872)  op(e2, e2) = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (160), (164), (168), (211), (360),
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2645), (2858), (2860), (2872), (function-axioms)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #877.
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2873)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2873) gives:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2874)  all_56_5 = e2 & op(e2, e1) = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2874) implies:
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2875)  all_56_5 = e2
% 152.03/21.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2681), (2875) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #593.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2876)  all_56_10 = e2 & op(e2, e0) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2876) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2877)  all_56_10 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2878)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (222), (2677), (2681), (2781),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2877), (2878), (function-axioms) are inconsistent
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #435.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2879)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2879) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2880)  all_56_6 = e0 & op(e1, e3) = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2880) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2881)  all_56_6 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2867), (2881) imply:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2882)  e2 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2882) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2883)  e2 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2877), (2883) imply:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2884)  all_56_10 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2885)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2885) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2886)  all_56_2 = e2 & op(e2, e3) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2886) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2887)  all_56_2 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2888)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (2781), (2887), (2888),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #557.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2889)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2889) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2890)  all_56_5 = e1 & op(e2, e1) = e1
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2681), (2890) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #437.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2891)  all_56_10 = e1 & op(e2, e0) = e1
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2884), (2891) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #434.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2892)  all_56_3 = e2 & op(e2, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2892) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2893)  op(e2, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2781), (2893), (function-axioms) are
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2873) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2894)  all_56_5 = e2 & op(e2, e1) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2894) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2895)  all_56_5 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2681), (2895) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #593.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2883) imply:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2896)  $false
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2896) is inconsistent.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2897)  all_56_12 = e0 & op(e0, e3) = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2897) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2898)  op(e0, e3) = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2864), (2898), (function-axioms) are
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2899)  all_56_7 = e2 & op(e1, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2899) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2900)  all_56_7 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2686), (2900) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #661.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2901)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (2669), (2860), (2901),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #815.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2902)  all_56_13 = e1 & op(e0, e2) = e1
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2902) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2903)  all_56_13 = e1
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2904)  op(e0, e2) = e1
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2905)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2905) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2906)  all_56_6 = e2 & op(e1, e3) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2906) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2907)  all_56_6 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2908)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2908) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2909)  all_56_1 = e2 & op(e3, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2909) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2910)  all_56_1 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2911)  op(e3, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2912)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2912) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2913)  all_56_2 = e2 & op(e2, e3) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2913) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2914)  op(e2, e3) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2856), (2914), (function-axioms) are
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2915)  all_56_3 = e2 & op(e2, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2915) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2916)  op(e2, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2917)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2910), (2916), (2917), (function-axioms) are
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #568.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2918)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2918) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2919)  all_56_7 = e0 & op(e1, e2) = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2919) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2920)  all_56_7 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2921)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (373), (2911), (2921),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #432.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2684) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2685), (2920) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #522.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2922)  all_56_13 = e3 & op(e0, e2) = e3
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2922) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2923)  all_56_13 = e3
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (225), (226), (2910),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2916), (2923), (function-axioms) are inconsistent
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #567.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2924)  all_56_13 = e0 & op(e0, e2) = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2924) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2925)  op(e0, e2) = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2904), (2925), (function-axioms) are
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #832.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2926)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2926) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2927)  all_56_5 = e2 & op(e2, e1) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2927) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2928)  all_56_5 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2681), (2928) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #593.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2929)  all_56_10 = e2 & op(e2, e0) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2929) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2930)  all_56_10 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2931)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (222), (2677), (2681), (2781),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2930), (2931), (function-axioms) are inconsistent
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #435.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2932)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2932) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2933)  all_56_6 = e0 & op(e1, e3) = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2933) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2934)  all_56_6 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2907), (2934) imply:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2935)  e2 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2935) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2936)  e2 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2910), (2936) imply:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2937)  all_56_1 = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (2677), (2781), (2903),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2937), (function-axioms) are inconsistent by
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #935.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2938)  all_56_12 = e0 & op(e0, e3) = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2938) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2939)  op(e0, e3) = e0
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2857), (2939), (function-axioms) are
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2940)  all_56_3 = e2 & op(e2, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2940) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2941)  op(e2, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (160), (164), (168), (211), (360),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2645), (2858), (2860), (2941), (function-axioms)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #877.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2942)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2942) gives:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2943)  all_56_7 = e2 & op(e1, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2943) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2944)  all_56_7 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2686), (2944) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #661.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2945)  all_56_13 = e2 & op(e0, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2945) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2946)  all_56_13 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2903), (2946) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #907.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2947)  all_56_7 = e2 & op(e1, e2) = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2947) implies:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2948)  all_56_7 = e2
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2686), (2948) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #661.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2949)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (2669), (2860), (2949),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #815.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2950)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (2645), (2665), (2950),
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #431.
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2951)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2951) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2952)  op(e2, e2) = e2
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (2845), (2952),
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2953)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2953) gives:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2954)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2954) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2955)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2645), (2842), (2955), (function-axioms) are
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #430.
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2956)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2956) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2957)  op(e0, e0) = e0
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2645), (2957), (function-axioms) are
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2958)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e1) = e0
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2958) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2959)  op(e1, e1) = e0
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2669), (2959), (function-axioms) are
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2960)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2960) gives:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2961)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 & 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2961) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2962)  op(e1, e0) = e1
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2666), (2962), (function-axioms) are
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2963)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = e0
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2963) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2964)  all_57_15 = e0
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2825), (2964) imply:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2965)  e3 = e0
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2681), (2965) imply:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2966)  all_56_5 = e0
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (222), (223), (224),
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (231), (233), (2677), (2781), (2966),
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #439.
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | |   (2967)  all_56_13 = e3 & op(e0, e2) = e3
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2640), (2967), (function-axioms) are
% 152.03/21.94  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | |   (2968)  all_56_10 = e3 & op(e2, e0) = e3
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | ALPHA: (2968) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | | |   (2969)  all_56_10 = e3
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (210), (211),
% 152.03/21.94  | | | | | | | | | | | | | | | | |            (2645), (2969), (function-axioms) are inconsistent
% 152.03/21.94  | | | | | | | | | | | | | | | | |            by sub-proof #466.
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | |   (2970)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (2673), (2970) are
% 152.03/21.94  | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | |   (2971)  all_26_2 = e1
% 152.03/21.94  | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | COMBINE_EQS: (307), (2971) imply:
% 152.03/21.94  | | | | | | | | | | | | | |   (2972)  all_6_2 = e1
% 152.03/21.94  | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | SIMP: (2972) implies:
% 152.03/21.94  | | | | | | | | | | | | | |   (2973)  all_6_2 = e1
% 152.03/21.94  | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | REDUCE: (342), (2973) imply:
% 152.03/21.94  | | | | | | | | | | | | | |   (2974)   ~ (all_52_3 = e1)
% 152.03/21.94  | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | REDUCE: (348), (2973) imply:
% 152.03/21.94  | | | | | | | | | | | | | |   (2975)   ~ (all_52_12 = e1)
% 152.03/21.94  | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | REDUCE: (39), (2973) imply:
% 152.03/21.94  | | | | | | | | | | | | | |   (2976)  op(e3, e3) = e1
% 152.03/21.94  | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 152.03/21.94  | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | Case 1:
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | |   (2977)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 152.03/21.94  | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | BETA: splitting (2977) gives:
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | Case 1:
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | |   (2978)  all_56_2 = e1 & op(e2, e3) = e1
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | ALPHA: (2978) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | |   (2979)  all_56_2 = e1
% 152.03/21.94  | | | | | | | | | | | | | | | |   (2980)  op(e2, e3) = e1
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (229), (233),
% 152.03/21.94  | | | | | | | | | | | | | | | |            (235), (2976), (2979), (2980), (function-axioms)
% 152.03/21.94  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #424.
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | |   (2981)  all_56_3 = e1 & op(e2, e2) = e1
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | ALPHA: (2981) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | |   (2982)  op(e2, e2) = e1
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (2671), (2982),
% 152.03/21.94  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.03/21.94  | | | | | | | | | | | | | | | |            #690.
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | End of split
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | |   (2983)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 152.03/21.94  | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | BETA: splitting (2983) gives:
% 152.03/21.94  | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | Case 1:
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | |   (2984)  all_56_5 = e1 & op(e2, e1) = e1
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2664), (2984), (function-axioms) are
% 152.03/21.94  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | |   (2985)  all_56_10 = e1 & op(e2, e0) = e1
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | ALPHA: (2985) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | |   (2986)  all_56_10 = e1
% 152.03/21.94  | | | | | | | | | | | | | | | |   (2987)  op(e2, e0) = e1
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 152.03/21.94  | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | |   (2988)   ~ (all_48_2 = e3)
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | REDUCE: (2638), (2988) imply:
% 152.03/21.94  | | | | | | | | | | | | | | | | |   (2989)  $false
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | CLOSE: (2989) is inconsistent.
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | |   (2990)  ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 &
% 152.03/21.94  | | | | | | | | | | | | | | | | |             $i(all_48_0)) | ( ~ (all_48_1 = e1) & op(e3, e3)
% 152.03/21.94  | | | | | | | | | | | | | | | | |             = all_48_1 & $i(all_48_1))
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | BETA: splitting (2990) gives:
% 152.03/21.94  | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | |   (2991)   ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 &
% 152.03/21.94  | | | | | | | | | | | | | | | | | |           $i(all_48_0)
% 152.03/21.94  | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | ALPHA: (2991) implies:
% 152.03/21.94  | | | | | | | | | | | | | | | | | |   (2992)   ~ (all_48_0 = e2)
% 152.03/21.94  | | | | | | | | | | | | | | | | | |   (2993)  op(e3, e0) = all_48_0
% 152.03/21.94  | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | |   (2994)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 152.03/21.94  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (2994) gives:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | |   (2995)  all_56_12 = e1 & op(e0, e3) = e1
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2974), (2995), (function-axioms) are
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #852.
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.03/21.94  | | | | | | | | | | | | | | | | | | | |   (2996)  all_56_13 = e1 & op(e0, e2) = e1
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (2996) implies:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (2997)  op(e0, e2) = e1
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e1,
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (2997) gives:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (2998)  all_52_7 = e1
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (164), (2987) gives:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (2999)  all_52_13 = e1
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |              all_48_0, e0, e3, simplifying with (168), (2993)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |              gives:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (3000)  all_52_12 = all_48_0
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3000) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (3001)  all_54_3 = all_48_0
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (2998) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (3002)   ~ (all_52_4 = e1)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (3000) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (3003)   ~ (all_52_14 = all_48_0)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | SIMP: (3003) implies:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (3004)   ~ (all_52_14 = all_48_0)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (2642), (3000) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (3005)   ~ (all_48_0 = e3)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (2975), (3000) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (3006)   ~ (all_48_0 = e1)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (2999) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (3007)   ~ (all_52_14 = e1)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (2999) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | |   (3008)   ~ (all_4_2 = e1)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | |   (3009)   ~ (all_36_2 = e0)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (3009) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | |   (3010)   ~ (all_4_2 = e0)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | |   (3011)  all_54_5 = e3
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3011) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | |   (3012)  all_4_2 = e3
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3012) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | |   (3013)  $false
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3013) is inconsistent.
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | |   (3014)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | |   (3015)  all_54_3 = e3
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3001), (3015) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | |   (3016)  all_48_0 = e3
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3005), (3016) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | |   (3017)  $false
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3017) is inconsistent.
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | |   (3018)   ~ (all_54_3 = e3)
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | |   (3019)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3019) gives:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | |   (3020)  all_54_3 = e2
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3001), (3020) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | |   (3021)  all_48_0 = e2
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2992), (3021) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | |   (3022)  $false
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3022) is inconsistent.
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | |   (3023)  all_54_3 = e1 | all_54_3 = e0
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3023) gives:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (3024)  all_54_3 = e1
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3001), (3024) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (3025)  all_48_0 = e1
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3006), (3025) imply:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (3026)  $false
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3026) is inconsistent.
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (3027)  all_54_3 = e0
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3001), (3027) imply:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (3028)  all_48_0 = e0
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3004), (3028) imply:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (3029)   ~ (all_52_14 = e0)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3005), (3028) imply:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (3030)   ~ (e3 = e0)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3006), (3028) imply:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (3031)   ~ (e1 = e0)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3014) gives:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3032)  all_54_5 = e2
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3032) imply:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3033)  all_4_2 = e2
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3033) implies:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3034)  all_4_2 = e2
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (3034) imply:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3035)   ~ (all_52_1 = e2)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (3034) imply:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3036)   ~ (all_52_9 = e2)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3037)  all_54_11 = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (2644), (3037) are inconsistent by
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #655.
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3038)   ~ (all_54_11 = e3)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3039)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3039) gives:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3040)  all_54_11 = e2
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (3040) imply:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3041)  all_52_14 = e2
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3041) implies:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3042)  all_52_14 = e2
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (3042) imply:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3043)   ~ (all_52_2 = e2)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2644), (3042) imply:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3044)   ~ (e3 = e2)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3045)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3045) gives:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3046)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (167), (2669), (3035), (3036), (3046),
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1000.
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3047)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3047) gives:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3048)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3048) gives:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3049)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3049) gives:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3050)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3050) implies:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3051)  op(e0, e3) = e0
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (159), (163), (167), (233), (2976),
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3035), (3043), (3051), (function-axioms) are
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #421.
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3052)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3052) implies:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3053)  op(e3, e3) = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2976), (3053), (function-axioms) are
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3054)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (2662), (2987), (3054),
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #812.
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3055)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3055) gives:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3056)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (2669), (2986), (3036), (3056),
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #841.
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3057)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (2645), (2662), (2669), (3057),
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #420.
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3058)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3058) gives:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3059)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3059) gives:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3060)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3060) gives:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3061)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (165), (221),
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (2663), (2986), (3036), (3061),
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #840.
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3062)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (133), (168), (170), (201),
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (238), (270), (272), (352), (2642), (2645),
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2975), (2976), (2990), (3002), (3062),
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #414.
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3063)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3063) gives:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3064)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (133), (162), (168), (170),
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (201), (203), (238), (270), (272), (352), (2642),
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2645), (2663), (2975), (2976), (2990), (3002),
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3064), (function-axioms) are inconsistent by
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #413.
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3065)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3065) gives:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3066)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3066) implies:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3067)  op(e0, e3) = e0
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (159), (163), (167), (233), (2976),
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3035), (3043), (3067), (function-axioms) are
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #421.
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3068)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2666), (2976), (3068), (function-axioms)
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #839.
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3069)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3069) gives:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3070)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3070) gives:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3071)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (2645), (3036), (3071),
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #412.
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3072)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3072) gives:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3073)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3073) implies:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3074)  op(e2, e2) = e1
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (2986), (3036), (3074), (function-axioms)
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #842.
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3075)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3075) implies:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3076)  op(e3, e0) = e3
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2642), (3076), (function-axioms) are
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3077)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3077) gives:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3078)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3078) gives:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3079)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3079) implies:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3080)  op(e0, e0) = e2
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2645), (3080), (function-axioms) are
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3081)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3081) implies:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3082)  op(e3, e3) = e3
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2976), (3082), (function-axioms) are
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3083)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3083) gives:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3084)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3084) implies:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3085)  op(e2, e0) = e2
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2987), (3085), (function-axioms) are
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3086)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3086) gives:
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3087)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3087) implies:
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3088)  op(e1, e0) = e1
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2666), (3088), (function-axioms) are
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3089)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3089) implies:
% 152.42/21.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3090)  op(e0, e0) = all_57_15
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3091)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3092)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (2976), (3035), (3092),
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #422.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3093)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3093) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3094)  all_56_6 = e2 & op(e1, e3) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3043), (3094), (function-axioms) are
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3095)  all_56_12 = e2 & op(e0, e3) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (103), (133),
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (168), (170), (201), (203), (238),
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (272), (352), (2638), (2642), (2645),
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2666), (2975), (2976), (2987), (2997), (3002),
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3090), (3091), (3095), (function-axioms) are
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #407.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3096)  all_54_11 = e1 | all_54_11 = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (2666), (3029), (3096) are inconsistent by
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #623.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3097)  all_54_5 = e1 | all_54_5 = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (2671), (3010), (3097) are inconsistent by
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | |   (3098)  all_36_2 = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (3098) imply:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | |   (3099)  all_4_2 = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | SIMP: (3099) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | |   (3100)  all_4_2 = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (3100) imply:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | |   (3101)   ~ (all_52_6 = e0)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3100) imply:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | |   (3102)   ~ (e3 = e0)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | REDUCE: (2671), (3100) imply:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | |   (3103)   ~ (e1 = e0)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3100) imply:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | |   (3104)  op(e2, e2) = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | |   (3105)  all_54_3 = e3
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3001), (3105) imply:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | |   (3106)  all_48_0 = e3
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3005), (3106) imply:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | |   (3107)  $false
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3107) is inconsistent.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | |   (3108)   ~ (all_54_3 = e3)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | |   (3109)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |   (3110)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (2976), (3104), (3110),
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |            #814.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |   (3111)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3111) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | |   (3112)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3112) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | |   (3113)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (3114)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3114) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3115)  all_56_9 = e2 & op(e3, e0) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3115) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3116)  all_56_9 = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (206), (2645), (2986), (2992), (3001),
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3004), (3005), (3006), (3109), (3116),
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            #404.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3117)  all_56_10 = e2 & op(e2, e0) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3117) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3118)  op(e2, e0) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2987), (3118), (function-axioms) are
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (3119)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3119) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3120)  all_56_11 = e2 & op(e1, e0) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3120) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3121)  op(e1, e0) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3122)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3122) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3123)  all_56_6 = e0 & op(e1, e3) = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3123) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3124)  all_56_6 = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3125)  op(e1, e3) = e0
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3126)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3126) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3127)  all_56_0 = e3 & op(e3, e3) = e3
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3127) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3128)  op(e3, e3) = e3
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2976), (3128), (function-axioms) are
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3129)  all_56_2 = e3 & op(e2, e3) = e3
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3129) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3130)  all_56_2 = e3
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3131)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3131) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3132)  all_56_2 = e2 & op(e2, e3) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3132) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3133)  all_56_2 = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3130), (3133) are inconsistent by sub-proof
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #848.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3134)  all_56_3 = e2 & op(e2, e2) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3134) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3135)  op(e2, e2) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3104), (3135), (function-axioms) are
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3136)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3136) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3137)  all_56_5 = e2 & op(e2, e1) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3137) implies:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3138)  all_56_5 = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3139)  op(e2, e1) = e2
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3140)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3140) gives:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3141)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3141) gives:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3142)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3142) gives:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3143)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (2976), (3104), (3143),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #827.
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3144)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3144) gives:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3145)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3145) implies:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3146)  op(e1, e1) = e2
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (133), (168), (170), (201),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (238), (270), (272), (352), (2642), (2645),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2975), (2976), (2990), (3002), (3146),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #415.
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3147)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3147) implies:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3148)  op(e2, e2) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3104), (3148), (function-axioms) are
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3149)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3149) gives:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3150)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3150) gives:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3151)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3151) implies:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3152)  op(e0, e0) = e2
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (163),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (2662), (2663), (2666), (2669), (2976),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2987), (2997), (3104), (3113), (3152),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #806.
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3153)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3153) implies:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3154)  op(e3, e0) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2642), (3154), (function-axioms) are
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3155)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (2669), (2976), (3104), (3155),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #824.
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3156)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3156) gives:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3157)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3157) gives:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3158)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3158) gives:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3159)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3159) implies:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3160)  op(e3, e2) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (134), (157), (169), (170), (203),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (272), (2641), (2669), (3139), (3160),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #401.
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3161)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3161) implies:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3162)  op(e3, e3) = e3
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3130), (3162), (function-axioms) are inconsistent
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #765.
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/21.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3163)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (2662), (2987), (3163),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #812.
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3164)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3164) gives:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3165)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (2669), (3104), (3165),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #921.
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3166)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (2645), (2662), (2669), (3166),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #420.
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3167)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3167) gives:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3168)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3168) gives:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3169)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3169) gives:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3170)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (2663), (3104), (3170),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #822.
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3171)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (133), (168), (170), (201),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (238), (270), (272), (352), (2642), (2645),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2975), (2976), (2990), (3002), (3171),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #414.
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3172)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3172) gives:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3173)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (133), (162), (168), (170),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (201), (203), (238), (270), (272), (352), (2642),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2645), (2663), (2975), (2976), (2990), (3002),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3173), (function-axioms) are inconsistent by
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #413.
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3174)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3174) gives:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3175)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3175) implies:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3176)  op(e0, e3) = e0
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3177)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (2976), (3130), (3177),
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #400.
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3178)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3178) gives:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3179)  all_56_6 = e2 & op(e1, e3) = e2
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3179) implies:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3180)  all_56_6 = e2
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3124), (3180) imply:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3181)  e2 = e0
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3181) implies:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3182)  e2 = e0
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (223), (2986), (3104), (3130),
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3138), (3182), (function-axioms) are inconsistent
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #399.
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3183)  all_56_12 = e2 & op(e0, e3) = e2
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3183) implies:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3184)  op(e0, e3) = e2
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (3176), (3184), (function-axioms) are
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #689.
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3185)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3185) gives:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3186)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3186) implies:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3187)  op(e3, e3) = e3
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3130), (3187), (function-axioms) are inconsistent
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #765.
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3188)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3188) implies:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3189)  op(e1, e0) = e1
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2666), (3189), (function-axioms) are
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3190)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3190) gives:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3191)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3191) gives:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3192)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3192) gives:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3193)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3193) implies:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3194)  op(e0, e0) = e2
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (163),
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (2662), (2663), (2666), (2669), (2976),
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2987), (2997), (3104), (3113), (3194),
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #806.
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3195)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3195) implies:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3196)  op(e2, e2) = e2
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3104), (3196), (function-axioms) are
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3197)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (168), (2642), (3104), (3197),
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #443.
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3198)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3198) gives:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3199)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3199) gives:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3200)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3200) implies:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3201)  op(e0, e0) = e2
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (163),
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (2662), (2663), (2666), (2669), (2976),
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2987), (2997), (3104), (3113), (3201),
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #806.
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3202)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3202) implies:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3203)  op(e3, e3) = e3
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3130), (3203), (function-axioms) are inconsistent
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #765.
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3204)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3204) gives:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3205)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3205) implies:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3206)  op(e2, e2) = e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3104), (3206), (function-axioms) are
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3207)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3207) gives:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3208)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3208) implies:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3209)  op(e1, e0) = e1
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2666), (3209), (function-axioms) are
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3210)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3210) implies:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3211)  op(e0, e0) = all_57_15
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3212)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3213)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (2976), (3130), (3213),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #400.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3214)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3214) gives:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3215)  all_56_6 = e2 & op(e1, e3) = e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3215) implies:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3216)  all_56_6 = e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3124), (3216) imply:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3217)  e2 = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (223), (2986), (3104), (3130),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3138), (3217), (function-axioms) are inconsistent
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #399.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3218)  all_56_12 = e2 & op(e0, e3) = e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (103), (133),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (168), (170), (201), (203), (238),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (272), (352), (2638), (2642), (2645),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2666), (2975), (2976), (2987), (2997), (3002),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3211), (3212), (3218), (function-axioms) are
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #407.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3219)  all_56_10 = e2 & op(e2, e0) = e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3219) implies:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3220)  op(e2, e0) = e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2987), (3220), (function-axioms) are
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3221)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3221) gives:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3222)  all_56_6 = e3 & op(e1, e3) = e3
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3222) implies:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3223)  op(e1, e3) = e3
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3125), (3223), (function-axioms) are
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #913.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3224)  all_56_12 = e3 & op(e0, e3) = e3
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2639), (3224), (function-axioms) are
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #398.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3225)  all_56_7 = e0 & op(e1, e2) = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3101), (3225), (function-axioms) are
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #898.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3226)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3226) gives:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3227)  all_56_8 = e0 & op(e1, e1) = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3227) implies:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3228)  op(e1, e1) = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (103), (133), (168),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (201), (203), (238), (270), (272), (352),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2638), (2642), (2645), (2975), (2976), (3002),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3228), (function-axioms) are inconsistent by
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #410.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3229)  all_56_11 = e0 & op(e1, e0) = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3229) implies:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3230)  op(e1, e0) = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3121), (3230), (function-axioms) are
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #397.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3231)  all_56_15 = e2 & op(e0, e0) = e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3231) implies:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3232)  op(e0, e0) = e2
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (163),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (2662), (2663), (2666), (2669), (2976),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2987), (2997), (3104), (3113), (3232),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            #806.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | |   (3233)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3233) implies:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | |   (3234)  op(e0, e0) = e0
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2645), (3234), (function-axioms) are
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | |   (3235)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 152.42/22.02  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (2645), (2665), (3235),
% 152.42/22.02  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.02  | | | | | | | | | | | | | | | | | | |            #431.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | |   (3236)   ~ (all_48_1 = e1) & op(e3, e3) = all_48_1 &
% 152.42/22.02  | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 152.42/22.02  | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2976), (3236), (function-axioms) are inconsistent
% 152.42/22.02  | | | | | | | | | | | | | | | | | |            by sub-proof #396.
% 152.42/22.02  | | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | | End of split
% 152.42/22.02  | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | Case 2:
% 152.42/22.02  | | | | | | | | | | | | | 
% 152.42/22.02  | | | | | | | | | | | | |   (3237)  all_24_2 = e1
% 152.42/22.03  | | | | | | | | | | | | |   (3238)  ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 &
% 152.42/22.03  | | | | | | | | | | | | |             $i(all_24_0)) | ( ~ (all_24_1 = e0) & op(e1, e1)
% 152.42/22.03  | | | | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 152.42/22.03  | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | COMBINE_EQS: (318), (3237) imply:
% 152.42/22.03  | | | | | | | | | | | | |   (3239)  all_4_2 = e1
% 152.42/22.03  | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | REDUCE: (356), (3239) imply:
% 152.42/22.03  | | | | | | | | | | | | |   (3240)   ~ (all_52_7 = e1)
% 152.42/22.03  | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | REDUCE: (360), (3239) imply:
% 152.42/22.03  | | | | | | | | | | | | |   (3241)   ~ (all_52_13 = e1)
% 152.42/22.03  | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | REDUCE: (36), (3239) imply:
% 152.42/22.03  | | | | | | | | | | | | |   (3242)  op(e2, e2) = e1
% 152.42/22.03  | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | BETA: splitting (207) gives:
% 152.42/22.03  | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | |   (3243)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 152.42/22.03  | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 152.42/22.03  | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | BETA: splitting (3243) gives:
% 152.42/22.03  | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | |   (3244)  all_56_12 = e1 & op(e0, e3) = e1
% 152.42/22.03  | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | ALPHA: (3244) implies:
% 152.42/22.03  | | | | | | | | | | | | | | |   (3245)  op(e0, e3) = e1
% 152.42/22.03  | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | |   (3246)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 152.42/22.03  | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 152.42/22.03  | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | BETA: splitting (3246) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | |   (3247)  all_56_9 = e1 & op(e3, e0) = e1
% 152.42/22.03  | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | ALPHA: (3247) implies:
% 152.42/22.03  | | | | | | | | | | | | | | | | |   (3248)  op(e3, e0) = e1
% 152.42/22.03  | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 152.42/22.03  | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (3245) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | |   (3249)  all_52_3 = e1
% 152.42/22.03  | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 152.42/22.03  | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (168), (3248) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | |   (3250)  all_52_12 = e1
% 152.42/22.03  | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | REDUCE: (112), (3250) imply:
% 152.42/22.03  | | | | | | | | | | | | | | | | |   (3251)   ~ (all_52_14 = e1)
% 152.42/22.03  | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | REDUCE: (348), (3250) imply:
% 152.42/22.03  | | | | | | | | | | | | | | | | |   (3252)   ~ (all_6_2 = e1)
% 152.42/22.03  | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | SIMP: (3252) implies:
% 152.42/22.03  | | | | | | | | | | | | | | | | |   (3253)   ~ (all_6_2 = e1)
% 152.42/22.03  | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | |   (3254)  all_54_0 = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (3254) imply:
% 152.42/22.03  | | | | | | | | | | | | | | | | | |   (3255)  all_6_2 = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | REDUCE: (344), (3255) imply:
% 152.42/22.03  | | | | | | | | | | | | | | | | | |   (3256)   ~ (all_52_4 = e3)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | REDUCE: (346), (3255) imply:
% 152.42/22.03  | | | | | | | | | | | | | | | | | |   (3257)   ~ (all_52_8 = e3)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | REDUCE: (39), (3255) imply:
% 152.42/22.03  | | | | | | | | | | | | | | | | | |   (3258)  op(e3, e3) = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | |   (3259)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 152.42/22.03  | | | | | | | | | | | | | | | | | | |            (3242), (3258), (3259), (function-axioms) are
% 152.42/22.03  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #762.
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | |   (3260)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | BETA: splitting (3260) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | |   (3261)  all_56_7 = e3 & op(e1, e2) = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | ALPHA: (3261) implies:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | |   (3262)  all_56_7 = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | |   (3263)  op(e1, e2) = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2636) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | |   (3264)   ~ (all_18_0 = e1) & op(e3, e0) = all_18_0 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | |           $i(all_18_0)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3264) implies:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | |   (3265)   ~ (all_18_0 = e1)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | |   (3266)  op(e3, e0) = all_18_0
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3248), (3265), (3266), (function-axioms) are
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #395.
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | |   (3267)   ~ (all_18_1 = e2) & op(e3, e3) = all_18_1 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3267) implies:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | |   (3268)  op(e3, e3) = all_18_1
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |   (3269)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3269) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |   (3270)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3270) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |   (3271)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3271) gives:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (3272)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3242), (3258), (3272),
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |            #801.
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (3273)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2669), (3242), (3273),
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | |            #800.
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |   (3274)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3274) gives:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (3275)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2642), (2645), (3275),
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |            #445.
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (3276)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3276) gives:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3277)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3277) implies:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3278)  op(e2, e2) = e2
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3242), (3278), (function-axioms) are
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3279)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3279) gives:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3280)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3280) implies:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3281)  op(e1, e1) = e3
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (2666), (3262), (3263), (3281),
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #457.
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3282)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3282) implies:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3283)   ~ (all_57_12 = e1)
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3284)  op(e2, e2) = all_57_12
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3242), (3283), (3284), (function-axioms) are
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #795.
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |   (3285)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3285) gives:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |   (3286)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3286) gives:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (3287)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.04  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3287) gives:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3288)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3288) implies:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3289)  op(e0, e3) = e0
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3245), (3289), (function-axioms) are
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3290)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3290) implies:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3291)  op(e3, e2) = e3
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (3256), (3291), (function-axioms) are
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (3292)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3258), (3292), (function-axioms) are
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |   (3293)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3293) gives:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (3294)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3294) gives:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3295)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3295) implies:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3296)  op(e1, e1) = e3
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (2666), (3262), (3263), (3296),
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            #457.
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3297)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3297) implies:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3298)  op(e1, e3) = e1
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2662), (3298), (function-axioms) are
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (3299)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (163), (213),
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (2645), (2662), (2666), (3262),
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (3263), (3299), (function-axioms) are inconsistent
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #454.
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |   (3300)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3300) gives:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |   (3301)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3301) gives:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |   (3302)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3302) gives:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (3303)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (2663), (3258), (3303),
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | |            #788.
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (3304)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2645), (2669), (3304),
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |            #453.
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |   (3305)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3305) gives:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (3306)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (2663), (2669), (3306),
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (3307)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3307) gives:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3308)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3308) implies:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3309)  op(e0, e3) = e0
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3245), (3309), (function-axioms) are
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3310)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (3257), (3258), (3310),
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            #981.
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |   (3311)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3311) gives:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |   (3312)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3312) gives:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (3313)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2645), (3242), (3313), (function-axioms) are
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #394.
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (3314)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (2666), (3245), (3314),
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |            #393.
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |   (3315)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3315) gives:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (3316)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2642), (2645), (3316),
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |            #451.
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (3317)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3317) gives:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3318)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3318) implies:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3319)  op(e2, e2) = e2
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3242), (3319), (function-axioms) are
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3320)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3320) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3321)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3321) implies:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3322)  op(e1, e0) = e1
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2666), (3322), (function-axioms) are
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3323)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3323) implies:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3324)  op(e0, e0) = all_57_15
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3325)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (2645), (3324)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3326)  all_57_15 = e3
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (3263) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3327)  all_52_6 = e3
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_18_1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (3258), (3268) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3328)  all_18_1 = e3
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (3327) imply:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3329)   ~ (all_52_14 = e3)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3325) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3330)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3330) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3331)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3331) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3332)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3332) implies:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3333)  op(e0, e3) = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3245), (3333), (function-axioms) are
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3334)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3334) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3335)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e3) = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3335) implies:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3336)  op(e0, e3) = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3245), (3336), (function-axioms) are
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3337)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e3) = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3337) implies:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3338)  op(e1, e1) = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (39), (160), (162), (163), (216),
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (340), (374), (2644), (2645), (3238),
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3242), (3338), (function-axioms) are inconsistent
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #392.
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3339)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (3242), (3245), (3258), (3339),
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #785.
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3340)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3340) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3341)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3341) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3342)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3342) implies:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3343)  op(e1, e1) = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (39), (160), (162), (163), (216),
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (340), (374), (2644), (2645), (3238),
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3242), (3343), (function-axioms) are inconsistent
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #392.
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3344)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3258), (3326), (3344), (function-axioms) are
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #448.
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3345)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3345) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3346)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3346) gives:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3347)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e1) = e0
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3347) implies:
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3348)  op(e2, e2) = e0
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3242), (3348), (function-axioms) are
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3349)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e1) = e0
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3349) implies:
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3350)  op(e1, e1) = e0
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (39), (160), (162), (163), (216),
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (340), (374), (2644), (2645), (3238),
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3242), (3350), (function-axioms) are inconsistent
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #392.
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3351)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (2666), (3326), (3351),
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #446.
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | |   (3352)  all_56_13 = e3 & op(e0, e2) = e3
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2640), (3352), (function-axioms) are
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | |   (3353)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.42/22.08  | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (3253), (3353) are
% 152.42/22.08  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 152.42/22.08  | | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | |   (3354)  all_56_10 = e1 & op(e2, e0) = e1
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3241), (3354), (function-axioms) are
% 152.42/22.08  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | |   (3355)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 152.42/22.08  | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (2645), (2666), (3355),
% 152.42/22.08  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.08  | | | | | | | | | | | | | | | |            #391.
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | |   (3356)  all_56_13 = e1 & op(e0, e2) = e1
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | REF_CLOSE: (158), (3240), (3356), (function-axioms) are
% 152.42/22.08  | | | | | | | | | | | | | | |            inconsistent by sub-proof #712.
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | |   (3357)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 152.42/22.08  | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (2645), (2665), (3357),
% 152.42/22.08  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.08  | | | | | | | | | | | | | |            #431.
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | |   (3358)  all_54_10 = e0
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | COMBINE_EQS: (336), (3358) imply:
% 152.42/22.08  | | | | | | | | | | | |   (3359)  all_10_2 = e0
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | REDUCE: (2647), (3359) imply:
% 152.42/22.08  | | | | | | | | | | | |   (3360)  $false
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | CLOSE: (3360) is inconsistent.
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | 
% 152.42/22.08  | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | 
% 152.42/22.08  | | | | | | | | |   (3361)  all_20_2 = e3
% 152.42/22.08  | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | COMBINE_EQS: (325), (3361) imply:
% 152.42/22.08  | | | | | | | | |   (3362)  all_10_2 = e3
% 152.42/22.08  | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | REDUCE: (361), (3362) imply:
% 152.42/22.08  | | | | | | | | |   (3363)   ~ (all_52_6 = e3)
% 152.42/22.08  | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | REDUCE: (45), (3362) imply:
% 152.42/22.08  | | | | | | | | |   (3364)  op(e1, e1) = e3
% 152.42/22.08  | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | BETA: splitting (228) gives:
% 152.42/22.08  | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | Case 1:
% 152.42/22.08  | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | |   (3365)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 152.42/22.08  | | | | | | | | | |             & op(e2, e2) = e3)
% 152.42/22.08  | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | BETA: splitting (3365) gives:
% 152.42/22.08  | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | Case 1:
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | |   (3366)  all_56_1 = e3 & op(e3, e2) = e3
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | ALPHA: (3366) implies:
% 152.42/22.08  | | | | | | | | | | |   (3367)  all_56_1 = e3
% 152.42/22.08  | | | | | | | | | | |   (3368)  op(e3, e2) = e3
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 152.42/22.08  | | | | | | | | | | |              e2, e3, simplifying with (170), (3368) gives:
% 152.42/22.08  | | | | | | | | | | |   (3369)  all_52_4 = e3
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | REDUCE: (344), (3369) imply:
% 152.42/22.08  | | | | | | | | | | |   (3370)   ~ (all_6_2 = e3)
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | SIMP: (3370) implies:
% 152.42/22.08  | | | | | | | | | | |   (3371)   ~ (all_6_2 = e3)
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | BETA: splitting (238) gives:
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | Case 1:
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | |   (3372)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 152.42/22.08  | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 152.42/22.08  | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 152.42/22.08  | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 152.42/22.08  | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 152.42/22.08  | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 152.42/22.08  | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 152.42/22.08  | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 152.42/22.08  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 152.42/22.08  | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 152.42/22.08  | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 152.42/22.08  | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 152.42/22.08  | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 152.42/22.08  | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 152.42/22.08  | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 152.42/22.08  | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | BETA: splitting (3372) gives:
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | Case 1:
% 152.42/22.08  | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | |   (3373)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 152.42/22.08  | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 152.42/22.08  | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 152.42/22.08  | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 152.42/22.08  | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 152.42/22.08  | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 152.42/22.08  | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 152.42/22.08  | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 152.42/22.08  | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | ALPHA: (3373) implies:
% 152.42/22.08  | | | | | | | | | | | | |   (3374)  op(e3, e3) = e3
% 152.42/22.08  | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 152.42/22.08  | | | | | | | | | | | | |            (3367), (3374), (function-axioms) are inconsistent
% 152.42/22.08  | | | | | | | | | | | | |            by sub-proof #946.
% 152.42/22.08  | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | |   (3375)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 152.42/22.08  | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 152.42/22.08  | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 152.42/22.08  | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 152.42/22.08  | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 152.42/22.08  | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 152.42/22.08  | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 152.42/22.08  | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 152.42/22.08  | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | ALPHA: (3375) implies:
% 152.42/22.08  | | | | | | | | | | | | |   (3376)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1
% 152.42/22.08  | | | | | | | | | | | | |               = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))
% 152.42/22.08  | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | BETA: splitting (204) gives:
% 152.42/22.08  | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | Case 1:
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | |   (3377)  all_54_0 = e3
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | REF_CLOSE: (279), (3371), (3377) are inconsistent by
% 152.42/22.08  | | | | | | | | | | | | | |            sub-proof #390.
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | |   (3378)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | BETA: splitting (3378) gives:
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | Case 1:
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | |   (3379)  all_54_0 = e2
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | COMBINE_EQS: (279), (3379) imply:
% 152.42/22.08  | | | | | | | | | | | | | | |   (3380)  all_6_2 = e2
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | SIMP: (3380) implies:
% 152.42/22.08  | | | | | | | | | | | | | | |   (3381)  all_6_2 = e2
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | REDUCE: (377), (3381) imply:
% 152.42/22.08  | | | | | | | | | | | | | | |   (3382)  $false
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | CLOSE: (3382) is inconsistent.
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | |   (3383)   ~ (all_54_0 = e2)
% 152.42/22.08  | | | | | | | | | | | | | | |   (3384)  all_54_0 = e1 | all_54_0 = e0
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | BETA: splitting (3384) gives:
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | Case 1:
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | |   (3385)  all_54_0 = e1
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (3385) imply:
% 152.42/22.08  | | | | | | | | | | | | | | | |   (3386)  all_6_2 = e1
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | SIMP: (3386) implies:
% 152.42/22.08  | | | | | | | | | | | | | | | |   (3387)  all_6_2 = e1
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | REDUCE: (377), (3387) imply:
% 152.42/22.08  | | | | | | | | | | | | | | | |   (3388)   ~ (e2 = e1)
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | REDUCE: (39), (3387) imply:
% 152.42/22.08  | | | | | | | | | | | | | | | |   (3389)  op(e3, e3) = e1
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | BETA: splitting (3376) gives:
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | |   (3390)  all_57_10 = e2 & op(e3, e3) = e2
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | ALPHA: (3390) implies:
% 152.42/22.08  | | | | | | | | | | | | | | | | |   (3391)  op(e3, e3) = e2
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3389), (3391), (function-axioms) are
% 152.42/22.08  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | |   (3392)   ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 152.42/22.08  | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | ALPHA: (3392) implies:
% 152.42/22.08  | | | | | | | | | | | | | | | | |   (3393)   ~ (all_57_1 = e3)
% 152.42/22.08  | | | | | | | | | | | | | | | | |   (3394)  op(e3, e2) = all_57_1
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_57_1,
% 152.42/22.08  | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (3368), (3394) gives:
% 152.42/22.08  | | | | | | | | | | | | | | | | |   (3395)  all_57_1 = e3
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | REDUCE: (3393), (3395) imply:
% 152.42/22.08  | | | | | | | | | | | | | | | | |   (3396)  $false
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | | CLOSE: (3396) is inconsistent.
% 152.42/22.08  | | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | |   (3397)  all_54_0 = e0
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (3397) imply:
% 152.42/22.08  | | | | | | | | | | | | | | | |   (3398)  all_6_2 = e0
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | SIMP: (3398) implies:
% 152.42/22.08  | | | | | | | | | | | | | | | |   (3399)  all_6_2 = e0
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | REDUCE: (374), (3399) imply:
% 152.42/22.08  | | | | | | | | | | | | | | | |   (3400)  $false
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | | CLOSE: (3400) is inconsistent.
% 152.42/22.08  | | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | |   (3401)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 152.42/22.08  | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 152.42/22.08  | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 152.42/22.08  | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 152.42/22.08  | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 152.42/22.08  | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 152.42/22.08  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 152.42/22.08  | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 152.42/22.08  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 152.42/22.08  | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 152.42/22.08  | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 152.42/22.08  | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 152.42/22.08  | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 152.42/22.08  | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 152.42/22.08  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 152.42/22.08  | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | | REF_CLOSE: (7), (8), (2645), (3364), (3401),
% 152.42/22.08  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.08  | | | | | | | | | | | |            #389.
% 152.42/22.08  | | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | |   (3402)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | ALPHA: (3402) implies:
% 152.42/22.08  | | | | | | | | | | |   (3403)  op(e2, e2) = e3
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | REF_CLOSE: (36), (373), (3403), (function-axioms) are
% 152.42/22.08  | | | | | | | | | | |            inconsistent by sub-proof #711.
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | |   (3404)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 152.42/22.08  | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 152.42/22.08  | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | BETA: splitting (3404) gives:
% 152.42/22.08  | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | Case 1:
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | |   (3405)  all_56_7 = e3 & op(e1, e2) = e3
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | REF_CLOSE: (162), (3363), (3405), (function-axioms) are
% 152.42/22.08  | | | | | | | | | | |            inconsistent by sub-proof #388.
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | |   (3406)  all_56_13 = e3 & op(e0, e2) = e3
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | | REF_CLOSE: (158), (2640), (3406), (function-axioms) are
% 152.42/22.08  | | | | | | | | | | |            inconsistent by sub-proof #429.
% 152.42/22.08  | | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | | 
% 152.42/22.08  | | | | | | | | End of split
% 152.42/22.08  | | | | | | | | 
% 152.42/22.08  | | | | | | | Case 2:
% 152.42/22.08  | | | | | | | | 
% 152.42/22.08  | | | | | | | |   (3407)  all_22_2 = e0
% 152.42/22.08  | | | | | | | |   (3408)  ( ~ (all_22_0 = e2) & op(e0, e1) = all_22_0 &
% 152.42/22.08  | | | | | | | |             $i(all_22_0)) | ( ~ (all_22_1 = e3) & op(e0, e0) =
% 152.42/22.08  | | | | | | | |             all_22_1 & $i(all_22_1))
% 152.42/22.08  | | | | | | | | 
% 152.42/22.08  | | | | | | | | COMBINE_EQS: (251), (3407) imply:
% 152.42/22.08  | | | | | | | |   (3409)  all_10_2 = e0
% 152.42/22.08  | | | | | | | | 
% 152.42/22.08  | | | | | | | | REDUCE: (363), (3409) imply:
% 152.42/22.08  | | | | | | | |   (3410)   ~ (all_52_8 = e0)
% 152.42/22.08  | | | | | | | | 
% 152.42/22.08  | | | | | | | | REDUCE: (366), (3409) imply:
% 152.42/22.08  | | | | | | | |   (3411)   ~ (all_52_11 = e0)
% 152.42/22.08  | | | | | | | | 
% 152.42/22.08  | | | | | | | | REDUCE: (375), (3409) imply:
% 152.42/22.08  | | | | | | | |   (3412)   ~ (e2 = e0)
% 152.42/22.08  | | | | | | | | 
% 152.42/22.08  | | | | | | | | REDUCE: (45), (3409) imply:
% 152.42/22.08  | | | | | | | |   (3413)  op(e1, e1) = e0
% 152.42/22.08  | | | | | | | | 
% 152.42/22.08  | | | | | | | | BETA: splitting (3408) gives:
% 152.42/22.08  | | | | | | | | 
% 152.42/22.08  | | | | | | | | Case 1:
% 152.42/22.08  | | | | | | | | | 
% 152.42/22.08  | | | | | | | | |   (3414)   ~ (all_22_0 = e2) & op(e0, e1) = all_22_0 &
% 152.42/22.08  | | | | | | | | |           $i(all_22_0)
% 152.42/22.08  | | | | | | | | | 
% 152.42/22.08  | | | | | | | | | ALPHA: (3414) implies:
% 152.42/22.08  | | | | | | | | |   (3415)   ~ (all_22_0 = e2)
% 152.42/22.08  | | | | | | | | |   (3416)  op(e0, e1) = all_22_0
% 152.42/22.09  | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 152.42/22.09  | | | | | | | | |              all_22_0, e1, e0, simplifying with (157), (3416)
% 152.42/22.09  | | | | | | | | |              gives:
% 152.42/22.09  | | | | | | | | |   (3417)  all_52_11 = all_22_0
% 152.42/22.09  | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | COMBINE_EQS: (247), (3417) imply:
% 152.42/22.09  | | | | | | | | |   (3418)  all_54_14 = all_22_0
% 152.42/22.09  | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | REDUCE: (125), (3417) imply:
% 152.42/22.09  | | | | | | | | |   (3419)   ~ (all_52_7 = all_22_0)
% 152.42/22.09  | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | REDUCE: (121), (3417) imply:
% 152.42/22.09  | | | | | | | | |   (3420)   ~ (all_52_8 = all_22_0)
% 152.42/22.09  | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | REDUCE: (2641), (3417) imply:
% 152.42/22.09  | | | | | | | | |   (3421)   ~ (all_22_0 = e3)
% 152.42/22.09  | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | REDUCE: (3411), (3417) imply:
% 152.42/22.09  | | | | | | | | |   (3422)   ~ (all_22_0 = e0)
% 152.42/22.09  | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | BETA: splitting (190) gives:
% 152.42/22.09  | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | |   (3423)  all_54_14 = e3
% 152.42/22.09  | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | REF_CLOSE: (3418), (3421), (3423) are inconsistent by
% 152.42/22.09  | | | | | | | | | |            sub-proof #387.
% 152.42/22.09  | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | |   (3424)   ~ (all_54_14 = e3)
% 152.42/22.09  | | | | | | | | | |   (3425)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 152.42/22.09  | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | BETA: splitting (3425) gives:
% 152.42/22.09  | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | |   (3426)  all_54_14 = e2
% 152.42/22.09  | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | REF_CLOSE: (3415), (3418), (3426) are inconsistent by
% 152.42/22.09  | | | | | | | | | | |            sub-proof #386.
% 152.42/22.09  | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | |   (3427)   ~ (all_54_14 = e2)
% 152.42/22.09  | | | | | | | | | | |   (3428)  all_54_14 = e1 | all_54_14 = e0
% 152.42/22.09  | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | BETA: splitting (3428) gives:
% 152.42/22.09  | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | |   (3429)  all_54_14 = e1
% 152.42/22.09  | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | COMBINE_EQS: (3418), (3429) imply:
% 152.42/22.09  | | | | | | | | | | | |   (3430)  all_22_0 = e1
% 152.42/22.09  | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | SIMP: (3430) implies:
% 152.42/22.09  | | | | | | | | | | | |   (3431)  all_22_0 = e1
% 152.42/22.09  | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | REDUCE: (3419), (3431) imply:
% 152.42/22.09  | | | | | | | | | | | |   (3432)   ~ (all_52_7 = e1)
% 152.42/22.09  | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | REDUCE: (3420), (3431) imply:
% 152.42/22.09  | | | | | | | | | | | |   (3433)   ~ (all_52_8 = e1)
% 152.42/22.09  | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | REDUCE: (3421), (3431) imply:
% 152.42/22.09  | | | | | | | | | | | |   (3434)   ~ (e3 = e1)
% 152.42/22.09  | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | REDUCE: (3415), (3431) imply:
% 152.42/22.09  | | | | | | | | | | | |   (3435)   ~ (e2 = e1)
% 152.42/22.09  | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | BETA: splitting (67) gives:
% 152.42/22.09  | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | |   (3436)   ~ (all_24_2 = e1)
% 152.42/22.09  | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | REDUCE: (318), (3436) imply:
% 152.42/22.09  | | | | | | | | | | | | |   (3437)   ~ (all_4_2 = e1)
% 152.42/22.09  | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | BETA: splitting (70) gives:
% 152.42/22.09  | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | |   (3438)   ~ (all_26_2 = e1)
% 152.42/22.09  | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | REDUCE: (307), (3438) imply:
% 152.42/22.09  | | | | | | | | | | | | | |   (3439)   ~ (all_6_2 = e1)
% 152.42/22.09  | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 152.42/22.09  | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | |   (3440)  all_54_0 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | COMBINE_EQS: (279), (3440) imply:
% 152.42/22.09  | | | | | | | | | | | | | | |   (3441)  all_6_2 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | REDUCE: (338), (3441) imply:
% 152.42/22.09  | | | | | | | | | | | | | | |   (3442)   ~ (all_52_1 = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | REDUCE: (344), (3441) imply:
% 152.42/22.09  | | | | | | | | | | | | | | |   (3443)   ~ (all_52_4 = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | REDUCE: (346), (3441) imply:
% 152.42/22.09  | | | | | | | | | | | | | | |   (3444)   ~ (all_52_8 = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | REDUCE: (39), (3441) imply:
% 152.42/22.09  | | | | | | | | | | | | | | |   (3445)  op(e3, e3) = e3
% 152.42/22.09  | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | |   (3446)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (230), (232),
% 152.42/22.09  | | | | | | | | | | | | | | | |            (234), (373), (3445), (3446), (function-axioms)
% 152.42/22.09  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #476.
% 152.42/22.09  | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | |   (3447)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 152.42/22.09  | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | BETA: splitting (3447) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | |   (3448)  all_56_7 = e3 & op(e1, e2) = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | ALPHA: (3448) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | |   (3449)  all_56_7 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | |   (3450)  op(e1, e2) = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | |   (3451)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (229), (231),
% 152.42/22.09  | | | | | | | | | | | | | | | | | |            (233), (373), (3445), (3451), (function-axioms)
% 152.42/22.09  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #475.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | |   (3452)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 152.42/22.09  | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | BETA: splitting (3452) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | |   (3453)  all_56_5 = e3 & op(e2, e1) = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | ALPHA: (3453) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | |   (3454)  all_56_5 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | |   (3455)  all_54_2 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (3455) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | |   (3456)  all_52_8 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | REDUCE: (3444), (3456) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | |   (3457)  $false
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | CLOSE: (3457) is inconsistent.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | |   (3458)   ~ (all_54_2 = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | |   (3459)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3459) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (3460)  all_54_2 = e2
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (3460) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (3461)  all_52_8 = e2
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (3461) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (3462)   ~ (all_52_4 = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (3461) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (3463)   ~ (all_52_9 = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | SIMP: (3463) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (3464)   ~ (all_52_9 = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3461) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (3465)   ~ (all_52_12 = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | SIMP: (3465) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (3466)   ~ (all_52_12 = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3444), (3461) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (3467)   ~ (e3 = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | |   (3468)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3468) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |   (3469)  all_56_1 = e1 & op(e3, e2) = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3469) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |   (3470)  all_56_1 = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |   (3471)  op(e3, e2) = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | |   (3472)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3472) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3473)  all_56_0 = e0 & op(e3, e3) = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3473) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3474)  op(e3, e3) = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3445), (3474), (function-axioms) are
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3475)  all_56_1 = e0 & op(e3, e2) = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3470), (3475) are inconsistent by sub-proof
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |            #760.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | |   (3476)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3476) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3477)  all_56_4 = e0 & op(e3, e1) = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3410), (3477), (function-axioms) are
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #700.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3478)  all_56_9 = e0 & op(e3, e0) = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3478) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3479)  all_56_9 = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3480)  op(e3, e0) = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (3450) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3481)  all_52_6 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (3480) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3482)  all_52_12 = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1,
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (3471) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3483)  all_52_4 = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (3483) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3484)   ~ (all_52_7 = e1)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (3483) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3485)   ~ (all_4_2 = e1)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (3481) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3486)   ~ (all_52_7 = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (3481) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3487)   ~ (all_4_2 = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (3482) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3488)   ~ (all_52_13 = e0)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3488) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (3489)   ~ (all_52_13 = e0)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3490)   ~ (all_32_2 = e0)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (3490) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3491)   ~ (all_4_2 = e0)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3492)  all_54_5 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (373), (3492) are inconsistent by sub-proof
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #930.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3493)   ~ (all_54_5 = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3494)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3494) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3495)  all_54_5 = e2
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3495) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3496)  all_4_2 = e2
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3496) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3497)  all_4_2 = e2
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (3497) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3498)   ~ (all_52_7 = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (3497) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3499)   ~ (all_52_13 = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3500)  all_54_13 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (2640), (3500) are inconsistent by
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #385.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3501)   ~ (all_54_13 = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3502)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3503)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (3466), (3499), (3503),
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #384.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3504)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3504) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3505)  all_56_11 = e2 & op(e1, e0) = e2
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3505) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3506)  all_56_11 = e2
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3502) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3507)  all_54_13 = e2
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (3498), (3507) are inconsistent by
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #505.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3508)   ~ (all_54_13 = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3509)  all_54_13 = e1 | all_54_13 = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3510)  all_54_7 = e3
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2643), (3510) are inconsistent by
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #383.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3511)   ~ (all_54_7 = e3)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3512)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3513)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3513) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3514)  all_56_9 = e1 & op(e3, e0) = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3514) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3515)  all_56_9 = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3479), (3515) are inconsistent by sub-proof
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #756.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3516)  all_56_10 = e1 & op(e2, e0) = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3516) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3517)  all_56_10 = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3512) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3518)  all_54_7 = e2
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (3499), (3518) are inconsistent by
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #382.
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3519)   ~ (all_54_7 = e2)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3520)  all_54_7 = e1 | all_54_7 = e0
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3520) gives:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3521)  all_54_7 = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3521) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3522)  all_52_13 = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3522) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3523)  all_52_13 = e1
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (3523) imply:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3524)   ~ (all_52_14 = e1)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3524) implies:
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3525)   ~ (all_52_14 = e1)
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (3523) imply:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3526)  op(e2, e0) = e1
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3527)  all_54_4 = e3
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (3442), (3527) are inconsistent by
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #931.
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3528)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3529)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3529) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3530)  all_56_6 = e1 & op(e1, e3) = e1
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3530) implies:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3531)  all_56_6 = e1
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3532)  op(e1, e3) = e1
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3509) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3533)  all_54_13 = e1
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (3432), (3533) are inconsistent by
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #504.
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3534)  all_54_13 = e0
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (3534) imply:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3535)  all_52_7 = e0
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3535) implies:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3536)  all_52_7 = e0
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (3536) imply:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3537)   ~ (all_52_3 = e0)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2640), (3536) imply:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3538)   ~ (e3 = e0)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3432), (3536) imply:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3539)   ~ (e1 = e0)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3540)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3540) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3541)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3541) implies:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3542)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (163), (3413), (3532), (3542),
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #606.
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3543)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3543) implies:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3544)  op(e2, e2) = e2
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3545)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3545) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3546)  all_57_15 = e2 & op(e0, e0) = e2
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3546) implies:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3547)  op(e0, e0) = e2
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2645), (3547), (function-axioms) are
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3548)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3548) implies:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3549)   ~ (all_57_7 = e0)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3550)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3550) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3551)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3551) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3552)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (268), (269), (349), (373),
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3437), (3528), (3544), (3552), (function-axioms)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #381.
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3553)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3553) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3554)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (268), (269), (349), (373),
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3437), (3528), (3544), (3554), (function-axioms)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #380.
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3555)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3555) gives:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3556)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3556) implies:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3557)  op(e2, e3) = e2
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (268), (269), (349), (373),
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3437), (3528), (3544), (3557), (function-axioms)
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #926.
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3558)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3558) gives:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3559)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3559) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3560)  op(e1, e1) = e3
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (213), (215), (3449),
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3531), (3560), (function-axioms) are inconsistent
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #458.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3561)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3561) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3562)  op(e2, e1) = e2
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3464), (3562), (function-axioms) are
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3563)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3563) gives:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3564)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3564) gives:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3565)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3565) gives:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3566)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3566) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3567)  op(e0, e3) = e0
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3537), (3567), (function-axioms) are
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3568)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3568) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3569)  op(e3, e2) = e3
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (3443), (3569), (function-axioms) are
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3570)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3570) gives:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3571)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3571) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3572)  op(e2, e0) = e2
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3526), (3572), (function-axioms) are
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3573)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3573) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3574)  op(e3, e3) = e1
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3445), (3574), (function-axioms) are
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3575)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3575) gives:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3576)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3576) gives:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3577)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3577) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3578)  op(e1, e1) = e3
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (213), (215), (3449),
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3531), (3578), (function-axioms) are inconsistent
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #458.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3579)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3579) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3580)  op(e2, e2) = e1
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (3464), (3517), (3580), (function-axioms)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #842.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3581)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3581) gives:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3582)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3582) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3583)  op(e0, e0) = e1
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (157), (160), (164), (165),
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (199), (239), (268),
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (349), (358), (360), (373), (2642), (3411),
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3413), (3437), (3443), (3444), (3445), (3491),
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3525), (3583), (function-axioms) are inconsistent
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #369.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3584)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3584) gives:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3585)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3585) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3586)  op(e1, e1) = e3
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (213), (215), (3449),
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3531), (3586), (function-axioms) are inconsistent
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #458.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3587)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e1
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3587) implies:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3588)  op(e1, e1) = e1
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3413), (3588), (function-axioms) are
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3589)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3589) gives:
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3590)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3590) gives:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3591)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3591) gives:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3592)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3592) gives:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3593)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3593) implies:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3594)  op(e3, e3) = e1
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3445), (3594), (function-axioms) are
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3595)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3595) implies:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3596)  op(e2, e2) = e1
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (3464), (3517), (3596), (function-axioms)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #842.
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3597)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3597) gives:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3598)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3598) implies:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3599)  op(e1, e1) = e2
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3413), (3599), (function-axioms) are
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3600)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3600) implies:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3601)  op(e0, e0) = e1
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (157), (160), (164), (165),
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (199), (239), (268),
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (349), (358), (360), (373), (2642), (3411),
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3413), (3437), (3443), (3444), (3445), (3491),
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3525), (3601), (function-axioms) are inconsistent
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #369.
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3602)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3602) gives:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3603)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (3413), (3603), (function-axioms) are
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3604)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3604) gives:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3605)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3605) implies:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3606)  op(e0, e3) = e0
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3537), (3606), (function-axioms) are
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3607)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (3444), (3445), (3607),
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #981.
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3608)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3608) gives:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3609)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3609) gives:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3610)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (2645), (3464), (3610),
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #412.
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3611)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3611) gives:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3612)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3612) implies:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3613)  op(e2, e2) = e1
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (3464), (3517), (3613), (function-axioms)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #842.
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3614)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3614) implies:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3615)  op(e0, e3) = e0
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3537), (3615), (function-axioms) are
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3616)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3616) gives:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3617)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2642), (2645), (3617),
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #451.
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3618)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3618) gives:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3619)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3619) implies:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3620)  op(e2, e0) = e2
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3526), (3620), (function-axioms) are
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3621)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3621) gives:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3622)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3622) implies:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3623)  op(e1, e1) = e1
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3413), (3623), (function-axioms) are
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3624)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3624) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3625)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3625) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3626)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3626) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3627)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3627) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3628)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3628) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3629)  op(e0, e3) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3537), (3629), (function-axioms) are
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3630)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3630) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3631)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e3) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3631) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3632)  op(e2, e0) = e2
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3526), (3632), (function-axioms) are
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3633)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e3) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3633) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3634)  op(e0, e3) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3537), (3634), (function-axioms) are
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3635)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3635) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3636)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3636) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3637)  op(e0, e3) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3537), (3637), (function-axioms) are
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3638)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3638) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3639)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e2) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3639) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3640)  op(e3, e3) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3445), (3640), (function-axioms) are
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3641)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e2) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3641) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3642)  op(e2, e0) = e2
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3526), (3642), (function-axioms) are
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3643)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3643) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3644)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3644) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3645)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3645) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3646)  op(e1, e0) = e1
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3525), (3646), (function-axioms) are
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3647)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3647) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3648)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3648) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3649)  all_57_7 = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3549), (3649) imply:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3650)  $false
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3650) is inconsistent.
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3651)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3651) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3652)  op(e3, e3) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3445), (3652), (function-axioms) are
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3653)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3653) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3654)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3654) gives:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3655)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e1) = e0
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3655) implies:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3656)  op(e2, e0) = e2
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3526), (3656), (function-axioms) are
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.76/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3657)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e1) = e0
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3657) implies:
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3658)  op(e0, e1) = e0
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3411), (3658), (function-axioms) are
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3659)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3411), (3659), (function-axioms) are
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3660)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (2645), (3413), (3660),
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #411.
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3661)  all_56_7 = e1 & op(e1, e2) = e1
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3661) implies:
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3662)  op(e1, e2) = e1
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3450), (3662), (function-axioms) are
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3663)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 153.10/22.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (3413), (3525), (3663),
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #902.
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3664)  all_54_7 = e0
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (3489), (3664) are inconsistent by
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #368.
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3665)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2645), (3506), (3665),
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #468.
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3666)  all_56_15 = e2 & op(e0, e0) = e2
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3666) implies:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3667)  op(e0, e0) = e2
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2645), (3667), (function-axioms) are
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3668)  all_54_5 = e1 | all_54_5 = e0
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3437), (3491), (3668) are inconsistent by
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3669)  all_32_2 = e0
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (3669) imply:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3670)  all_4_2 = e0
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (3670) imply:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3671)   ~ (all_52_7 = e0)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3670) imply:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3672)   ~ (e3 = e0)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3437), (3670) imply:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3673)   ~ (e1 = e0)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3670) imply:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3674)  op(e2, e2) = e0
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3675)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3675) gives:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3676)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3676) gives:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3677)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3677) gives:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3678)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (3445), (3674), (3678),
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #934.
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3679)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (3413), (3674), (3679),
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #367.
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3680)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3680) gives:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3681)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2642), (2645), (3681),
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #445.
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3682)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3682) gives:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3683)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3683) implies:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3684)  op(e2, e2) = e2
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3674), (3684), (function-axioms) are
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3685)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (3413), (3464), (3685),
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #708.
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3686)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3686) gives:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3687)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3687) gives:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3688)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (3443), (3688), (function-axioms) are
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #792.
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3689)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3445), (3689), (function-axioms) are
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3690)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3690) gives:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3691)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (3413), (3674), (3691),
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #366.
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3692)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3692) gives:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3693)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3693) implies:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3694)  op(e0, e0) = e1
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2645), (3694), (function-axioms) are
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3695)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (3413), (3695), (function-axioms) are
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #704.
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3696)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3696) gives:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3697)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3697) gives:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3698)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3698) gives:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3699)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (3445), (3674), (3699),
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #920.
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3700)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3700) gives:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3701)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3701) implies:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3702)  op(e1, e1) = e2
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3413), (3702), (function-axioms) are
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3703)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3703) implies:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3704)  op(e0, e0) = e1
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2645), (3704), (function-axioms) are
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3705)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3705) gives:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3706)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (3413), (3706), (function-axioms) are
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3707)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (3444), (3445), (3707),
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #787.
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3708)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3708) gives:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3709)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (168), (2642), (2645), (3674),
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3709), (function-axioms) are inconsistent by
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #442.
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3710)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3710) gives:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3711)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2642), (2645), (3711),
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #451.
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3712)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3712) gives:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3713)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3713) implies:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3714)  op(e2, e2) = e2
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3674), (3714), (function-axioms) are
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3715)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3715) gives:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3716)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3716) implies:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3717)  op(e1, e1) = e1
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3413), (3717), (function-axioms) are
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3718)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3718) implies:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3719)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3720)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3720) gives:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3721)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3721) implies:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3722)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3722) gives:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3723)  all_57_15 = e3 & op(e0, e0) = e3
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3723) implies:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3724)  all_57_15 = e3
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3719) gives:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3725)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3725) gives:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3726)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3722), (3726) are inconsistent by sub-proof #365.
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3727)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (222), (223),
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (229), (231), (233), (3445), (3454),
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3671), (3674), (3724), (3727), (function-axioms)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #438.
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3728)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3728) gives:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3729)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (3445), (3671), (3729),
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #967.
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3730)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3411), (3730), (function-axioms) are
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #744.
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3731)   ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_6)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3731) implies:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3732)   ~ (all_57_6 = e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3719) gives:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3733)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3733) gives:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3734)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3722), (3734) are inconsistent by sub-proof #365.
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3735)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3735) gives:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3736)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3736) implies:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3737)  all_57_6 = e0
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3732), (3737) imply:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3738)  $false
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3738) is inconsistent.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3739)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (3445), (3671), (3739),
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #900.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3740)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3740) gives:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3741)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (3445), (3671), (3741),
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #967.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3742)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3411), (3742), (function-axioms) are
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #744.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3743)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3743) implies:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3744)  op(e2, e2) = e2
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3674), (3744), (function-axioms) are
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3745)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (2645), (3413), (3745),
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #411.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | |   (3746)  all_56_3 = e1 & op(e2, e2) = e1
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3746) implies:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | |   (3747)  op(e2, e2) = e1
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (3437), (3747),
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | |            #690.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | |   (3748)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3748) gives:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | |   (3749)  all_56_7 = e1 & op(e1, e2) = e1
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3749) implies:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | |   (3750)  op(e1, e2) = e1
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3450), (3750), (function-axioms) are
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | |   (3751)  all_56_13 = e1 & op(e0, e2) = e1
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3432), (3751), (function-axioms) are
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #712.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | |   (3752)  all_54_2 = e1 | all_54_2 = e0
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (3410), (3433), (3752) are inconsistent by
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | |            sub-proof #364.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | |   (3753)  all_56_10 = e3 & op(e2, e0) = e3
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (157), (199),
% 153.10/22.19  | | | | | | | | | | | | | | | | | | |            (206), (209), (210), (211), (225), (226), (227),
% 153.10/22.19  | | | | | | | | | | | | | | | | | | |            (229), (231), (233), (268), (373), (2641), (3437),
% 153.10/22.19  | | | | | | | | | | | | | | | | | | |            (3445), (3449), (3450), (3753), (function-axioms)
% 153.10/22.19  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #465.
% 153.10/22.19  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | |   (3754)  all_56_13 = e3 & op(e0, e2) = e3
% 153.10/22.19  | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2640), (3754), (function-axioms) are
% 153.10/22.19  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 153.10/22.19  | | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | |   (3755)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.10/22.19  | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (3439), (3755) are
% 153.10/22.19  | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 153.10/22.19  | | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | |   (3756)  all_26_2 = e1
% 153.10/22.19  | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | COMBINE_EQS: (307), (3756) imply:
% 153.10/22.19  | | | | | | | | | | | | | |   (3757)  all_6_2 = e1
% 153.10/22.19  | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | SIMP: (3757) implies:
% 153.10/22.19  | | | | | | | | | | | | | |   (3758)  all_6_2 = e1
% 153.10/22.19  | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | REDUCE: (344), (3758) imply:
% 153.10/22.19  | | | | | | | | | | | | | |   (3759)   ~ (all_52_4 = e1)
% 153.10/22.19  | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | REDUCE: (348), (3758) imply:
% 153.10/22.19  | | | | | | | | | | | | | |   (3760)   ~ (all_52_12 = e1)
% 153.10/22.19  | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | REDUCE: (39), (3758) imply:
% 153.10/22.19  | | | | | | | | | | | | | |   (3761)  op(e3, e3) = e1
% 153.10/22.19  | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (103), (133), (168),
% 153.10/22.19  | | | | | | | | | | | | | |            (170), (201), (203), (238), (270), (272), (352),
% 153.10/22.19  | | | | | | | | | | | | | |            (2638), (2642), (2645), (3413), (3759), (3760),
% 153.10/22.19  | | | | | | | | | | | | | |            (3761), (function-axioms) are inconsistent by
% 153.10/22.19  | | | | | | | | | | | | | |            sub-proof #410.
% 153.10/22.19  | | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | |   (3762)  all_24_2 = e1
% 153.10/22.19  | | | | | | | | | | | | |   (3763)  ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 &
% 153.10/22.19  | | | | | | | | | | | | |             $i(all_24_0)) | ( ~ (all_24_1 = e0) & op(e1, e1)
% 153.10/22.19  | | | | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 153.10/22.19  | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | COMBINE_EQS: (318), (3762) imply:
% 153.10/22.19  | | | | | | | | | | | | |   (3764)  all_4_2 = e1
% 153.10/22.19  | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | SIMP: (3764) implies:
% 153.10/22.19  | | | | | | | | | | | | |   (3765)  all_4_2 = e1
% 153.10/22.19  | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | REDUCE: (36), (3765) imply:
% 153.10/22.19  | | | | | | | | | | | | |   (3766)  op(e2, e2) = e1
% 153.10/22.19  | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (39), (160), (162), (163), (216),
% 153.10/22.19  | | | | | | | | | | | | |            (238), (340), (374), (2644), (2645), (3413),
% 153.10/22.19  | | | | | | | | | | | | |            (3763), (3766), (function-axioms) are inconsistent
% 153.10/22.19  | | | | | | | | | | | | |            by sub-proof #392.
% 153.10/22.19  | | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | |   (3767)  all_54_14 = e0
% 153.10/22.19  | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | | REF_CLOSE: (3418), (3422), (3767) are inconsistent by
% 153.10/22.19  | | | | | | | | | | | |            sub-proof #363.
% 153.10/22.19  | | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | | 
% 153.10/22.19  | | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | | 
% 153.10/22.19  | | | | | | | | |   (3768)   ~ (all_22_1 = e3) & op(e0, e0) = all_22_1 &
% 153.10/22.19  | | | | | | | | |           $i(all_22_1)
% 153.10/22.19  | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | REF_CLOSE: (2645), (3768), (function-axioms) are inconsistent
% 153.10/22.19  | | | | | | | | |            by sub-proof #362.
% 153.10/22.19  | | | | | | | | | 
% 153.10/22.19  | | | | | | | | End of split
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | End of split
% 153.10/22.19  | | | | | | | 
% 153.10/22.19  | | | | | | End of split
% 153.10/22.19  | | | | | | 
% 153.10/22.19  | | | | | Case 2:
% 153.10/22.19  | | | | | | 
% 153.10/22.19  | | | | | |   (3769)  all_14_2 = e1
% 153.10/22.19  | | | | | |   (3770)  ( ~ (all_14_0 = e2) & op(e1, e0) = all_14_0 &
% 153.10/22.19  | | | | | |             $i(all_14_0)) | ( ~ (all_14_1 = e3) & op(e1, e1) =
% 153.10/22.19  | | | | | |             all_14_1 & $i(all_14_1))
% 153.10/22.19  | | | | | | 
% 153.10/22.19  | | | | | | REDUCE: (351), (3769) imply:
% 153.10/22.19  | | | | | |   (3771)   ~ (all_52_3 = e1)
% 153.10/22.19  | | | | | | 
% 153.10/22.19  | | | | | | REDUCE: (362), (3769) imply:
% 153.10/22.19  | | | | | |   (3772)   ~ (all_52_7 = e1)
% 153.10/22.19  | | | | | | 
% 153.10/22.19  | | | | | | REDUCE: (369), (3769) imply:
% 153.10/22.19  | | | | | |   (3773)   ~ (all_52_11 = e1)
% 153.10/22.19  | | | | | | 
% 153.10/22.19  | | | | | | REDUCE: (370), (3769) imply:
% 153.10/22.19  | | | | | |   (3774)   ~ (all_52_12 = e1)
% 153.10/22.19  | | | | | | 
% 153.10/22.19  | | | | | | REDUCE: (371), (3769) imply:
% 153.10/22.19  | | | | | |   (3775)   ~ (all_52_13 = e1)
% 153.10/22.19  | | | | | | 
% 153.10/22.19  | | | | | | REDUCE: (372), (3769) imply:
% 153.10/22.19  | | | | | |   (3776)   ~ (all_52_14 = e1)
% 153.10/22.19  | | | | | | 
% 153.10/22.19  | | | | | | BETA: splitting (207) gives:
% 153.10/22.19  | | | | | | 
% 153.10/22.19  | | | | | | Case 1:
% 153.10/22.19  | | | | | | | 
% 153.10/22.19  | | | | | | |   (3777)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 &
% 153.10/22.19  | | | | | | |             op(e0, e2) = e1)
% 153.10/22.19  | | | | | | | 
% 153.10/22.19  | | | | | | | BETA: splitting (3777) gives:
% 153.10/22.19  | | | | | | | 
% 153.10/22.19  | | | | | | | Case 1:
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | |   (3778)  all_56_12 = e1 & op(e0, e3) = e1
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | | REF_CLOSE: (159), (3771), (3778), (function-axioms) are
% 153.10/22.19  | | | | | | | |            inconsistent by sub-proof #852.
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | |   (3779)  all_56_13 = e1 & op(e0, e2) = e1
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | | REF_CLOSE: (158), (3772), (3779), (function-axioms) are
% 153.10/22.19  | | | | | | | |            inconsistent by sub-proof #712.
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | End of split
% 153.10/22.19  | | | | | | | 
% 153.10/22.19  | | | | | | Case 2:
% 153.10/22.19  | | | | | | | 
% 153.10/22.19  | | | | | | |   (3780)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 &
% 153.10/22.19  | | | | | | |             op(e0, e0) = e1)
% 153.10/22.19  | | | | | | | 
% 153.10/22.19  | | | | | | | BETA: splitting (3780) gives:
% 153.10/22.19  | | | | | | | 
% 153.10/22.19  | | | | | | | Case 1:
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | |   (3781)  all_56_14 = e1 & op(e0, e1) = e1
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | | REF_CLOSE: (157), (3773), (3781), (function-axioms) are
% 153.10/22.19  | | | | | | | |            inconsistent by sub-proof #803.
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | Case 2:
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | |   (3782)  all_56_15 = e1 & op(e0, e0) = e1
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | | ALPHA: (3782) implies:
% 153.10/22.19  | | | | | | | |   (3783)  all_56_15 = e1
% 153.10/22.19  | | | | | | | |   (3784)  op(e0, e0) = e1
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | | BETA: splitting (61) gives:
% 153.10/22.19  | | | | | | | | 
% 153.10/22.19  | | | | | | | | Case 1:
% 153.10/22.19  | | | | | | | | | 
% 153.10/22.19  | | | | | | | | |   (3785)   ~ (all_20_2 = e3)
% 153.10/22.19  | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | REDUCE: (325), (3785) imply:
% 153.10/22.19  | | | | | | | | |   (3786)   ~ (all_10_2 = e3)
% 153.10/22.19  | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | BETA: splitting (64) gives:
% 153.10/22.19  | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | Case 1:
% 153.10/22.19  | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | |   (3787)   ~ (all_22_2 = e0)
% 153.10/22.19  | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | REDUCE: (251), (3787) imply:
% 153.10/22.19  | | | | | | | | | |   (3788)   ~ (all_10_2 = e0)
% 153.10/22.19  | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | BETA: splitting (194) gives:
% 153.10/22.19  | | | | | | | | | | 
% 153.10/22.19  | | | | | | | | | | Case 1:
% 153.10/22.19  | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | |   (3789)  all_54_10 = e3
% 153.10/22.20  | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | REF_CLOSE: (336), (3786), (3789) are inconsistent by
% 153.10/22.20  | | | | | | | | | | |            sub-proof #361.
% 153.10/22.20  | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | Case 2:
% 153.10/22.20  | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | |   (3790)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.10/22.20  | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | BETA: splitting (3790) gives:
% 153.10/22.20  | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | |   (3791)  all_54_10 = e2
% 153.10/22.20  | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | REF_CLOSE: (336), (375), (3791) are inconsistent by sub-proof
% 153.10/22.20  | | | | | | | | | | | |            #360.
% 153.10/22.20  | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | Case 2:
% 153.10/22.20  | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | |   (3792)   ~ (all_54_10 = e2)
% 153.10/22.20  | | | | | | | | | | | |   (3793)  all_54_10 = e1 | all_54_10 = e0
% 153.10/22.20  | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | BETA: splitting (3793) gives:
% 153.10/22.20  | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | |   (3794)  all_54_10 = e1
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | COMBINE_EQS: (336), (3794) imply:
% 153.10/22.20  | | | | | | | | | | | | |   (3795)  all_10_2 = e1
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | SIMP: (3795) implies:
% 153.10/22.20  | | | | | | | | | | | | |   (3796)  all_10_2 = e1
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | REDUCE: (350), (3796) imply:
% 153.10/22.20  | | | | | | | | | | | | |   (3797)   ~ (all_52_2 = e1)
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | REDUCE: (361), (3796) imply:
% 153.10/22.20  | | | | | | | | | | | | |   (3798)   ~ (all_52_6 = e1)
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | REDUCE: (363), (3796) imply:
% 153.10/22.20  | | | | | | | | | | | | |   (3799)   ~ (all_52_8 = e1)
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | REDUCE: (364), (3796) imply:
% 153.10/22.20  | | | | | | | | | | | | |   (3800)   ~ (all_52_9 = e1)
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | REDUCE: (375), (3796) imply:
% 153.10/22.20  | | | | | | | | | | | | |   (3801)   ~ (e2 = e1)
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | REDUCE: (45), (3796) imply:
% 153.10/22.20  | | | | | | | | | | | | |   (3802)  op(e1, e1) = e1
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | BETA: splitting (67) gives:
% 153.10/22.20  | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | |   (3803)   ~ (all_24_2 = e1)
% 153.10/22.20  | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | REDUCE: (318), (3803) imply:
% 153.10/22.20  | | | | | | | | | | | | | |   (3804)   ~ (all_4_2 = e1)
% 153.10/22.20  | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 153.10/22.20  | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | |   (3805)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 153.10/22.20  | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 153.10/22.20  | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | BETA: splitting (3805) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | |   (3806)  all_56_2 = e1 & op(e2, e3) = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | ALPHA: (3806) implies:
% 153.10/22.20  | | | | | | | | | | | | | | | |   (3807)  all_56_2 = e1
% 153.10/22.20  | | | | | | | | | | | | | | | |   (3808)  op(e2, e3) = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | |   (3809)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | BETA: splitting (3809) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3810)  all_56_1 = e1 & op(e3, e2) = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | ALPHA: (3810) implies:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3811)  all_56_1 = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3812)  op(e3, e2) = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 153.10/22.20  | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (3808) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3813)  all_52_1 = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1,
% 153.10/22.20  | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (3812) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3814)  all_52_4 = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | REDUCE: (149), (3813) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3815)   ~ (all_52_2 = e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | REDUCE: (148), (3813) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3816)   ~ (all_52_3 = e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | REDUCE: (145), (3813) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3817)   ~ (all_52_13 = e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | REDUCE: (136), (3814) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3818)   ~ (all_52_6 = e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | REDUCE: (135), (3814) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3819)   ~ (all_52_7 = e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | REDUCE: (344), (3814) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3820)   ~ (all_6_2 = e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | SIMP: (3820) implies:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3821)   ~ (all_6_2 = e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | REDUCE: (352), (3814) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | |   (3822)   ~ (all_4_2 = e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | |   (3823)  all_54_0 = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (3823) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | |   (3824)  all_6_2 = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | REDUCE: (342), (3824) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | |   (3825)   ~ (all_52_3 = e3)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | REDUCE: (346), (3824) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | |   (3826)   ~ (all_52_8 = e3)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | REDUCE: (348), (3824) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | |   (3827)   ~ (all_52_12 = e3)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (3824) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | |   (3828)  op(e3, e3) = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | |   (3829)   ~ (all_32_2 = e0)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (3829) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | |   (3830)   ~ (all_4_2 = e0)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | |   (3831)  all_54_5 = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3831) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | |   (3832)  all_4_2 = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3832) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | |   (3833)  $false
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | CLOSE: (3833) is inconsistent.
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | |   (3834)   ~ (all_54_5 = e3)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | |   (3835)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3835) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | |   (3836)  all_54_5 = e2
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3836) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | |   (3837)  all_4_2 = e2
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (3837) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | |   (3838)   ~ (all_52_9 = e2)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (3837) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | |   (3839)   ~ (all_52_13 = e2)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3837) imply:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | |   (3840)   ~ (e3 = e2)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |   (3841)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3841) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |   (3842)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3842) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3843)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3843) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3844)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3808), (3844), (function-axioms) are
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #359.
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3845)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3845) gives:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3846)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3846) implies:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3847)  op(e1, e1) = e2
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3802), (3847), (function-axioms) are
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3848)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3848) implies:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3849)  op(e2, e3) = e2
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3808), (3849), (function-axioms) are
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #428.
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (3850)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3850) gives:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3851)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3851) gives:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3852)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3852) implies:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3853)  op(e0, e0) = e2
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3784), (3853), (function-axioms) are
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3854)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3854) implies:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3855)  op(e2, e3) = e2
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3808), (3855), (function-axioms) are
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #428.
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3856)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3856) gives:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3857)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3857) implies:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3858)  op(e2, e3) = e2
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e3,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (3808), (3858) gives:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3859)  e2 = e1
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3859) imply:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3860)  $false
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3860) is inconsistent.
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3861)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (3802), (3838), (3861),
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1001.
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |   (3862)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3862) gives:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (3863)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3863) gives:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3864)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3864) gives:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3865)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3865) implies:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3866)  op(e0, e0) = e3
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3784), (3866), (function-axioms) are
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3867)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3867) implies:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3868)  op(e3, e2) = e3
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e2,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (3812), (3868) gives:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3869)  e3 = e1
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (3869) imply:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3870)  $false
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3870) is inconsistent.
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3871)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (3828), (3839), (3871),
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            #994.
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (3872)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (165), (221),
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (3797), (3802), (3807), (3838),
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |            (3872), (function-axioms) are inconsistent by
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #353.
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.10/22.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |   (3873)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 153.38/22.21  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3873) gives:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |   (3874)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3874) gives:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (3875)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3875) gives:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3876)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (3807), (3828), (3838), (3876),
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            #352.
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3877)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (3798), (3802), (3877),
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            #351.
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (3878)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3878) gives:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3879)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (3798), (3802), (3879),
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3880)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (3784), (3826), (3828), (3880),
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            #375.
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |   (3881)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3881) gives:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (3882)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (3784), (3807), (3838), (3882),
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |            #350.
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (3883)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3883) gives:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3884)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (3784), (3827), (3884),
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            #373.
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3885)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3885) gives:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3886)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3886) implies:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3887)  op(e2, e0) = e2
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3839), (3887), (function-axioms) are
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3888)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3888) gives:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3889)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3889) implies:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3890)  op(e1, e0) = e1
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3776), (3890), (function-axioms) are
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3891)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3891) implies:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3892)  op(e0, e0) = all_57_15
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3893)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (3784), (3892)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3894)  all_57_15 = e1
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3893) gives:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3895)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3895) gives:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3896)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (164), (3802), (3828), (3839), (3896),
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #866.
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3897)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3897) gives:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3898)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3894), (3898) are inconsistent by sub-proof
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #372.
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3899)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (164), (3828), (3839), (3899),
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #864.
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3900)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3900) gives:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3901)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3901) gives:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3902)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3902) implies:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3903)  op(e1, e1) = e0
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3802), (3903), (function-axioms) are
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3904)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (3828), (3894), (3904),
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #370.
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3905)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3905) gives:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3906)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 153.38/22.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (3802), (3839), (3906),
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #862.
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3907)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3776), (3894), (3907), (function-axioms)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #349.
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |   (3908)  all_54_5 = e1 | all_54_5 = e0
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3804), (3830), (3908) are inconsistent by
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |   (3909)  all_32_2 = e0
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |   (3910)  ( ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |             $i(all_32_0)) | ( ~ (all_32_1 = e1) & op(e0, e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |             = all_32_1 & $i(all_32_1))
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (3909) imply:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |   (3911)  all_4_2 = e0
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (3911) imply:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |   (3912)   ~ (all_52_6 = e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (3911) imply:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |   (3913)   ~ (all_52_7 = e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (3911) imply:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |   (3914)   ~ (all_52_13 = e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3911) imply:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |   (3915)   ~ (e3 = e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (3804), (3911) imply:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |   (3916)   ~ (e1 = e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3911) imply:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | |   (3917)  op(e2, e2) = e0
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |   (3918)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3918) gives:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |   (3919)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (3802), (3808), (3828), (3919),
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |            #346.
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |   (3920)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3920) gives:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |   (3921)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3921) gives:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |   (3922)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3784), (3812), (3922), (function-axioms) are
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #344.
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |   (3923)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3828), (3923), (function-axioms) are
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |   (3924)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3924) gives:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |   (3925)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (3802), (3917), (3925),
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |            #921.
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |   (3926)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (3797), (3802), (3926),
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | |            #354.
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.24  | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |   (3927)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3927) gives:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |   (3928)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3928) gives:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |   (3929)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3929) gives:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |   (3930)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (3828), (3917), (3930),
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |            #920.
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |   (3931)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (3798), (3802), (3931),
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |            #351.
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |   (3932)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3932) gives:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |   (3933)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (3798), (3802), (3933),
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |   (3934)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (3784), (3826), (3828), (3934),
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | |            #375.
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |   (3935)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3935) gives:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |   (3936)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (3784), (3917), (3936),
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | |            #342.
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |   (3937)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3937) gives:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |   (3938)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (3784), (3827), (3938),
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |            #373.
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |   (3939)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3939) gives:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (3940)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3940) implies:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (3941)  op(e2, e2) = e2
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3917), (3941), (function-axioms) are
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (3942)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3942) gives:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3943)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3943) implies:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3944)  op(e1, e0) = e1
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3776), (3944), (function-axioms) are
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3945)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3945) implies:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3946)  op(e0, e0) = all_57_15
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3947)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (3784), (3946)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3948)  all_57_15 = e1
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3910) gives:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3949)   ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_32_0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3949) implies:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3950)   ~ (all_32_0 = e3)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3951)  op(e0, e2) = all_32_0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3947) gives:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3952)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3952) gives:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3953)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3953) gives:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3954)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3954) implies:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3955)  op(e3, e3) = e0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3828), (3955), (function-axioms) are
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3956)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3956) gives:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3957)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e3) = e0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3957) implies:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3958)  all_57_6 = e0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3959)   ~ (all_57_15 = e3)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3960)  op(e0, e3) = e0
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3961)  op(e2, e0) = e2
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3948), (3959) imply:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3962)   ~ (e3 = e1)
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3963)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3963) gives:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3964)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3964) implies:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3965)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3958), (3959), (3965) are inconsistent by
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #684.
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3966)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3966) implies:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3967)  op(e2, e2) = e2
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (3961), (3967),
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3968)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3968) gives:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3969)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3969) implies:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3970)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3970) gives:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3971)  all_57_12 = e1 & op(e2, e2) = e1
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3971) implies:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3972)  op(e2, e2) = e1
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3917), (3972), (function-axioms) are
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_0, e2, e0, simplifying with (158), (3951)
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3973)  all_52_7 = all_32_0
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (3960) gives:
% 153.38/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3974)  all_52_3 = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (3961) gives:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3975)  all_52_13 = e2
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (3973) imply:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3976)  all_54_13 = all_32_0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (3973) imply:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3977)   ~ (all_52_6 = all_32_0)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3978)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3978) gives:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3979)  all_56_9 = e3 & op(e3, e0) = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3979) implies:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3980)  all_56_9 = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3828), (3980), (function-axioms) are inconsistent
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #632.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3981)  all_56_10 = e3 & op(e2, e0) = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3981) implies:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3982)  op(e2, e0) = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3961), (3982), (function-axioms) are
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #580.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3983)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3983) gives:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3984)  all_56_11 = e3 & op(e1, e0) = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3984) implies:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3985)  op(e1, e0) = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3986)  all_54_13 = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3976), (3986) imply:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3987)  all_32_0 = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3987) implies:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3988)  all_32_0 = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3950), (3988) imply:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3989)  $false
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3989) is inconsistent.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3990)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3990) gives:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3991)  all_54_13 = e2
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3976), (3991) imply:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3992)  all_32_0 = e2
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3992) implies:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3993)  all_32_0 = e2
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3977), (3993) imply:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3994)   ~ (all_52_6 = e2)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (160), (195), (258), (3798), (3912),
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3985), (3994), (function-axioms) are inconsistent
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #672.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3995)  all_54_13 = e1 | all_54_13 = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3995) gives:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3996)  all_54_13 = e1
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (3772), (3996) are inconsistent by
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #504.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3997)  all_54_13 = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (3913), (3997) are inconsistent by
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #503.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3998)  all_56_15 = e3 & op(e0, e0) = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3998) implies:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3999)  op(e0, e0) = e3
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3784), (3999), (function-axioms) are
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4000)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4000) implies:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4001)  op(e0, e0) = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (3784), (4001), (function-axioms) are
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4002)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e3) = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4002) implies:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4003)  op(e1, e1) = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3802), (4003), (function-axioms) are
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4004)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4004) gives:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4005)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4005) implies:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4006)  all_57_15 = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3948), (4006) imply:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4007)  e1 = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3811), (4007) imply:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4008)  all_56_1 = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (226), (227),
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (230), (232), (234), (3772), (3828),
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3917), (4008), (function-axioms) are inconsistent
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #340.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4009)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (3828), (3913), (4009),
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #900.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4010)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4010) gives:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4011)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (158), (3802), (3828), (3913), (4011),
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #784.
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4012)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4012) gives:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4013)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3802), (3948), (4013), (function-axioms) are
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #339.
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4014)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4014) gives:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4015)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 & 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4015) implies:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4016)  op(e1, e0) = e1
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3776), (4016), (function-axioms) are
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4017)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4017) implies:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4018)  all_57_15 = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3948), (4018) imply:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4019)  e1 = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3811), (4019) imply:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4020)  all_56_1 = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (226), (227),
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (230), (232), (234), (3772), (3828),
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3917), (4020), (function-axioms) are inconsistent
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #340.
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4021)   ~ (all_32_1 = e1) & op(e0, e0) = all_32_1 &
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_32_1)
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4021) implies:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4022)   ~ (all_32_1 = e1)
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4023)  op(e0, e0) = all_32_1
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3784), (3946), (4022), (4023), (function-axioms)
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #513.
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | |   (4024)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (3821), (4024) are
% 153.60/22.28  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | |   (4025)  all_56_3 = e1 & op(e2, e2) = e1
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | ALPHA: (4025) implies:
% 153.60/22.28  | | | | | | | | | | | | | | | | | |   (4026)  op(e2, e2) = e1
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (3804), (4026),
% 153.60/22.28  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.28  | | | | | | | | | | | | | | | | | |            #690.
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | |   (4027)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 153.60/22.28  | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 153.60/22.28  | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (3772), (3798), (4027),
% 153.60/22.28  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.28  | | | | | | | | | | | | | | | | |            #338.
% 153.60/22.28  | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | |   (4028)  all_56_3 = e1 & op(e2, e2) = e1
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | ALPHA: (4028) implies:
% 153.60/22.28  | | | | | | | | | | | | | | | |   (4029)  op(e2, e2) = e1
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (3804), (4029),
% 153.60/22.28  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.28  | | | | | | | | | | | | | | | |            #690.
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | |   (4030)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 153.60/22.28  | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 153.60/22.28  | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | BETA: splitting (4030) gives:
% 153.60/22.28  | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | |   (4031)  all_56_5 = e1 & op(e2, e1) = e1
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3800), (4031), (function-axioms) are
% 153.60/22.28  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | |   (4032)  all_56_10 = e1 & op(e2, e0) = e1
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3775), (4032), (function-axioms) are
% 153.60/22.28  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | |   (4033)  all_24_2 = e1
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | COMBINE_EQS: (318), (4033) imply:
% 153.60/22.28  | | | | | | | | | | | | | |   (4034)  all_4_2 = e1
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | SIMP: (4034) implies:
% 153.60/22.28  | | | | | | | | | | | | | |   (4035)  all_4_2 = e1
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | REDUCE: (373), (4035) imply:
% 153.60/22.28  | | | | | | | | | | | | | |   (4036)   ~ (e3 = e1)
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | REDUCE: (36), (4035) imply:
% 153.60/22.28  | | | | | | | | | | | | | |   (4037)  op(e2, e2) = e1
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (160), (162),
% 153.60/22.28  | | | | | | | | | | | | | |            (163), (168), (169), (214), (225), (227), (228),
% 153.60/22.28  | | | | | | | | | | | | | |            (232), (238), (239), (3774), (3776), (3784),
% 153.60/22.28  | | | | | | | | | | | | | |            (3797), (3798), (3799), (3802), (4037),
% 153.60/22.28  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.28  | | | | | | | | | | | | | |            #330.
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | |   (4038)  all_54_10 = e0
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | REF_CLOSE: (336), (3788), (4038) are inconsistent by
% 153.60/22.28  | | | | | | | | | | | | |            sub-proof #329.
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | End of split
% 153.60/22.28  | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | |   (4039)  all_22_2 = e0
% 153.60/22.28  | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | COMBINE_EQS: (251), (4039) imply:
% 153.60/22.28  | | | | | | | | | |   (4040)  all_10_2 = e0
% 153.60/22.28  | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | SIMP: (4040) implies:
% 153.60/22.28  | | | | | | | | | |   (4041)  all_10_2 = e0
% 153.60/22.28  | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | REDUCE: (366), (4041) imply:
% 153.60/22.28  | | | | | | | | | |   (4042)   ~ (all_52_11 = e0)
% 153.60/22.28  | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | REDUCE: (3786), (4041) imply:
% 153.60/22.28  | | | | | | | | | |   (4043)   ~ (e3 = e0)
% 153.60/22.28  | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | REDUCE: (375), (4041) imply:
% 153.60/22.28  | | | | | | | | | |   (4044)   ~ (e2 = e0)
% 153.60/22.28  | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | REDUCE: (45), (4041) imply:
% 153.60/22.28  | | | | | | | | | |   (4045)  op(e1, e1) = e0
% 153.60/22.28  | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | BETA: splitting (67) gives:
% 153.60/22.28  | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | |   (4046)   ~ (all_24_2 = e1)
% 153.60/22.28  | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | REDUCE: (318), (4046) imply:
% 153.60/22.28  | | | | | | | | | | |   (4047)   ~ (all_4_2 = e1)
% 153.60/22.28  | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | BETA: splitting (70) gives:
% 153.60/22.28  | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | |   (4048)   ~ (all_26_2 = e1)
% 153.60/22.28  | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | REDUCE: (307), (4048) imply:
% 153.60/22.28  | | | | | | | | | | | |   (4049)   ~ (all_6_2 = e1)
% 153.60/22.28  | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | BETA: splitting (204) gives:
% 153.60/22.28  | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | |   (4050)  all_54_0 = e3
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | COMBINE_EQS: (279), (4050) imply:
% 153.60/22.28  | | | | | | | | | | | | |   (4051)  all_6_2 = e3
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | SIMP: (4051) implies:
% 153.60/22.28  | | | | | | | | | | | | |   (4052)  all_6_2 = e3
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | REDUCE: (344), (4052) imply:
% 153.60/22.28  | | | | | | | | | | | | |   (4053)   ~ (all_52_4 = e3)
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | REDUCE: (346), (4052) imply:
% 153.60/22.28  | | | | | | | | | | | | |   (4054)   ~ (all_52_8 = e3)
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | REDUCE: (348), (4052) imply:
% 153.60/22.28  | | | | | | | | | | | | |   (4055)   ~ (all_52_12 = e3)
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | REDUCE: (39), (4052) imply:
% 153.60/22.28  | | | | | | | | | | | | |   (4056)  op(e3, e3) = e3
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | BETA: splitting (79) gives:
% 153.60/22.28  | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | |   (4057)   ~ (all_32_2 = e0)
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | REDUCE: (314), (4057) imply:
% 153.60/22.28  | | | | | | | | | | | | | |   (4058)   ~ (all_4_2 = e0)
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (157), (160), (164), (165),
% 153.60/22.28  | | | | | | | | | | | | | |            (167), (168), (169), (170), (199), (239), (268),
% 153.60/22.28  | | | | | | | | | | | | | |            (349), (358), (360), (373), (3776), (3784),
% 153.60/22.28  | | | | | | | | | | | | | |            (4042), (4045), (4047), (4053), (4054), (4055),
% 153.60/22.28  | | | | | | | | | | | | | |            (4056), (4058), (function-axioms) are inconsistent
% 153.60/22.28  | | | | | | | | | | | | | |            by sub-proof #369.
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | |   (4059)  all_32_2 = e0
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | COMBINE_EQS: (314), (4059) imply:
% 153.60/22.28  | | | | | | | | | | | | | |   (4060)  all_4_2 = e0
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | REDUCE: (356), (4060) imply:
% 153.60/22.28  | | | | | | | | | | | | | |   (4061)   ~ (all_52_7 = e0)
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | REDUCE: (4047), (4060) imply:
% 153.60/22.28  | | | | | | | | | | | | | |   (4062)   ~ (e1 = e0)
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | REDUCE: (36), (4060) imply:
% 153.60/22.28  | | | | | | | | | | | | | |   (4063)  op(e2, e2) = e0
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 153.60/22.28  | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | |   (4064)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 153.60/22.28  | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 153.60/22.28  | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | BETA: splitting (4064) gives:
% 153.60/22.28  | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | |   (4065)  all_56_2 = e0 & op(e2, e3) = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | ALPHA: (4065) implies:
% 153.60/22.28  | | | | | | | | | | | | | | | |   (4066)  all_56_2 = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (164), (222),
% 153.60/22.28  | | | | | | | | | | | | | | | |            (223), (224), (229), (231), (233), (3771), (3775),
% 153.60/22.28  | | | | | | | | | | | | | | | |            (4056), (4063), (4066), (function-axioms) are
% 153.60/22.28  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #328.
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | |   (4067)  all_56_3 = e0 & op(e2, e2) = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | ALPHA: (4067) implies:
% 153.60/22.28  | | | | | | | | | | | | | | | |   (4068)  all_56_3 = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 153.60/22.28  | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | |   (4069)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 153.60/22.28  | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (164), (222),
% 153.60/22.28  | | | | | | | | | | | | | | | | |            (223), (224), (229), (231), (233), (3771), (3775),
% 153.60/22.28  | | | | | | | | | | | | | | | | |            (4056), (4063), (4069), (function-axioms) are
% 153.60/22.28  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #327.
% 153.60/22.28  | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | |   (4070)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 153.60/22.28  | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 153.60/22.28  | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | BETA: splitting (4070) gives:
% 153.60/22.28  | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | |   (4071)  all_56_6 = e0 & op(e1, e3) = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | ALPHA: (4071) implies:
% 153.60/22.28  | | | | | | | | | | | | | | | | | |   (4072)  all_56_6 = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | |   (4073)  op(e1, e3) = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (214), (215),
% 153.60/22.28  | | | | | | | | | | | | | | | | | |            (216), (225), (226), (227), (228), (230), (232),
% 153.60/22.28  | | | | | | | | | | | | | | | | | |            (234), (3776), (4045), (4056), (4063), (4068),
% 153.60/22.28  | | | | | | | | | | | | | | | | | |            (4072), (4073), (function-axioms) are inconsistent
% 153.60/22.28  | | | | | | | | | | | | | | | | | |            by sub-proof #901.
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | |   (4074)  all_56_12 = e0 & op(e0, e3) = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | ALPHA: (4074) implies:
% 153.60/22.28  | | | | | | | | | | | | | | | | | |   (4075)  op(e0, e3) = e0
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | 
% 153.60/22.28  | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.28  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |   (4076)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | BETA: splitting (4076) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |   (4077)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | ALPHA: (4077) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |   (4078)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |   (4079)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (139), (157), (158),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |            (159), (160), (168), (169), (170), (208), (214),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |            (218), (220), (223), (224), (226), (227), (228),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (239),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |            (3772), (3773), (3774), (3776), (3784), (4042),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |            (4045), (4053), (4054), (4055), (4056), (4061),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |            (4063), (4075), (4078), (4079), (function-axioms)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #320.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |   (4080)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | ALPHA: (4080) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |   (4081)  op(e2, e2) = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4063), (4081), (function-axioms) are
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |   (4082)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (3784), (4045), (4082),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |            #629.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.29  | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | End of split
% 153.60/22.29  | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | End of split
% 153.60/22.29  | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | End of split
% 153.60/22.29  | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | |   (4083)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 153.60/22.29  | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 153.60/22.29  | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | BETA: splitting (4083) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | |   (4084)  all_56_5 = e0 & op(e2, e1) = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | ALPHA: (4084) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | |   (4085)  all_56_5 = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (222), (223), (224),
% 153.60/22.29  | | | | | | | | | | | | | | | |            (229), (231), (233), (4056), (4063), (4085),
% 153.60/22.29  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.29  | | | | | | | | | | | | | | | |            #439.
% 153.60/22.29  | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | |   (4086)  all_56_10 = e0 & op(e2, e0) = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | ALPHA: (4086) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | |   (4087)  all_56_10 = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | |   (4088)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.60/22.29  | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 153.60/22.29  | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.60/22.29  | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.60/22.29  | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.60/22.29  | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 153.60/22.29  | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 153.60/22.29  | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 153.60/22.29  | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.60/22.29  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 153.60/22.29  | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.60/22.29  | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.60/22.29  | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.60/22.29  | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 153.60/22.29  | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 153.60/22.29  | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 153.60/22.29  | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | BETA: splitting (4088) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | |   (4089)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.60/22.29  | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 153.60/22.29  | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.60/22.29  | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.60/22.29  | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.60/22.29  | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 153.60/22.29  | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 153.60/22.29  | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 153.60/22.29  | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | ALPHA: (4089) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | |   (4090)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 153.60/22.29  | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 153.60/22.29  | | | | | | | | | | | | | | | | | |   (4091)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0
% 153.60/22.29  | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))
% 153.60/22.29  | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |   (4092)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | BETA: splitting (4092) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |   (4093)  all_56_4 = e1 & op(e3, e1) = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | ALPHA: (4093) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | |   (4094)  all_56_4 = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | |   (4095)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (226), (227),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | |            (228), (230), (232), (234), (3772), (4056),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | |            (4063), (4095), (function-axioms) are inconsistent
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #326.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | |   (4096)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4096) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | |   (4097)  all_56_4 = e0 & op(e3, e1) = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (160), (169),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | |            (208), (214), (218), (220), (223), (224), (228),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (3773),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | |            (3776), (3784), (4045), (4054), (4056), (4063),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | |            (4091), (4097), (function-axioms) are inconsistent
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #323.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | |   (4098)  all_56_9 = e0 & op(e3, e0) = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4098) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | |   (4099)  all_56_9 = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | |   (4100)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4100) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | |   (4101)  all_56_0 = e2 & op(e3, e3) = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4101) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | |   (4102)  op(e3, e3) = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4056), (4102), (function-axioms) are
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | |   (4103)  all_56_1 = e2 & op(e3, e2) = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4103) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | |   (4104)  all_56_1 = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (4105)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (164), (222),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (229), (231), (233), (3771), (3775),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | |            (4056), (4063), (4105), (function-axioms) are
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #327.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (4106)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4106) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4107)  all_56_6 = e0 & op(e1, e3) = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4107) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4108)  all_56_6 = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4109)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4109) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4110)  all_56_1 = e1 & op(e3, e2) = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4104), (4110) are inconsistent by sub-proof
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #911.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4111)  all_56_3 = e1 & op(e2, e2) = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4111) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4112)  op(e2, e2) = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4063), (4112), (function-axioms) are
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4113)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4113) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4114)  all_56_7 = e1 & op(e1, e2) = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4114) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4115)  all_56_7 = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4116)  op(e1, e2) = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4117)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4117) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4118)  all_56_6 = e2 & op(e1, e3) = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4118) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4119)  all_56_6 = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4108), (4119) imply:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4120)  e2 = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4120) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4121)  e2 = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4104), (4121) imply:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4122)  all_56_1 = e0
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (226), (227),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (230), (232), (234), (3772), (4056),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4063), (4116), (4122), (function-axioms) are
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #341.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4123)  all_56_7 = e2 & op(e1, e2) = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4115), (4123) are inconsistent by sub-proof
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #915.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4124)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4124) gives:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4125)  all_56_8 = e2 & op(e1, e1) = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4125) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4126)  op(e1, e1) = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4045), (4126), (function-axioms) are
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4127)  all_56_11 = e2 & op(e1, e0) = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4127) implies:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4128)  all_56_11 = e2
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (230), (232),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (3783), (4056), (4087), (4128),
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #318.
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4129)  all_56_13 = e1 & op(e0, e2) = e1
% 153.60/22.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3772), (4129), (function-axioms) are
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #712.
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4130)  all_56_12 = e0 & op(e0, e3) = e0
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4130) implies:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4131)  op(e0, e3) = e0
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (139), (157), (158),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (168), (169), (170), (208), (214),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (223), (224), (226), (227), (228),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (239),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3772), (3773), (3774), (3776), (3784), (4042),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4045), (4053), (4054), (4055), (4056), (4061),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4063), (4090), (4091), (4131), (function-axioms)
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #320.
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | |   (4132)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4132) gives:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | |   (4133)  all_56_4 = e2 & op(e3, e1) = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4094), (4133) are inconsistent by sub-proof
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | |            #317.
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | |   (4134)  all_56_9 = e2 & op(e3, e0) = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4134) implies:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | |   (4135)  all_56_9 = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4099), (4135) are inconsistent by sub-proof
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | |            #316.
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | |   (4136)  all_56_5 = e1 & op(e2, e1) = e1
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | ALPHA: (4136) implies:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | |   (4137)  all_56_5 = e1
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (169), (208),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | |            (214), (220), (223), (224), (228), (229), (230),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (3776), (3784),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | |            (4045), (4054), (4056), (4063), (4091), (4137),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | |            #325.
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | |   (4138)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 153.60/22.30  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (3773), (4045), (4138),
% 153.60/22.30  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.30  | | | | | | | | | | | | | | | | | | |            #324.
% 153.60/22.30  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | |   (4139)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.60/22.30  | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 153.60/22.30  | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.60/22.30  | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.60/22.30  | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.60/22.30  | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 153.60/22.30  | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 153.60/22.30  | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 153.60/22.30  | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | ALPHA: (4139) implies:
% 153.60/22.30  | | | | | | | | | | | | | | | | | |   (4140)  op(e2, e2) = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4063), (4140), (function-axioms) are
% 153.60/22.30  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 153.60/22.30  | | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | |   (4141)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 153.60/22.30  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 153.60/22.30  | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 153.60/22.30  | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 153.60/22.30  | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 153.60/22.30  | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 153.60/22.30  | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 153.60/22.30  | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 153.60/22.30  | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 153.60/22.30  | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 153.60/22.30  | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 153.60/22.30  | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 153.60/22.30  | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 153.60/22.30  | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 153.60/22.30  | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 153.60/22.30  | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (3784), (4045), (4141),
% 153.60/22.30  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.30  | | | | | | | | | | | | | | | | |            #629.
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | |   (4142)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (4049), (4142) are
% 153.60/22.30  | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | |   (4143)  all_26_2 = e1
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | COMBINE_EQS: (307), (4143) imply:
% 153.60/22.30  | | | | | | | | | | | |   (4144)  all_6_2 = e1
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | SIMP: (4144) implies:
% 153.60/22.30  | | | | | | | | | | | |   (4145)  all_6_2 = e1
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | REDUCE: (340), (4145) imply:
% 153.60/22.30  | | | | | | | | | | | |   (4146)   ~ (all_52_2 = e1)
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | REDUCE: (39), (4145) imply:
% 153.60/22.30  | | | | | | | | | | | |   (4147)  op(e3, e3) = e1
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (51), (160), (163), (214), (238),
% 153.60/22.30  | | | | | | | | | | | |            (3776), (3784), (4045), (4146), (4147),
% 153.60/22.30  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.30  | | | | | | | | | | | |            #628.
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | |   (4148)  all_24_2 = e1
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | COMBINE_EQS: (318), (4148) imply:
% 153.60/22.30  | | | | | | | | | | |   (4149)  all_4_2 = e1
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | REDUCE: (354), (4149) imply:
% 153.60/22.30  | | | | | | | | | | |   (4150)   ~ (all_52_6 = e1)
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | REDUCE: (36), (4149) imply:
% 153.60/22.30  | | | | | | | | | | |   (4151)  op(e2, e2) = e1
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (51), (160), (162), (163), (214),
% 153.60/22.30  | | | | | | | | | | |            (238), (3776), (3784), (4045), (4150), (4151),
% 153.60/22.30  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.30  | | | | | | | | | | |            #592.
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | |   (4152)  all_20_2 = e3
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | COMBINE_EQS: (325), (4152) imply:
% 153.60/22.30  | | | | | | | | |   (4153)  all_10_2 = e3
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | SIMP: (4153) implies:
% 153.60/22.30  | | | | | | | | |   (4154)  all_10_2 = e3
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | REDUCE: (350), (4154) imply:
% 153.60/22.30  | | | | | | | | |   (4155)   ~ (all_52_2 = e3)
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | REDUCE: (361), (4154) imply:
% 153.60/22.30  | | | | | | | | |   (4156)   ~ (all_52_6 = e3)
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | REDUCE: (366), (4154) imply:
% 153.60/22.30  | | | | | | | | |   (4157)   ~ (all_52_11 = e3)
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | REDUCE: (368), (4154) imply:
% 153.60/22.30  | | | | | | | | |   (4158)   ~ (all_52_14 = e3)
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | REDUCE: (45), (4154) imply:
% 153.60/22.30  | | | | | | | | |   (4159)  op(e1, e1) = e3
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | BETA: splitting (3770) gives:
% 153.60/22.30  | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | |   (4160)   ~ (all_14_0 = e2) & op(e1, e0) = all_14_0 &
% 153.60/22.30  | | | | | | | | | |           $i(all_14_0)
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | ALPHA: (4160) implies:
% 153.60/22.30  | | | | | | | | | |   (4161)   ~ (all_14_0 = e2)
% 153.60/22.30  | | | | | | | | | |   (4162)  op(e1, e0) = all_14_0
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 153.60/22.30  | | | | | | | | | |              all_14_0, e0, e1, simplifying with (160), (4162)
% 153.60/22.30  | | | | | | | | | |              gives:
% 153.60/22.30  | | | | | | | | | |   (4163)  all_52_14 = all_14_0
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | COMBINE_EQS: (250), (4163) imply:
% 153.60/22.30  | | | | | | | | | |   (4164)  all_54_11 = all_14_0
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | REDUCE: (141), (4163) imply:
% 153.60/22.30  | | | | | | | | | |   (4165)   ~ (all_52_2 = all_14_0)
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | REDUCE: (126), (4163) imply:
% 153.60/22.30  | | | | | | | | | |   (4166)   ~ (all_52_6 = all_14_0)
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | REDUCE: (112), (4163) imply:
% 153.60/22.30  | | | | | | | | | |   (4167)   ~ (all_52_12 = all_14_0)
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | REDUCE: (4158), (4163) imply:
% 153.60/22.30  | | | | | | | | | |   (4168)   ~ (all_14_0 = e3)
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | REDUCE: (3776), (4163) imply:
% 153.60/22.30  | | | | | | | | | |   (4169)   ~ (all_14_0 = e1)
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | BETA: splitting (193) gives:
% 153.60/22.30  | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | |   (4170)  all_54_11 = e3
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | COMBINE_EQS: (4164), (4170) imply:
% 153.60/22.30  | | | | | | | | | | |   (4171)  all_14_0 = e3
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | REDUCE: (4168), (4171) imply:
% 153.60/22.30  | | | | | | | | | | |   (4172)  $false
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | CLOSE: (4172) is inconsistent.
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | |   (4173)   ~ (all_54_11 = e3)
% 153.60/22.30  | | | | | | | | | | |   (4174)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | BETA: splitting (4174) gives:
% 153.60/22.30  | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | |   (4175)  all_54_11 = e2
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | COMBINE_EQS: (4164), (4175) imply:
% 153.60/22.30  | | | | | | | | | | | |   (4176)  all_14_0 = e2
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | REDUCE: (4161), (4176) imply:
% 153.60/22.30  | | | | | | | | | | | |   (4177)  $false
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | CLOSE: (4177) is inconsistent.
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | |   (4178)   ~ (all_54_11 = e2)
% 153.60/22.30  | | | | | | | | | | | |   (4179)  all_54_11 = e1 | all_54_11 = e0
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | BETA: splitting (4179) gives:
% 153.60/22.30  | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | |   (4180)  all_54_11 = e1
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | COMBINE_EQS: (4164), (4180) imply:
% 153.60/22.30  | | | | | | | | | | | | |   (4181)  all_14_0 = e1
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | REDUCE: (4169), (4181) imply:
% 153.60/22.30  | | | | | | | | | | | | |   (4182)  $false
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | CLOSE: (4182) is inconsistent.
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | |   (4183)  all_54_11 = e0
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | COMBINE_EQS: (4164), (4183) imply:
% 153.60/22.30  | | | | | | | | | | | | |   (4184)  all_14_0 = e0
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | REDUCE: (4165), (4184) imply:
% 153.60/22.30  | | | | | | | | | | | | |   (4185)   ~ (all_52_2 = e0)
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | REDUCE: (4166), (4184) imply:
% 153.60/22.30  | | | | | | | | | | | | |   (4186)   ~ (all_52_6 = e0)
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | REDUCE: (4167), (4184) imply:
% 153.60/22.30  | | | | | | | | | | | | |   (4187)   ~ (all_52_12 = e0)
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | REDUCE: (4168), (4184) imply:
% 153.60/22.30  | | | | | | | | | | | | |   (4188)   ~ (e3 = e0)
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | REDUCE: (4161), (4184) imply:
% 153.60/22.30  | | | | | | | | | | | | |   (4189)   ~ (e2 = e0)
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | REDUCE: (4169), (4184) imply:
% 153.60/22.30  | | | | | | | | | | | | |   (4190)   ~ (e1 = e0)
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | REDUCE: (4162), (4184) imply:
% 153.60/22.30  | | | | | | | | | | | | |   (4191)  op(e1, e0) = e0
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | BETA: splitting (213) gives:
% 153.60/22.30  | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | |   (4192)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 153.60/22.30  | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 153.60/22.30  | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | BETA: splitting (4192) gives:
% 153.60/22.30  | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | |   (4193)  all_56_6 = e0 & op(e1, e3) = e0
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | ALPHA: (4193) implies:
% 153.60/22.30  | | | | | | | | | | | | | | |   (4194)  all_56_6 = e0
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | |   (4195)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 153.60/22.30  | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 153.60/22.30  | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | BETA: splitting (4195) gives:
% 153.60/22.30  | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | |   (4196)  all_56_6 = e2 & op(e1, e3) = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | ALPHA: (4196) implies:
% 153.60/22.30  | | | | | | | | | | | | | | | | |   (4197)  all_56_6 = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4194), (4197) are inconsistent by sub-proof
% 153.60/22.30  | | | | | | | | | | | | | | | | |            #916.
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | |   (4198)  all_56_7 = e2 & op(e1, e2) = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | ALPHA: (4198) implies:
% 153.60/22.30  | | | | | | | | | | | | | | | | |   (4199)  all_56_7 = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (214), (4159), (4191), (4194),
% 153.60/22.30  | | | | | | | | | | | | | | | | |            (4199), (function-axioms) are inconsistent by
% 153.60/22.30  | | | | | | | | | | | | | | | | |            sub-proof #315.
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | |   (4200)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 153.60/22.30  | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 153.60/22.30  | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | BETA: splitting (4200) gives:
% 153.60/22.30  | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | |   (4201)  all_56_8 = e2 & op(e1, e1) = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | ALPHA: (4201) implies:
% 153.60/22.30  | | | | | | | | | | | | | | | | |   (4202)  op(e1, e1) = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4159), (4202), (function-axioms) are
% 153.60/22.30  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | |   (4203)  all_56_11 = e2 & op(e1, e0) = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | ALPHA: (4203) implies:
% 153.60/22.30  | | | | | | | | | | | | | | | | |   (4204)  op(e1, e0) = e2
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4191), (4204), (function-axioms) are
% 153.60/22.30  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #397.
% 153.60/22.30  | | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | |   (4205)  all_56_7 = e0 & op(e1, e2) = e0
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | ALPHA: (4205) implies:
% 153.60/22.30  | | | | | | | | | | | | | | |   (4206)  all_56_7 = e0
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (214), (215), (216),
% 153.60/22.30  | | | | | | | | | | | | | | |            (4159), (4191), (4206), (function-axioms) are
% 153.60/22.30  | | | | | | | | | | | | | | |            inconsistent by sub-proof #311.
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | End of split
% 153.60/22.30  | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | Case 2:
% 153.60/22.30  | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | |   (4207)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 153.60/22.30  | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 153.60/22.30  | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | BETA: splitting (4207) gives:
% 153.60/22.30  | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | Case 1:
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | |   (4208)  all_56_8 = e0 & op(e1, e1) = e0
% 153.60/22.30  | | | | | | | | | | | | | | | 
% 153.60/22.30  | | | | | | | | | | | | | | | ALPHA: (4208) implies:
% 153.60/22.31  | | | | | | | | | | | | | | |   (4209)  op(e1, e1) = e0
% 153.60/22.31  | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | REF_CLOSE: (7), (4159), (4209), (function-axioms) are
% 153.60/22.31  | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 153.60/22.31  | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | |   (4210)  all_56_11 = e0 & op(e1, e0) = e0
% 153.60/22.31  | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | ALPHA: (4210) implies:
% 153.60/22.31  | | | | | | | | | | | | | | |   (4211)  all_56_11 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | |   (4212)   ~ (all_24_2 = e1)
% 153.60/22.31  | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | REDUCE: (318), (4212) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | |   (4213)   ~ (all_4_2 = e1)
% 153.60/22.31  | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | |   (4214)   ~ (all_26_2 = e1)
% 153.60/22.31  | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | REDUCE: (307), (4214) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | |   (4215)   ~ (all_6_2 = e1)
% 153.60/22.31  | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | |   (4216)  all_54_0 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (4216) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | |   (4217)  all_6_2 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | REDUCE: (346), (4217) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | |   (4218)   ~ (all_52_8 = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | REDUCE: (348), (4217) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | |   (4219)   ~ (all_52_12 = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | REDUCE: (39), (4217) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | |   (4220)  op(e3, e3) = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | |   (4221)  all_54_3 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (4219), (4221) are inconsistent by
% 153.60/22.31  | | | | | | | | | | | | | | | | | | |            sub-proof #310.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | |   (4222)   ~ (all_54_3 = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | |   (4223)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (4223) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | |   (4224)  all_54_3 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (4224) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | |   (4225)  all_52_12 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | SIMP: (4225) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | |   (4226)  all_52_12 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (4226) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | |   (4227)   ~ (all_52_4 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (4226) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | |   (4228)   ~ (all_52_8 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (4226) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | |   (4229)   ~ (all_52_13 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | SIMP: (4229) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | |   (4230)   ~ (all_52_13 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (4219), (4226) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | |   (4231)   ~ (e3 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | |   (4232)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4232) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | |   (4233)  all_56_12 = e3 & op(e0, e3) = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4233) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | |   (4234)  all_56_12 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | |            (4220), (4234), (function-axioms) are inconsistent
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | |   (4235)  all_56_13 = e3 & op(e0, e2) = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4235) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | |   (4236)  all_56_13 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | |   (4237)  op(e0, e2) = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | |   (4238)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4238) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | |   (4239)  all_56_9 = e3 & op(e3, e0) = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4239) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | |   (4240)  all_56_9 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | |            (4220), (4240), (function-axioms) are inconsistent
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #632.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | |   (4241)  all_56_10 = e3 & op(e2, e0) = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4241) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | |   (4242)  all_56_10 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (4243)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4243) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4244)  all_56_9 = e2 & op(e3, e0) = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4244) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4245)  all_56_9 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (4237) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4246)  all_52_7 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (4246) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4247)   ~ (all_52_3 = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (4246) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4248)   ~ (all_52_4 = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (4246) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4249)   ~ (all_4_2 = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4250)   ~ (all_32_2 = e0)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (4250) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4251)   ~ (all_4_2 = e0)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4252)  all_54_5 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (4252) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4253)  all_4_2 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (4253) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4254)  $false
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4254) is inconsistent.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4255)   ~ (all_54_5 = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4256)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4256) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4257)  all_54_5 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (4257) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4258)  all_4_2 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (4258) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4259)   ~ (all_52_6 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (4258) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4260)   ~ (all_52_9 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4258) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4261)  op(e2, e2) = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4262)  all_54_9 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (4156), (4262) are inconsistent by
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #656.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4263)   ~ (all_54_9 = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4264)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4264) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4265)  all_54_9 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (4259), (4265) are inconsistent by
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #676.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4266)   ~ (all_54_9 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4267)  all_54_9 = e1 | all_54_9 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4268)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4268) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4269)  all_56_6 = e2 & op(e1, e3) = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4269) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4270)  all_56_6 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4271)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4271) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4272)  all_56_0 = e1 & op(e3, e3) = e1
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4272) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4273)  op(e3, e3) = e1
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4220), (4273), (function-axioms) are
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4274)  all_56_2 = e1 & op(e2, e3) = e1
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4274) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4275)  all_56_2 = e1
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4267) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4276)  all_54_9 = e1
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (4276) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4277)  all_52_6 = e1
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4277) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4278)  all_52_6 = e1
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (4278) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4279)   ~ (all_52_2 = e1)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4156), (4278) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4280)   ~ (e3 = e1)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4281)  all_54_8 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4155), (4281) are inconsistent by
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #309.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4282)   ~ (all_54_8 = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4283)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4283) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4284)  all_54_8 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (4284) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4285)  all_52_2 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4285) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4286)  all_52_2 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (4286) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4287)   ~ (all_52_1 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (4286) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4288)   ~ (all_52_3 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4288) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4289)   ~ (all_52_3 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4290)  all_54_12 = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (4247), (4290) are inconsistent by
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #697.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4291)   ~ (all_54_12 = e3)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4292)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4292) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4293)  all_54_12 = e2
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (4289), (4293) are inconsistent by
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #696.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4294)   ~ (all_54_12 = e2)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4295)  all_54_12 = e1 | all_54_12 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4295) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4296)  all_54_12 = e1
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (3771), (4296) are inconsistent by
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #695.
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4297)  all_54_12 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (4297) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4298)  all_52_3 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4298) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4299)  all_52_3 = e0
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (4299) imply:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4300)   ~ (all_52_11 = e0)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4300) implies:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4301)   ~ (all_52_11 = e0)
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4302)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.60/22.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4302) gives:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4303)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (165), (167), (4260), (4279), (4287),
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4303), (function-axioms) are inconsistent by
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #652.
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4304)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4304) gives:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4305)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4305) gives:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4306)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (170), (206), (210),
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4242), (4245), (4248), (4306), (function-axioms)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #308.
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4307)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (164), (360), (4220), (4261), (4307),
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #706.
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4308)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4308) gives:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4309)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4309) gives:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4310)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4310) implies:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4311)  op(e1, e3) = e1
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4279), (4311), (function-axioms) are
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4312)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4312) implies:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4313)  op(e2, e2) = e1
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (4260), (4275), (4313), (function-axioms)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #355.
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4314)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4314) gives:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4315)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4315) implies:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4316)  op(e0, e1) = e0
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4301), (4316), (function-axioms) are
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4317)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4159), (4279), (4317), (function-axioms)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #649.
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4318)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 153.60/22.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4318) gives:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4319)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4319) gives:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4320)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4320) gives:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4321)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (4220), (4260), (4275), (4321),
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #352.
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4322)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4322) gives:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4323)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4323) implies:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4324)  op(e1, e1) = e2
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4159), (4324), (function-axioms) are
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4325)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4325) implies:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4326)  op(e0, e1) = e0
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4301), (4326), (function-axioms) are
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4327)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (206), (210),
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4159), (4218), (4220), (4242), (4245), (4327),
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #307.
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4328)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4328) gives:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4329)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4329) gives:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4330)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (165), (3784), (4260), (4330),
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #374.
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4331)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4331) gives:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4332)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4332) implies:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4333)  op(e2, e2) = e1
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (4260), (4275), (4333), (function-axioms)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #355.
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4334)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4334) implies:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4335)  op(e0, e0) = e3
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (206), (210), (4242),
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4245), (4335), (function-axioms) are inconsistent
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #471.
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4336)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 153.60/22.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4336) gives:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4337)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (3784), (4219), (4337),
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #373.
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4338)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4338) gives:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4339)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4339) implies:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4340)  op(e2, e0) = e2
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (4261), (4340),
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4341)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4341) gives:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4342)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4342) implies:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4343)  op(e1, e1) = e1
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4159), (4343), (function-axioms) are
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4344)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4344) implies:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4345)  op(e0, e0) = all_57_15
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4346)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4346) gives:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4347)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4347) gives:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4348)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4348) gives:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4349)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4349) implies:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4350)  op(e3, e3) = e0
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4220), (4350), (function-axioms) are
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4351)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (164), (360), (4159), (4261), (4351),
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #462.
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4352)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4352) gives:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4353)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4353) implies:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4354)  all_57_15 = e0
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4345), (4354) imply:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4355)  op(e0, e0) = e0
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (3784), (4355), (function-axioms) are
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4356)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (164), (360), (4220), (4261), (4356),
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #970.
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4357)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4357) gives:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4358)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (51), (3784), (4159), (4220), (4345),
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4358), (function-axioms) are inconsistent by
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #305.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4359)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4359) gives:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4360)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (164), (360), (4159), (4261), (4360),
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #461.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4361)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4301), (4361), (function-axioms) are
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4362)  all_54_8 = e1 | all_54_8 = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4185), (4279), (4362) are inconsistent by
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #612.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4363)  all_54_9 = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (4186), (4363) are inconsistent by
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #674.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4364)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (3771), (4270), (4364),
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #304.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4365)  all_56_7 = e2 & op(e1, e2) = e2
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4259), (4365), (function-axioms) are
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4366)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4366) gives:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4367)  all_56_8 = e2 & op(e1, e1) = e2
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4367) implies:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4368)  op(e1, e1) = e2
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4159), (4368), (function-axioms) are
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4369)  all_56_11 = e2 & op(e1, e0) = e2
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4369) implies:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4370)  all_56_11 = e2
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4371)  all_56_15 = e0 & op(e0, e0) = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4371) implies:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4372)  all_56_15 = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (210), (212), (230),
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (234), (4220), (4245), (4370), (4372),
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #302.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4373)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4373) implies:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4374)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4374) gives:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4375)  all_56_9 = e0 & op(e3, e0) = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4245), (4375) are inconsistent by sub-proof
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #950.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4376)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4376) gives:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4377)  all_56_10 = e0 & op(e2, e0) = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4377) implies:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4378)  all_56_10 = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4379)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4379) gives:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4380)  all_56_9 = e1 & op(e3, e0) = e1
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4245), (4380) are inconsistent by sub-proof
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #948.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4381)  all_56_10 = e1 & op(e2, e0) = e1
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4381) implies:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4382)  all_56_10 = e1
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4378), (4382) imply:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4383)  e1 = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4383) implies:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4384)  e1 = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (4384) imply:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4385)  $false
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4385) is inconsistent.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4386)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4386) gives:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4387)  all_56_11 = e1 & op(e1, e0) = e1
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4370), (4387) are inconsistent by sub-proof
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #469.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (230), (232),
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (3783), (4220), (4370), (4378),
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #318.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4210), (4370) are inconsistent by sub-proof
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #739.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4388)  all_54_5 = e1 | all_54_5 = e0
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (4213), (4251), (4388) are inconsistent by
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.60/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4389)  all_32_2 = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (4389) imply:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4390)  all_4_2 = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4390) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4391)  all_4_2 = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (4391) imply:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4392)   ~ (all_52_4 = e0)
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4391) imply:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4393)  op(e2, e2) = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4394)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4394) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4395)  all_56_0 = e0 & op(e3, e3) = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4395) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4396)  op(e3, e3) = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4220), (4396), (function-axioms) are
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4397)  all_56_1 = e0 & op(e3, e2) = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4397) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4398)  all_56_1 = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4399)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4399) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4400)  all_56_1 = e2 & op(e3, e2) = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (230), (232), (4220),
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4245), (4400), (function-axioms) are inconsistent
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #301.
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4401)  all_56_3 = e2 & op(e2, e2) = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4401) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4402)  op(e2, e2) = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4393), (4402), (function-axioms) are
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4403)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4403) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4404)  all_56_7 = e2 & op(e1, e2) = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4404) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4405)  all_56_7 = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (158), (226), (3772), (4393), (4398),
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4405), (function-axioms) are inconsistent by
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #603.
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4406)  all_56_13 = e2 & op(e0, e2) = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4406) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4407)  all_56_13 = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4236), (4407) are inconsistent by sub-proof
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #688.
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4408)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4408) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4409)  all_56_4 = e0 & op(e3, e1) = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4409) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4410)  all_56_4 = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4411)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4411) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4412)  all_56_1 = e2 & op(e3, e2) = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4412) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4413)  all_56_1 = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (232), (4220), (4245), (4410),
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4413), (function-axioms) are inconsistent by
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #300.
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4414)  all_56_3 = e2 & op(e2, e2) = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4414) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4415)  op(e2, e2) = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4393), (4415), (function-axioms) are
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4416)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4416) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4417)  all_56_7 = e2 & op(e1, e2) = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4417) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4418)  all_56_7 = e2
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4419)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4419) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4420)  all_56_0 = e0 & op(e3, e3) = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4420) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4421)  op(e3, e3) = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4220), (4421), (function-axioms) are
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4422)  all_56_2 = e0 & op(e2, e3) = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4422) implies:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4423)  all_56_2 = e0
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4424)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (4220), (4423), (4424),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #732.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4425)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4425) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4426)  all_56_6 = e1 & op(e1, e3) = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4426) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4427)  all_56_6 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4428)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4428) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4429)  all_56_2 = e1 & op(e2, e3) = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4429) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4430)  all_56_2 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4423), (4430) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4431)  e1 = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4431) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4432)  e1 = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4427), (4432) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4433)  all_56_6 = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (214), (4159), (4191), (4418),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4433), (function-axioms) are inconsistent by
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #315.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4434)  all_56_3 = e1 & op(e2, e2) = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4434) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4435)  op(e2, e2) = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4393), (4435), (function-axioms) are
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4436)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4436) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4437)  all_56_5 = e1 & op(e2, e1) = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4437) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4438)  all_56_5 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4439)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4439) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4440)  all_56_4 = e2 & op(e3, e1) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4440) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4441)  op(e3, e1) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4228), (4441), (function-axioms) are
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4442)  all_56_5 = e2 & op(e2, e1) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4438), (4442) are inconsistent by sub-proof
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #548.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4443)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4443) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4444)  all_56_8 = e2 & op(e1, e1) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4444) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4445)  op(e1, e1) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4159), (4445), (function-axioms) are
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4446)  all_56_14 = e2 & op(e0, e1) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4446) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4447)  all_56_14 = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (51), (136), (143), (159),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (169), (195), (203), (206), (210), (211),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (232), (233), (234), (238), (258), (272),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3784), (4156), (4159), (4186), (4211), (4227),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4228), (4236), (4245), (4248), (4392), (4393),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4410), (4447), (function-axioms) are inconsistent
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #296.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4448)  all_56_10 = e1 & op(e2, e0) = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (230), (232),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (3784), (4191), (4220), (4448),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #293.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4449)  all_56_12 = e1 & op(e0, e3) = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3771), (4449), (function-axioms) are
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #852.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4450)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4450) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4451)  all_56_6 = e0 & op(e1, e3) = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4451) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4452)  all_56_6 = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (214), (4159), (4191), (4418),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4452), (function-axioms) are inconsistent by
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #315.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4453)  all_56_12 = e0 & op(e0, e3) = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4453) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4454)  op(e0, e3) = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4455)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (159), (4236), (4454), (4455),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #687.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4456)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4456) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4457)  all_56_14 = e2 & op(e0, e1) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4457) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4458)  all_56_14 = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (51), (136), (143), (159),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (169), (195), (203), (206), (210), (211),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (232), (233), (234), (238), (258), (272),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3784), (4156), (4159), (4186), (4211), (4227),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4228), (4236), (4245), (4248), (4392), (4393),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4410), (4458), (function-axioms) are inconsistent
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #296.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4459)  all_56_15 = e2 & op(e0, e0) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4459) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4460)  op(e0, e0) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3784), (4460), (function-axioms) are
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4461)  all_56_13 = e2 & op(e0, e2) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4461) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4462)  all_56_13 = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4236), (4462) are inconsistent by sub-proof
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #688.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4463)  all_56_9 = e0 & op(e3, e0) = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4245), (4463) are inconsistent by sub-proof
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #950.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4464)  all_56_10 = e2 & op(e2, e0) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4464) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4465)  op(e2, e0) = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4230), (4465), (function-axioms) are
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (4466)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (3784), (4191), (4466),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            #292.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |   (4467)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (3784), (4158), (4467),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |            #291.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | |   (4468)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (3784), (4157), (4468),
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | |            #290.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | |   (4469)  all_54_3 = e1 | all_54_3 = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (3774), (4187), (4469) are inconsistent by
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | |            sub-proof #582.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | |   (4470)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (4215), (4470) are
% 153.80/22.36  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | End of split
% 153.80/22.36  | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | |   (4471)  all_26_2 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (4471) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | |   (4472)  all_6_2 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | SIMP: (4472) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | |   (4473)  all_6_2 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | REDUCE: (340), (4473) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | |   (4474)   ~ (all_52_2 = e1)
% 153.80/22.36  | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | REDUCE: (39), (4473) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | |   (4475)  op(e3, e3) = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | |   (4476)  all_54_8 = e3
% 153.80/22.36  | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4155), (4476) are inconsistent by
% 153.80/22.36  | | | | | | | | | | | | | | | | | |            sub-proof #309.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | |   (4477)   ~ (all_54_8 = e3)
% 153.80/22.36  | | | | | | | | | | | | | | | | | |   (4478)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | BETA: splitting (4478) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | |   (4479)  all_54_8 = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (4479) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | |   (4480)  all_52_2 = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | SIMP: (4480) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | |   (4481)  all_52_2 = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | REDUCE: (143), (4481) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | |   (4482)   ~ (all_52_6 = e2)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | SIMP: (4482) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | |   (4483)   ~ (all_52_6 = e2)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | REDUCE: (4155), (4481) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | |   (4484)   ~ (e3 = e2)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | |   (4485)  all_54_9 = e3
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (4156), (4485) are inconsistent by
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | |            sub-proof #656.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | |   (4486)   ~ (all_54_9 = e3)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | |   (4487)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4487) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | |   (4488)  all_54_9 = e2
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (4483), (4488) are inconsistent by
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | |            sub-proof #676.
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | |   (4489)  all_54_9 = e1 | all_54_9 = e0
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4489) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | |   (4490)  all_54_9 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (4490) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | |   (4491)  all_52_6 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | SIMP: (4491) implies:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | |   (4492)  all_52_6 = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4156), (4492) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | |   (4493)   ~ (e3 = e1)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (4492) imply:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | |   (4494)  op(e1, e2) = e1
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |   (4495)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4495) gives:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4496)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4496) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4497)  op(e3, e3) = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4475), (4497), (function-axioms) are
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4498)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4498) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4499)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4499) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (4500)  all_57_14 = e2 & op(e1, e1) = e2
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4500) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (4501)  op(e1, e1) = e2
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4159), (4501), (function-axioms) are
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (4502)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4502) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (4503)   ~ (all_57_3 = e1)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (4504)  op(e1, e2) = all_57_3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4494), (4503), (4504), (function-axioms) are
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #631.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |   (4505)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (3784), (4159), (4505),
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |            #297.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | |   (4506)  all_54_9 = e0
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (4186), (4506) are inconsistent by
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #674.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | |   (4507)  all_54_8 = e1 | all_54_8 = e0
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4185), (4474), (4507) are inconsistent by
% 153.80/22.37  | | | | | | | | | | | | | | | | | | |            sub-proof #612.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.37  | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | End of split
% 153.80/22.37  | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | End of split
% 153.80/22.37  | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | |   (4508)  all_24_2 = e1
% 153.80/22.37  | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (4508) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | |   (4509)  all_4_2 = e1
% 153.80/22.37  | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | REDUCE: (354), (4509) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | |   (4510)   ~ (all_52_6 = e1)
% 153.80/22.37  | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | REDUCE: (373), (4509) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | |   (4511)   ~ (e3 = e1)
% 153.80/22.37  | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | REDUCE: (36), (4509) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | |   (4512)  op(e2, e2) = e1
% 153.80/22.37  | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | |   (4513)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.80/22.37  | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 153.80/22.37  | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.80/22.37  | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.80/22.37  | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.80/22.37  | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 153.80/22.37  | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 153.80/22.37  | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 153.80/22.37  | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 153.80/22.37  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 153.80/22.37  | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 153.80/22.37  | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 153.80/22.37  | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 153.80/22.37  | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 153.80/22.37  | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 153.80/22.37  | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 153.80/22.37  | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | BETA: splitting (4513) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | |   (4514)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 153.80/22.37  | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 153.80/22.37  | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 153.80/22.37  | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | ALPHA: (4514) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | |   (4515)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 153.80/22.37  | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 153.80/22.37  | | | | | | | | | | | | | | | | | |   (4516)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2
% 153.80/22.37  | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))
% 153.80/22.37  | | | | | | | | | | | | | | | | | |   (4517)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0
% 153.80/22.37  | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))
% 153.80/22.37  | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | |   (4518)  all_54_9 = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (4156), (4518) are inconsistent by
% 153.80/22.37  | | | | | | | | | | | | | | | | | | |            sub-proof #656.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | |   (4519)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (4519) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | |   (4520)  all_54_9 = e2
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (4520) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | |   (4521)  all_52_6 = e2
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | SIMP: (4521) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | |   (4522)  all_52_6 = e2
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (4522) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | |   (4523)   ~ (all_52_2 = e2)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | |   (4524)  all_54_8 = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4155), (4524) are inconsistent by
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | |            sub-proof #309.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | |   (4525)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4525) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | |   (4526)  all_54_8 = e2
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4523), (4526) are inconsistent by
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #608.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | |   (4527)   ~ (all_54_8 = e2)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | |   (4528)  all_54_8 = e1 | all_54_8 = e0
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4528) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |   (4529)  all_54_8 = e1
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (4529) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |   (4530)  all_52_2 = e1
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4530) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |   (4531)  all_52_2 = e1
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (340), (4531) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |   (4532)   ~ (all_6_2 = e1)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4532) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |   (4533)   ~ (all_6_2 = e1)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4523), (4531) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | |   (4534)   ~ (e2 = e1)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4535)  all_54_0 = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (4535) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4536)  all_6_2 = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (4536) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4537)   ~ (all_52_4 = e3)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (4536) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4538)   ~ (all_52_8 = e3)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (4536) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4539)   ~ (all_52_12 = e3)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (4536) imply:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4540)  op(e3, e3) = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (4541)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4541) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4542)  all_56_9 = e3 & op(e3, e0) = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4542) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4543)  all_56_9 = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4540), (4543), (function-axioms) are inconsistent
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #632.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4544)  all_56_10 = e3 & op(e2, e0) = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4544) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4545)  all_56_10 = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4546)  op(e2, e0) = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4547)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4547) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4548)  all_56_9 = e2 & op(e3, e0) = e2
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4548) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4549)  all_56_9 = e2
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4515) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4550)  all_57_15 = e3 & op(e0, e0) = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4550) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4551)  op(e0, e0) = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (206), (210), (4545),
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4549), (4551), (function-axioms) are inconsistent
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #471.
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4552)   ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_6)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4552) implies:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4553)   ~ (all_57_6 = e0)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4554)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4554) gives:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4555)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4555) gives:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4556)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4556) gives:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4557)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4557) gives:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4558)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4558) implies:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4559)  op(e2, e3) = e2
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4512), (4517), (4559), (function-axioms) are
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #782.
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4560)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4560) implies:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4561)  op(e2, e3) = e2
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4512), (4517), (4561), (function-axioms) are
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #782.
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4562)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4562) gives:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4563)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4563) implies:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4564)  op(e2, e3) = e2
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4512), (4517), (4564), (function-axioms) are
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #782.
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4565)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4565) implies:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4566)  op(e2, e3) = e2
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4512), (4517), (4566), (function-axioms) are
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #782.
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4567)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4567) gives:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.80/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4568)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4568) gives:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4569)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4569) implies:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4570)  op(e2, e3) = e2
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4512), (4517), (4570), (function-axioms) are
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #782.
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4571)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4571) implies:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4572)  op(e2, e3) = e2
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4512), (4517), (4572), (function-axioms) are
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #782.
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4573)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4573) gives:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4574)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4574) implies:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4575)  op(e2, e3) = e2
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4512), (4517), (4575), (function-axioms) are
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #782.
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4576)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (4537), (4540), (4576),
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #538.
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4577)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4577) gives:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4578)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4578) gives:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4579)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (170), (206), (210),
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4537), (4545), (4549), (4579), (function-axioms)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #308.
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4580)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (4540), (4546), (4580),
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #579.
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4581)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4581) gives:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4582)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4582) gives:
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4583)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4583) implies:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4584)  op(e3, e1) = e3
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4538), (4584), (function-axioms) are
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4585)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4585) implies:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4586)  all_57_2 = e1
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4587)   ~ (all_57_14 = e3)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4516), (4586), (4587) are inconsistent by
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #749.
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4588)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4588) gives:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4589)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4589) implies:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4590)  all_57_2 = e1
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4591)   ~ (all_57_14 = e3)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4516), (4590), (4591) are inconsistent by
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #749.
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4592)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4159), (4539), (4592), (function-axioms)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #578.
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4593)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4593) gives:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4594)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4594) gives:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4595)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4595) gives:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4596)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (4510), (4540), (4596),
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #788.
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4597)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4597) gives:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4598)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4598) implies:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4599)  op(e1, e1) = e2
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4159), (4599), (function-axioms) are
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4600)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4600) implies:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4601)  op(e1, e2) = e1
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4510), (4601), (function-axioms) are
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #984.
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4602)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (206), (210),
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4159), (4538), (4540), (4545), (4549), (4602),
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #307.
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4603)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4603) gives:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4604)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4604) gives:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4605)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3784), (4512), (4605), (function-axioms) are
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #337.
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4606)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4606) gives:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4607)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4607) implies:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4608)  op(e1, e0) = e1
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4191), (4608), (function-axioms) are
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #545.
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4609)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4609) implies:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4610)  op(e0, e0) = e3
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (206), (210), (4545),
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4549), (4610), (function-axioms) are inconsistent
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #471.
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4611)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4611) gives:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4612)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (3784), (4539), (4612),
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #373.
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4613)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4613) gives:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4614)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4614) implies:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4615)  op(e2, e2) = e2
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4512), (4615), (function-axioms) are
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.86/22.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4616)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.04/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4616) gives:
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4617)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4617) implies:
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4618)  op(e1, e1) = e1
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4159), (4618), (function-axioms) are
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4619)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4619) implies:
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4620)  op(e0, e0) = all_57_15
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4621)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4621) gives:
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4622)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4622) gives:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4623)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (4159), (4515), (4546), (4623),
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #517.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4624)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4624) gives:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4625)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4625) implies:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4626)  all_57_6 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4553), (4626) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4627)  $false
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4627) is inconsistent.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4628)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (4540), (4546), (4628),
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #574.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4629)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4629) gives:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4630)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (51), (3784), (4159), (4540), (4620),
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4630), (function-axioms) are inconsistent by
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #305.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4631)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4631) gives:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4632)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (4159), (4546), (4632),
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #572.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4633)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (3784), (4191), (4620), (4633),
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #289.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4634)  all_56_10 = e2 & op(e2, e0) = e2
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4634) implies:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4635)  op(e2, e0) = e2
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4546), (4635), (function-axioms) are
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #580.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4636)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (3784), (4191), (4636),
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #292.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (4637)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (3784), (4158), (4637),
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | |            #291.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | |   (4638)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (377), (4533), (4638) are
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | |   (4639)  all_54_8 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4185), (4639) are inconsistent by
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #613.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | |   (4640)  all_54_9 = e1 | all_54_9 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (4186), (4510), (4640) are inconsistent by
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | |            sub-proof #478.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | |   (4641)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.13/22.45  | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 154.13/22.45  | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.13/22.45  | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.13/22.45  | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.13/22.45  | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 154.13/22.45  | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | ALPHA: (4641) implies:
% 154.13/22.45  | | | | | | | | | | | | | | | | | |   (4642)  op(e2, e2) = e2
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4512), (4642), (function-axioms) are
% 154.13/22.45  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | |   (4643)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.13/22.45  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.13/22.45  | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.13/22.45  | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.13/22.45  | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.13/22.45  | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.13/22.45  | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.13/22.45  | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.13/22.45  | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.13/22.45  | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.13/22.45  | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.13/22.45  | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.13/22.45  | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.13/22.45  | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.13/22.45  | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.13/22.45  | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (3784), (4159), (4643),
% 154.13/22.45  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.45  | | | | | | | | | | | | | | | | |            #297.
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | |   (4644)   ~ (all_14_1 = e3) & op(e1, e1) = all_14_1 &
% 154.13/22.45  | | | | | | | | | |           $i(all_14_1)
% 154.13/22.45  | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | REF_CLOSE: (4159), (4644), (function-axioms) are inconsistent
% 154.13/22.45  | | | | | | | | | |            by sub-proof #288.
% 154.13/22.45  | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | | 
% 154.13/22.45  | | | | | | | | End of split
% 154.13/22.45  | | | | | | | | 
% 154.13/22.45  | | | | | | | End of split
% 154.13/22.45  | | | | | | | 
% 154.13/22.45  | | | | | | End of split
% 154.13/22.45  | | | | | | 
% 154.13/22.45  | | | | | End of split
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | Case 2:
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | |   (4645)  all_12_2 = e2
% 154.13/22.45  | | | | |   (4646)  ( ~ (all_12_0 = e0) & op(e2, e3) = all_12_0 & $i(all_12_0))
% 154.13/22.45  | | | | |           | ( ~ (all_12_1 = e1) & op(e2, e2) = all_12_1 &
% 154.13/22.45  | | | | |             $i(all_12_1))
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | | COMBINE_EQS: (324), (4645) imply:
% 154.13/22.45  | | | | |   (4647)  all_6_2 = e2
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | | COMBINE_EQS: (281), (4647) imply:
% 154.13/22.45  | | | | |   (4648)  all_46_2 = e2
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | | REDUCE: (338), (4647) imply:
% 154.13/22.45  | | | | |   (4649)   ~ (all_52_1 = e2)
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | | REDUCE: (340), (4647) imply:
% 154.13/22.45  | | | | |   (4650)   ~ (all_52_2 = e2)
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | | REDUCE: (342), (4647) imply:
% 154.13/22.45  | | | | |   (4651)   ~ (all_52_3 = e2)
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | | REDUCE: (344), (4647) imply:
% 154.13/22.45  | | | | |   (4652)   ~ (all_52_4 = e2)
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | | REDUCE: (346), (4647) imply:
% 154.13/22.45  | | | | |   (4653)   ~ (all_52_8 = e2)
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | | REDUCE: (348), (4647) imply:
% 154.13/22.45  | | | | |   (4654)   ~ (all_52_12 = e2)
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | | BETA: splitting (234) gives:
% 154.13/22.45  | | | | | 
% 154.13/22.45  | | | | | Case 1:
% 154.13/22.45  | | | | | | 
% 154.13/22.45  | | | | | |   (4655)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 &
% 154.13/22.45  | | | | | |             op(e3, e2) = e2)
% 154.13/22.45  | | | | | | 
% 154.13/22.45  | | | | | | BETA: splitting (4655) gives:
% 154.13/22.45  | | | | | | 
% 154.13/22.45  | | | | | | Case 1:
% 154.13/22.45  | | | | | | | 
% 154.13/22.45  | | | | | | |   (4656)  all_56_0 = e2 & op(e3, e3) = e2
% 154.13/22.45  | | | | | | | 
% 154.13/22.45  | | | | | | | ALPHA: (4656) implies:
% 154.13/22.45  | | | | | | |   (4657)  all_56_0 = e2
% 154.13/22.45  | | | | | | |   (4658)  op(e3, e3) = e2
% 154.13/22.45  | | | | | | | 
% 154.13/22.45  | | | | | | | BETA: splitting (52) gives:
% 154.13/22.45  | | | | | | | 
% 154.13/22.45  | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | 
% 154.13/22.45  | | | | | | | |   (4659)   ~ (all_14_2 = e1)
% 154.13/22.45  | | | | | | | | 
% 154.13/22.45  | | | | | | | | BETA: splitting (58) gives:
% 154.13/22.45  | | | | | | | | 
% 154.13/22.45  | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | 
% 154.13/22.45  | | | | | | | | |   (4660)   ~ (all_18_2 = e3)
% 154.13/22.45  | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | REDUCE: (301), (4660) imply:
% 154.13/22.45  | | | | | | | | |   (4661)   ~ (all_14_2 = e3)
% 154.13/22.45  | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | BETA: splitting (61) gives:
% 154.13/22.45  | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | |   (4662)   ~ (all_20_2 = e3)
% 154.13/22.45  | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | REDUCE: (325), (4662) imply:
% 154.13/22.45  | | | | | | | | | |   (4663)   ~ (all_10_2 = e3)
% 154.13/22.45  | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | BETA: splitting (64) gives:
% 154.13/22.45  | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | |   (4664)   ~ (all_22_2 = e0)
% 154.13/22.45  | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | REDUCE: (251), (4664) imply:
% 154.13/22.45  | | | | | | | | | | |   (4665)   ~ (all_10_2 = e0)
% 154.13/22.45  | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | BETA: splitting (194) gives:
% 154.13/22.45  | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | |   (4666)  all_54_10 = e3
% 154.13/22.45  | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | COMBINE_EQS: (336), (4666) imply:
% 154.13/22.45  | | | | | | | | | | | |   (4667)  all_10_2 = e3
% 154.13/22.45  | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | REDUCE: (4663), (4667) imply:
% 154.13/22.45  | | | | | | | | | | | |   (4668)  $false
% 154.13/22.45  | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | CLOSE: (4668) is inconsistent.
% 154.13/22.45  | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | |   (4669)   ~ (all_54_10 = e3)
% 154.13/22.45  | | | | | | | | | | | |   (4670)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.13/22.45  | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | BETA: splitting (4670) gives:
% 154.13/22.45  | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | |   (4671)  all_54_10 = e2
% 154.13/22.45  | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | COMBINE_EQS: (336), (4671) imply:
% 154.13/22.45  | | | | | | | | | | | | |   (4672)  all_10_2 = e2
% 154.13/22.45  | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | REDUCE: (375), (4672) imply:
% 154.13/22.45  | | | | | | | | | | | | |   (4673)  $false
% 154.13/22.45  | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | CLOSE: (4673) is inconsistent.
% 154.13/22.45  | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | |   (4674)   ~ (all_54_10 = e2)
% 154.13/22.45  | | | | | | | | | | | | |   (4675)  all_54_10 = e1 | all_54_10 = e0
% 154.13/22.45  | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | BETA: splitting (4675) gives:
% 154.13/22.45  | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | |   (4676)  all_54_10 = e1
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | COMBINE_EQS: (336), (4676) imply:
% 154.13/22.45  | | | | | | | | | | | | | |   (4677)  all_10_2 = e1
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | REDUCE: (350), (4677) imply:
% 154.13/22.45  | | | | | | | | | | | | | |   (4678)   ~ (all_52_2 = e1)
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | REDUCE: (361), (4677) imply:
% 154.13/22.45  | | | | | | | | | | | | | |   (4679)   ~ (all_52_6 = e1)
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | REDUCE: (363), (4677) imply:
% 154.13/22.45  | | | | | | | | | | | | | |   (4680)   ~ (all_52_8 = e1)
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | REDUCE: (364), (4677) imply:
% 154.13/22.45  | | | | | | | | | | | | | |   (4681)   ~ (all_52_9 = e1)
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | REDUCE: (366), (4677) imply:
% 154.13/22.45  | | | | | | | | | | | | | |   (4682)   ~ (all_52_11 = e1)
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | REDUCE: (368), (4677) imply:
% 154.13/22.45  | | | | | | | | | | | | | |   (4683)   ~ (all_52_14 = e1)
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | REDUCE: (4663), (4677) imply:
% 154.13/22.45  | | | | | | | | | | | | | |   (4684)   ~ (e3 = e1)
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | REDUCE: (375), (4677) imply:
% 154.13/22.45  | | | | | | | | | | | | | |   (4685)   ~ (e2 = e1)
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | REDUCE: (45), (4677) imply:
% 154.13/22.45  | | | | | | | | | | | | | |   (4686)  op(e1, e1) = e1
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 154.13/22.45  | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | |   (4687)   ~ (all_24_2 = e1)
% 154.13/22.45  | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | REDUCE: (318), (4687) imply:
% 154.13/22.45  | | | | | | | | | | | | | | |   (4688)   ~ (all_4_2 = e1)
% 154.13/22.45  | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 154.13/22.45  | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | |   (4689)   ~ (all_28_2 = e2)
% 154.13/22.45  | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | REDUCE: (330), (4689) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | |   (4690)   ~ (all_14_2 = e2)
% 154.13/22.45  | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 154.13/22.45  | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | |   (4691)  all_54_15 = e3
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4691) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | |   (4692)  all_14_2 = e3
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | REDUCE: (4661), (4692) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | |   (4693)  $false
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | CLOSE: (4693) is inconsistent.
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | |   (4694)   ~ (all_54_15 = e3)
% 154.13/22.45  | | | | | | | | | | | | | | | | |   (4695)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | BETA: splitting (4695) gives:
% 154.13/22.45  | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | |   (4696)  all_54_15 = e2
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4696) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | |   (4697)  all_14_2 = e2
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | REDUCE: (4690), (4697) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | |   (4698)  $false
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | CLOSE: (4698) is inconsistent.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | |   (4699)   ~ (all_54_15 = e2)
% 154.13/22.45  | | | | | | | | | | | | | | | | | |   (4700)  all_54_15 = e1 | all_54_15 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | BETA: splitting (4700) gives:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4701)  all_54_15 = e1
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4701) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4702)  all_14_2 = e1
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | REDUCE: (4659), (4702) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4703)  $false
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | CLOSE: (4703) is inconsistent.
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4704)  all_54_15 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4704) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4705)  all_14_2 = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | REDUCE: (351), (4705) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4706)   ~ (all_52_3 = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | REDUCE: (362), (4705) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4707)   ~ (all_52_7 = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | REDUCE: (369), (4705) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4708)   ~ (all_52_11 = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | REDUCE: (4661), (4705) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4709)   ~ (e3 = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | REDUCE: (4690), (4705) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4710)   ~ (e2 = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | REDUCE: (4659), (4705) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4711)   ~ (e1 = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | REDUCE: (51), (4705) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | |   (4712)  op(e0, e0) = e0
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | |   (4713)   ~ (all_32_2 = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (4713) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | |   (4714)   ~ (all_4_2 = e0)
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | |   (4715)  all_54_5 = e3
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (4715) imply:
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | |   (4716)  all_4_2 = e3
% 154.13/22.45  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (4716) imply:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | |   (4717)  $false
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | CLOSE: (4717) is inconsistent.
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | |   (4718)   ~ (all_54_5 = e3)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | |   (4719)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4719) gives:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | |   (4720)  all_54_5 = e2
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (4720) imply:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | |   (4721)  all_4_2 = e2
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (4721) imply:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | |   (4722)   ~ (all_52_9 = e2)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (4721) imply:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | |   (4723)   ~ (all_52_13 = e2)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (4721) imply:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | |   (4724)   ~ (e3 = e2)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4721) imply:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | |   (4725)  op(e2, e2) = e2
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |   (4726)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4726) gives:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |   (4727)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (167), (4649), (4686), (4722), (4727),
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |            #1000.
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |   (4728)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4728) gives:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (4729)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4729) gives:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4730)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4658), (4712), (4730), (function-axioms) are
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #287.
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4731)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (4658), (4723), (4731),
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            #286.
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (4732)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4732) gives:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4733)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4686), (4725), (4733),
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            #992.
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4734)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (163), (4678), (4686), (4712),
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4734), (function-axioms) are inconsistent by
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #988.
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |   (4735)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4735) gives:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |   (4736)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4736) gives:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (4737)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4737) gives:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4738)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4658), (4725), (4738), (function-axioms) are
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #285.
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4739)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (4686), (4712), (4739),
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            #985.
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (4740)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.13/22.46  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4740) gives:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4741)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (4679), (4686), (4741),
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4742)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (4658), (4712), (4742),
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            #283.
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |   (4743)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4743) gives:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (4744)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4744) gives:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4745)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (165), (4712), (4722), (4745),
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            #978.
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4746)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (4712), (4725), (4746),
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            #977.
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (4747)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4747) gives:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4748)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (4658), (4712), (4748),
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            #282.
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4749)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4749) gives:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4750)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4750) implies:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4751)  op(e2, e0) = e2
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4723), (4751), (function-axioms) are
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4752)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (157), (158), (159), (160), (4658),
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4683), (4686), (4706), (4707), (4708), (4752),
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #276.
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | |   (4753)  all_54_5 = e1 | all_54_5 = e0
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (4688), (4714), (4753) are inconsistent by
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.47  | | | | | | | | | | | | | | | | | | | |   (4754)  all_32_2 = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (4754) imply:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | |   (4755)  all_4_2 = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (4755) imply:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | |   (4756)   ~ (all_52_4 = e0)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (4755) imply:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | |   (4757)   ~ (all_52_9 = e0)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4755) imply:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | |   (4758)  op(e2, e2) = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | |   (4759)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4759) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | |   (4760)  all_56_0 = e0 & op(e3, e3) = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4760) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | |   (4761)  op(e3, e3) = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (4761), (function-axioms) are
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | |   (4762)  all_56_2 = e0 & op(e2, e3) = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4762) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | |   (4763)  all_56_2 = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | |   (4764)  op(e2, e3) = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |   (4765)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4758), (4763), (4765), (function-axioms) are
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #535.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |   (4766)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4766) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |   (4767)  all_56_5 = e1 & op(e2, e1) = e1
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4681), (4767), (function-axioms) are
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |   (4768)  all_56_10 = e1 & op(e2, e0) = e1
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4768) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |   (4769)  all_56_10 = e1
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (4770)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4770) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4771)  all_56_2 = e3 & op(e2, e3) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4771) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4772)  all_56_2 = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4763), (4772) are inconsistent by sub-proof
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |            #275.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4773)  all_56_3 = e3 & op(e2, e2) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4773) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4774)  op(e2, e2) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4758), (4774), (function-axioms) are
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (4775)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4775) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4776)  all_56_5 = e3 & op(e2, e1) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4776) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4777)  all_56_5 = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4778)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4778) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4779)  all_56_2 = e2 & op(e2, e3) = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4779) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4780)  op(e2, e3) = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4764), (4780), (function-axioms) are
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #709.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4781)  all_56_3 = e2 & op(e2, e2) = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4781) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4782)  op(e2, e2) = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4758), (4782), (function-axioms) are
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4783)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4783) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4784)  all_56_5 = e2 & op(e2, e1) = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4777), (4784) are inconsistent by sub-proof
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #668.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4785)  all_56_10 = e2 & op(e2, e0) = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4785) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4786)  all_56_10 = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (222), (4758), (4763), (4777),
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4786), (function-axioms) are inconsistent by
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #436.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4787)  all_56_10 = e3 & op(e2, e0) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4787) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4788)  all_56_10 = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4769), (4788) are inconsistent by sub-proof
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |            #887.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | |   (4789)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4789) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | |   (4790)  all_56_6 = e0 & op(e1, e3) = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4790) implies:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | |   (4791)  op(e1, e3) = e0
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |   (4792)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4792) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |   (4793)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4793) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (4794)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (4794), (function-axioms) are
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (4795)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4795) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4796)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (4796), (function-axioms) are
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4797)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4797) gives:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4798)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4798) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4799)  op(e2, e3) = e2
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (4799), (function-axioms) are
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4800)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4800) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4801)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4801) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4802)  op(e1, e1) = e3
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4686), (4802), (function-axioms) are
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4803)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4803) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4804)  all_57_5 = e2
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4805)   ~ (all_57_12 = e1)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4806)  op(e2, e1) = e2
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4807)  op(e2, e2) = all_57_12
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4808)  op(e3, e2) = e3
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4809)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4809) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4810)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4810) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4811)  op(e3, e3) = e3
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (4811), (function-axioms) are
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4812)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4812) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4813)  op(e2, e2) = e2
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4758), (4813), (function-axioms) are
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4814)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4814) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4815)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4815) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4816)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4804), (4805), (4807), (4816), (function-axioms)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #274.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4817)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4817) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4818)  (all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4818) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4819)  all_57_10 = e0 & op(e3, e3) = e0
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4819) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4820)  op(e3, e3) = e0
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (4820), (function-axioms) are
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4821)   ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_9)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4821) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4822)  op(e3, e0) = all_57_9
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (4791) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4823)  all_52_2 = e0
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (4806) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4824)  all_52_9 = e2
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9, e0, e3, simplifying with (168), (4822)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4825)  all_57_9 = all_52_12
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (4808) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4826)  all_52_4 = e3
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (4826) imply:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4827)   ~ (all_52_6 = e3)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4827) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4828)   ~ (all_52_6 = e3)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (4824) imply:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4829)   ~ (all_52_13 = e2)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4829) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4830)   ~ (all_52_13 = e2)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4831)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (4654), (4830), (4831),
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #384.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4832)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4832) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4833)  all_56_11 = e2 & op(e1, e0) = e2
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4833) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4834)  all_56_11 = e2
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (162), (216), (4686), (4791),
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4828), (4834), (function-axioms) are inconsistent
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #273.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4835)  all_56_15 = e2 & op(e0, e0) = e2
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4835) implies:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4836)  op(e0, e0) = e2
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4712), (4836), (function-axioms) are
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |   (4837)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4837) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (4838)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (4658), (4712), (4758), (4838),
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |            #272.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (4839)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4839) gives:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4840)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (4686), (4758), (4840),
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            #921.
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4841)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (163), (4678), (4686), (4712),
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4841), (function-axioms) are inconsistent by
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #988.
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |   (4842)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4842) gives:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |   (4843)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4843) gives:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (4844)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4844) gives:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4845)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (4658), (4758), (4845),
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            #271.
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4846)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (4686), (4712), (4846),
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            #985.
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (4847)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4847) gives:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4848)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (4679), (4686), (4848),
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4849)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (4658), (4712), (4849),
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            #283.
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |   (4850)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4850) gives:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (4851)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.13/22.50  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (4712), (4758), (4851),
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |            #918.
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (4852)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4852) gives:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4853)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (4658), (4712), (4853),
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            #282.
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4854)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4854) gives:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4855)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4855) implies:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4856)  op(e2, e2) = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4758), (4856), (function-axioms) are
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4857)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (157), (158), (159), (160), (4658),
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4683), (4686), (4706), (4707), (4708), (4857),
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #276.
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | |   (4858)  all_56_12 = e0 & op(e0, e3) = e0
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4858) implies:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | |   (4859)  op(e0, e3) = e0
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4706), (4859), (function-axioms) are
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | End of split
% 154.13/22.51  | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | Case 2:
% 154.13/22.51  | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | |   (4860)  all_28_2 = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (4860) imply:
% 154.13/22.51  | | | | | | | | | | | | | | | |   (4861)  all_14_2 = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | SIMP: (4861) implies:
% 154.13/22.51  | | | | | | | | | | | | | | | |   (4862)  all_14_2 = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | REDUCE: (369), (4862) imply:
% 154.13/22.51  | | | | | | | | | | | | | | | |   (4863)   ~ (all_52_11 = e2)
% 154.13/22.51  | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | REDUCE: (4661), (4862) imply:
% 154.13/22.51  | | | | | | | | | | | | | | | |   (4864)   ~ (e3 = e2)
% 154.13/22.51  | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | REDUCE: (51), (4862) imply:
% 154.13/22.51  | | | | | | | | | | | | | | | |   (4865)  op(e0, e0) = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 154.13/22.51  | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.51  | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | |   (4866)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 154.13/22.51  | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | BETA: splitting (4866) gives:
% 154.13/22.51  | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | |   (4867)  all_56_4 = e2 & op(e3, e1) = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | ALPHA: (4867) implies:
% 154.13/22.51  | | | | | | | | | | | | | | | | | |   (4868)  op(e3, e1) = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4653), (4868), (function-axioms) are
% 154.13/22.51  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | Case 2:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | |   (4869)  all_56_5 = e2 & op(e2, e1) = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | ALPHA: (4869) implies:
% 154.13/22.51  | | | | | | | | | | | | | | | | | |   (4870)  op(e2, e1) = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 154.13/22.51  | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (4870) gives:
% 154.13/22.51  | | | | | | | | | | | | | | | | | |   (4871)  all_52_9 = e2
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | REDUCE: (117), (4871) imply:
% 154.13/22.51  | | | | | | | | | | | | | | | | | |   (4872)   ~ (all_52_13 = e2)
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | SIMP: (4872) implies:
% 154.13/22.51  | | | | | | | | | | | | | | | | | |   (4873)   ~ (all_52_13 = e2)
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | REDUCE: (358), (4871) imply:
% 154.13/22.51  | | | | | | | | | | | | | | | | | |   (4874)   ~ (all_4_2 = e2)
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | SIMP: (4874) implies:
% 154.13/22.51  | | | | | | | | | | | | | | | | | |   (4875)   ~ (all_4_2 = e2)
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |   (4876)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.13/22.51  | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | BETA: splitting (4876) gives:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | 
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.13/22.51  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |   (4877)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | ALPHA: (4877) implies:
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |   (4878)  op(e3, e3) = e3
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (4878), (function-axioms) are
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |   (4879)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | ALPHA: (4879) implies:
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |   (4880)  op(e2, e2) = e2
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (4688), (4875), (4880),
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | |            #927.
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.51  | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.51  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.51  | | | | | | | | | | | | | | | | | | |   (4881)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.28/22.51  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.28/22.51  | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.28/22.51  | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.28/22.51  | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.28/22.51  | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.28/22.51  | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.28/22.51  | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.28/22.51  | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.28/22.52  | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (4881) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |   (4882)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (4882) implies:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |   (4883)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |   (4884)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4883) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | |   (4885)  all_57_15 = e1 & op(e0, e0) = e1
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4885) implies:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | |   (4886)  op(e0, e0) = e1
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4865), (4886), (function-axioms) are
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | |   (4887)   ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_8)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4887) implies:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | |   (4888)   ~ (all_57_8 = e0)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | |   (4889)  all_54_5 = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (4889) imply:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | |   (4890)  all_4_2 = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (4890) imply:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | |   (4891)  $false
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4891) is inconsistent.
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | |   (4892)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4892) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | |   (4893)  all_54_5 = e2
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (4893) imply:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | |   (4894)  all_4_2 = e2
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4875), (4894) imply:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | |   (4895)  $false
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4895) is inconsistent.
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | |   (4896)   ~ (all_54_5 = e2)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | |   (4897)  all_54_5 = e1 | all_54_5 = e0
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |   (4898)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4898) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (4899)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4899) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4900)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (4900), (function-axioms) are
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4901)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4901) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4902)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (4902), (function-axioms) are
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4903)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4903) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4904)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4904) implies:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4905)  op(e2, e3) = e2
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (4905), (function-axioms) are
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4906)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4686), (4884), (4906), (function-axioms) are
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (4907)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4907) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4908)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4908) gives:
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4909)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (4865), (4909), (function-axioms) are
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #269.
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4910)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (4658), (4873), (4910),
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #286.
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4911)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4911) gives:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4912)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4912) gives:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4913)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4913) implies:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4914)  op(e1, e1) = e3
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4686), (4914), (function-axioms) are
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4915)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4915) implies:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4916)  op(e2, e2) = e1
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (268), (4688), (4875), (4892), (4916),
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #267.
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4917)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (163), (4678), (4686), (4865), (4917),
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #874.
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |   (4918)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4918) gives:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (4919)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4919) gives:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4920)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4920) gives:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4921)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4921) gives:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4922)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4922) implies:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4923)  op(e3, e3) = e1
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4658), (4923), (function-axioms) are
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4924)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4924) implies:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4925)  op(e2, e2) = e1
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (268), (4688), (4875), (4892), (4925),
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #267.
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4926)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4686), (4865), (4926), (function-axioms) are
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4927)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.28/22.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4927) gives:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4928)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (4679), (4686), (4928),
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4929)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4929) gives:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4930)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4930) implies:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4931)  op(e0, e0) = e3
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4865), (4931), (function-axioms) are
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4932)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (4658), (4932), (function-axioms) are
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #284.
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (4933)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4933) gives:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4934)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4934) gives:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4935)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4935) gives:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4936)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4936) implies:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4937)  all_57_5 = e2
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4938)   ~ (all_57_12 = e1)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4939)  op(e2, e2) = all_57_12
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4884), (4937), (4938), (4939), (function-axioms)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #274.
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4940)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4940) implies:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4941)  op(e2, e2) = e2
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (268), (4688), (4875), (4897), (4941),
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #929.
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4942)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4942) gives:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4943)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4943) implies:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4944)  op(e2, e2) = e1
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (268), (4688), (4875), (4892), (4944),
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #267.
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4945)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4945) implies:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4946)  op(e0, e0) = e3
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4865), (4946), (function-axioms) are
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4947)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4947) gives:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4948)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (4658), (4873), (4948),
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #266.
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4949)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4949) gives:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4950)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4950) implies:
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4951)  op(e2, e2) = e2
% 154.28/22.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (268), (4688), (4875), (4897), (4951),
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #929.
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4952)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4952) gives:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4953)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4953) implies:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4954)  op(e1, e0) = e1
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4683), (4954), (function-axioms) are
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4955)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4955) implies:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4956)  op(e0, e0) = all_57_15
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4957)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4897) gives:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4958)  all_54_5 = e1
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (4958) imply:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4959)  all_4_2 = e1
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4688), (4959) imply:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4960)  $false
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4960) is inconsistent.
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4961)  all_54_5 = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (4961) imply:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4962)  all_4_2 = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (4962) imply:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4963)   ~ (all_52_7 = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4875), (4962) imply:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4964)   ~ (e2 = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4688), (4962) imply:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4965)   ~ (e1 = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4957) gives:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4966)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4966) gives:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4967)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (164), (4658), (4686), (4873), (4967),
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #265.
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4968)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4968) gives:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4969)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4969) implies:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4970)  all_57_15 = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4956), (4970) imply:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4971)  op(e0, e0) = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4865), (4971), (function-axioms) are
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4972)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (4658), (4873), (4972),
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #264.
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4973)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4973) gives:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4974)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (158), (4658), (4686), (4963), (4974),
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #278.
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4975)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4975) gives:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4976)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (4686), (4873), (4976),
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #862.
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4977)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4683), (4888), (4977), (function-axioms)
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #807.
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |   (4978)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (4978) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |   (4979)  op(e0, e0) = e0
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4865), (4979), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | |   (4980)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 154.28/22.56  | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 154.28/22.56  | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | BETA: splitting (4980) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | |   (4981)  all_56_8 = e2 & op(e1, e1) = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | ALPHA: (4981) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | |   (4982)  op(e1, e1) = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4686), (4982), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | |   (4983)  all_56_14 = e2 & op(e0, e1) = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4863), (4983), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | |   (4984)  all_24_2 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | COMBINE_EQS: (318), (4984) imply:
% 154.28/22.56  | | | | | | | | | | | | | | |   (4985)  all_4_2 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | REDUCE: (349), (4985) imply:
% 154.28/22.56  | | | | | | | | | | | | | | |   (4986)   ~ (all_52_1 = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | REDUCE: (356), (4985) imply:
% 154.28/22.56  | | | | | | | | | | | | | | |   (4987)   ~ (all_52_7 = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | REDUCE: (360), (4985) imply:
% 154.28/22.56  | | | | | | | | | | | | | | |   (4988)   ~ (all_52_13 = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | REDUCE: (36), (4985) imply:
% 154.28/22.56  | | | | | | | | | | | | | | |   (4989)  op(e2, e2) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | |   (4990)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 154.28/22.56  | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | BETA: splitting (4990) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | |   (4991)  all_56_12 = e1 & op(e0, e3) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | ALPHA: (4991) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | |   (4992)  all_56_12 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | |   (4993)  op(e0, e3) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | |   (4994)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | BETA: splitting (4994) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |   (4995)  all_56_0 = e1 & op(e3, e3) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | ALPHA: (4995) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |   (4996)  op(e3, e3) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |            (235), (4650), (4992), (4996), (function-axioms)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #495.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |   (4997)  all_56_1 = e1 & op(e3, e2) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | ALPHA: (4997) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |   (4998)  all_56_1 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (225), (227), (228),
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |            (4989), (4998), (function-axioms) are inconsistent
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |            by sub-proof #332.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | |   (4999)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | BETA: splitting (4999) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |   (5000)  all_56_4 = e1 & op(e3, e1) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4680), (5000), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #331.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |   (5001)  all_56_9 = e1 & op(e3, e0) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | ALPHA: (5001) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |   (5002)  all_56_9 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | |   (5003)  op(e3, e0) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (4646) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |   (5004)   ~ (all_12_0 = e0) & op(e2, e3) = all_12_0 &
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |           $i(all_12_0)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (5004) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |   (5005)   ~ (all_12_0 = e0)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | |   (5006)  op(e2, e3) = all_12_0
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | |   (5007)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5007) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5008)  all_56_2 = e1 & op(e2, e3) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5008) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5009)  all_56_2 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5010)  op(e2, e3) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (223), (224),
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |            (4989), (5009), (5010), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #259.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5011)  all_56_3 = e1 & op(e2, e2) = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (4993) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5012)  all_52_3 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |              all_12_0, e3, e2, simplifying with (167), (5006)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5013)  all_52_1 = all_12_0
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (168), (5003) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5014)  all_52_12 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (5013) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5015)  all_54_4 = all_12_0
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (5013) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5016)   ~ (all_52_2 = all_12_0)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | SIMP: (5016) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5017)   ~ (all_52_2 = all_12_0)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (5013) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5018)   ~ (all_52_9 = all_12_0)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | SIMP: (5018) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5019)   ~ (all_52_9 = all_12_0)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4649), (5013) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5020)   ~ (all_12_0 = e2)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4986), (5013) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5021)   ~ (all_12_0 = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5012) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5022)   ~ (all_52_7 = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (5012) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5023)   ~ (all_52_11 = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (5014) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5024)   ~ (all_52_13 = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5014) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5025)   ~ (all_52_14 = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (5014) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | |   (5026)   ~ (all_14_2 = e1)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | |   (5027)  all_54_4 = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5015), (5027) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | |   (5028)  all_12_0 = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5028) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | |   (5029)  all_12_0 = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5017), (5029) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | |   (5030)   ~ (all_52_2 = e3)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5019), (5029) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | |   (5031)   ~ (all_52_9 = e3)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5032)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5032) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5033)  all_56_9 = e3 & op(e3, e0) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5033) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5034)  op(e3, e0) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5003), (5034), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #796.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5035)  all_56_10 = e3 & op(e2, e0) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5035) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5036)  all_56_10 = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5037)  op(e2, e0) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5038)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5038) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5039)  all_56_0 = e3 & op(e3, e3) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5039) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5040)  op(e3, e3) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (5040), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5041)  all_56_2 = e3 & op(e2, e3) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5041) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5042)  all_56_2 = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5043)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (4649), (4989), (5043),
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #258.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5044)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5044) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5045)  all_56_5 = e2 & op(e2, e1) = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5045) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5046)  all_56_5 = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5047)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5047) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5048)  all_56_2 = e0 & op(e2, e3) = e0
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5042), (5048) are inconsistent by sub-proof
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #777.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5049)  all_56_3 = e0 & op(e2, e2) = e0
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5049) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5050)  op(e2, e2) = e0
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4989), (5050), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5051)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5051) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5052)  all_56_5 = e0 & op(e2, e1) = e0
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5046), (5052) are inconsistent by sub-proof
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #257.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5053)  all_56_10 = e0 & op(e2, e0) = e0
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5036), (5053) are inconsistent by sub-proof
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #551.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5054)  all_56_10 = e2 & op(e2, e0) = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5054) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5055)  op(e2, e0) = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5037), (5055), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #580.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5056)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5056) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5057)  all_56_6 = e3 & op(e1, e3) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5030), (5057), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #681.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5058)  all_56_12 = e3 & op(e0, e3) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5058) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5059)  all_56_12 = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4992), (5059) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5060)  e3 = e1
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (5060) imply:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5061)  $false
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5061) is inconsistent.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5062)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5062) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5063)  all_56_11 = e3 & op(e1, e0) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5063) implies:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5064)  all_56_11 = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5065)  op(e1, e0) = e3
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5066)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5066) gives:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5067)  all_56_6 = e2 & op(e1, e3) = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4650), (5067), (function-axioms) are
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5068)  all_56_7 = e2 & op(e1, e2) = e2
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5068) implies:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5069)  all_56_7 = e2
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5070)  op(e1, e2) = e2
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5071)  all_54_8 = e3
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (5071) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5072)  all_52_2 = e3
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5030), (5072) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5073)  $false
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5073) is inconsistent.
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5074)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5074) gives:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5075)  all_54_8 = e2
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (5075) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5076)  all_52_2 = e2
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4650), (5076) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5077)  $false
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5077) is inconsistent.
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5078)   ~ (all_54_8 = e2)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5079)  all_54_8 = e1 | all_54_8 = e0
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5079) gives:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5080)  all_54_8 = e1
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (5080) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5081)  all_52_2 = e1
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4678), (5081) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5082)  $false
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5082) is inconsistent.
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5083)  all_54_8 = e0
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (5083) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5084)  all_52_2 = e0
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (5084) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5085)   ~ (all_52_6 = e0)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5085) implies:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5086)   ~ (all_52_6 = e0)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (5084) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5087)   ~ (all_52_14 = e0)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5087) implies:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5088)   ~ (all_52_14 = e0)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4678), (5084) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5089)   ~ (e1 = e0)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (160), (5065) gives:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5090)  all_52_14 = e3
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (5070) gives:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5091)  all_52_6 = e2
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (5091) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5092)   ~ (all_52_7 = e2)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5092) implies:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5093)   ~ (all_52_7 = e2)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (5090), (5091) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5094)   ~ (e3 = e2)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (5090) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5095)   ~ (all_52_13 = e3)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (5090) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5096)   ~ (all_14_2 = e3)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5097)   ~ (all_28_2 = e2)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (5097) imply:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5098)   ~ (all_14_2 = e2)
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5099)  all_54_15 = e3
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (4661), (5099) are inconsistent by
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1010.
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.28/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5100)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5101)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5101) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5102)  all_56_12 = e2 & op(e0, e3) = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4651), (5102), (function-axioms) are
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5103)  all_56_13 = e2 & op(e0, e2) = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5093), (5103), (function-axioms) are
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #594.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5104)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5104) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5105)  all_56_14 = e2 & op(e0, e1) = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5105) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5106)  all_56_14 = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5107)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5107) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5108)  all_56_4 = e3 & op(e3, e1) = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5108) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5109)  all_56_4 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5110)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5110) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5111)  all_56_0 = e0 & op(e3, e3) = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5111) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5112)  op(e3, e3) = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (5112), (function-axioms) are
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5113)  all_56_1 = e0 & op(e3, e2) = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5113) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5114)  all_56_1 = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5115)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5115) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5116)  all_56_9 = e2 & op(e3, e0) = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4654), (5116), (function-axioms) are
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #880.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5117)  all_56_10 = e2 & op(e2, e0) = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5117) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5118)  op(e2, e0) = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5100) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5119)  all_54_15 = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (5098), (5119) are inconsistent by
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1009.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5120)  all_54_15 = e1 | all_54_15 = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5120) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5121)  all_54_15 = e1
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (4659), (5121) are inconsistent by
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1008.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5122)  all_54_15 = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (5122) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5123)  all_14_2 = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5123) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5124)  all_14_2 = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (5124) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5125)   ~ (all_52_7 = e0)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (5124) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5126)   ~ (all_52_11 = e0)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (5124) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5127)   ~ (all_52_13 = e0)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (5124) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5128)  op(e0, e0) = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5129)  all_54_7 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (5129) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5130)  all_52_13 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5095), (5130) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5131)  $false
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5131) is inconsistent.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5132)   ~ (all_54_7 = e3)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5133)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5134)  all_54_13 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (5134) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5135)  all_52_7 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5135) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5136)  all_52_7 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (5136) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5137)   ~ (all_52_4 = e3)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (5136) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5138)   ~ (all_52_11 = e3)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5138) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5139)   ~ (all_52_11 = e3)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5133) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5140)  all_54_7 = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (5140) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5141)  all_52_13 = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5141) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5142)  all_52_13 = e2
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (5142) imply:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5143)   ~ (all_52_9 = e2)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5144)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5144) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5145)  all_56_1 = e3 & op(e3, e2) = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5145) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5146)  op(e3, e2) = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5137), (5146), (function-axioms) are
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5147)  all_56_3 = e3 & op(e2, e2) = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5147) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5148)  op(e2, e2) = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4989), (5148), (function-axioms) are
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5149)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5149) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5150)  all_56_7 = e3 & op(e1, e2) = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5150) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5151)  all_56_7 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5069), (5151) are inconsistent by sub-proof
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #661.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5152)  all_56_13 = e3 & op(e0, e2) = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5152) implies:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5153)  all_56_13 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5154)  op(e0, e2) = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5155)  all_54_14 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (5139), (5155) are inconsistent by
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #587.
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5156)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5157)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.40/22.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5157) gives:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5158)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (4649), (4686), (4989), (5158),
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #256.
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5159)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5159) gives:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5160)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5160) gives:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5161)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4658), (5128), (5161), (function-axioms) are
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #287.
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5162)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5162) gives:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5163)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5163) implies:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5164)  op(e3, e2) = e3
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5137), (5164), (function-axioms) are
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5165)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5165) implies:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5166)  op(e3, e3) = e1
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (4992), (5166), (function-axioms)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #495.
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5167)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5167) gives:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5168)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (4678), (4686), (5168),
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #791.
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5169)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (51), (163), (246), (4659), (4678), (4686),
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5120), (5169), (function-axioms) are inconsistent
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #255.
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5170)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5170) gives:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5171)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5171) gives:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5172)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5172) gives:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5173)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5173) gives:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5174)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5174) implies:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5175)  op(e3, e3) = e1
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (4992), (5175), (function-axioms)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #495.
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5176)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5176) implies:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5177)  op(e2, e1) = e2
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (165), (247), (4682), (5126), (5156),
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5177), (function-axioms) are inconsistent by
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #584.
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5178)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5178) gives:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5179)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5179) implies:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5180)  op(e1, e1) = e2
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (164), (165), (167), (223), (238),
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4649), (4658), (4989), (5143), (5180),
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #253.
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5181)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5181) implies:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5182)  op(e0, e0) = e1
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (4659), (5120), (5182),
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #790.
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5183)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5183) gives:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5184)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5184) gives:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5185)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5185) implies:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5186)  op(e1, e1) = e2
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (164), (165), (167), (223), (238),
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4649), (4658), (4989), (5143), (5186),
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #253.
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5187)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = e1
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5187) implies:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5188)  op(e1, e2) = e1
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4679), (5188), (function-axioms) are
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #984.
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5189)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5189) gives:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5190)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5190) implies:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5191)  op(e0, e0) = e3
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5128), (5191), (function-axioms) are
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5192)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (4658), (4992), (5192),
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #252.
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5193)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5193) gives:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5194)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5194) gives:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5195)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5195) gives:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5196)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5196) implies:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5197)  op(e0, e0) = e2
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (206), (207), (5106),
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5153), (5154), (5197), (function-axioms) are
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #724.
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5198)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5198) implies:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5199)  op(e2, e2) = e2
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (5118), (5199),
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5200)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5200) gives:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5201)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5201) implies:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5202)  op(e2, e1) = e2
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (165), (247), (4682), (5126), (5156),
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5202), (function-axioms) are inconsistent by
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #584.
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5203)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5203) implies:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5204)  op(e0, e0) = e3
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5128), (5204), (function-axioms) are
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5205)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5205) gives:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5206)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5206) gives:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5207)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5207) implies:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5208)  op(e0, e0) = e2
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (206), (207), (5106),
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5153), (5154), (5208), (function-axioms) are
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #724.
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5209)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5209) implies:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5210)  op(e3, e3) = e3
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (5210), (function-axioms) are
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5211)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5211) gives:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5212)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5212) implies:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5213)  op(e2, e2) = e2
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (5118), (5213),
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5214)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5214) gives:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5215)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5215) implies:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5216)  op(e1, e0) = e1
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4683), (5216), (function-axioms) are
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5217)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5217) implies:
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5218)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.40/22.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5218) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5219)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5219) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5220)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4686), (4993), (5220), (function-axioms) are
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #251.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5221)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5221) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5222)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5222) implies:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5223)  op(e0, e3) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4993), (5223), (function-axioms) are
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5224)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5224) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5225)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e2) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5225) implies:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5226)  op(e3, e3) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (5226), (function-axioms) are
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5227)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e2) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5227) implies:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5228)  op(e2, e2) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (158), (226), (4987), (5069), (5114),
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5228), (function-axioms) are inconsistent by
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #603.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5229)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5229) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5230)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5230) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5231)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5231) implies:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5232)  op(e1, e1) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4686), (5232), (function-axioms) are
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5233)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (4658), (5154), (5233),
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #250.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5234)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5234) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5235)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5235) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5236)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e1) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5236) implies:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5237)  op(e2, e2) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (158), (226), (4987), (5069), (5114),
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5237), (function-axioms) are inconsistent by
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #603.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5238)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e1) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5238) implies:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5239)  op(e1, e1) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4686), (5239), (function-axioms) are
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5240)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (5126), (5240), (function-axioms) are
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5241)   ~ (all_54_7 = e2)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (260), (5241) imply:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5242)   ~ (all_52_13 = e2)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5118), (5242), (function-axioms) are
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5243)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (4987), (5093), (5125), (5243) are
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5244)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5244) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5245)  all_56_11 = e2 & op(e1, e0) = e2
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5064), (5245) are inconsistent by sub-proof
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #249.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5246)  all_56_15 = e2 & op(e0, e0) = e2
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5246) implies:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5247)  op(e0, e0) = e2
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (4659), (5098), (5100), (5247),
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #798.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5248)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5248) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5249)  all_56_4 = e0 & op(e3, e1) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5109), (5249) are inconsistent by sub-proof
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #248.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5250)  all_56_9 = e0 & op(e3, e0) = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5250) implies:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5251)  all_56_9 = e0
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5002), (5251) are inconsistent by sub-proof
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #756.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5252)  all_56_5 = e3 & op(e2, e1) = e3
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5252) implies:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5253)  op(e2, e1) = e3
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5031), (5253), (function-axioms) are
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #763.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5254)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (4686), (5106), (5254),
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #247.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5255)  all_56_15 = e2 & op(e0, e0) = e2
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5255) implies:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5256)  op(e0, e0) = e2
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (4659), (5098), (5100), (5256),
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #798.
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5257)  all_28_2 = e2
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (5257) imply:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5258)  all_14_2 = e2
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (5258) imply:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5259)  all_50_2 = e2
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (5258) imply:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5260)   ~ (all_52_13 = e2)
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (5258) imply:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5261)  op(e0, e0) = e2
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5262)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5262) gives:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5263)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (4649), (4686), (4989), (5263),
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #256.
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5264)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5264) gives:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5265)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5265) gives:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5266)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (5261), (5266), (function-axioms) are
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #269.
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5267)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5267) gives:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5268)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5268) implies:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5269)  op(e2, e0) = e2
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5260), (5269), (function-axioms) are
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5270)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5270) implies:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5271)  op(e3, e3) = e1
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (4992), (5271), (function-axioms)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #495.
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5272)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5272) gives:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5273)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (4678), (4686), (5273),
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #791.
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5274)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (163), (4678), (4686), (5261), (5274),
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #874.
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5275)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5275) gives:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5276)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5276) gives:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5277)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5277) gives:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5278)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5278) gives:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5279)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5279) implies:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5280)  op(e3, e3) = e1
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (4992), (5280), (function-axioms)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #495.
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5281)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5281) implies:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5282)  op(e1, e2) = e1
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4679), (5282), (function-axioms) are
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #984.
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5283)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4686), (5261), (5283), (function-axioms) are
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5284)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5284) gives:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5285)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (4679), (4686), (5285),
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5286)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5286) gives:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5287)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5287) implies:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5288)  op(e0, e0) = e3
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5261), (5288), (function-axioms) are
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5289)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (4658), (4992), (5289),
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #252.
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5290)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5290) gives:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5291)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (4683), (4989), (5261), (5291),
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #716.
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5292)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5292) gives:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5293)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (4658), (5260), (5293),
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #266.
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5294)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5294) gives:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5295)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5295) implies:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5296)  op(e2, e2) = e2
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4989), (5296), (function-axioms) are
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5297)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5297) gives:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5298)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5298) implies:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5299)  op(e1, e0) = e1
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4683), (5299), (function-axioms) are
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5300)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5300) implies:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5301)  op(e0, e0) = all_57_15
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5302)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5303)   ~ (all_50_2 = e2)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5259), (5303) imply:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5304)  $false
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5304) is inconsistent.
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5305)  ( ~ (all_50_0 = e3) & op(e2, e0) = all_50_0 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_50_0)) | ( ~ (all_50_1 = e1) & op(e2, e2)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5306)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5306) gives:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5307)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5307) implies:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5308)  op(e3, e3) = e3
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (160), (164), (4683), (4686),
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4989), (5260), (5261), (5301), (5302), (5305),
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5308), (function-axioms) are inconsistent by
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #714.
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5309)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5309) implies:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5310)  op(e2, e2) = e2
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4989), (5310), (function-axioms) are
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5311)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5311) gives:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5312)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 154.40/22.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5312) implies:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5313)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5313) gives:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5314)  all_57_15 = e1 & op(e0, e0) = e1
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5314) implies:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5315)  op(e0, e0) = e1
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (110), (160), (164), (168), (211),
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4654), (4658), (4683), (4686), (5260), (5301),
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5302), (5315), (function-axioms) are inconsistent
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #246.
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5316)   ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_8)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5316) implies:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5317)   ~ (all_57_8 = e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5302) gives:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5318)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5318) gives:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5319)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5319) gives:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5320)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5320) implies:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5321)  op(e0, e3) = e0
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4993), (5321), (function-axioms) are
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5322)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (4686), (5260), (5322),
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #867.
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5323)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5323) gives:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5324)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5324) implies:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5325)  op(e0, e3) = e0
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4993), (5325), (function-axioms) are
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5326)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (4658), (5260), (5326),
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #264.
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5327)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5327) gives:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5328)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5328) gives:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5329)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5329) implies:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5330)  op(e1, e1) = e0
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4686), (5330), (function-axioms) are
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5331)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5331) gives:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5332)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5332) implies:
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5333)  all_57_15 = e0
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.40/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5301), (5333) imply:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5334)  op(e0, e0) = e0
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5261), (5334), (function-axioms) are
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5335)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5335) implies:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5336)  op(e3, e3) = e0
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (5336), (function-axioms) are
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5337)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5337) gives:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5338)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (4686), (5260), (5338),
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #862.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5339)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4683), (5317), (5339), (function-axioms)
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #807.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5340)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5340) implies:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5341)  op(e0, e0) = e0
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5261), (5341), (function-axioms) are
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5342)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5342) gives:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5343)  all_56_8 = e2 & op(e1, e1) = e2
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5343) implies:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5344)  op(e1, e1) = e2
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4686), (5344), (function-axioms) are
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5345)  all_56_11 = e2 & op(e1, e0) = e2
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5345) implies:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5346)  all_56_11 = e2
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5064), (5346) are inconsistent by sub-proof
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #319.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (5347)  all_56_15 = e3 & op(e0, e0) = e3
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5347) implies:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (5348)  op(e0, e0) = e3
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (4661), (5348), (function-axioms) are
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #245.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | |   (5349)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5005), (5015), (5020), (5021), (5349) are
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #244.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | |   (5350)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5350) gives:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | |   (5351)  all_56_5 = e1 & op(e2, e1) = e1
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4681), (5351), (function-axioms) are
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | |   (5352)  all_56_10 = e1 & op(e2, e0) = e1
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4988), (5352), (function-axioms) are
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.65  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | | | | |   (5353)   ~ (all_12_1 = e1) & op(e2, e2) = all_12_1 &
% 154.49/22.66  | | | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 154.49/22.66  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4989), (5353), (function-axioms) are inconsistent
% 154.49/22.66  | | | | | | | | | | | | | | | | | | | |            by sub-proof #243.
% 154.49/22.66  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | |   (5354)  all_56_13 = e1 & op(e0, e2) = e1
% 154.49/22.66  | | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4987), (5354), (function-axioms) are
% 154.49/22.66  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #712.
% 154.49/22.66  | | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5355)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 154.49/22.66  | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REF_CLOSE: (51), (157), (4659), (4682), (5355),
% 154.49/22.66  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.66  | | | | | | | | | | | | | | | |            #802.
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | |   (5356)  all_54_10 = e0
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | COMBINE_EQS: (336), (5356) imply:
% 154.49/22.66  | | | | | | | | | | | | | |   (5357)  all_10_2 = e0
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | REDUCE: (4665), (5357) imply:
% 154.49/22.66  | | | | | | | | | | | | | |   (5358)  $false
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | CLOSE: (5358) is inconsistent.
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | |   (5359)  all_22_2 = e0
% 154.49/22.66  | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | COMBINE_EQS: (251), (5359) imply:
% 154.49/22.66  | | | | | | | | | | |   (5360)  all_10_2 = e0
% 154.49/22.66  | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | REDUCE: (350), (5360) imply:
% 154.49/22.66  | | | | | | | | | | |   (5361)   ~ (all_52_2 = e0)
% 154.49/22.66  | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | REDUCE: (363), (5360) imply:
% 154.49/22.66  | | | | | | | | | | |   (5362)   ~ (all_52_8 = e0)
% 154.49/22.66  | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | REDUCE: (375), (5360) imply:
% 154.49/22.66  | | | | | | | | | | |   (5363)   ~ (e2 = e0)
% 154.49/22.66  | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | REDUCE: (45), (5360) imply:
% 154.49/22.66  | | | | | | | | | | |   (5364)  op(e1, e1) = e0
% 154.49/22.66  | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | BETA: splitting (67) gives:
% 154.49/22.66  | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | |   (5365)   ~ (all_24_2 = e1)
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | REDUCE: (318), (5365) imply:
% 154.49/22.66  | | | | | | | | | | | |   (5366)   ~ (all_4_2 = e1)
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | BETA: splitting (73) gives:
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | |   (5367)   ~ (all_28_2 = e2)
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | REDUCE: (330), (5367) imply:
% 154.49/22.66  | | | | | | | | | | | | |   (5368)   ~ (all_14_2 = e2)
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | BETA: splitting (189) gives:
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | |   (5369)  all_54_15 = e3
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | REF_CLOSE: (246), (4661), (5369) are inconsistent by
% 154.49/22.66  | | | | | | | | | | | | | |            sub-proof #1010.
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | |   (5370)   ~ (all_54_15 = e3)
% 154.49/22.66  | | | | | | | | | | | | | |   (5371)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | BETA: splitting (5371) gives:
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | |   (5372)  all_54_15 = e2
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | REF_CLOSE: (246), (5368), (5372) are inconsistent by
% 154.49/22.66  | | | | | | | | | | | | | | |            sub-proof #1009.
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | |   (5373)   ~ (all_54_15 = e2)
% 154.49/22.66  | | | | | | | | | | | | | | |   (5374)  all_54_15 = e1 | all_54_15 = e0
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | BETA: splitting (5374) gives:
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5375)  all_54_15 = e1
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REF_CLOSE: (246), (4659), (5375) are inconsistent by
% 154.49/22.66  | | | | | | | | | | | | | | | |            sub-proof #1008.
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5376)  all_54_15 = e0
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (5376) imply:
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5377)  all_14_2 = e0
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | SIMP: (5377) implies:
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5378)  all_14_2 = e0
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REDUCE: (351), (5378) imply:
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5379)   ~ (all_52_3 = e0)
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REDUCE: (369), (5378) imply:
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5380)   ~ (all_52_11 = e0)
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REDUCE: (370), (5378) imply:
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5381)   ~ (all_52_12 = e0)
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REDUCE: (4661), (5378) imply:
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5382)   ~ (e3 = e0)
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REDUCE: (4659), (5378) imply:
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5383)   ~ (e1 = e0)
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REDUCE: (51), (5378) imply:
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5384)  op(e0, e0) = e0
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (135), (148), (157),
% 154.49/22.66  | | | | | | | | | | | | | | | |            (158), (159), (163), (164), (165), (167), (168),
% 154.49/22.66  | | | | | | | | | | | | | | | |            (169), (170), (199), (229), (230), (239), (268),
% 154.49/22.66  | | | | | | | | | | | | | | | |            (352), (358), (360), (373), (4658), (5361),
% 154.49/22.66  | | | | | | | | | | | | | | | |            (5362), (5364), (5366), (5379), (5380), (5381),
% 154.49/22.66  | | | | | | | | | | | | | | | |            (5384), (function-axioms) are inconsistent by
% 154.49/22.66  | | | | | | | | | | | | | | | |            sub-proof #238.
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | |   (5385)  all_28_2 = e2
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | COMBINE_EQS: (330), (5385) imply:
% 154.49/22.66  | | | | | | | | | | | | |   (5386)  all_14_2 = e2
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | SIMP: (5386) implies:
% 154.49/22.66  | | | | | | | | | | | | |   (5387)  all_14_2 = e2
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | REDUCE: (369), (5387) imply:
% 154.49/22.66  | | | | | | | | | | | | |   (5388)   ~ (all_52_11 = e2)
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | REDUCE: (4661), (5387) imply:
% 154.49/22.66  | | | | | | | | | | | | |   (5389)   ~ (e3 = e2)
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | REDUCE: (51), (5387) imply:
% 154.49/22.66  | | | | | | | | | | | | |   (5390)  op(e0, e0) = e2
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | BETA: splitting (219) gives:
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | |   (5391)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 154.49/22.66  | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | BETA: splitting (5391) gives:
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | |   (5392)  all_56_4 = e2 & op(e3, e1) = e2
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | ALPHA: (5392) implies:
% 154.49/22.66  | | | | | | | | | | | | | | |   (5393)  op(e3, e1) = e2
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | REF_CLOSE: (169), (4653), (5393), (function-axioms) are
% 154.49/22.66  | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | |   (5394)  all_56_5 = e2 & op(e2, e1) = e2
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | ALPHA: (5394) implies:
% 154.49/22.66  | | | | | | | | | | | | | | |   (5395)  op(e2, e1) = e2
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5396)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.49/22.66  | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.49/22.66  | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.49/22.66  | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.49/22.66  | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.49/22.66  | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.49/22.66  | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.49/22.66  | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.49/22.66  | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.49/22.66  | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.49/22.66  | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.49/22.66  | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.49/22.66  | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.66  | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.49/22.66  | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.49/22.66  | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (165), (358), (4658), (5395), (5396),
% 154.49/22.66  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.66  | | | | | | | | | | | | | | | |            #236.
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | |   (5397)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.49/22.66  | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.49/22.66  | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.49/22.66  | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.49/22.66  | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.49/22.66  | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.49/22.66  | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.49/22.66  | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.49/22.66  | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.49/22.66  | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.49/22.66  | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.49/22.66  | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.66  | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.66  | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.49/22.66  | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.49/22.66  | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (5364), (5390), (5397),
% 154.49/22.66  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.66  | | | | | | | | | | | | | | | |            #671.
% 154.49/22.66  | | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | |   (5398)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 154.49/22.66  | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | BETA: splitting (5398) gives:
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | |   (5399)  all_56_8 = e2 & op(e1, e1) = e2
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | ALPHA: (5399) implies:
% 154.49/22.66  | | | | | | | | | | | | | | |   (5400)  op(e1, e1) = e2
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | REF_CLOSE: (5), (5364), (5400), (function-axioms) are
% 154.49/22.66  | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | |   (5401)  all_56_14 = e2 & op(e0, e1) = e2
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | | REF_CLOSE: (157), (5388), (5401), (function-axioms) are
% 154.49/22.66  | | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 154.49/22.66  | | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | End of split
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | |   (5402)  all_24_2 = e1
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | COMBINE_EQS: (318), (5402) imply:
% 154.49/22.66  | | | | | | | | | | | |   (5403)  all_4_2 = e1
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | SIMP: (5403) implies:
% 154.49/22.66  | | | | | | | | | | | |   (5404)  all_4_2 = e1
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | REDUCE: (349), (5404) imply:
% 154.49/22.66  | | | | | | | | | | | |   (5405)   ~ (all_52_1 = e1)
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | REDUCE: (360), (5404) imply:
% 154.49/22.66  | | | | | | | | | | | |   (5406)   ~ (all_52_13 = e1)
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | REDUCE: (36), (5404) imply:
% 154.49/22.66  | | | | | | | | | | | |   (5407)  op(e2, e2) = e1
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | BETA: splitting (4646) gives:
% 154.49/22.66  | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | |   (5408)   ~ (all_12_0 = e0) & op(e2, e3) = all_12_0 &
% 154.49/22.66  | | | | | | | | | | | | |           $i(all_12_0)
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | ALPHA: (5408) implies:
% 154.49/22.66  | | | | | | | | | | | | |   (5409)   ~ (all_12_0 = e0)
% 154.49/22.66  | | | | | | | | | | | | |   (5410)  op(e2, e3) = all_12_0
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.49/22.66  | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | Case 1:
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | |   (5411)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.49/22.66  | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.49/22.66  | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.49/22.66  | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.49/22.66  | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.49/22.66  | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.49/22.66  | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.49/22.66  | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.49/22.66  | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.49/22.66  | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.49/22.66  | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.49/22.66  | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.49/22.66  | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.66  | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.49/22.66  | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.49/22.66  | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (4658), (5407), (5411),
% 154.49/22.66  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.66  | | | | | | | | | | | | | |            #254.
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.66  | | | | | | | | | | | | | Case 2:
% 154.49/22.66  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | |   (5412)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.49/22.67  | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.49/22.67  | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.49/22.67  | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.49/22.67  | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.49/22.67  | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.49/22.67  | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.49/22.67  | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.49/22.67  | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.49/22.67  | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.49/22.67  | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.49/22.67  | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.67  | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.67  | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.49/22.67  | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.49/22.67  | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | BETA: splitting (5412) gives:
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | |   (5413)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.49/22.67  | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 154.49/22.67  | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.49/22.67  | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.49/22.67  | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.49/22.67  | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 154.49/22.67  | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 154.49/22.67  | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | ALPHA: (5413) implies:
% 154.49/22.67  | | | | | | | | | | | | | | |   (5414)  op(e1, e1) = e1
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5364), (5414), (function-axioms) are
% 154.49/22.67  | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | |   (5415)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.49/22.67  | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 154.49/22.67  | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.49/22.67  | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.67  | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.67  | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.49/22.67  | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.49/22.67  | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | ALPHA: (5415) implies:
% 154.49/22.67  | | | | | | | | | | | | | | |   (5416)  op(e0, e0) = e0
% 154.49/22.67  | | | | | | | | | | | | | | |   (5417)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.67  | | | | | | | | | | | | | | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.67  | | | | | | | | | | | | | | |             $i(all_57_11))
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | BETA: splitting (5417) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5418)  all_57_12 = e0 & op(e2, e2) = e0
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | ALPHA: (5418) implies:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5419)  op(e2, e2) = e0
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5407), (5419), (function-axioms) are
% 154.49/22.67  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5420)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.67  | | | | | | | | | | | | | | | |           $i(all_57_11)
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | ALPHA: (5420) implies:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5421)   ~ (all_57_11 = e2)
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5422)  op(e2, e0) = all_57_11
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e0,
% 154.49/22.67  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (51), (5416) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5423)  all_14_2 = e0
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 154.49/22.67  | | | | | | | | | | | | | | | |              all_57_11, e0, e2, simplifying with (164), (5422)
% 154.49/22.67  | | | | | | | | | | | | | | | |              gives:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5424)  all_57_11 = all_52_13
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 154.49/22.67  | | | | | | | | | | | | | | | |              all_12_0, e3, e2, simplifying with (167), (5410)
% 154.49/22.67  | | | | | | | | | | | | | | | |              gives:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5425)  all_52_1 = all_12_0
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (5425) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5426)  all_54_4 = all_12_0
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | REDUCE: (5421), (5424) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5427)   ~ (all_52_13 = e2)
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | REDUCE: (145), (5425) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5428)   ~ (all_52_13 = all_12_0)
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | SIMP: (5428) implies:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5429)   ~ (all_52_13 = all_12_0)
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | REDUCE: (4649), (5425) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5430)   ~ (all_12_0 = e2)
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | REDUCE: (5405), (5425) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5431)   ~ (all_12_0 = e1)
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | REDUCE: (371), (5423) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5432)   ~ (all_52_13 = e0)
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | |   (5433)  all_54_4 = e3
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | COMBINE_EQS: (5426), (5433) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | |   (5434)  all_12_0 = e3
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | SIMP: (5434) implies:
% 154.49/22.67  | | | | | | | | | | | | | | | | |   (5435)  all_12_0 = e3
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | REDUCE: (5429), (5435) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | |   (5436)   ~ (all_52_13 = e3)
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (260), (5406), (5427), (5432), (5436) are
% 154.49/22.67  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #234.
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | |   (5437)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (5409), (5426), (5430), (5431), (5437) are
% 154.49/22.67  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #244.
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | End of split
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | End of split
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | End of split
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | End of split
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | |   (5438)   ~ (all_12_1 = e1) & op(e2, e2) = all_12_1 &
% 154.49/22.67  | | | | | | | | | | | | |           $i(all_12_1)
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | REF_CLOSE: (5407), (5438), (function-axioms) are inconsistent
% 154.49/22.67  | | | | | | | | | | | | |            by sub-proof #243.
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | End of split
% 154.49/22.67  | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | End of split
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | End of split
% 154.49/22.67  | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | |   (5439)  all_20_2 = e3
% 154.49/22.67  | | | | | | | | | |   (5440)  ( ~ (all_20_0 = e0) & op(e3, e1) = all_20_0 &
% 154.49/22.67  | | | | | | | | | |             $i(all_20_0)) | ( ~ (all_20_1 = e2) & op(e3, e3)
% 154.49/22.67  | | | | | | | | | |             = all_20_1 & $i(all_20_1))
% 154.49/22.67  | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | COMBINE_EQS: (325), (5439) imply:
% 154.49/22.67  | | | | | | | | | |   (5441)  all_10_2 = e3
% 154.49/22.67  | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | SIMP: (5441) implies:
% 154.49/22.67  | | | | | | | | | |   (5442)  all_10_2 = e3
% 154.49/22.67  | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | REDUCE: (361), (5442) imply:
% 154.49/22.67  | | | | | | | | | |   (5443)   ~ (all_52_6 = e3)
% 154.49/22.67  | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | REDUCE: (363), (5442) imply:
% 154.49/22.67  | | | | | | | | | |   (5444)   ~ (all_52_8 = e3)
% 154.49/22.67  | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | REDUCE: (366), (5442) imply:
% 154.49/22.67  | | | | | | | | | |   (5445)   ~ (all_52_11 = e3)
% 154.49/22.67  | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | REDUCE: (45), (5442) imply:
% 154.49/22.67  | | | | | | | | | |   (5446)  op(e1, e1) = e3
% 154.49/22.67  | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | BETA: splitting (5440) gives:
% 154.49/22.67  | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | |   (5447)   ~ (all_20_0 = e0) & op(e3, e1) = all_20_0 &
% 154.49/22.67  | | | | | | | | | | |           $i(all_20_0)
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | ALPHA: (5447) implies:
% 154.49/22.67  | | | | | | | | | | |   (5448)   ~ (all_20_0 = e0)
% 154.49/22.67  | | | | | | | | | | |   (5449)  op(e3, e1) = all_20_0
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 154.49/22.67  | | | | | | | | | | |              all_20_0, e1, e3, simplifying with (169), (5449)
% 154.49/22.67  | | | | | | | | | | |              gives:
% 154.49/22.67  | | | | | | | | | | |   (5450)  all_52_8 = all_20_0
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | COMBINE_EQS: (271), (5450) imply:
% 154.49/22.67  | | | | | | | | | | |   (5451)  all_54_2 = all_20_0
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | REDUCE: (134), (5450) imply:
% 154.49/22.67  | | | | | | | | | | |   (5452)   ~ (all_52_4 = all_20_0)
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | REDUCE: (123), (5450) imply:
% 154.49/22.67  | | | | | | | | | | |   (5453)   ~ (all_52_9 = all_20_0)
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | SIMP: (5453) implies:
% 154.49/22.67  | | | | | | | | | | |   (5454)   ~ (all_52_9 = all_20_0)
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | REDUCE: (121), (5450) imply:
% 154.49/22.67  | | | | | | | | | | |   (5455)   ~ (all_52_11 = all_20_0)
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | SIMP: (5455) implies:
% 154.49/22.67  | | | | | | | | | | |   (5456)   ~ (all_52_11 = all_20_0)
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | REDUCE: (120), (5450) imply:
% 154.49/22.67  | | | | | | | | | | |   (5457)   ~ (all_52_12 = all_20_0)
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | SIMP: (5457) implies:
% 154.49/22.67  | | | | | | | | | | |   (5458)   ~ (all_52_12 = all_20_0)
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | REDUCE: (5444), (5450) imply:
% 154.49/22.67  | | | | | | | | | | |   (5459)   ~ (all_20_0 = e3)
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | REDUCE: (4653), (5450) imply:
% 154.49/22.67  | | | | | | | | | | |   (5460)   ~ (all_20_0 = e2)
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | BETA: splitting (202) gives:
% 154.49/22.67  | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | |   (5461)  all_54_2 = e3
% 154.49/22.67  | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | COMBINE_EQS: (5451), (5461) imply:
% 154.49/22.67  | | | | | | | | | | | |   (5462)  all_20_0 = e3
% 154.49/22.67  | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | REDUCE: (5459), (5462) imply:
% 154.49/22.67  | | | | | | | | | | | |   (5463)  $false
% 154.49/22.67  | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | CLOSE: (5463) is inconsistent.
% 154.49/22.67  | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | |   (5464)   ~ (all_54_2 = e3)
% 154.49/22.67  | | | | | | | | | | | |   (5465)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.49/22.67  | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | BETA: splitting (5465) gives:
% 154.49/22.67  | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | |   (5466)  all_54_2 = e2
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | COMBINE_EQS: (5451), (5466) imply:
% 154.49/22.67  | | | | | | | | | | | | |   (5467)  all_20_0 = e2
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | REDUCE: (5460), (5467) imply:
% 154.49/22.67  | | | | | | | | | | | | |   (5468)  $false
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | CLOSE: (5468) is inconsistent.
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | |   (5469)   ~ (all_54_2 = e2)
% 154.49/22.67  | | | | | | | | | | | | |   (5470)  all_54_2 = e1 | all_54_2 = e0
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | BETA: splitting (5470) gives:
% 154.49/22.67  | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | |   (5471)  all_54_2 = e1
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | COMBINE_EQS: (5451), (5471) imply:
% 154.49/22.67  | | | | | | | | | | | | | |   (5472)  all_20_0 = e1
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | REDUCE: (5452), (5472) imply:
% 154.49/22.67  | | | | | | | | | | | | | |   (5473)   ~ (all_52_4 = e1)
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | REDUCE: (5454), (5472) imply:
% 154.49/22.67  | | | | | | | | | | | | | |   (5474)   ~ (all_52_9 = e1)
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | REDUCE: (5456), (5472) imply:
% 154.49/22.67  | | | | | | | | | | | | | |   (5475)   ~ (all_52_11 = e1)
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | REDUCE: (5458), (5472) imply:
% 154.49/22.67  | | | | | | | | | | | | | |   (5476)   ~ (all_52_12 = e1)
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | REDUCE: (5459), (5472) imply:
% 154.49/22.67  | | | | | | | | | | | | | |   (5477)   ~ (e3 = e1)
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | REDUCE: (5460), (5472) imply:
% 154.49/22.67  | | | | | | | | | | | | | |   (5478)   ~ (e2 = e1)
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 154.49/22.67  | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | |   (5479)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 154.49/22.67  | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | BETA: splitting (5479) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5480)  all_56_0 = e1 & op(e3, e3) = e1
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | ALPHA: (5480) implies:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5481)  op(e3, e3) = e1
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4658), (5481), (function-axioms) are
% 154.49/22.67  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5482)  all_56_1 = e1 & op(e3, e2) = e1
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | ALPHA: (5482) implies:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5483)  all_56_1 = e1
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5484)  op(e3, e2) = e1
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (157), (165), (169),
% 154.49/22.67  | | | | | | | | | | | | | | | |            (218), (230), (236), (4658), (5444), (5446),
% 154.49/22.67  | | | | | | | | | | | | | | | |            (5474), (5475), (5483), (5484), (function-axioms)
% 154.49/22.67  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #228.
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | End of split
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | |   (5485)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 154.49/22.67  | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | BETA: splitting (5485) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5486)  all_56_4 = e1 & op(e3, e1) = e1
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | ALPHA: (5486) implies:
% 154.49/22.67  | | | | | | | | | | | | | | | |   (5487)  all_56_4 = e1
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | |   (5488)   ~ (all_24_2 = e1)
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | REDUCE: (318), (5488) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | |   (5489)   ~ (all_4_2 = e1)
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | |   (5490)   ~ (all_28_2 = e2)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | REDUCE: (330), (5490) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | |   (5491)   ~ (all_14_2 = e2)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | |   (5492)  all_54_15 = e3
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (5492) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | |   (5493)  all_14_2 = e3
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | REDUCE: (4661), (5493) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | |   (5494)  $false
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | CLOSE: (5494) is inconsistent.
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | |   (5495)   ~ (all_54_15 = e3)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | |   (5496)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (5496) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | |   (5497)  all_54_15 = e2
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (5497) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | |   (5498)  all_14_2 = e2
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (5491), (5498) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | |   (5499)  $false
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | CLOSE: (5499) is inconsistent.
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | |   (5500)   ~ (all_54_15 = e2)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | |   (5501)  all_54_15 = e1 | all_54_15 = e0
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5501) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5502)  all_54_15 = e1
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (5502) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5503)  all_14_2 = e1
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (4659), (5503) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5504)  $false
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | CLOSE: (5504) is inconsistent.
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5505)  all_54_15 = e0
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (5505) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5506)  all_14_2 = e0
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (5506) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5507)   ~ (all_52_3 = e0)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (5506) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5508)   ~ (all_52_7 = e0)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (5506) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5509)   ~ (all_52_11 = e0)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (5506) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5510)   ~ (all_52_12 = e0)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (4661), (5506) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5511)   ~ (e3 = e0)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (5491), (5506) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5512)   ~ (e2 = e0)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (4659), (5506) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5513)   ~ (e1 = e0)
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (5506) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | |   (5514)  op(e0, e0) = e0
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | |   (5515)  all_54_3 = e3
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (5515) imply:
% 154.49/22.67  | | | | | | | | | | | | | | | | | | | | | |   (5516)  all_52_12 = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (5516) imply:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | |   (5517)   ~ (all_52_4 = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5516) imply:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | |   (5518)   ~ (all_52_14 = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | SIMP: (5518) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | |   (5519)   ~ (all_52_14 = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (5516) imply:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | |   (5520)  op(e3, e0) = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | |   (5521)  all_54_1 = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (5521) imply:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | |   (5522)  all_52_4 = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5517), (5522) imply:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | |   (5523)  $false
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5523) is inconsistent.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | |   (5524)   ~ (all_54_1 = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | |   (5525)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | |   (5526)  all_54_14 = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (5445), (5526) are inconsistent by
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #587.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | |   (5527)   ~ (all_54_14 = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | |   (5528)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (5529)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5529) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5530)  all_56_9 = e3 & op(e3, e0) = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5530) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5531)  all_56_9 = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5532)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5532) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5533)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5533) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5534)  op(e3, e3) = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5531), (5534), (function-axioms) are inconsistent
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #632.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5535)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5535) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5536)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5536) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5537)  all_57_14 = e2 & op(e1, e1) = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5537) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5538)  op(e1, e1) = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5446), (5538), (function-axioms) are
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5539)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5539) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5540)   ~ (all_57_3 = e1)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5541)  op(e1, e2) = all_57_3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5542)  all_54_5 = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (373), (5542) are inconsistent by sub-proof
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #930.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5543)   ~ (all_54_5 = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5544)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5545)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (170), (373), (5517), (5545),
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #227.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5546)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5546) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5547)  all_56_7 = e3 & op(e1, e2) = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5443), (5547), (function-axioms) are
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #388.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5548)  all_56_13 = e3 & op(e0, e2) = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5548) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5549)  all_56_13 = e3
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5550)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (157), (165), (218),
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (268), (4658), (5446), (5474), (5475),
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5489), (5531), (5544), (5550), (function-axioms)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #226.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5551)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5551) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5552)  all_56_7 = e1 & op(e1, e2) = e1
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5552) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5553)  op(e1, e2) = e1
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5540), (5541), (5553), (function-axioms) are
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #631.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5554)  all_56_13 = e1 & op(e0, e2) = e1
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5554) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5555)  all_56_13 = e1
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5549), (5555) are inconsistent by sub-proof
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5556)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5556) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5557)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5557) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5558)  op(e1, e1) = e1
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5446), (5558), (function-axioms) are
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5559)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5559) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5560)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13))
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5561)  (all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5562)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5562) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5563)  all_56_4 = e2 & op(e3, e1) = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5563) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5564)  op(e3, e1) = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4653), (5564), (function-axioms) are
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5565)  all_56_5 = e2 & op(e2, e1) = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5565) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5566)  op(e2, e1) = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (165), (247), (5475), (5509), (5528),
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5566), (function-axioms) are inconsistent by
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #584.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5567)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5567) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5568)  all_56_8 = e2 & op(e1, e1) = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5568) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5569)  op(e1, e1) = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5446), (5569), (function-axioms) are
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5570)  all_56_14 = e2 & op(e0, e1) = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5570) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5571)  all_56_14 = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5560) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5572)  all_57_14 = e0 & op(e1, e1) = e0
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5572) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5573)  op(e1, e1) = e0
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5446), (5573), (function-axioms) are
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5574)   ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5574) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5575)   ~ (all_57_13 = e1)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5576)  op(e1, e0) = all_57_13
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5561) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5577)  all_57_10 = e0 & op(e3, e3) = e0
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5577) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5578)  op(e3, e3) = e0
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (5578), (function-axioms) are
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5579)   ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_9)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5579) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5580)   ~ (all_57_9 = e3)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5581)  all_56_15 = e0 & op(e0, e0) = e0
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5581) implies:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5582)  all_56_15 = e0
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5525) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5583)  all_54_1 = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (5583) imply:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5584)  all_52_4 = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4652), (5584) imply:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5585)  $false
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5585) is inconsistent.
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5586)   ~ (all_54_1 = e2)
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5587)  all_54_1 = e1 | all_54_1 = e0
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5528) gives:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5588)  all_54_14 = e2
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (5588) imply:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5589)  all_52_11 = e2
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5589) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5590)  all_52_11 = e2
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (5590) imply:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5591)   ~ (all_52_7 = e2)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5445), (5590) imply:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5592)   ~ (e3 = e2)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5593)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5593) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5594)  all_56_2 = e3 & op(e2, e3) = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5594) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5595)  all_56_2 = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5596)  all_54_5 = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (373), (5596) are inconsistent by sub-proof
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #930.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5597)   ~ (all_54_5 = e3)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5598)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5599)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (170), (373), (5517), (5599),
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #227.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5600)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5600) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5601)  all_56_7 = e3 & op(e1, e2) = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5443), (5601), (function-axioms) are
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #388.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5602)  all_56_13 = e3 & op(e0, e2) = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5602) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5603)  all_56_13 = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5604)  op(e0, e2) = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5605)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5605) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5606)  all_56_2 = e1 & op(e2, e3) = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5595), (5606) are inconsistent by sub-proof
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #774.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5607)  all_56_3 = e1 & op(e2, e2) = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5607) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5608)  op(e2, e2) = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (268), (5489), (5598), (5608),
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #691.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5609)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5609) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5610)  all_56_5 = e1 & op(e2, e1) = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5474), (5610), (function-axioms) are
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5611)  all_56_10 = e1 & op(e2, e0) = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5611) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5612)  all_56_10 = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5613)  op(e2, e0) = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5614)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5614) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5615)  all_56_12 = e1 & op(e0, e3) = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5615) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5616)  all_56_12 = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5617)  op(e0, e3) = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5618)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (157), (165), (218),
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (268), (4658), (5446), (5474), (5475),
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5489), (5531), (5598), (5618), (function-axioms)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #226.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5619)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5619) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5620)  all_56_7 = e1 & op(e1, e2) = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5620) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5621)  all_56_7 = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5587) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5622)  all_54_1 = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (5473), (5622) are inconsistent by
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #419.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5623)  all_54_1 = e0
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (5623) imply:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5624)  all_52_4 = e0
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5624) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5625)  all_52_4 = e0
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (5625) imply:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5626)   ~ (all_52_6 = e0)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5626) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5627)   ~ (all_52_6 = e0)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5628)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (4654), (5613), (5628),
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #225.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5629)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5629) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5630)  all_56_11 = e2 & op(e1, e0) = e2
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5630) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5631)  all_56_11 = e2
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5632)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5632) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5633)  all_56_6 = e0 & op(e1, e3) = e0
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5633) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5634)  op(e1, e3) = e0
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5635)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5635) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5636)  all_56_1 = e2 & op(e3, e2) = e2
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (4652), (5636), (function-axioms) are
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #224.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5637)  all_56_3 = e2 & op(e2, e2) = e2
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5637) implies:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5638)  op(e2, e2) = e2
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5639)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5639) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5640)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5640) gives:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5641)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (5641), (function-axioms) are
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5642)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 154.49/22.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5642) gives:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5643)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (5643), (function-axioms) are
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5644)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5644) gives:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5645)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5645) implies:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5646)  op(e2, e3) = e2
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (5646), (function-axioms) are
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5647)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5647) gives:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5648)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5648) implies:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5649)  op(e3, e2) = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5517), (5649), (function-axioms) are
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5650)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5650) implies:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5651)  op(e2, e1) = e2
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (5638), (5651),
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5652)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5652) gives:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5653)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5653) gives:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5654)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5654) gives:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5655)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5655) implies:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5656)  op(e0, e0) = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5514), (5656), (function-axioms) are
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5657)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5657) implies:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5658)  op(e3, e3) = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (230), (232),
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (5582), (5612), (5631), (5658),
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #303.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5659)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (5613), (5616), (5659),
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #223.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5660)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5660) gives:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5661)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (268), (5444), (5489), (5598),
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5661), (function-axioms) are inconsistent by
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #222.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5662)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5662) gives:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5663)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5663) implies:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5664)  op(e0, e0) = e1
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (5514), (5664), (function-axioms) are
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5665)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5665) gives:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5666)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5666) implies:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5667)  all_57_9 = e3
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5580), (5667) imply:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5668)  $false
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5668) is inconsistent.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5669)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e1
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5669) implies:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5670)  op(e1, e1) = e1
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (162), (216), (5443), (5631),
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5634), (5670), (function-axioms) are inconsistent
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #273.
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5671)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5671) gives:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5672)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5672) gives:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5673)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5673) gives:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5674)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5674) gives:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5675)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5675) implies:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5676)  op(e3, e3) = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (5616), (5676), (function-axioms)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #495.
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5677)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5677) implies:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5678)  op(e2, e2) = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (268), (5489), (5598), (5678),
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #691.
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5679)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (51), (5446), (5514), (5679),
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #645.
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5680)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5680) gives:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5681)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5681) gives:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5682)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5682) implies:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5683)  op(e1, e1) = e2
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5446), (5683), (function-axioms) are
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5684)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5684) implies:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5685)  op(e1, e1) = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (162), (216), (5443), (5631),
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5634), (5685), (function-axioms) are inconsistent
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #273.
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5686)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5686) gives:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5687)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5687) implies:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5688)  op(e0, e0) = e3
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5514), (5688), (function-axioms) are
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5689)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5689) gives:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5690)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5690) implies:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5691)  op(e3, e3) = e3
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (230), (232),
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (5582), (5612), (5631), (5691),
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #303.
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5692)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5692) implies:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5693)  op(e3, e3) = e1
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (5616), (5693), (function-axioms)
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #495.
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5694)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5694) gives:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5695)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5695) gives:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5696)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5696) gives:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5697)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5697) implies:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5698)  op(e0, e0) = e2
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (206), (207), (5571),
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5603), (5604), (5698), (function-axioms) are
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #724.
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5699)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5699) implies:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5700)  op(e2, e1) = e2
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (5638), (5700),
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5701)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (268), (5489), (5514), (5598), (5701),
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #221.
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5702)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5702) gives:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5703)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5703) gives:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5704)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5704) implies:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5705)  op(e0, e0) = e2
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (206), (207), (5571),
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5603), (5604), (5705), (function-axioms) are
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #724.
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5706)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5706) implies:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5707)  op(e3, e3) = e3
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (230), (232),
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (5582), (5612), (5631), (5707),
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #303.
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5708)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5708) gives:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5709)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5709) implies:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5710)  op(e2, e0) = e2
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5613), (5710), (function-axioms) are
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5711)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5711) gives:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5712)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5712) implies:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5713)  op(e1, e1) = e1
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (162), (216), (5443), (5631),
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5634), (5713), (function-axioms) are inconsistent
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #273.
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5714)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5714) implies:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5715)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5715) gives:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5716)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5716) gives:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5717)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5717) gives:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5718)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5718) implies:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5719)  op(e0, e3) = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5617), (5719), (function-axioms) are
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5720)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (5446), (5613), (5720),
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #220.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5721)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (4658), (5613), (5617), (5721),
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #218.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5722)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5722) gives:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5723)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5723) gives:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5724)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5724) implies:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5725)  op(e1, e1) = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5446), (5725), (function-axioms) are
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5726)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (4658), (5604), (5726),
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #250.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5727)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (157), (5446), (5509), (5613), (5727),
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #217.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5728)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5728) gives:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5729)  all_56_7 = e2 & op(e1, e2) = e2
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5621), (5729) are inconsistent by sub-proof
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #915.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5730)  all_56_13 = e2 & op(e0, e2) = e2
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5591), (5730), (function-axioms) are
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #594.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5731)  all_56_7 = e0 & op(e1, e2) = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5627), (5731), (function-axioms) are
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #898.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5732)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (210), (211), (212),
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5446), (5514), (5582), (5732), (function-axioms)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #216.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5733)  all_56_15 = e2 & op(e0, e0) = e2
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5733) implies:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5734)  op(e0, e0) = e2
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (206), (207), (5571),
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5603), (5604), (5734), (function-axioms) are
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #724.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5735)  all_56_13 = e1 & op(e0, e2) = e1
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5735) implies:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5736)  all_56_13 = e1
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5603), (5736) are inconsistent by sub-proof
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5737)  all_56_13 = e1 & op(e0, e2) = e1
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5737) implies:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5738)  all_56_13 = e1
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5603), (5738) are inconsistent by sub-proof
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5739)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (157), (5475), (5514), (5739),
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #215.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5740)  all_56_3 = e3 & op(e2, e2) = e3
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5740) implies:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5741)  op(e2, e2) = e3
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (5741), (function-axioms) are
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #711.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5742)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5742) gives:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5743)  all_56_5 = e3 & op(e2, e1) = e3
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5743) implies:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5744)  all_56_5 = e3
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5745)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5745) gives:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5746)  all_56_4 = e0 & op(e3, e1) = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5487), (5746) are inconsistent by sub-proof
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #951.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5747)  all_56_5 = e0 & op(e2, e1) = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5744), (5747) are inconsistent by sub-proof
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #845.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5748)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5748) gives:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5749)  all_56_8 = e0 & op(e1, e1) = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5749) implies:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5750)  op(e1, e1) = e0
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5446), (5750), (function-axioms) are
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5751)  all_56_14 = e0 & op(e0, e1) = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5751) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5752)  all_56_14 = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5753)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5753) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5754)  all_56_4 = e2 & op(e3, e1) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5487), (5754) are inconsistent by sub-proof
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #317.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5755)  all_56_5 = e2 & op(e2, e1) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5744), (5755) are inconsistent by sub-proof
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #668.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5567) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5756)  all_56_8 = e2 & op(e1, e1) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5756) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5757)  op(e1, e1) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5446), (5757), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5571), (5752) are inconsistent by sub-proof
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #214.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5758)  all_56_10 = e3 & op(e2, e0) = e3
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5758) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5759)  all_56_10 = e3
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5760)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5760) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5761)  all_56_9 = e1 & op(e3, e0) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5476), (5761), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #851.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5762)  all_56_10 = e1 & op(e2, e0) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5759), (5762) are inconsistent by sub-proof
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #556.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5763)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (160), (5514), (5575), (5576), (5763),
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #213.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5764)  all_54_14 = e1 | all_54_14 = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (5475), (5509), (5764) are inconsistent by
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #585.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5765)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5765) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5766)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (5507), (5508), (5509),
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5766), (function-axioms) are inconsistent by
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #881.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5767)  all_56_10 = e3 & op(e2, e0) = e3
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5767) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5768)  all_56_10 = e3
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5769)  op(e2, e0) = e3
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5770)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5770) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5771)  all_56_9 = e2 & op(e3, e0) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4654), (5771), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #880.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5772)  all_56_10 = e2 & op(e2, e0) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5772) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5773)  op(e2, e0) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5769), (5773), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #580.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5774)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5774) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5775)  all_56_11 = e2 & op(e1, e0) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5775) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5776)  all_56_11 = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5777)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5777) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5778)  all_56_9 = e1 & op(e3, e0) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5778) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5779)  op(e3, e0) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5520), (5779), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #796.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5780)  all_56_10 = e1 & op(e2, e0) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5780) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5781)  all_56_10 = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5768), (5781) are inconsistent by sub-proof
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #887.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5782)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5782) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5783)  all_56_11 = e1 & op(e1, e0) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5776), (5783) are inconsistent by sub-proof
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #469.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5784)  all_56_15 = e1 & op(e0, e0) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5784) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5785)  op(e0, e0) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (5514), (5785), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5786)  all_56_15 = e2 & op(e0, e0) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5786) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5787)  op(e0, e0) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5514), (5787), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (5788)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (5514), (5519), (5788),
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | |            #622.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | |   (5789)   ~ (all_54_3 = e3)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (5789) imply:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | |   (5790)   ~ (all_52_12 = e3)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | |   (5791)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5791) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5792)  all_56_0 = e0 & op(e3, e3) = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5792) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5793)  op(e3, e3) = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (5793), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5794)  all_56_1 = e0 & op(e3, e2) = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5794) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5795)  all_56_1 = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (168), (169), (236), (4658), (5444),
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            (5790), (5795), (function-axioms) are inconsistent
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #212.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | |   (5796)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5796) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5797)  all_56_4 = e0 & op(e3, e1) = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5797) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5798)  all_56_4 = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (157), (165), (218), (5446), (5474),
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            (5475), (5798), (function-axioms) are inconsistent
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #230.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5799)  all_56_9 = e0 & op(e3, e0) = e0
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5510), (5799), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #620.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | |   (5800)  all_28_2 = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (5800) imply:
% 154.49/22.74  | | | | | | | | | | | | | | | | | |   (5801)  all_14_2 = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | SIMP: (5801) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | |   (5802)  all_14_2 = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | REDUCE: (369), (5802) imply:
% 154.49/22.74  | | | | | | | | | | | | | | | | | |   (5803)   ~ (all_52_11 = e2)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | REDUCE: (372), (5802) imply:
% 154.49/22.74  | | | | | | | | | | | | | | | | | |   (5804)   ~ (all_52_14 = e2)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | REDUCE: (4661), (5802) imply:
% 154.49/22.74  | | | | | | | | | | | | | | | | | |   (5805)   ~ (e3 = e2)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | REDUCE: (51), (5802) imply:
% 154.49/22.74  | | | | | | | | | | | | | | | | | |   (5806)  op(e0, e0) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | |   (5807)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | BETA: splitting (5807) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | |   (5808)  all_56_4 = e2 & op(e3, e1) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | ALPHA: (5808) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | |   (5809)  op(e3, e1) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4653), (5809), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | |   (5810)  all_56_5 = e2 & op(e2, e1) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | ALPHA: (5810) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | |   (5811)  op(e2, e1) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | |   (5812)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5812) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | |   (5813)  all_56_6 = e2 & op(e1, e3) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4650), (5813), (function-axioms) are
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | |   (5814)  all_56_7 = e2 & op(e1, e2) = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5814) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | |   (5815)  all_56_7 = e2
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | |   (5816)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5816) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5817)  all_56_1 = e1 & op(e3, e2) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5817) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5818)  all_56_1 = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5819)  op(e3, e2) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (157), (165), (169),
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            (218), (230), (236), (4658), (5444), (5446),
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            (5474), (5475), (5818), (5819), (function-axioms)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #228.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5820)  all_56_3 = e1 & op(e2, e2) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5820) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5821)  op(e2, e2) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (5489), (5821),
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            #690.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | |   (5822)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5822) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5823)  all_56_7 = e1 & op(e1, e2) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5815), (5823) are inconsistent by sub-proof
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |            #604.
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5824)  all_56_13 = e1 & op(e0, e2) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5824) implies:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5825)  all_56_13 = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | |   (5826)  op(e0, e2) = e1
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (5827)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5827) gives:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5828)  all_56_12 = e3 & op(e0, e3) = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5828) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5829)  all_56_12 = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5830)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5830) gives:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5831)  all_56_1 = e3 & op(e3, e2) = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5831) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5832)  all_56_1 = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5833)  op(e3, e2) = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5834)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5834) gives:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5835)  all_56_1 = e0 & op(e3, e2) = e0
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5832), (5835) are inconsistent by sub-proof
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #955.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5836)  all_56_3 = e0 & op(e2, e2) = e0
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5836) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5837)  op(e2, e2) = e0
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5838)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5838) gives:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5839)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5839) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5840)  op(e3, e3) = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5829), (5840), (function-axioms) are inconsistent
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5841)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5841) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5842)  op(e2, e2) = e2
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5837), (5842), (function-axioms) are
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5843)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5843) gives:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5844)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5844) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5845)  op(e1, e1) = e1
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (134), (157), (169), (170), (203),
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (272), (5445), (5811), (5833), (5845),
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #401.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5846)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5846) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5847)  op(e0, e0) = e0
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5806), (5847), (function-axioms) are
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5848)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5848) gives:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5849)  all_56_7 = e0 & op(e1, e2) = e0
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5849) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5850)  all_56_7 = e0
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5815), (5850) are inconsistent by sub-proof
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #523.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5851)  all_56_13 = e0 & op(e0, e2) = e0
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5851) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5852)  op(e0, e2) = e0
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5826), (5852), (function-axioms) are
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #832.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5853)  all_56_3 = e3 & op(e2, e2) = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5853) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5854)  op(e2, e2) = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (5854), (function-axioms) are
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #711.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5855)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (5443), (5825), (5855),
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5856)  all_56_13 = e3 & op(e0, e2) = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5856) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5857)  all_56_13 = e3
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5825), (5857) are inconsistent by sub-proof
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (5858)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (5445), (5806), (5858),
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | |            #719.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | |   (5859)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (5446), (5804), (5859),
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | |            #509.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | |   (5860)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (5446), (5803), (5860),
% 154.49/22.75  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.75  | | | | | | | | | | | | | | | | | | |            #210.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | |   (5861)  all_24_2 = e1
% 154.49/22.75  | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (5861) imply:
% 154.49/22.75  | | | | | | | | | | | | | | | | |   (5862)  all_4_2 = e1
% 154.49/22.75  | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | SIMP: (5862) implies:
% 154.49/22.75  | | | | | | | | | | | | | | | | |   (5863)  all_4_2 = e1
% 154.49/22.75  | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | REDUCE: (360), (5863) imply:
% 154.49/22.75  | | | | | | | | | | | | | | | | |   (5864)   ~ (all_52_13 = e1)
% 154.49/22.75  | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | REDUCE: (36), (5863) imply:
% 154.49/22.75  | | | | | | | | | | | | | | | | |   (5865)  op(e2, e2) = e1
% 154.49/22.75  | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.49/22.75  | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | |   (5866)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.49/22.75  | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.49/22.75  | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (4658), (5865), (5866),
% 154.49/22.75  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.75  | | | | | | | | | | | | | | | | | |            #254.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | |   (5867)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.49/22.75  | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.49/22.75  | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.49/22.75  | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.49/22.75  | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (51), (160), (164), (168), (210),
% 154.49/22.75  | | | | | | | | | | | | | | | | | |            (5446), (5476), (5864), (5867), (function-axioms)
% 154.49/22.75  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #209.
% 154.49/22.75  | | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | |   (5868)  all_56_9 = e1 & op(e3, e0) = e1
% 154.49/22.75  | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5476), (5868), (function-axioms) are
% 154.49/22.75  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #851.
% 154.49/22.75  | | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | |   (5869)  all_54_2 = e0
% 154.49/22.75  | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | COMBINE_EQS: (5451), (5869) imply:
% 154.49/22.75  | | | | | | | | | | | | | |   (5870)  all_20_0 = e0
% 154.49/22.75  | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | REDUCE: (5448), (5870) imply:
% 154.49/22.75  | | | | | | | | | | | | | |   (5871)  $false
% 154.49/22.75  | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | | CLOSE: (5871) is inconsistent.
% 154.49/22.75  | | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | |   (5872)   ~ (all_20_1 = e2) & op(e3, e3) = all_20_1 &
% 154.49/22.75  | | | | | | | | | | |           $i(all_20_1)
% 154.49/22.75  | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | ALPHA: (5872) implies:
% 154.49/22.75  | | | | | | | | | | |   (5873)   ~ (all_20_1 = e2)
% 154.49/22.75  | | | | | | | | | | |   (5874)  op(e3, e3) = all_20_1
% 154.49/22.75  | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_20_1,
% 154.49/22.75  | | | | | | | | | | |              e3, e3, simplifying with (4658), (5874) gives:
% 154.49/22.75  | | | | | | | | | | |   (5875)  all_20_1 = e2
% 154.49/22.75  | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | REDUCE: (5873), (5875) imply:
% 154.49/22.75  | | | | | | | | | | |   (5876)  $false
% 154.49/22.75  | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | | CLOSE: (5876) is inconsistent.
% 154.49/22.75  | | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | End of split
% 154.49/22.75  | | | | | | | | | 
% 154.49/22.75  | | | | | | | | Case 2:
% 154.49/22.75  | | | | | | | | | 
% 154.49/22.75  | | | | | | | | |   (5877)  all_18_2 = e3
% 154.49/22.75  | | | | | | | | |   (5878)  ( ~ (all_18_0 = e1) & op(e3, e0) = all_18_0 &
% 154.49/22.75  | | | | | | | | |             $i(all_18_0)) | ( ~ (all_18_1 = e2) & op(e3, e3) =
% 154.49/22.75  | | | | | | | | |             all_18_1 & $i(all_18_1))
% 154.49/22.75  | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | COMBINE_EQS: (301), (5877) imply:
% 154.49/22.75  | | | | | | | | |   (5879)  all_14_2 = e3
% 154.49/22.75  | | | | | | | | | 
% 154.49/22.75  | | | | | | | | | REDUCE: (351), (5879) imply:
% 154.49/22.75  | | | | | | | | |   (5880)   ~ (all_52_3 = e3)
% 154.49/22.75  | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | REDUCE: (362), (5879) imply:
% 154.49/22.76  | | | | | | | | |   (5881)   ~ (all_52_7 = e3)
% 154.49/22.76  | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | REDUCE: (369), (5879) imply:
% 154.49/22.76  | | | | | | | | |   (5882)   ~ (all_52_11 = e3)
% 154.49/22.76  | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | REDUCE: (370), (5879) imply:
% 154.49/22.76  | | | | | | | | |   (5883)   ~ (all_52_12 = e3)
% 154.49/22.76  | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | REDUCE: (371), (5879) imply:
% 154.49/22.76  | | | | | | | | |   (5884)   ~ (all_52_13 = e3)
% 154.49/22.76  | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | REDUCE: (372), (5879) imply:
% 154.49/22.76  | | | | | | | | |   (5885)   ~ (all_52_14 = e3)
% 154.49/22.76  | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | REDUCE: (51), (5879) imply:
% 154.49/22.76  | | | | | | | | |   (5886)  op(e0, e0) = e3
% 154.49/22.76  | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | BETA: splitting (5878) gives:
% 154.49/22.76  | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | |   (5887)   ~ (all_18_0 = e1) & op(e3, e0) = all_18_0 &
% 154.49/22.76  | | | | | | | | | |           $i(all_18_0)
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | ALPHA: (5887) implies:
% 154.49/22.76  | | | | | | | | | |   (5888)   ~ (all_18_0 = e1)
% 154.49/22.76  | | | | | | | | | |   (5889)  op(e3, e0) = all_18_0
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 154.49/22.76  | | | | | | | | | |              all_18_0, e0, e3, simplifying with (168), (5889)
% 154.49/22.76  | | | | | | | | | |              gives:
% 154.49/22.76  | | | | | | | | | |   (5890)  all_52_12 = all_18_0
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | COMBINE_EQS: (270), (5890) imply:
% 154.49/22.76  | | | | | | | | | |   (5891)  all_54_3 = all_18_0
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | REDUCE: (133), (5890) imply:
% 154.49/22.76  | | | | | | | | | |   (5892)   ~ (all_52_4 = all_18_0)
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | REDUCE: (120), (5890) imply:
% 154.49/22.76  | | | | | | | | | |   (5893)   ~ (all_52_8 = all_18_0)
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | REDUCE: (113), (5890) imply:
% 154.49/22.76  | | | | | | | | | |   (5894)   ~ (all_52_13 = all_18_0)
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | SIMP: (5894) implies:
% 154.49/22.76  | | | | | | | | | |   (5895)   ~ (all_52_13 = all_18_0)
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | REDUCE: (112), (5890) imply:
% 154.49/22.76  | | | | | | | | | |   (5896)   ~ (all_52_14 = all_18_0)
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | SIMP: (5896) implies:
% 154.49/22.76  | | | | | | | | | |   (5897)   ~ (all_52_14 = all_18_0)
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | REDUCE: (5883), (5890) imply:
% 154.49/22.76  | | | | | | | | | |   (5898)   ~ (all_18_0 = e3)
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | REDUCE: (4654), (5890) imply:
% 154.49/22.76  | | | | | | | | | |   (5899)   ~ (all_18_0 = e2)
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | BETA: splitting (201) gives:
% 154.49/22.76  | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | |   (5900)  all_54_3 = e3
% 154.49/22.76  | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | COMBINE_EQS: (5891), (5900) imply:
% 154.49/22.76  | | | | | | | | | | |   (5901)  all_18_0 = e3
% 154.49/22.76  | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | SIMP: (5901) implies:
% 154.49/22.76  | | | | | | | | | | |   (5902)  all_18_0 = e3
% 154.49/22.76  | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | REDUCE: (5898), (5902) imply:
% 154.49/22.76  | | | | | | | | | | |   (5903)  $false
% 154.49/22.76  | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | CLOSE: (5903) is inconsistent.
% 154.49/22.76  | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | |   (5904)   ~ (all_54_3 = e3)
% 154.49/22.76  | | | | | | | | | | |   (5905)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 154.49/22.76  | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | BETA: splitting (5905) gives:
% 154.49/22.76  | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | |   (5906)  all_54_3 = e2
% 154.49/22.76  | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | COMBINE_EQS: (5891), (5906) imply:
% 154.49/22.76  | | | | | | | | | | | |   (5907)  all_18_0 = e2
% 154.49/22.76  | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | SIMP: (5907) implies:
% 154.49/22.76  | | | | | | | | | | | |   (5908)  all_18_0 = e2
% 154.49/22.76  | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | REDUCE: (5899), (5908) imply:
% 154.49/22.76  | | | | | | | | | | | |   (5909)  $false
% 154.49/22.76  | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | CLOSE: (5909) is inconsistent.
% 154.49/22.76  | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | |   (5910)   ~ (all_54_3 = e2)
% 154.49/22.76  | | | | | | | | | | | |   (5911)  all_54_3 = e1 | all_54_3 = e0
% 154.49/22.76  | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | BETA: splitting (5911) gives:
% 154.49/22.76  | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | |   (5912)  all_54_3 = e1
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | COMBINE_EQS: (5891), (5912) imply:
% 154.49/22.76  | | | | | | | | | | | | |   (5913)  all_18_0 = e1
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | SIMP: (5913) implies:
% 154.49/22.76  | | | | | | | | | | | | |   (5914)  all_18_0 = e1
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | REDUCE: (5888), (5914) imply:
% 154.49/22.76  | | | | | | | | | | | | |   (5915)  $false
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | CLOSE: (5915) is inconsistent.
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | |   (5916)  all_54_3 = e0
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | COMBINE_EQS: (5891), (5916) imply:
% 154.49/22.76  | | | | | | | | | | | | |   (5917)  all_18_0 = e0
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | SIMP: (5917) implies:
% 154.49/22.76  | | | | | | | | | | | | |   (5918)  all_18_0 = e0
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | REDUCE: (5892), (5918) imply:
% 154.49/22.76  | | | | | | | | | | | | |   (5919)   ~ (all_52_4 = e0)
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | REDUCE: (5893), (5918) imply:
% 154.49/22.76  | | | | | | | | | | | | |   (5920)   ~ (all_52_8 = e0)
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | REDUCE: (5895), (5918) imply:
% 154.49/22.76  | | | | | | | | | | | | |   (5921)   ~ (all_52_13 = e0)
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | REDUCE: (5897), (5918) imply:
% 154.49/22.76  | | | | | | | | | | | | |   (5922)   ~ (all_52_14 = e0)
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | REDUCE: (5898), (5918) imply:
% 154.49/22.76  | | | | | | | | | | | | |   (5923)   ~ (e3 = e0)
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | REDUCE: (5899), (5918) imply:
% 154.49/22.76  | | | | | | | | | | | | |   (5924)   ~ (e2 = e0)
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | REDUCE: (5888), (5918) imply:
% 154.49/22.76  | | | | | | | | | | | | |   (5925)   ~ (e1 = e0)
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | BETA: splitting (206) gives:
% 154.49/22.76  | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | |   (5926)  all_56_15 = e0 & op(e0, e0) = e0
% 154.49/22.76  | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | ALPHA: (5926) implies:
% 154.49/22.76  | | | | | | | | | | | | | |   (5927)  op(e0, e0) = e0
% 154.49/22.76  | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | REF_CLOSE: (7), (5886), (5927), (function-axioms) are
% 154.49/22.76  | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 154.49/22.76  | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | |   (5928)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 154.49/22.76  | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 154.49/22.76  | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 154.49/22.76  | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 154.49/22.76  | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 154.49/22.76  | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | ALPHA: (5928) implies:
% 154.49/22.76  | | | | | | | | | | | | | |   (5929)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 154.49/22.76  | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 154.49/22.76  | | | | | | | | | | | | | |               e0) = e0)
% 154.49/22.76  | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 154.49/22.76  | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | |   (5930)   ~ (all_20_2 = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | REDUCE: (325), (5930) imply:
% 154.49/22.76  | | | | | | | | | | | | | | |   (5931)   ~ (all_10_2 = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | |   (5932)   ~ (all_22_2 = e0)
% 154.49/22.76  | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | REDUCE: (251), (5932) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | |   (5933)   ~ (all_10_2 = e0)
% 154.49/22.76  | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | |   (5934)  all_54_10 = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (5931), (5934) are inconsistent by
% 154.49/22.76  | | | | | | | | | | | | | | | | |            sub-proof #361.
% 154.49/22.76  | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | |   (5935)   ~ (all_54_10 = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | | |   (5936)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.49/22.76  | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | BETA: splitting (5936) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | |   (5937)  all_54_10 = e2
% 154.49/22.76  | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (375), (5937) are inconsistent by sub-proof
% 154.49/22.76  | | | | | | | | | | | | | | | | | |            #360.
% 154.49/22.76  | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | |   (5938)   ~ (all_54_10 = e2)
% 154.49/22.76  | | | | | | | | | | | | | | | | | |   (5939)  all_54_10 = e1 | all_54_10 = e0
% 154.49/22.76  | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | BETA: splitting (5939) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | |   (5940)  all_54_10 = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (5940) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | |   (5941)  all_10_2 = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | SIMP: (5941) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | |   (5942)  all_10_2 = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | REDUCE: (350), (5942) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | |   (5943)   ~ (all_52_2 = e1)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | REDUCE: (363), (5942) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | |   (5944)   ~ (all_52_8 = e1)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | REDUCE: (368), (5942) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | |   (5945)   ~ (all_52_14 = e1)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | REDUCE: (5931), (5942) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | |   (5946)   ~ (e3 = e1)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | REDUCE: (375), (5942) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | |   (5947)   ~ (e2 = e1)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | REDUCE: (45), (5942) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | |   (5948)  op(e1, e1) = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | |   (5949)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5949) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | |   (5950)  all_56_0 = e1 & op(e3, e3) = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5950) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | |   (5951)  op(e3, e3) = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4658), (5951), (function-axioms) are
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | |   (5952)  all_56_1 = e1 & op(e3, e2) = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5952) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | |   (5953)  all_56_1 = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | |   (5954)  op(e3, e2) = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | |   (5955)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (4658), (5954), (5955),
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | |            #233.
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | |   (5956)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5956) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | |   (5957)  all_56_4 = e3 & op(e3, e1) = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5957) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | |   (5958)  op(e3, e1) = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | |   (5959)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5959) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (5960)  all_56_9 = e1 & op(e3, e0) = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5960) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (5961)  op(e3, e0) = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5888), (5889), (5961), (function-axioms) are
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #395.
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (5962)  all_56_10 = e1 & op(e2, e0) = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5962) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (5963)  all_56_10 = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (5964)  op(e2, e0) = e1
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5965)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5965) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5966)  all_56_9 = e2 & op(e3, e0) = e2
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5966) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5967)  all_56_9 = e2
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (160), (206), (5886), (5922),
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5963), (5967), (function-axioms) are inconsistent
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #405.
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5968)  all_56_10 = e2 & op(e2, e0) = e2
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5968) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5969)  op(e2, e0) = e2
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5964), (5969), (function-axioms) are
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5970)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5970) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5971)  all_56_11 = e2 & op(e1, e0) = e2
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5971) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5972)  all_56_11 = e2
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5973)  all_54_2 = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (5973) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5974)  all_52_8 = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (5974) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5975)   ~ (all_52_4 = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (5974) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5976)   ~ (all_52_9 = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5976) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5977)   ~ (all_52_9 = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (5974) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5978)   ~ (all_52_11 = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5979)  all_54_1 = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (5979) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5980)  all_52_4 = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5975), (5980) imply:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5981)  $false
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5981) is inconsistent.
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5982)   ~ (all_54_1 = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5983)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5984)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5984) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5985)  all_56_1 = e3 & op(e3, e2) = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5985) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5986)  op(e3, e2) = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (169), (170), (203), (272), (5958), (5986),
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #403.
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5987)  all_56_3 = e3 & op(e2, e2) = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5987) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5988)  op(e2, e2) = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (5988), (function-axioms) are
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #711.
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5989)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5989) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5990)  all_56_7 = e3 & op(e1, e2) = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5990) implies:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5991)  all_56_7 = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5992)  op(e1, e2) = e3
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5983) gives:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5993)  all_54_1 = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (4652), (5993) are inconsistent by
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #609.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5994)   ~ (all_54_1 = e2)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5995)  all_54_1 = e1 | all_54_1 = e0
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5996)  all_54_11 = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (5885), (5996) are inconsistent by
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #655.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5997)   ~ (all_54_11 = e3)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5998)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5998) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5999)  all_54_11 = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (5999) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6000)  all_52_14 = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6000) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6001)  all_52_14 = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (6001) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6002)   ~ (all_52_13 = e2)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5885), (6001) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6003)   ~ (e3 = e2)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6004)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6004) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6005)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6005) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6006)  op(e3, e3) = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6006), (function-axioms) are
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6007)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6007) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6008)  op(e2, e2) = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6009)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6010)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6011)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6011) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6012)  all_56_2 = e3 & op(e2, e3) = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6012) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6013)  all_56_2 = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6009) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6014)  all_57_15 = e2 & op(e0, e0) = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6014) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6015)  op(e0, e0) = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5886), (6015), (function-axioms) are
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6016)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6016) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6017)   ~ (all_57_7 = e0)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6018)  op(e0, e2) = all_57_7
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6019)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4658), (6013), (6019),
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #208.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6020)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6020) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6021)  all_56_6 = e1 & op(e1, e3) = e1
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6021) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6022)  op(e1, e3) = e1
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5943), (6022), (function-axioms) are
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6023)  all_56_12 = e1 & op(e0, e3) = e1
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6010) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6024)  all_57_14 = e2 & op(e1, e1) = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6024) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6025)  op(e1, e1) = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5948), (6025), (function-axioms) are
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6026)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6026) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6027)  op(e1, e2) = all_57_3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6028)  all_54_7 = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (6028) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6029)  all_52_13 = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5884), (6029) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6030)  $false
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6030) is inconsistent.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6031)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6031) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6032)  all_54_7 = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (6032) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6033)  all_52_13 = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6002), (6033) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6034)  $false
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6034) is inconsistent.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6035)  all_54_7 = e1 | all_54_7 = e0
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6035) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6023) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6036)  op(e0, e3) = e1
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_7, e2, e0, simplifying with (158), (6018)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6037)  all_57_7 = all_52_7
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (6036) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6038)  all_52_3 = e1
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_3, e2, e1, simplifying with (162), (6027)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6039)  all_57_3 = all_52_6
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_57_3,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (5992), (6027) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6040)  all_57_3 = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e2,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (6008) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6041)  all_4_2 = e2
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6039), (6040) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6042)  all_52_6 = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6042) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6043)  all_52_6 = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6017), (6037) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6044)   ~ (all_52_7 = e0)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (6038) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6045)   ~ (all_52_7 = e1)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6045) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6046)   ~ (all_52_7 = e1)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (6043) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6047)   ~ (all_52_7 = e3)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (6041) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6048)   ~ (all_52_7 = e2)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (248), (5881), (6044), (6046), (6048) are
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #207.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6049)  all_54_7 = e0
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (6049) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6050)  all_52_13 = e0
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5921), (6050) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6051)  $false
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6051) is inconsistent.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6052)  all_56_3 = e3 & op(e2, e2) = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6052) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6053)  op(e2, e2) = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (6053), (function-axioms) are
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #711.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6054)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (165), (210), (5886),
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5929), (5972), (5977), (6054), (function-axioms)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #206.
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6055)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6055) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6056)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6056) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6057)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6058)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6059)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6059) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6060)  all_56_2 = e3 & op(e2, e3) = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6060) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6061)  all_56_2 = e3
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5995) gives:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6062)  all_54_1 = e1
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6062) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6063)  all_52_4 = e1
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6063) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6064)  all_52_4 = e1
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (6064) imply:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6065)   ~ (all_52_6 = e1)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6065) implies:
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6066)   ~ (all_52_6 = e1)
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.49/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (6064) imply:
% 154.54/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6067)   ~ (all_4_2 = e1)
% 154.54/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6067) implies:
% 154.54/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6068)   ~ (all_4_2 = e1)
% 154.54/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 154.54/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6069)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4658), (6061), (6069),
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #208.
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6070)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6070) gives:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6071)  all_56_6 = e1 & op(e1, e3) = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6071) implies:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6072)  op(e1, e3) = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5943), (6072), (function-axioms) are
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6073)  all_56_12 = e1 & op(e0, e3) = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6073) implies:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6074)  all_56_12 = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6075)  op(e0, e3) = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6058) gives:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6076)  all_57_12 = e1 & op(e2, e2) = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6076) implies:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6077)  op(e2, e2) = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (225), (227), (228),
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5953), (6077), (function-axioms) are inconsistent
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #332.
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6078)   ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_5)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6078) implies:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6079)   ~ (all_57_5 = e2)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6080)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6080) gives:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6081)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6081) gives:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6082)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (6082), (function-axioms) are
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6083)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6083) gives:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6084)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (6084), (function-axioms) are
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6085)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6085) gives:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6086)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6086) implies:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6087)  op(e2, e3) = e2
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (6087), (function-axioms) are
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6088)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6088) gives:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6089)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6089) implies:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6090)  op(e1, e1) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (5945), (5991), (5992), (6090),
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #457.
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6091)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6091) implies:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6092)  op(e2, e1) = e2
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6093)  op(e3, e2) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (134), (157), (169), (170), (203),
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (272), (5882), (5948), (6092), (6093),
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #401.
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6094)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6094) gives:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6095)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6095) gives:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6096)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6096) gives:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6097)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6097) implies:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6098)  op(e0, e3) = e0
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6075), (6098), (function-axioms) are
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6099)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6099) implies:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6100)  op(e3, e3) = e3
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (157), (165),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (206), (209), (210), (211), (224), (225),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (229), (231), (233), (268), (373),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5882), (5977), (5991), (5992), (6068), (6100),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #464.
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6101)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (5964), (6074), (6101),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #223.
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6102)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6102) gives:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6103)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6103) gives:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6104)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6104) implies:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6105)  op(e1, e1) = e3
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (5945), (5991), (5992), (6105),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #457.
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6106)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6106) implies:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6107)  op(e2, e2) = e1
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (225), (227), (228),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5953), (6107), (function-axioms) are inconsistent
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #332.
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6108)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (163), (213),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (5886), (5943), (5945), (5991),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5992), (6108), (function-axioms) are inconsistent
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #454.
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6109)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6109) gives:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6110)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6110) gives:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6111)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6111) gives:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6112)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6112) gives:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6113)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6113) implies:
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6114)  op(e3, e3) = e1
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (6074), (6114), (function-axioms)
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #495.
% 154.54/22.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6115)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6115) implies:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6116)  op(e2, e2) = e1
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (225), (227), (228),
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5953), (6116), (function-axioms) are inconsistent
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #332.
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6117)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (5886), (5948), (6117),
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #453.
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6118)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6118) gives:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6119)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (5948), (6066), (6119),
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6120)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6120) gives:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6121)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6121) implies:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6122)  op(e0, e3) = e0
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6075), (6122), (function-axioms) are
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6123)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6123) gives:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6124)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6124) implies:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6125)  op(e3, e3) = e3
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (157), (165),
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (206), (209), (210), (211), (224), (225),
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (229), (231), (233), (268), (373),
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5882), (5977), (5991), (5992), (6068), (6125),
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #464.
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6126)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6126) implies:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6127)  op(e3, e3) = e1
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (4650), (6074), (6127), (function-axioms)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #495.
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6128)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6128) gives:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6129)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6129) gives:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6130)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6130) gives:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6131)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6131) implies:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6132)  op(e0, e0) = e2
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5886), (6132), (function-axioms) are
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6133)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6133) implies:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6134)  all_57_5 = e2
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6079), (6134) imply:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6135)  $false
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6135) is inconsistent.
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6136)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6136) gives:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6137)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6137) implies:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6138)  op(e2, e2) = e1
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (225), (227), (228),
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5953), (6138), (function-axioms) are inconsistent
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #332.
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6139)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6139) implies:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6140)  op(e0, e3) = e0
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6075), (6140), (function-axioms) are
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6141)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 154.54/22.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6141) gives:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6142)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6142) gives:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6143)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6143) implies:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6144)  op(e0, e0) = e2
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5886), (6144), (function-axioms) are
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6145)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6145) implies:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6146)  op(e3, e3) = e3
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (157), (165),
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (206), (209), (210), (211), (224), (225),
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (229), (231), (233), (268), (373),
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5882), (5977), (5991), (5992), (6068), (6146),
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #464.
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6147)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6147) gives:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6148)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6148) implies:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6149)  op(e2, e0) = e2
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5964), (6149), (function-axioms) are
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6150)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6150) gives:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6151)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6151) implies:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6152)  op(e1, e0) = e1
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (5945), (6152), (function-axioms) are
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6153)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6153) implies:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6154)  op(e0, e0) = all_57_15
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6155)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6155) gives:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6156)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6156) gives:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6157)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6157) gives:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6158)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6158) implies:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6159)  op(e0, e3) = e0
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6075), (6159), (function-axioms) are
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6160)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (5948), (5964), (6160),
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #810.
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6161)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (4658), (5964), (6075), (6161),
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #218.
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6162)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6162) gives:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6163)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6163) gives:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6164)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6164) implies:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6165)  op(e1, e1) = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5948), (6165), (function-axioms) are
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6166)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6166) gives:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6167)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6167) implies:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6168)  all_57_15 = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6154), (6168) imply:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6169)  op(e0, e0) = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5886), (6169), (function-axioms) are
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6170)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6170) implies:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6171)  op(e3, e3) = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (6171), (function-axioms) are
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6172)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6172) gives:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6173)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6173) gives:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6174)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e1) = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6174) implies:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6175)  op(e2, e0) = e2
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5964), (6175), (function-axioms) are
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6176)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e1) = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6176) implies:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6177)  op(e1, e1) = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5948), (6177), (function-axioms) are
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6178)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5886), (6057), (6178), (function-axioms) are
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #205.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6179)  all_54_1 = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (5919), (6179) are inconsistent by
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #418.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6180)  all_56_3 = e3 & op(e2, e2) = e3
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6180) implies:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6181)  op(e2, e2) = e3
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (6181), (function-axioms) are
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #711.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6182)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (165), (210), (5886),
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5929), (5972), (5977), (6182), (function-axioms)
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #206.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6183)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6183) implies:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6184)  op(e0, e0) = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5886), (6184), (function-axioms) are
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6185)  all_54_11 = e1 | all_54_11 = e0
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (5922), (5945), (6185) are inconsistent by
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #623.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6186)  all_56_13 = e3 & op(e0, e2) = e3
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5881), (6186), (function-axioms) are
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.54/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6187)   ~ (all_54_2 = e3)
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (271), (6187) imply:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6188)   ~ (all_52_8 = e3)
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5958), (6188), (function-axioms) are
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6189)  all_56_15 = e2 & op(e0, e0) = e2
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6189) implies:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6190)  op(e0, e0) = e2
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5886), (6190), (function-axioms) are
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | |   (6191)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (5886), (5945), (6191),
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | |            #391.
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | |   (6192)  all_56_9 = e3 & op(e3, e0) = e3
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6192) implies:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | |   (6193)  op(e3, e0) = e3
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5883), (6193), (function-axioms) are
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | |   (6194)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6194) gives:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | |   (6195)  all_56_4 = e1 & op(e3, e1) = e1
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5944), (6195), (function-axioms) are
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #331.
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | |   (6196)  all_56_9 = e1 & op(e3, e0) = e1
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6196) implies:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | |   (6197)  op(e3, e0) = e1
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5888), (5889), (6197), (function-axioms) are
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #395.
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | |   (6198)  all_54_10 = e0
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (5933), (6198) are inconsistent by
% 154.77/22.82  | | | | | | | | | | | | | | | | | | |            sub-proof #329.
% 154.77/22.82  | | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | |   (6199)  all_22_2 = e0
% 154.77/22.82  | | | | | | | | | | | | | | | |   (6200)  ( ~ (all_22_0 = e2) & op(e0, e1) = all_22_0 &
% 154.77/22.82  | | | | | | | | | | | | | | | |             $i(all_22_0)) | ( ~ (all_22_1 = e3) & op(e0, e0)
% 154.77/22.82  | | | | | | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 154.77/22.82  | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (6199) imply:
% 154.77/22.82  | | | | | | | | | | | | | | | |   (6201)  all_10_2 = e0
% 154.77/22.82  | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | SIMP: (6201) implies:
% 154.77/22.82  | | | | | | | | | | | | | | | |   (6202)  all_10_2 = e0
% 154.77/22.82  | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | REDUCE: (366), (6202) imply:
% 154.77/22.82  | | | | | | | | | | | | | | | |   (6203)   ~ (all_52_11 = e0)
% 154.77/22.82  | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | REDUCE: (45), (6202) imply:
% 154.77/22.82  | | | | | | | | | | | | | | | |   (6204)  op(e1, e1) = e0
% 154.77/22.82  | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.77/22.82  | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.82  | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | |   (6205)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.77/22.82  | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.77/22.82  | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.77/22.82  | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.77/22.82  | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.77/22.82  | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.77/22.82  | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.77/22.82  | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.77/22.82  | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | BETA: splitting (6205) gives:
% 154.77/22.82  | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | |   (6206)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.77/22.82  | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 154.77/22.82  | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | ALPHA: (6206) implies:
% 154.77/22.82  | | | | | | | | | | | | | | | | | |   (6207)  op(e3, e3) = e3
% 154.77/22.82  | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6207), (function-axioms) are
% 154.77/22.82  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.77/22.82  | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | |   (6208)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.77/22.82  | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 154.77/22.82  | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 154.77/22.82  | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (125), (157), (158), (190), (191),
% 154.77/22.82  | | | | | | | | | | | | | | | | | |            (247), (248), (356), (5881), (5882), (5886),
% 154.77/22.82  | | | | | | | | | | | | | | | | | |            (6200), (6203), (6208), (function-axioms) are
% 154.77/22.82  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #204.
% 154.77/22.82  | | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | |   (6209)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.77/22.82  | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.77/22.82  | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.77/22.82  | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.77/22.82  | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.77/22.82  | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.77/22.82  | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.77/22.82  | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.77/22.82  | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.77/22.82  | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (5886), (6204), (6209),
% 154.77/22.82  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.77/22.82  | | | | | | | | | | | | | | | | |            #411.
% 154.77/22.82  | | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | | End of split
% 154.77/22.82  | | | | | | | | | | | | | | | 
% 154.77/22.82  | | | | | | | | | | | | | | Case 2:
% 154.77/22.82  | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | |   (6210)  all_20_2 = e3
% 154.77/22.83  | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | COMBINE_EQS: (325), (6210) imply:
% 154.77/22.83  | | | | | | | | | | | | | | |   (6211)  all_10_2 = e3
% 154.77/22.83  | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | SIMP: (6211) implies:
% 154.77/22.83  | | | | | | | | | | | | | | |   (6212)  all_10_2 = e3
% 154.77/22.83  | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | REDUCE: (350), (6212) imply:
% 154.77/22.83  | | | | | | | | | | | | | | |   (6213)   ~ (all_52_2 = e3)
% 154.77/22.83  | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | REDUCE: (361), (6212) imply:
% 154.77/22.83  | | | | | | | | | | | | | | |   (6214)   ~ (all_52_6 = e3)
% 154.77/22.83  | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | REDUCE: (363), (6212) imply:
% 154.77/22.83  | | | | | | | | | | | | | | |   (6215)   ~ (all_52_8 = e3)
% 154.77/22.83  | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | REDUCE: (45), (6212) imply:
% 154.77/22.83  | | | | | | | | | | | | | | |   (6216)  op(e1, e1) = e3
% 154.77/22.83  | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | |   (6217)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.77/22.83  | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 154.77/22.83  | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.77/22.83  | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.77/22.83  | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.77/22.83  | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 154.77/22.83  | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 154.77/22.83  | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 154.77/22.83  | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.77/22.83  | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 154.77/22.83  | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.77/22.83  | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.77/22.83  | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.77/22.83  | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 154.77/22.83  | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 154.77/22.83  | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 154.77/22.83  | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | BETA: splitting (6217) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | |   (6218)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 154.77/22.83  | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 154.77/22.83  | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 154.77/22.83  | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 154.77/22.83  | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 154.77/22.83  | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 154.77/22.83  | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 154.77/22.83  | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 154.77/22.83  | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | ALPHA: (6218) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | |   (6219)  op(e3, e3) = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6219), (function-axioms) are
% 154.77/22.83  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.77/22.83  | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | |   (6220)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 154.77/22.83  | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 154.77/22.83  | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 154.77/22.83  | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 154.77/22.83  | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.77/22.83  | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 154.77/22.83  | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 154.77/22.83  | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 154.77/22.83  | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | ALPHA: (6220) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | |   (6221)  op(e2, e2) = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | |   (6222)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7
% 154.77/22.83  | | | | | | | | | | | | | | | | |               = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))
% 154.77/22.83  | | | | | | | | | | | | | | | | |   (6223)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 154.77/22.83  | | | | | | | | | | | | | | | | |               = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))
% 154.77/22.83  | | | | | | | | | | | | | | | | |   (6224)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1
% 154.77/22.83  | | | | | | | | | | | | | | | | |               = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))
% 154.77/22.83  | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | BETA: splitting (6223) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | |   (6225)  all_57_14 = e2 & op(e1, e1) = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | ALPHA: (6225) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | |   (6226)  op(e1, e1) = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6216), (6226), (function-axioms) are
% 154.77/22.83  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 154.77/22.83  | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | |   (6227)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 154.77/22.83  | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | ALPHA: (6227) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | |   (6228)   ~ (all_57_3 = e1)
% 154.77/22.83  | | | | | | | | | | | | | | | | | |   (6229)  op(e1, e2) = all_57_3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | |   (6230)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | BETA: splitting (6230) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | |   (6231)  all_56_0 = e3 & op(e3, e3) = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | ALPHA: (6231) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | |   (6232)  op(e3, e3) = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6232), (function-axioms) are
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | |   (6233)  all_56_2 = e3 & op(e2, e3) = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | ALPHA: (6233) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | |   (6234)  all_56_2 = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | |   (6235)  op(e2, e3) = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | |   (6236)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6236) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | |   (6237)  all_56_1 = e3 & op(e3, e2) = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6237) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | |   (6238)  op(e3, e2) = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6222) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | |   (6239)  all_57_15 = e2 & op(e0, e0) = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6239) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | |   (6240)  op(e0, e0) = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5886), (6240), (function-axioms) are
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | |   (6241)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6241) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | |   (6242)  op(e0, e2) = all_57_7
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6224) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6243)  all_57_10 = e2 & op(e3, e3) = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6243) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6244)  all_57_10 = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_7, e2, e0, simplifying with (158), (6242)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6245)  all_57_7 = all_52_7
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_3, e2, e1, simplifying with (162), (6229)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6246)  all_57_3 = all_52_6
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e2,
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (6221) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6247)  all_4_2 = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (6235) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6248)  all_52_1 = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6228), (6246) imply:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6249)   ~ (all_52_6 = e1)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (6248) imply:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6250)   ~ (all_52_3 = e3)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (6247) imply:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6251)   ~ (all_52_6 = e2)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (6247) imply:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6252)   ~ (all_52_7 = e2)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (6247) imply:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6253)   ~ (all_52_9 = e2)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (6247) imply:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6254)   ~ (all_52_13 = e2)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (6247) imply:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | |   (6255)   ~ (e3 = e2)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (6256)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (4654), (6254), (6256),
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | |            #384.
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (6257)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6257) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6258)  all_56_11 = e2 & op(e1, e0) = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6258) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6259)  all_56_11 = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6260)  all_54_9 = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (6214), (6260) are inconsistent by
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #656.
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6261)   ~ (all_54_9 = e3)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6262)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6262) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6263)  all_54_9 = e2
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (6251), (6263) are inconsistent by
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #676.
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6264)   ~ (all_54_9 = e2)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6265)  all_54_9 = e1 | all_54_9 = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6265) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6266)  all_54_9 = e1
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (6249), (6266) are inconsistent by
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #675.
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6267)  all_54_9 = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (6267) imply:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6268)  all_52_6 = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6268) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6269)  all_52_6 = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (6269) imply:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6270)   ~ (all_52_2 = e0)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (6269) imply:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6271)   ~ (all_52_7 = e0)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6271) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6272)   ~ (all_52_7 = e0)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6273)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6273) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6274)  all_56_0 = e0 & op(e3, e3) = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6274) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6275)  op(e3, e3) = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (6275), (function-axioms) are
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6276)  all_56_2 = e0 & op(e2, e3) = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6276) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6277)  all_56_2 = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6234), (6277) are inconsistent by sub-proof
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #275.
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6278)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6278) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6279)  all_56_6 = e0 & op(e1, e3) = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6270), (6279), (function-axioms) are
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #699.
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6280)  all_56_12 = e0 & op(e0, e3) = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6280) implies:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6281)  op(e0, e3) = e0
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6282)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.77/22.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6282) gives:
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6283)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6283) gives:
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6284)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (6284), (function-axioms) are
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.77/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6285)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6285) gives:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6286)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (6286), (function-axioms) are
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6287)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6287) gives:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6288)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6288) implies:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6289)  op(e2, e3) = e2
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4649), (6289), (function-axioms) are
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6290)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6290) gives:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6291)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6291) implies:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6292)   ~ (all_57_10 = e2)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6244), (6292) imply:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6293)  $false
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6293) is inconsistent.
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6294)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6294) implies:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6295)  op(e2, e1) = e2
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6253), (6295), (function-axioms) are
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6296)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6296) gives:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6297)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6297) gives:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6298)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6298) gives:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6299)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6299) implies:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6300)   ~ (all_57_10 = e2)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6244), (6300) imply:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6301)  $false
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6301) is inconsistent.
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6302)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6302) implies:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6303)  op(e3, e3) = e3
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6303), (function-axioms) are
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6304)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6304) gives:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6305)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6305) implies:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6306)  op(e2, e0) = e2
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6254), (6306), (function-axioms) are
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6307)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6307) implies:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6308)  op(e3, e3) = e1
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (159), (163), (167), (233), (4649),
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4650), (6281), (6308), (function-axioms) are
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #421.
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6309)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6309) gives:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6310)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 154.81/22.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (6215), (6221), (6310),
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #565.
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6311)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6311) gives:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6312)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6312) implies:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6313)  op(e0, e0) = e1
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5886), (6313), (function-axioms) are
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6314)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5883), (6216), (6314), (function-axioms)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #578.
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6315)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6315) gives:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6316)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6316) gives:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6317)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6317) gives:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6318)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6318) gives:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6319)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6319) implies:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6320)  op(e3, e3) = e1
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (159), (163), (167), (233), (4649),
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4650), (6281), (6320), (function-axioms) are
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #421.
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6321)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6321) implies:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6322)  op(e2, e2) = e1
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6221), (6322), (function-axioms) are
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6323)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6323) gives:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6324)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6324) implies:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6325)  op(e1, e1) = e2
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6216), (6325), (function-axioms) are
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6326)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6326) implies:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6327)  op(e0, e0) = e1
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5886), (6327), (function-axioms) are
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6328)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6328) gives:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6329)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (6216), (6329), (function-axioms) are
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #644.
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6330)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6330) gives:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6331)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6331) implies:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6332)  op(e3, e1) = e3
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6215), (6332), (function-axioms) are
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6333)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6333) gives:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6334)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6334) implies:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6335)  op(e3, e3) = e3
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6335), (function-axioms) are
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6336)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6336) implies:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6337)  op(e3, e3) = e1
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (159), (163), (167), (233), (4649),
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4650), (6281), (6337), (function-axioms) are
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #421.
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6338)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6338) gives:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6339)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6339) gives:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6340)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (5886), (6253), (6340),
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #412.
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6341)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (5883), (6221), (6341),
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #452.
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6342)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6342) gives:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6343)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6343) gives:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6344)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6344) implies:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6345)  op(e0, e0) = e2
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5886), (6345), (function-axioms) are
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6346)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6346) implies:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6347)  op(e3, e3) = e3
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6347), (function-axioms) are
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6348)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6348) gives:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6349)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6349) implies:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6350)  op(e2, e0) = e2
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6254), (6350), (function-axioms) are
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6351)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.81/22.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6351) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6352)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6352) implies:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6353)  op(e1, e1) = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6216), (6353), (function-axioms) are
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6354)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6354) implies:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6355)  op(e0, e0) = all_57_15
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6356)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6357)  all_54_13 = e3
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (5881), (6357) are inconsistent by
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #385.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6358)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6359)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6359) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6360)  all_56_9 = e1 & op(e3, e0) = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6360) implies:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6361)  op(e3, e0) = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5888), (5889), (6361), (function-axioms) are
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #395.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6362)  all_56_10 = e1 & op(e2, e0) = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6362) implies:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6363)  op(e2, e0) = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6358) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6364)  all_54_13 = e2
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (6252), (6364) are inconsistent by
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #505.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6365)   ~ (all_54_13 = e2)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6366)  all_54_13 = e1 | all_54_13 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6366) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6367)  all_54_13 = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (6367) imply:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6368)  all_52_7 = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6368) implies:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6369)  all_52_7 = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (6369) imply:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6370)   ~ (all_52_3 = e1)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6252), (6369) imply:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6371)   ~ (e2 = e1)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (6369) imply:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6372)  op(e0, e2) = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6373)  all_54_12 = e3
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5880), (6373) are inconsistent by
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #697.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6374)   ~ (all_54_12 = e3)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6375)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6375) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6376)  all_54_12 = e2
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (4651), (6376) are inconsistent by
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #696.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6377)   ~ (all_54_12 = e2)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6378)  all_54_12 = e1 | all_54_12 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6378) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6379)  all_54_12 = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6379) imply:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6380)  all_52_3 = e1
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6370), (6380) imply:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6381)  $false
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6381) is inconsistent.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6382)  all_54_12 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6382) imply:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6383)  all_52_3 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (6383) imply:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6384)   ~ (all_52_11 = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6384) implies:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6385)   ~ (all_52_11 = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6356) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6386)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6386) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6387)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6387) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6388)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6388) implies:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6389)  op(e3, e3) = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (6389), (function-axioms) are
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6390)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (6216), (6363), (6390),
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #220.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6391)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6391) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6392)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6392) implies:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6393)  all_57_15 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6355), (6393) imply:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6394)  op(e0, e0) = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5886), (6394), (function-axioms) are
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6395)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (4658), (6363), (6395),
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #219.
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6396)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6396) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6397)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6397) gives:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6398)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6398) implies:
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6399)  op(e1, e1) = e0
% 154.81/22.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6216), (6399), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6400)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6400) gives:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6401)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6401) implies:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6402)  op(e0, e2) = e0
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6372), (6402), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #832.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6403)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6403) implies:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6404)  op(e3, e3) = e0
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4658), (6404), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6405)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (157), (6216), (6363), (6385), (6405),
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #217.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6406)  all_54_13 = e0
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (6272), (6406) are inconsistent by
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #503.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6407)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6407) gives:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6408)  all_56_11 = e1 & op(e1, e0) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6408) implies:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6409)  all_56_11 = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6259), (6409) imply:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6410)  e2 = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6410) implies:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6411)  e2 = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4657), (6411) imply:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6412)  all_56_0 = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (159), (163), (233), (4650),
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6234), (6281), (6412), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #203.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6413)  all_56_15 = e1 & op(e0, e0) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6413) implies:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6414)  op(e0, e0) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5886), (6414), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6415)  all_56_15 = e2 & op(e0, e0) = e2
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6415) implies:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6416)  op(e0, e0) = e2
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5886), (6416), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | |   (6417)   ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6417) implies:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | |   (6418)   ~ (all_57_1 = e3)
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | |   (6419)  op(e3, e2) = all_57_1
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_57_1,
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (6238), (6419) gives:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | |   (6420)  all_57_1 = e3
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6418), (6420) imply:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | |   (6421)  $false
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6421) is inconsistent.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | |   (6422)  all_56_3 = e3 & op(e2, e2) = e3
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6422) implies:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | |   (6423)  op(e2, e2) = e3
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (6423), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #711.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | |   (6424)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6424) gives:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | |   (6425)  all_56_7 = e3 & op(e1, e2) = e3
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (6214), (6425), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #388.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | |   (6426)  all_56_13 = e3 & op(e0, e2) = e3
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5881), (6426), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | |   (6427)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 154.81/22.88  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | BETA: splitting (6427) gives:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | |   (6428)  all_56_6 = e3 & op(e1, e3) = e3
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6213), (6428), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #681.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | |   (6429)  all_56_12 = e3 & op(e0, e3) = e3
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (5880), (6429), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #398.
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | |   (6430)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 154.81/22.88  | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 154.81/22.88  | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 154.81/22.88  | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 154.81/22.88  | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 154.81/22.88  | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 154.81/22.88  | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 154.81/22.88  | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 154.81/22.88  | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 154.81/22.88  | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 154.81/22.88  | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 154.81/22.88  | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 154.81/22.88  | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 154.81/22.88  | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 154.81/22.88  | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 154.81/22.88  | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 154.81/22.88  | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (5886), (6216), (6430),
% 154.81/22.88  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.88  | | | | | | | | | | | | | | | |            #389.
% 154.81/22.88  | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | |   (6431)   ~ (all_18_1 = e2) & op(e3, e3) = all_18_1 &
% 154.81/22.88  | | | | | | | | | |           $i(all_18_1)
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | ALPHA: (6431) implies:
% 154.81/22.88  | | | | | | | | | |   (6432)   ~ (all_18_1 = e2)
% 154.81/22.88  | | | | | | | | | |   (6433)  op(e3, e3) = all_18_1
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_18_1,
% 154.81/22.88  | | | | | | | | | |              e3, e3, simplifying with (4658), (6433) gives:
% 154.81/22.88  | | | | | | | | | |   (6434)  all_18_1 = e2
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | REDUCE: (6432), (6434) imply:
% 154.81/22.88  | | | | | | | | | |   (6435)  $false
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | CLOSE: (6435) is inconsistent.
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | | 
% 154.81/22.88  | | | | | | | | End of split
% 154.81/22.88  | | | | | | | | 
% 154.81/22.88  | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | 
% 154.81/22.88  | | | | | | | |   (6436)  all_14_2 = e1
% 154.81/22.88  | | | | | | | |   (6437)  ( ~ (all_14_0 = e2) & op(e1, e0) = all_14_0 &
% 154.81/22.88  | | | | | | | |             $i(all_14_0)) | ( ~ (all_14_1 = e3) & op(e1, e1) =
% 154.81/22.88  | | | | | | | |             all_14_1 & $i(all_14_1))
% 154.81/22.88  | | | | | | | | 
% 154.81/22.88  | | | | | | | | REDUCE: (351), (6436) imply:
% 154.81/22.88  | | | | | | | |   (6438)   ~ (all_52_3 = e1)
% 154.81/22.88  | | | | | | | | 
% 154.81/22.88  | | | | | | | | REDUCE: (362), (6436) imply:
% 154.81/22.88  | | | | | | | |   (6439)   ~ (all_52_7 = e1)
% 154.81/22.88  | | | | | | | | 
% 154.81/22.88  | | | | | | | | REDUCE: (370), (6436) imply:
% 154.81/22.88  | | | | | | | |   (6440)   ~ (all_52_12 = e1)
% 154.81/22.88  | | | | | | | | 
% 154.81/22.88  | | | | | | | | REDUCE: (372), (6436) imply:
% 154.81/22.88  | | | | | | | |   (6441)   ~ (all_52_14 = e1)
% 154.81/22.88  | | | | | | | | 
% 154.81/22.88  | | | | | | | | REDUCE: (51), (6436) imply:
% 154.81/22.88  | | | | | | | |   (6442)  op(e0, e0) = e1
% 154.81/22.88  | | | | | | | | 
% 154.81/22.88  | | | | | | | | BETA: splitting (61) gives:
% 154.81/22.88  | | | | | | | | 
% 154.81/22.88  | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | 
% 154.81/22.88  | | | | | | | | |   (6443)   ~ (all_20_2 = e3)
% 154.81/22.88  | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | REDUCE: (325), (6443) imply:
% 154.81/22.88  | | | | | | | | |   (6444)   ~ (all_10_2 = e3)
% 154.81/22.88  | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | BETA: splitting (64) gives:
% 154.81/22.88  | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | |   (6445)   ~ (all_22_2 = e0)
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | REDUCE: (251), (6445) imply:
% 154.81/22.88  | | | | | | | | | |   (6446)   ~ (all_10_2 = e0)
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | BETA: splitting (194) gives:
% 154.81/22.88  | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | |   (6447)  all_54_10 = e3
% 154.81/22.88  | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | REF_CLOSE: (336), (6444), (6447) are inconsistent by
% 154.81/22.88  | | | | | | | | | | |            sub-proof #361.
% 154.81/22.88  | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | |   (6448)   ~ (all_54_10 = e3)
% 154.81/22.88  | | | | | | | | | | |   (6449)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.81/22.88  | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | BETA: splitting (6449) gives:
% 154.81/22.88  | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | |   (6450)  all_54_10 = e2
% 154.81/22.88  | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | REF_CLOSE: (336), (375), (6450) are inconsistent by sub-proof
% 154.81/22.88  | | | | | | | | | | | |            #360.
% 154.81/22.88  | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | |   (6451)   ~ (all_54_10 = e2)
% 154.81/22.88  | | | | | | | | | | | |   (6452)  all_54_10 = e1 | all_54_10 = e0
% 154.81/22.88  | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | BETA: splitting (6452) gives:
% 154.81/22.88  | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | |   (6453)  all_54_10 = e1
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | COMBINE_EQS: (336), (6453) imply:
% 154.81/22.88  | | | | | | | | | | | | |   (6454)  all_10_2 = e1
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | SIMP: (6454) implies:
% 154.81/22.88  | | | | | | | | | | | | |   (6455)  all_10_2 = e1
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | REDUCE: (350), (6455) imply:
% 154.81/22.88  | | | | | | | | | | | | |   (6456)   ~ (all_52_2 = e1)
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | REDUCE: (363), (6455) imply:
% 154.81/22.88  | | | | | | | | | | | | |   (6457)   ~ (all_52_8 = e1)
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | REDUCE: (6444), (6455) imply:
% 154.81/22.88  | | | | | | | | | | | | |   (6458)   ~ (e3 = e1)
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | REDUCE: (375), (6455) imply:
% 154.81/22.88  | | | | | | | | | | | | |   (6459)   ~ (e2 = e1)
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | REDUCE: (45), (6455) imply:
% 154.81/22.88  | | | | | | | | | | | | |   (6460)  op(e1, e1) = e1
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | BETA: splitting (231) gives:
% 154.81/22.88  | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | |   (6461)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 154.81/22.88  | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 154.81/22.88  | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | BETA: splitting (6461) gives:
% 154.81/22.88  | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | |   (6462)  all_56_0 = e1 & op(e3, e3) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | ALPHA: (6462) implies:
% 154.81/22.88  | | | | | | | | | | | | | | |   (6463)  op(e3, e3) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | REF_CLOSE: (6), (4658), (6463), (function-axioms) are
% 154.81/22.88  | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 154.81/22.88  | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | |   (6464)  all_56_2 = e1 & op(e2, e3) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | ALPHA: (6464) implies:
% 154.81/22.88  | | | | | | | | | | | | | | |   (6465)  all_56_2 = e1
% 154.81/22.88  | | | | | | | | | | | | | | |   (6466)  op(e2, e3) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 154.81/22.88  | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | |   (6467)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 154.81/22.88  | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 154.81/22.88  | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | BETA: splitting (6467) gives:
% 154.81/22.88  | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.88  | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | |   (6468)  all_56_0 = e1 & op(e3, e3) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | ALPHA: (6468) implies:
% 154.81/22.88  | | | | | | | | | | | | | | | | |   (6469)  op(e3, e3) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (229), (233),
% 154.81/22.88  | | | | | | | | | | | | | | | | |            (235), (6465), (6466), (6469), (function-axioms)
% 154.81/22.88  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #424.
% 154.81/22.88  | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.88  | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | |   (6470)  all_56_1 = e1 & op(e3, e2) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | 
% 154.81/22.88  | | | | | | | | | | | | | | | | | ALPHA: (6470) implies:
% 154.81/22.88  | | | | | | | | | | | | | | | | |   (6471)  op(e3, e2) = e1
% 154.81/22.88  | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 154.81/22.89  | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (6466) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | |   (6472)  all_52_1 = e1
% 154.81/22.89  | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1,
% 154.81/22.89  | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (6471) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | |   (6473)  all_52_4 = e1
% 154.81/22.89  | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | REDUCE: (149), (6472) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | |   (6474)   ~ (all_52_2 = e1)
% 154.81/22.89  | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | REDUCE: (136), (6473) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | |   (6475)   ~ (all_52_6 = e1)
% 154.81/22.89  | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | SIMP: (6475) implies:
% 154.81/22.89  | | | | | | | | | | | | | | | | |   (6476)   ~ (all_52_6 = e1)
% 154.81/22.89  | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | REDUCE: (352), (6473) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | |   (6477)   ~ (all_4_2 = e1)
% 154.81/22.89  | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | SIMP: (6477) implies:
% 154.81/22.89  | | | | | | | | | | | | | | | | |   (6478)   ~ (all_4_2 = e1)
% 154.81/22.89  | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | |   (6479)   ~ (all_46_2 = e2)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | REDUCE: (4648), (6479) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | | |   (6480)  $false
% 154.81/22.89  | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | CLOSE: (6480) is inconsistent.
% 154.81/22.89  | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | |   (6481)  ( ~ (all_46_0 = e1) & op(e2, e3) = all_46_0 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | |             $i(all_46_0)) | ( ~ (all_46_1 = e0) & op(e2, e2)
% 154.81/22.89  | | | | | | | | | | | | | | | | | |             = all_46_1 & $i(all_46_1))
% 154.81/22.89  | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | BETA: splitting (6481) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |   (6482)   ~ (all_46_0 = e1) & op(e2, e3) = all_46_0 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |           $i(all_46_0)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | ALPHA: (6482) implies:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |   (6483)   ~ (all_46_0 = e1)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |   (6484)  op(e2, e3) = all_46_0
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_46_0,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (6466), (6484) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |   (6485)  all_46_0 = e1
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | REDUCE: (6483), (6485) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |   (6486)  $false
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | CLOSE: (6486) is inconsistent.
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |   (6487)   ~ (all_46_1 = e0) & op(e2, e2) = all_46_1 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |           $i(all_46_1)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | ALPHA: (6487) implies:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |   (6488)   ~ (all_46_1 = e0)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |   (6489)  op(e2, e2) = all_46_1
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |              all_46_1, e2, e2, simplifying with (36), (6489)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |              gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |   (6490)  all_46_1 = all_4_2
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | REDUCE: (6488), (6490) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | |   (6491)   ~ (all_4_2 = e0)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | |   (6492)  all_54_5 = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (6492) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | |   (6493)  all_4_2 = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (6493) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | |   (6494)  $false
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | CLOSE: (6494) is inconsistent.
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | |   (6495)   ~ (all_54_5 = e3)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | |   (6496)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6496) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | |   (6497)  all_54_5 = e2
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (6497) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | |   (6498)  all_4_2 = e2
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (6498) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | |   (6499)   ~ (all_52_9 = e2)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (6498) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | |   (6500)   ~ (all_52_13 = e2)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (6498) imply:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | |   (6501)   ~ (e3 = e2)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |   (6502)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6502) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |   (6503)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (167), (4649), (6460), (6499), (6503),
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |            #1000.
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |   (6504)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6504) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |   (6505)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6505) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (6506)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6506) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6507)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6507) implies:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6508)  op(e0, e0) = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6442), (6508), (function-axioms) are
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6509)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6509) implies:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6510)  op(e3, e3) = e3
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6510), (function-axioms) are
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (6511)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6511) gives:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6512)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6512) implies:
% 154.81/22.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6513)  op(e2, e0) = e2
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6500), (6513), (function-axioms) are
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6514)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6514) implies:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6515)  op(e3, e3) = e1
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (229), (233),
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (6465), (6466), (6515), (function-axioms)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #424.
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |   (6516)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (165), (221),
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (6456), (6460), (6465), (6499),
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |            (6516), (function-axioms) are inconsistent by
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #353.
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |   (6517)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6517) gives:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |   (6518)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6518) gives:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |   (6519)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6519) gives:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (6520)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6520) gives:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6521)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6521) implies:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6522)  op(e3, e3) = e1
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (229), (233),
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (6465), (6466), (6522), (function-axioms)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #424.
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6523)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6523) implies:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6524)  op(e2, e2) = e1
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (6465), (6499), (6524), (function-axioms)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #355.
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (6525)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (6460), (6476), (6525),
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |            #351.
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |   (6526)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6526) gives:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (6527)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (6460), (6476), (6527),
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (6528)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6528) gives:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6529)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6529) implies:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6530)  op(e0, e0) = e3
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6442), (6530), (function-axioms) are
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6531)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6531) gives:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6532)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6532) implies:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6533)  op(e3, e3) = e3
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6533), (function-axioms) are
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6534)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6534) implies:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6535)  op(e3, e3) = e1
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (229), (233),
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (6465), (6466), (6535), (function-axioms)
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #424.
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |   (6536)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6536) gives:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |   (6537)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |            (224), (6442), (6465), (6499), (6537),
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |            #350.
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |   (6538)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6538) gives:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (6539)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6539) gives:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6540)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6540) implies:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6541)  op(e0, e0) = e2
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6442), (6541), (function-axioms) are
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6542)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6542) implies:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6543)  op(e3, e3) = e3
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6543), (function-axioms) are
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (6544)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6544) gives:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6545)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6545) implies:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6546)  op(e2, e0) = e2
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6500), (6546), (function-axioms) are
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.81/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6547)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6547) gives:
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6548)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6548) implies:
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6549)  op(e1, e0) = e1
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6441), (6549), (function-axioms) are
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6550)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6550) implies:
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6551)  op(e0, e0) = all_57_15
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6552)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (110), (160), (164), (168), (211),
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4654), (4658), (6441), (6442), (6460), (6500),
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6551), (6552), (function-axioms) are inconsistent
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #246.
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | |   (6553)  all_54_5 = e1 | all_54_5 = e0
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (6478), (6491), (6553) are inconsistent by
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | |   (6554)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 155.02/22.92  | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 155.02/22.92  | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | BETA: splitting (6554) gives:
% 155.02/22.92  | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.92  | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | |   (6555)  all_56_4 = e1 & op(e3, e1) = e1
% 155.02/22.92  | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6457), (6555), (function-axioms) are
% 155.02/22.92  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #331.
% 155.02/22.92  | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | |   (6556)  all_56_9 = e1 & op(e3, e0) = e1
% 155.02/22.92  | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (6440), (6556), (function-axioms) are
% 155.02/22.92  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #851.
% 155.02/22.92  | | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | |   (6557)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 155.02/22.92  | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 155.02/22.92  | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (6438), (6456), (6557),
% 155.02/22.92  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.02/22.92  | | | | | | | | | | | | | |            #202.
% 155.02/22.92  | | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | |   (6558)  all_54_10 = e0
% 155.02/22.92  | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | | REF_CLOSE: (336), (6446), (6558) are inconsistent by
% 155.02/22.92  | | | | | | | | | | | | |            sub-proof #329.
% 155.02/22.92  | | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | |   (6559)  all_22_2 = e0
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | COMBINE_EQS: (251), (6559) imply:
% 155.02/22.92  | | | | | | | | | |   (6560)  all_10_2 = e0
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | REDUCE: (361), (6560) imply:
% 155.02/22.92  | | | | | | | | | |   (6561)   ~ (all_52_6 = e0)
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | REDUCE: (375), (6560) imply:
% 155.02/22.92  | | | | | | | | | |   (6562)   ~ (e2 = e0)
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | REDUCE: (45), (6560) imply:
% 155.02/22.92  | | | | | | | | | |   (6563)  op(e1, e1) = e0
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | BETA: splitting (238) gives:
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | Case 1:
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | |   (6564)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.02/22.92  | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.02/22.92  | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.02/22.92  | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.02/22.92  | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.02/22.92  | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.02/22.92  | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.02/22.92  | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.02/22.92  | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.02/22.92  | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.02/22.92  | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.02/22.92  | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.02/22.92  | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.02/22.92  | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.02/22.92  | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.02/22.92  | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | BETA: splitting (6564) gives:
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | Case 1:
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | |   (6565)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.02/22.92  | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.02/22.92  | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.02/22.92  | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.02/22.92  | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.02/22.92  | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.02/22.92  | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.02/22.92  | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | ALPHA: (6565) implies:
% 155.02/22.92  | | | | | | | | | | | |   (6566)  op(e3, e3) = e3
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6566), (function-axioms) are
% 155.02/22.92  | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | |   (6567)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.02/22.92  | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.02/22.92  | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.02/22.92  | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.02/22.92  | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.02/22.92  | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.02/22.92  | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.02/22.92  | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (128), (158), (162), (191), (195),
% 155.02/22.92  | | | | | | | | | | | |            (248), (258), (354), (356), (6439), (6442),
% 155.02/22.92  | | | | | | | | | | | |            (6561), (6563), (6567), (function-axioms) are
% 155.02/22.92  | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | |   (6568)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.02/22.92  | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.02/22.92  | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.02/22.92  | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.02/22.92  | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.02/22.92  | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.02/22.92  | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.02/22.92  | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.02/22.92  | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.02/22.92  | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.02/22.92  | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.02/22.92  | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.02/22.92  | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.02/22.92  | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.02/22.92  | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.02/22.92  | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | REF_CLOSE: (4), (51), (6442), (6563), (6568),
% 155.02/22.92  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.02/22.92  | | | | | | | | | | |            #629.
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | End of split
% 155.02/22.92  | | | | | | | | | 
% 155.02/22.92  | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | 
% 155.02/22.92  | | | | | | | | |   (6569)  all_20_2 = e3
% 155.02/22.92  | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | COMBINE_EQS: (325), (6569) imply:
% 155.02/22.92  | | | | | | | | |   (6570)  all_10_2 = e3
% 155.02/22.92  | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | REDUCE: (368), (6570) imply:
% 155.02/22.92  | | | | | | | | |   (6571)   ~ (all_52_14 = e3)
% 155.02/22.92  | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | REDUCE: (45), (6570) imply:
% 155.02/22.92  | | | | | | | | |   (6572)  op(e1, e1) = e3
% 155.02/22.92  | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | BETA: splitting (6437) gives:
% 155.02/22.92  | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | Case 1:
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | |   (6573)   ~ (all_14_0 = e2) & op(e1, e0) = all_14_0 &
% 155.02/22.92  | | | | | | | | | |           $i(all_14_0)
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | ALPHA: (6573) implies:
% 155.02/22.92  | | | | | | | | | |   (6574)   ~ (all_14_0 = e2)
% 155.02/22.92  | | | | | | | | | |   (6575)  op(e1, e0) = all_14_0
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | BETA: splitting (238) gives:
% 155.02/22.92  | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | Case 1:
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | |   (6576)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.02/22.92  | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.02/22.92  | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.02/22.92  | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.02/22.92  | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.02/22.92  | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.02/22.92  | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.02/22.92  | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.02/22.92  | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.02/22.92  | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.02/22.92  | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.02/22.92  | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.02/22.92  | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.02/22.92  | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.02/22.92  | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.02/22.92  | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | BETA: splitting (6576) gives:
% 155.02/22.92  | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | Case 1:
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | |   (6577)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.02/22.92  | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.02/22.92  | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.02/22.92  | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.02/22.92  | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.02/22.92  | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.02/22.92  | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.02/22.92  | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | ALPHA: (6577) implies:
% 155.02/22.92  | | | | | | | | | | | |   (6578)  op(e3, e3) = e3
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | REF_CLOSE: (9), (4658), (6578), (function-axioms) are
% 155.02/22.92  | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | Case 2:
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | |   (6579)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.02/22.92  | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.02/22.92  | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.02/22.92  | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.02/22.92  | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.02/22.92  | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.02/22.92  | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.02/22.92  | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.02/22.92  | | | | | | | | | | | | 
% 155.02/22.92  | | | | | | | | | | | | ALPHA: (6579) implies:
% 155.02/22.93  | | | | | | | | | | | |   (6580)  op(e2, e2) = e2
% 155.02/22.93  | | | | | | | | | | | |   (6581)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7
% 155.02/22.93  | | | | | | | | | | | |               = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))
% 155.02/22.93  | | | | | | | | | | | |   (6582)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 155.02/22.93  | | | | | | | | | | | |               = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))
% 155.02/22.93  | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | BETA: splitting (6582) gives:
% 155.02/22.93  | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | |   (6583)  all_57_14 = e2 & op(e1, e1) = e2
% 155.02/22.93  | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | ALPHA: (6583) implies:
% 155.02/22.93  | | | | | | | | | | | | |   (6584)  op(e1, e1) = e2
% 155.02/22.93  | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | REF_CLOSE: (9), (6572), (6584), (function-axioms) are
% 155.02/22.93  | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 155.02/22.93  | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | |   (6585)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.02/22.93  | | | | | | | | | | | | |           $i(all_57_3)
% 155.02/22.93  | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | ALPHA: (6585) implies:
% 155.02/22.93  | | | | | | | | | | | | |   (6586)   ~ (all_57_3 = e1)
% 155.02/22.93  | | | | | | | | | | | | |   (6587)  op(e1, e2) = all_57_3
% 155.02/22.93  | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | BETA: splitting (6581) gives:
% 155.02/22.93  | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | |   (6588)  all_57_15 = e2 & op(e0, e0) = e2
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | ALPHA: (6588) implies:
% 155.02/22.93  | | | | | | | | | | | | | |   (6589)  op(e0, e0) = e2
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | REF_CLOSE: (6), (6442), (6589), (function-axioms) are
% 155.02/22.93  | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | |   (6590)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 155.02/22.93  | | | | | | | | | | | | | |           $i(all_57_7)
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | ALPHA: (6590) implies:
% 155.02/22.93  | | | | | | | | | | | | | |   (6591)   ~ (all_57_7 = e0)
% 155.02/22.93  | | | | | | | | | | | | | |   (6592)  op(e0, e2) = all_57_7
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 155.02/22.93  | | | | | | | | | | | | | |              all_57_7, e2, e0, simplifying with (158), (6592)
% 155.02/22.93  | | | | | | | | | | | | | |              gives:
% 155.02/22.93  | | | | | | | | | | | | | |   (6593)  all_57_7 = all_52_7
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 155.02/22.93  | | | | | | | | | | | | | |              all_14_0, e0, e1, simplifying with (160), (6575)
% 155.02/22.93  | | | | | | | | | | | | | |              gives:
% 155.02/22.93  | | | | | | | | | | | | | |   (6594)  all_52_14 = all_14_0
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e2,
% 155.02/22.93  | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (6580) gives:
% 155.02/22.93  | | | | | | | | | | | | | |   (6595)  all_4_2 = e2
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | COMBINE_EQS: (250), (6594) imply:
% 155.02/22.93  | | | | | | | | | | | | | |   (6596)  all_54_11 = all_14_0
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | REDUCE: (6591), (6593) imply:
% 155.02/22.93  | | | | | | | | | | | | | |   (6597)   ~ (all_52_7 = e0)
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | REDUCE: (6571), (6594) imply:
% 155.02/22.93  | | | | | | | | | | | | | |   (6598)   ~ (all_14_0 = e3)
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | REDUCE: (6441), (6594) imply:
% 155.02/22.93  | | | | | | | | | | | | | |   (6599)   ~ (all_14_0 = e1)
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | REDUCE: (373), (6595) imply:
% 155.02/22.93  | | | | | | | | | | | | | |   (6600)   ~ (e3 = e2)
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | |   (6601)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 155.02/22.93  | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.02/22.93  | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | BETA: splitting (6601) gives:
% 155.02/22.93  | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | |   (6602)  all_56_1 = e1 & op(e3, e2) = e1
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | ALPHA: (6602) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | |   (6603)  all_56_1 = e1
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | |   (6604)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 155.02/22.93  | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | BETA: splitting (6604) gives:
% 155.02/22.93  | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | |   (6605)  all_56_1 = e0 & op(e3, e2) = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | ALPHA: (6605) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | | | |   (6606)  all_56_1 = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6603), (6606) are inconsistent by sub-proof
% 155.02/22.93  | | | | | | | | | | | | | | | | | |            #961.
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | |   (6607)  all_56_3 = e0 & op(e2, e2) = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | ALPHA: (6607) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | | | |   (6608)  op(e2, e2) = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6580), (6608), (function-axioms) are
% 155.02/22.93  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | |   (6609)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 155.02/22.93  | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 155.02/22.93  | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | BETA: splitting (6609) gives:
% 155.02/22.93  | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | |   (6610)  all_56_7 = e0 & op(e1, e2) = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | ALPHA: (6610) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | | | |   (6611)  all_56_7 = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | |   (6612)  all_54_11 = e3
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6596), (6612) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | |   (6613)  all_14_0 = e3
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | SIMP: (6613) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | |   (6614)  all_14_0 = e3
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | REDUCE: (6598), (6614) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | |   (6615)  $false
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | CLOSE: (6615) is inconsistent.
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | |   (6616)   ~ (all_54_11 = e3)
% 155.02/22.93  | | | | | | | | | | | | | | | | | | |   (6617)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | BETA: splitting (6617) gives:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | |   (6618)  all_54_11 = e2
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6596), (6618) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | |   (6619)  all_14_0 = e2
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | SIMP: (6619) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | |   (6620)  all_14_0 = e2
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (6574), (6620) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | |   (6621)  $false
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | CLOSE: (6621) is inconsistent.
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | |   (6622)   ~ (all_54_11 = e2)
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | |   (6623)  all_54_11 = e1 | all_54_11 = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6623) gives:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6624)  all_54_11 = e1
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6596), (6624) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6625)  all_14_0 = e1
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | SIMP: (6625) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6626)  all_14_0 = e1
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6599), (6626) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6627)  $false
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | CLOSE: (6627) is inconsistent.
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6628)  all_54_11 = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6596), (6628) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6629)  all_14_0 = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | SIMP: (6629) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6630)  all_14_0 = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6598), (6630) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6631)   ~ (e3 = e0)
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6574), (6630) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6632)   ~ (e2 = e0)
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6599), (6630) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6633)   ~ (e1 = e0)
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6575), (6630) imply:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |   (6634)  op(e1, e0) = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (214), (215), (216),
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |            (6572), (6611), (6634), (function-axioms) are
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #311.
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | |   (6635)  all_56_13 = e0 & op(e0, e2) = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | ALPHA: (6635) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | | | |   (6636)  op(e0, e2) = e0
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (6597), (6636), (function-axioms) are
% 155.02/22.93  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 155.02/22.93  | | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | |   (6637)  all_56_3 = e1 & op(e2, e2) = e1
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | ALPHA: (6637) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | |   (6638)  op(e2, e2) = e1
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6580), (6638), (function-axioms) are
% 155.02/22.93  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | |   (6639)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 155.02/22.93  | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 155.02/22.93  | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | BETA: splitting (6639) gives:
% 155.02/22.93  | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | |   (6640)  all_56_7 = e1 & op(e1, e2) = e1
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | ALPHA: (6640) implies:
% 155.02/22.93  | | | | | | | | | | | | | | | |   (6641)  op(e1, e2) = e1
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | REF_CLOSE: (6586), (6587), (6641), (function-axioms) are
% 155.02/22.93  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #631.
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | |   (6642)  all_56_13 = e1 & op(e0, e2) = e1
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | | REF_CLOSE: (158), (6439), (6642), (function-axioms) are
% 155.02/22.93  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #712.
% 155.02/22.93  | | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | |   (6643)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.02/22.93  | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.02/22.93  | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.02/22.93  | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.02/22.93  | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.02/22.93  | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.02/22.93  | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.02/22.93  | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.02/22.93  | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.02/22.93  | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.02/22.93  | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.02/22.93  | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.02/22.93  | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.02/22.93  | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.02/22.93  | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.02/22.93  | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.02/22.93  | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (6442), (6572), (6643),
% 155.02/22.93  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.02/22.93  | | | | | | | | | | |            #297.
% 155.02/22.93  | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | Case 2:
% 155.02/22.93  | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | |   (6644)   ~ (all_14_1 = e3) & op(e1, e1) = all_14_1 &
% 155.02/22.93  | | | | | | | | | |           $i(all_14_1)
% 155.02/22.93  | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | REF_CLOSE: (6572), (6644), (function-axioms) are inconsistent
% 155.02/22.93  | | | | | | | | | |            by sub-proof #288.
% 155.02/22.93  | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | | 
% 155.02/22.93  | | | | | | | | End of split
% 155.02/22.93  | | | | | | | | 
% 155.02/22.93  | | | | | | | End of split
% 155.02/22.93  | | | | | | | 
% 155.02/22.93  | | | | | | Case 2:
% 155.02/22.93  | | | | | | | 
% 155.02/22.93  | | | | | | |   (6645)  all_56_1 = e2 & op(e3, e2) = e2
% 155.02/22.93  | | | | | | | 
% 155.02/22.93  | | | | | | | REF_CLOSE: (170), (4652), (6645), (function-axioms) are
% 155.02/22.93  | | | | | | |            inconsistent by sub-proof #224.
% 155.02/22.93  | | | | | | | 
% 155.02/22.93  | | | | | | End of split
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | Case 2:
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | |   (6646)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 &
% 155.02/22.93  | | | | | |             op(e3, e0) = e2)
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | | REF_CLOSE: (168), (169), (4653), (4654), (6646), (function-axioms)
% 155.02/22.93  | | | | | |            are inconsistent by sub-proof #511.
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | End of split
% 155.02/22.93  | | | | | 
% 155.02/22.93  | | | | End of split
% 155.02/22.93  | | | | 
% 155.02/22.93  | | | Case 2:
% 155.02/22.93  | | | | 
% 155.02/22.93  | | | |   (6647)  all_10_2 = e2
% 155.02/22.93  | | | |   (6648)  ( ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 & $i(all_10_0)) |
% 155.02/22.93  | | | |           ( ~ (all_10_1 = e0) & op(e2, e2) = all_10_1 & $i(all_10_1))
% 155.02/22.93  | | | | 
% 155.02/22.93  | | | | REDUCE: (350), (6647) imply:
% 155.02/22.93  | | | |   (6649)   ~ (all_52_2 = e2)
% 155.02/22.93  | | | | 
% 155.02/22.93  | | | | REDUCE: (361), (6647) imply:
% 155.02/22.93  | | | |   (6650)   ~ (all_52_6 = e2)
% 155.02/22.93  | | | | 
% 155.02/22.93  | | | | REDUCE: (363), (6647) imply:
% 155.02/22.93  | | | |   (6651)   ~ (all_52_8 = e2)
% 155.02/22.93  | | | | 
% 155.02/22.93  | | | | REDUCE: (364), (6647) imply:
% 155.02/22.93  | | | |   (6652)   ~ (all_52_9 = e2)
% 155.02/22.93  | | | | 
% 155.02/22.93  | | | | REDUCE: (368), (6647) imply:
% 155.02/22.93  | | | |   (6653)   ~ (all_52_14 = e2)
% 155.02/22.93  | | | | 
% 155.02/22.93  | | | | BETA: splitting (215) gives:
% 155.02/22.93  | | | | 
% 155.02/22.93  | | | | Case 1:
% 155.02/22.93  | | | | | 
% 155.02/22.93  | | | | |   (6654)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1,
% 155.02/22.93  | | | | |               e2) = e2)
% 155.02/22.93  | | | | | 
% 155.02/22.93  | | | | | BETA: splitting (6654) gives:
% 155.02/22.93  | | | | | 
% 155.02/22.93  | | | | | Case 1:
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | |   (6655)  all_56_6 = e2 & op(e1, e3) = e2
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | | REF_CLOSE: (163), (6649), (6655), (function-axioms) are inconsistent
% 155.02/22.93  | | | | | |            by sub-proof #761.
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | Case 2:
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | |   (6656)  all_56_7 = e2 & op(e1, e2) = e2
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | | REF_CLOSE: (162), (6650), (6656), (function-axioms) are inconsistent
% 155.02/22.93  | | | | | |            by sub-proof #816.
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | End of split
% 155.02/22.93  | | | | | 
% 155.02/22.93  | | | | Case 2:
% 155.02/22.93  | | | | | 
% 155.02/22.93  | | | | |   (6657)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1,
% 155.02/22.93  | | | | |               e0) = e2)
% 155.02/22.93  | | | | | 
% 155.02/22.93  | | | | | BETA: splitting (6657) gives:
% 155.02/22.93  | | | | | 
% 155.02/22.93  | | | | | Case 1:
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | |   (6658)  all_56_8 = e2 & op(e1, e1) = e2
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | | ALPHA: (6658) implies:
% 155.02/22.93  | | | | | |   (6659)  all_56_8 = e2
% 155.02/22.93  | | | | | |   (6660)  op(e1, e1) = e2
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | | BETA: splitting (49) gives:
% 155.02/22.93  | | | | | | 
% 155.02/22.93  | | | | | | Case 1:
% 155.02/22.93  | | | | | | | 
% 155.02/22.93  | | | | | | |   (6661)   ~ (all_12_2 = e2)
% 155.02/22.93  | | | | | | | 
% 155.02/22.93  | | | | | | | REDUCE: (324), (6661) imply:
% 155.02/22.93  | | | | | | |   (6662)   ~ (all_6_2 = e2)
% 155.02/22.93  | | | | | | | 
% 155.02/22.93  | | | | | | | BETA: splitting (52) gives:
% 155.02/22.93  | | | | | | | 
% 155.02/22.93  | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | 
% 155.02/22.93  | | | | | | | |   (6663)   ~ (all_14_2 = e1)
% 155.02/22.93  | | | | | | | | 
% 155.02/22.93  | | | | | | | | BETA: splitting (58) gives:
% 155.02/22.93  | | | | | | | | 
% 155.02/22.93  | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | 
% 155.02/22.93  | | | | | | | | |   (6664)   ~ (all_18_2 = e3)
% 155.02/22.93  | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | REDUCE: (301), (6664) imply:
% 155.02/22.93  | | | | | | | | |   (6665)   ~ (all_14_2 = e3)
% 155.02/22.93  | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | BETA: splitting (67) gives:
% 155.02/22.93  | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | |   (6666)   ~ (all_24_2 = e1)
% 155.02/22.93  | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | REDUCE: (318), (6666) imply:
% 155.02/22.93  | | | | | | | | | |   (6667)   ~ (all_4_2 = e1)
% 155.02/22.93  | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | BETA: splitting (70) gives:
% 155.02/22.93  | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | |   (6668)   ~ (all_26_2 = e1)
% 155.02/22.93  | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | REDUCE: (307), (6668) imply:
% 155.02/22.93  | | | | | | | | | | |   (6669)   ~ (all_6_2 = e1)
% 155.02/22.93  | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | BETA: splitting (204) gives:
% 155.02/22.93  | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | Case 1:
% 155.02/22.93  | | | | | | | | | | | | 
% 155.02/22.93  | | | | | | | | | | | |   (6670)  all_54_0 = e3
% 155.02/22.94  | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | COMBINE_EQS: (279), (6670) imply:
% 155.02/22.94  | | | | | | | | | | | |   (6671)  all_6_2 = e3
% 155.02/22.94  | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | REDUCE: (338), (6671) imply:
% 155.02/22.94  | | | | | | | | | | | |   (6672)   ~ (all_52_1 = e3)
% 155.02/22.94  | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | REDUCE: (340), (6671) imply:
% 155.02/22.94  | | | | | | | | | | | |   (6673)   ~ (all_52_2 = e3)
% 155.02/22.94  | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | REDUCE: (344), (6671) imply:
% 155.02/22.94  | | | | | | | | | | | |   (6674)   ~ (all_52_4 = e3)
% 155.02/22.94  | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | REDUCE: (346), (6671) imply:
% 155.02/22.94  | | | | | | | | | | | |   (6675)   ~ (all_52_8 = e3)
% 155.02/22.94  | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | REDUCE: (348), (6671) imply:
% 155.02/22.94  | | | | | | | | | | | |   (6676)   ~ (all_52_12 = e3)
% 155.02/22.94  | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | REDUCE: (39), (6671) imply:
% 155.02/22.94  | | | | | | | | | | | |   (6677)  op(e3, e3) = e3
% 155.02/22.94  | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | BETA: splitting (73) gives:
% 155.02/22.94  | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | |   (6678)   ~ (all_28_2 = e2)
% 155.02/22.94  | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | REDUCE: (330), (6678) imply:
% 155.02/22.94  | | | | | | | | | | | | |   (6679)   ~ (all_14_2 = e2)
% 155.02/22.94  | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | BETA: splitting (189) gives:
% 155.02/22.94  | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | |   (6680)  all_54_15 = e3
% 155.02/22.94  | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | COMBINE_EQS: (246), (6680) imply:
% 155.02/22.94  | | | | | | | | | | | | | |   (6681)  all_14_2 = e3
% 155.02/22.94  | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | REDUCE: (6665), (6681) imply:
% 155.02/22.94  | | | | | | | | | | | | | |   (6682)  $false
% 155.02/22.94  | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | CLOSE: (6682) is inconsistent.
% 155.02/22.94  | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | Case 2:
% 155.02/22.94  | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | |   (6683)   ~ (all_54_15 = e3)
% 155.02/22.94  | | | | | | | | | | | | | |   (6684)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 155.02/22.94  | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | BETA: splitting (6684) gives:
% 155.02/22.94  | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | |   (6685)  all_54_15 = e2
% 155.02/22.94  | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | COMBINE_EQS: (246), (6685) imply:
% 155.02/22.94  | | | | | | | | | | | | | | |   (6686)  all_14_2 = e2
% 155.02/22.94  | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | REDUCE: (6679), (6686) imply:
% 155.02/22.94  | | | | | | | | | | | | | | |   (6687)  $false
% 155.02/22.94  | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | CLOSE: (6687) is inconsistent.
% 155.02/22.94  | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | Case 2:
% 155.02/22.94  | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | |   (6688)   ~ (all_54_15 = e2)
% 155.02/22.94  | | | | | | | | | | | | | | |   (6689)  all_54_15 = e1 | all_54_15 = e0
% 155.02/22.94  | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | BETA: splitting (6689) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | |   (6690)  all_54_15 = e1
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (6690) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | |   (6691)  all_14_2 = e1
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | REDUCE: (6663), (6691) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | |   (6692)  $false
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | CLOSE: (6692) is inconsistent.
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | Case 2:
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | |   (6693)  all_54_15 = e0
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (6693) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | |   (6694)  all_14_2 = e0
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | REDUCE: (351), (6694) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | |   (6695)   ~ (all_52_3 = e0)
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | REDUCE: (362), (6694) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | |   (6696)   ~ (all_52_7 = e0)
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | REDUCE: (369), (6694) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | |   (6697)   ~ (all_52_11 = e0)
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | REDUCE: (6665), (6694) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | |   (6698)   ~ (e3 = e0)
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | REDUCE: (6679), (6694) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | |   (6699)   ~ (e2 = e0)
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | |   (6700)  all_56_15 = e0 & op(e0, e0) = e0
% 155.02/22.94  | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | ALPHA: (6700) implies:
% 155.02/22.94  | | | | | | | | | | | | | | | | |   (6701)  all_56_15 = e0
% 155.02/22.94  | | | | | | | | | | | | | | | | |   (6702)  op(e0, e0) = e0
% 155.02/22.94  | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | |   (6703)   ~ (all_32_2 = e0)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | REDUCE: (314), (6703) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | | | |   (6704)   ~ (all_4_2 = e0)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | |   (6705)  all_54_5 = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (6705) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | |   (6706)  all_4_2 = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (6706) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | |   (6707)  $false
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | CLOSE: (6707) is inconsistent.
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | |   (6708)   ~ (all_54_5 = e3)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | |   (6709)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (6709) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | |   (6710)  all_54_5 = e2
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (6710) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | |   (6711)  all_4_2 = e2
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (6711) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | |   (6712)   ~ (all_52_1 = e2)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (6711) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | |   (6713)   ~ (all_52_13 = e2)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (6711) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | |   (6714)   ~ (e3 = e2)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (6711) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | |   (6715)  op(e2, e2) = e2
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | |   (6716)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (6677), (6712), (6716),
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | |            #868.
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | |   (6717)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6717) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | |   (6718)  all_56_6 = e2 & op(e1, e3) = e2
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6649), (6718), (function-axioms) are
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | |   (6719)  all_56_12 = e2 & op(e0, e3) = e2
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6719) implies:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | |   (6720)  op(e0, e3) = e2
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |   (6721)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6721) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |   (6722)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6722) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (6723)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6723) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6724)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (6712), (6724), (function-axioms) are
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6725)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6725) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6726)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6726) implies:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6727)  op(e2, e3) = e2
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (6727) gives:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6728)  all_52_1 = e2
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6712), (6728) imply:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6729)  $false
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6729) is inconsistent.
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6730)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6730) implies:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6731)  op(e3, e1) = e3
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6675), (6731), (function-axioms) are
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (6732)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (167), (170), (6652), (6674), (6712),
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (6732), (function-axioms) are inconsistent by
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #566.
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |   (6733)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6733) gives:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (6734)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6734) gives:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6735)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6735) gives:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6736)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6736) implies:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6737)  op(e0, e3) = e0
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (6720), (6737), (function-axioms) are
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #689.
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6738)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6738) implies:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6739)  op(e3, e2) = e3
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (6739) gives:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6740)  all_52_4 = e3
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6674), (6740) imply:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6741)  $false
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6741) is inconsistent.
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6742)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (6677), (6713), (6742),
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            #994.
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (6743)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6743) gives:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6744)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (6675), (6715), (6744),
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            #565.
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6745)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (168), (6660), (6676), (6697), (6745),
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            #200.
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |   (6746)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6746) gives:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |   (6747)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6747) gives:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (6748)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6748) gives:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6749)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6749) gives:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6750)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6750) implies:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6751)  op(e3, e3) = e1
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6677), (6751), (function-axioms) are
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6752)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6752) implies:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6753)  op(e2, e2) = e1
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (6715), (6753) gives:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6754)  e2 = e1
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (6754) imply:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6755)  $false
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6755) is inconsistent.
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6756)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (165), (6652), (6697), (6756),
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            #199.
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (6757)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (159), (164), (169), (6660), (6675),
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |            (6677), (6713), (6720), (6757), (function-axioms)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #197.
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |   (6758)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6758) gives:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (6759)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6759) gives:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6760)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6760) gives:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6761)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6761) implies:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6762)  op(e0, e0) = e2
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6702), (6762), (function-axioms) are
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6763)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6763) implies:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6764)  op(e2, e1) = e2
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (6764) gives:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6765)  all_52_9 = e2
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6652), (6765) imply:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6766)  $false
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6766) is inconsistent.
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6767)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (159), (6715), (6720), (6767),
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            #196.
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (6768)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6768) gives:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6769)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (6676), (6702), (6769),
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            #975.
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6770)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6770) gives:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6771)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6771) implies:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6772)  op(e2, e0) = e2
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6713), (6772), (function-axioms) are
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6773)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6773) gives:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6774)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6774) implies:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6775)  op(e1, e1) = e1
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6660), (6775), (function-axioms) are
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6776)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6776) implies:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6777)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6777) gives:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6778)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6778) gives:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6779)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6779) gives:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6780)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6780) implies:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6781)  op(e0, e3) = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (6720), (6781), (function-axioms) are
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #689.
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6782)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6782) gives:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6783)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e3) = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6783) implies:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6784)  op(e2, e0) = e2
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6713), (6784), (function-axioms) are
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6785)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e3) = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6785) implies:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6786)  op(e0, e3) = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (6720), (6786), (function-axioms) are
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #689.
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6787)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (159), (164), (6677), (6713), (6720),
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6787), (function-axioms) are inconsistent by
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #195.
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6788)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6788) gives:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6789)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6789) gives:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6790)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6790) implies:
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6791)  op(e0, e2) = e0
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (6696), (6791), (function-axioms) are
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 155.02/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6792)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6792) gives:
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6793)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6793) implies:
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6794)  op(e0, e2) = e0
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (6794) gives:
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6795)  all_52_7 = e0
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6696), (6795) imply:
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6796)  $false
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6796) is inconsistent.
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6797)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6797) implies:
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6798)  op(e3, e3) = e0
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6677), (6798), (function-axioms) are
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6799)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 155.13/22.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6799) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6800)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (164), (6697), (6713), (6800),
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #682.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6801)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6801) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6802)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 & 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6802) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6803)  op(e0, e1) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (6697), (6803), (function-axioms) are
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6804)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6804) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6805)  op(e0, e1) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (6805) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6806)  all_52_11 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6697), (6806) imply:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6807)  $false
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6807) is inconsistent.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | |   (6808)  all_54_5 = e1 | all_54_5 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (6667), (6704), (6808) are inconsistent by
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | |   (6809)  all_32_2 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (6809) imply:
% 155.13/22.98  | | | | | | | | | | | | | | | | | |   (6810)  all_4_2 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | REDUCE: (354), (6810) imply:
% 155.13/22.98  | | | | | | | | | | | | | | | | | |   (6811)   ~ (all_52_6 = e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | REDUCE: (6667), (6810) imply:
% 155.13/22.98  | | | | | | | | | | | | | | | | | |   (6812)   ~ (e1 = e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | REDUCE: (36), (6810) imply:
% 155.13/22.98  | | | | | | | | | | | | | | | | | |   (6813)  op(e2, e2) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | BETA: splitting (6648) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | |   (6814)   ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | |           $i(all_10_0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | ALPHA: (6814) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | |   (6815)  op(e2, e1) = all_10_0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | |   (6816)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6816) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | |   (6817)  all_56_0 = e0 & op(e3, e3) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6817) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | |   (6818)  op(e3, e3) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6677), (6818), (function-axioms) are
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | |   (6819)  all_56_2 = e0 & op(e2, e3) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6819) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | |   (6820)  all_56_2 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | |   (6821)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6821) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |   (6822)  all_56_4 = e0 & op(e3, e1) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6822) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |   (6823)  all_56_4 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (165), (169),
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |            (207), (209), (210), (211), (212), (213), (216),
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (226), (227), (228), (229),
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (6649), (6651),
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6659), (6673), (6677), (6701), (6702),
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |            (6813), (6815), (6820), (6823), (function-axioms)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #188.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |   (6824)  all_56_5 = e0 & op(e2, e1) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6824) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |   (6825)  all_56_5 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |   (6826)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (6677), (6820), (6826),
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |            #534.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |   (6827)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6827) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (6828)  all_56_6 = e2 & op(e1, e3) = e2
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6649), (6828), (function-axioms) are
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (6829)  all_56_12 = e2 & op(e0, e3) = e2
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6829) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (6830)  all_56_12 = e2
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6831)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (229), (231), (6677),
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6813), (6830), (6831), (function-axioms) are
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #532.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6832)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6832) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6833)  all_56_5 = e3 & op(e2, e1) = e3
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6833) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6834)  all_56_5 = e3
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6825), (6834) are inconsistent by sub-proof
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #591.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6835)  all_56_10 = e3 & op(e2, e0) = e3
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6835) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6836)  all_56_10 = e3
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6837)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6813), (6820), (6837), (function-axioms) are
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #535.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6838)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6838) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6839)  all_56_5 = e1 & op(e2, e1) = e1
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6839) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6840)  all_56_5 = e1
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6825), (6840) imply:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6841)  e1 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6841) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6842)  e1 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (6842) imply:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6843)  $false
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6843) is inconsistent.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6844)  all_56_10 = e1 & op(e2, e0) = e1
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6836), (6844) are inconsistent by sub-proof
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #556.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | |   (6845)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (6659), (6697), (6845),
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | |            #186.
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | |   (6846)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6846) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | |   (6847)  all_56_6 = e0 & op(e1, e3) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6847) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | |   (6848)  all_56_6 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | |   (6849)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6849) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |   (6850)  all_56_4 = e0 & op(e3, e1) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6850) implies:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | |   (6851)  op(e3, e1) = e0
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |   (6852)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6852) gives:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (6853)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6853) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6854)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6854) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6855)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (6677), (6813), (6855),
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #934.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6856)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6856) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6857)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6857) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6858)  op(e1, e2) = e1
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6859)  op(e2, e3) = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6860)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6860) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6861)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6861) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6862)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6813), (6859), (6862), (function-axioms) are
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #322.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6863)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6863) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6864)  op(e2, e2) = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6813), (6864), (function-axioms) are
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6865)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6865) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6866)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6866) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6867)  op(e1, e1) = e1
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6660), (6867), (function-axioms) are
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6868)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6868) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6869)  (all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6869) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6870)  all_57_10 = e0 & op(e3, e3) = e0
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6870) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6871)  op(e3, e3) = e0
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6677), (6871), (function-axioms) are
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6872)   ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_9)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6872) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6873)  op(e3, e0) = all_57_9
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (6858) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6874)  all_52_6 = e1
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (6859) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6875)  all_52_1 = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9, e0, e3, simplifying with (168), (6873)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6876)  all_57_9 = all_52_12
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (6851) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6877)  all_52_8 = e0
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (6875) imply:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6878)   ~ (all_52_3 = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6878) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6879)   ~ (all_52_3 = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (6875) imply:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6880)   ~ (all_52_13 = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6880) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6881)   ~ (all_52_13 = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6672), (6875) imply:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6882)   ~ (e3 = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (6874) imply:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6883)   ~ (all_52_4 = e1)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (6877) imply:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6884)   ~ (all_52_4 = e0)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6885)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6885) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6886)  all_56_0 = e2 & op(e3, e3) = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6886) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6887)  op(e3, e3) = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6677), (6887), (function-axioms) are
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6888)  all_56_2 = e2 & op(e2, e3) = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6888) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6889)  all_56_2 = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6890)  all_54_1 = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (6674), (6890) are inconsistent by
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #299.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6891)   ~ (all_54_1 = e3)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6892)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6892) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6893)  all_54_1 = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6893) imply:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6894)  all_52_4 = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6894) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6895)  all_52_4 = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (6895) imply:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6896)   ~ (all_52_12 = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6896) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6897)   ~ (all_52_12 = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6898)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6898) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6899)  all_56_6 = e3 & op(e1, e3) = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6673), (6899), (function-axioms) are
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #681.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6900)  all_56_7 = e3 & op(e1, e2) = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6900) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6901)  all_56_7 = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6902)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (6881), (6897), (6902),
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #384.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6903)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6903) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6904)  all_56_11 = e2 & op(e1, e0) = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6904) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6905)  all_56_11 = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (213), (214),
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (6659), (6673), (6901), (6905),
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #183.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6906)  all_56_15 = e2 & op(e0, e0) = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6906) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6907)  op(e0, e0) = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (159), (163), (167), (168),
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (199), (233), (234), (238), (268),
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (352), (373), (6649), (6651), (6660), (6667),
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6677), (6879), (6897), (6907), (function-axioms)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #181.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6908)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6908) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6909)  all_56_8 = e3 & op(e1, e1) = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6909) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6910)  all_56_8 = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6659), (6910) imply:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6911)  e3 = e2
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (6911) imply:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6912)  $false
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6912) is inconsistent.
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6913)  all_56_11 = e3 & op(e1, e0) = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6913) implies:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6914)  all_56_11 = e3
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/22.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6915)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (6677), (6889), (6915),
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #737.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6916)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6916) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6917)  all_56_6 = e1 & op(e1, e3) = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6848), (6917) are inconsistent by sub-proof
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #599.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6918)  all_56_12 = e1 & op(e0, e3) = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6918) implies:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6919)  all_56_12 = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6920)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6920) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6921)  all_56_6 = e1 & op(e1, e3) = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6921) implies:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6922)  all_56_6 = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6923)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (6677), (6889), (6923),
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #601.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6846) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6847), (6922) are inconsistent by sub-proof
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #459.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6924)  all_56_12 = e0 & op(e0, e3) = e0
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6919), (6924) are inconsistent by sub-proof
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #497.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6925)  all_56_7 = e1 & op(e1, e2) = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6925) implies:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6926)  all_56_7 = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6927)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (6881), (6897), (6927),
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #384.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6928)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6928) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6929)  all_56_11 = e2 & op(e1, e0) = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6929) implies:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6930)  all_56_11 = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (163), (216), (6659), (6673), (6926),
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6930), (function-axioms) are inconsistent by
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #185.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6931)  all_56_15 = e2 & op(e0, e0) = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6931) implies:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6932)  op(e0, e0) = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (159), (163), (167), (168),
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (199), (233), (234), (238), (268),
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (352), (373), (6649), (6651), (6660), (6667),
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6677), (6879), (6897), (6932), (function-axioms)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #181.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6933)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (6660), (6914), (6933),
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #180.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6934)  all_54_1 = e1 | all_54_1 = e0
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6934) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6935)  all_54_1 = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (6883), (6935) are inconsistent by
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #419.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6936)  all_54_1 = e0
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (6884), (6936) are inconsistent by
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #418.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6937)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6937) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6938)  all_56_6 = e2 & op(e1, e3) = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6649), (6938), (function-axioms) are
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6939)  all_56_12 = e2 & op(e0, e3) = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (6879), (6939), (function-axioms) are
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6940)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6940) implies:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6941)  op(e2, e2) = e3
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6813), (6941), (function-axioms) are
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6942)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6942) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6943)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (6676), (6702), (6943),
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #932.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6944)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6944) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6945)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6945) implies:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6946)  op(e2, e2) = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6813), (6946), (function-axioms) are
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6947)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6947) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6948)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6948) implies:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6949)  op(e3, e2) = e3
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (6674), (6949), (function-axioms) are
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6950)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6950) implies:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6951)  op(e2, e1) = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6652), (6815), (6951), (function-axioms)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #194.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (6952)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6952) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6953)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6953) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6954)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (6674), (6954), (function-axioms) are
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #792.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6955)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (6677), (6955), (function-axioms) are
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6956)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6956) gives:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6957)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.13/23.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (169), (6675), (6813), (6957),
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #537.
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6958)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (168), (6660), (6676), (6697), (6958),
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #200.
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |   (6959)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6959) gives:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (6960)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6960) gives:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6961)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6961) gives:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6962)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (6677), (6813), (6962),
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #920.
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6963)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6963) gives:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6964)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6964) implies:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6965)  op(e2, e1) = e2
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6652), (6815), (6965), (function-axioms)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #194.
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6966)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6966) implies:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6967)  op(e0, e1) = e0
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (6697), (6967), (function-axioms) are
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6968)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6968) gives:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6969)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6660), (6813), (6969), (function-axioms) are
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #179.
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6970)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (6675), (6677), (6970),
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #787.
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (6971)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6971) gives:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6972)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6972) gives:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6973)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6702), (6813), (6973), (function-axioms) are
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #919.
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6974)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6974) gives:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6975)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6975) implies:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6976)  op(e2, e2) = e1
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6813), (6976), (function-axioms) are
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6977)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6977) implies:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6978)  op(e0, e3) = e0
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (6695), (6978), (function-axioms) are
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6979)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6979) gives:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6980)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (6676), (6702), (6980),
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #975.
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6981)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6981) gives:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6982)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6982) implies:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6983)  op(e2, e2) = e2
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6813), (6983), (function-axioms) are
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6984)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6984) gives:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6985)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6985) implies:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6986)  op(e1, e1) = e1
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6660), (6986), (function-axioms) are
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6987)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6987) implies:
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6988)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.13/23.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (157), (158), (159), (6660), (6677),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6695), (6696), (6697), (6988), (function-axioms)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #743.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | |   (6989)  all_56_5 = e0 & op(e2, e1) = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6989) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | |   (6990)  all_56_5 = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | |   (6991)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | |            (6677), (6813), (6991), (function-axioms) are
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #441.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | |   (6992)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6992) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (6993)  all_56_5 = e3 & op(e2, e1) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6993) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (6994)  all_56_5 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6990), (6994) are inconsistent by sub-proof
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | |            #591.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (6995)  all_56_10 = e3 & op(e2, e0) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6995) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (6996)  all_56_10 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6997)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6997) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6998)  all_56_4 = e3 & op(e3, e1) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6998) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6999)  op(e3, e1) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6675), (6999), (function-axioms) are
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7000)  all_56_5 = e3 & op(e2, e1) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7000) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7001)  all_56_5 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6990), (7001) are inconsistent by sub-proof
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #591.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7002)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7002) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7003)  all_56_8 = e3 & op(e1, e1) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6659), (7003) are inconsistent by sub-proof
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #193.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7004)  all_56_14 = e3 & op(e0, e1) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7004) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7005)  all_56_14 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7006)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (222), (6813), (6990), (6996),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7006), (function-axioms) are inconsistent by
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #554.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7007)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7007) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7008)  all_56_5 = e2 & op(e2, e1) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7008) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7009)  op(e2, e1) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6652), (6815), (7009), (function-axioms)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #194.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7010)  all_56_10 = e2 & op(e2, e0) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7010) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7011)  all_56_10 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6996), (7011) imply:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7012)  e3 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7005), (7012) imply:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7013)  all_56_14 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (217), (218),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (6659), (6675), (7013), (function-axioms)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #178.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | |   (7014)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (6659), (6697), (7014),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | |            #186.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | |   (7015)  all_56_12 = e0 & op(e0, e3) = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7015) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | |   (7016)  all_56_12 = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | |   (7017)  op(e0, e3) = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | |   (7018)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7018) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | |   (7019)  all_56_4 = e0 & op(e3, e1) = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7019) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | |   (7020)  all_56_4 = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | |   (7021)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7021) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (7022)  all_56_0 = e2 & op(e3, e3) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7022) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (7023)  op(e3, e3) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6677), (7023), (function-axioms) are
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (7024)  all_56_2 = e2 & op(e2, e3) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7024) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (7025)  all_56_2 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7026)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7026) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7027)  all_56_12 = e2 & op(e0, e3) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7027) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7028)  all_56_12 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (229), (231), (6677),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7025), (7028), (function-axioms) are inconsistent
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #597.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7029)  all_56_13 = e2 & op(e0, e2) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7029) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7030)  all_56_13 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7031)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7031) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7032)  all_56_1 = e0 & op(e3, e2) = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7032) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7033)  all_56_1 = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (165), (169),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (209), (210), (211), (212), (213), (216),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (226), (227), (228), (229),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (6649), (6651),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6659), (6673), (6677), (6701), (6702),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6813), (6815), (7020), (7025), (7033),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #176.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7034)  all_56_3 = e0 & op(e2, e2) = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7034) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7035)  all_56_3 = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7036)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6677), (6813), (7036), (function-axioms) are
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #944.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7037)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7037) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7038)  all_56_7 = e3 & op(e1, e2) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7038) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7039)  all_56_7 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7040)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7040) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7041)  all_56_1 = e1 & op(e3, e2) = e1
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7041) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7042)  all_56_1 = e1
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7043)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7043) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7044)  all_56_12 = e3 & op(e0, e3) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7044) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7045)  all_56_12 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (229), (231), (6677),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7025), (7045), (function-axioms) are inconsistent
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #734.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7046)  all_56_13 = e3 & op(e0, e2) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7046) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7047)  all_56_13 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7030), (7047) are inconsistent by sub-proof
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #688.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7048)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7048) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7049)  all_56_14 = e3 & op(e0, e1) = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7049) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7050)  all_56_14 = e3
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7051)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (225), (226), (228),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (6677), (7030), (7035),
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7051), (function-axioms) are inconsistent by
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #512.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7052)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7052) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7053)  all_56_4 = e2 & op(e3, e1) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7053) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7054)  op(e3, e1) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6651), (7054), (function-axioms) are
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7055)  all_56_9 = e2 & op(e3, e0) = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7055) implies:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7056)  all_56_9 = e2
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7057)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7057) gives:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7058)  all_56_6 = e0 & op(e1, e3) = e0
% 155.13/23.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7058) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7059)  all_56_6 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7060)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (6677), (7025), (7060),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #737.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7061)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7061) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7062)  all_56_6 = e1 & op(e1, e3) = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7062) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7063)  all_56_6 = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7059), (7063) imply:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7064)  e1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7064) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7065)  e1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7042), (7065) imply:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7066)  all_56_1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (165), (169),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (209), (210), (211), (212), (213), (216),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (226), (227), (228), (229),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (6649), (6651),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6659), (6673), (6677), (6701), (6702),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6813), (6815), (7020), (7025), (7066),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #176.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7067)  all_56_12 = e1 & op(e0, e3) = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7067) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7068)  all_56_12 = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7016), (7068) imply:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7069)  e1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7069) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7070)  e1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7042), (7070) imply:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7071)  all_56_1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (165), (169),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (209), (210), (211), (212), (213), (216),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (226), (227), (228), (229),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (6649), (6651),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6659), (6673), (6677), (6701), (6702),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6813), (6815), (7020), (7025), (7071),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #176.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7072)  all_56_7 = e0 & op(e1, e2) = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7039), (7072) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #909.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7073)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7073) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7074)  all_56_8 = e0 & op(e1, e1) = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7074) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7075)  all_56_8 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6659), (7075) imply:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7076)  e2 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7025), (7076) imply:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7077)  all_56_2 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (165), (169),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (209), (210), (211), (212), (213), (216),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (226), (227), (228), (229),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (6649), (6651),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6659), (6673), (6677), (6701), (6702),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6813), (6815), (7020), (7077), (function-axioms)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #188.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7078)  all_56_11 = e0 & op(e1, e0) = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7078) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7079)  all_56_11 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7080)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7080) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7081)  all_56_9 = e1 & op(e3, e0) = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7056), (7081) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #948.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7082)  all_56_10 = e1 & op(e2, e0) = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7082) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7083)  all_56_10 = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7084)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6677), (6813), (7084), (function-axioms) are
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #441.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7085)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7085) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7086)  all_56_5 = e3 & op(e2, e1) = e3
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (217), (218), (6659),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7050), (7086) are inconsistent by sub-proof #174.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7087)  all_56_10 = e3 & op(e2, e0) = e3
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7083), (7087) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #295.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7088)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7088) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7089)  all_56_11 = e1 & op(e1, e0) = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7089) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7090)  all_56_11 = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7079), (7090) imply:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7091)  e1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7091) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7092)  e1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7042), (7092) imply:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7093)  all_56_1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (165), (169),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (209), (210), (211), (212), (213), (216),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (226), (227), (228), (229),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (6649), (6651),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6659), (6673), (6677), (6701), (6702),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6813), (6815), (7020), (7025), (7093),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #176.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7094)  all_56_15 = e1 & op(e0, e0) = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7094) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7095)  all_56_15 = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6701), (7095) imply:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7096)  e1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7096) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7097)  e1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7042), (7097) imply:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7098)  all_56_1 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (165), (169),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (209), (210), (211), (212), (213), (216),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (226), (227), (228), (229),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (6649), (6651),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6659), (6673), (6677), (6701), (6702),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6813), (6815), (7020), (7025), (7098),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #176.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7099)  all_56_15 = e3 & op(e0, e0) = e3
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6701), (7099) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #892.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7100)  all_56_3 = e1 & op(e2, e2) = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7100) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7101)  op(e2, e2) = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6813), (7101), (function-axioms) are
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7102)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7102) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7103)  all_56_7 = e1 & op(e1, e2) = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7039), (7103) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #173.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7104)  all_56_13 = e1 & op(e0, e2) = e1
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7030), (7104) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #938.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7105)  all_56_13 = e3 & op(e0, e2) = e3
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7030), (7105) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #906.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7106)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7106) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7107)  all_56_7 = e0 & op(e1, e2) = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7107) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7108)  all_56_7 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230), (232),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (6677), (6813), (7030), (7108),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #521.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7109)  all_56_13 = e0 & op(e0, e2) = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7109) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7110)  op(e0, e2) = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (6696), (7110), (function-axioms) are
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7111)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7111) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7112)  all_56_14 = e2 & op(e0, e1) = e2
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7112) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7113)  all_56_14 = e2
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (217), (218),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (6659), (6675), (7113), (function-axioms)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #178.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7114)  all_56_15 = e2 & op(e0, e0) = e2
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7114) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7115)  op(e0, e0) = e2
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6702), (7115), (function-axioms) are
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | |   (7116)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (163), (6649), (7017), (7116),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | |            #589.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | |   (7117)  all_56_5 = e0 & op(e2, e1) = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7117) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | |   (7118)  all_56_5 = e0
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | |   (7119)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7119) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (7120)  all_56_0 = e2 & op(e3, e3) = e2
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7120) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (7121)  op(e3, e3) = e2
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6677), (7121), (function-axioms) are
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (7122)  all_56_2 = e2 & op(e2, e3) = e2
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7122) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (7123)  all_56_2 = e2
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7124)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6677), (6813), (7124), (function-axioms) are
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #441.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7125)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7125) gives:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7126)  all_56_5 = e3 & op(e2, e1) = e3
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7126) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7127)  all_56_5 = e3
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7118), (7127) are inconsistent by sub-proof
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #591.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7128)  all_56_10 = e3 & op(e2, e0) = e3
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7128) implies:
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7129)  all_56_10 = e3
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (222), (6813), (7118), (7123),
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7129), (function-axioms) are inconsistent by
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #555.
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | |   (7130)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (163), (6649), (7017), (7130),
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | |            #589.
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | |   (7131)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7131) gives:
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | |   (7132)  all_56_8 = e0 & op(e1, e1) = e0
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6659), (7132) are inconsistent by sub-proof
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | |            #191.
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | |   (7133)  all_56_14 = e0 & op(e0, e1) = e0
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7133) implies:
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | |   (7134)  op(e0, e1) = e0
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (6697), (7134), (function-axioms) are
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | |   (7135)   ~ (all_10_1 = e0) & op(e2, e2) = all_10_1 &
% 155.13/23.05  | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | ALPHA: (7135) implies:
% 155.13/23.05  | | | | | | | | | | | | | | | | | | |   (7136)   ~ (all_10_1 = e0)
% 155.13/23.05  | | | | | | | | | | | | | | | | | | |   (7137)  op(e2, e2) = all_10_1
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6813), (7136), (7137), (function-axioms) are
% 155.13/23.05  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #172.
% 155.13/23.05  | | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | |   (7138)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 155.13/23.05  | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 155.13/23.05  | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 155.13/23.05  | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 155.13/23.05  | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 155.13/23.05  | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | ALPHA: (7138) implies:
% 155.13/23.05  | | | | | | | | | | | | | | | | |   (7139)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 155.13/23.05  | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 155.13/23.05  | | | | | | | | | | | | | | | | |               e1) = e0)
% 155.13/23.05  | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (6695), (6696), (6697),
% 155.13/23.05  | | | | | | | | | | | | | | | | |            (7139), (function-axioms) are inconsistent by
% 155.13/23.05  | | | | | | | | | | | | | | | | |            sub-proof #881.
% 155.13/23.05  | | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | |   (7140)  all_28_2 = e2
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | COMBINE_EQS: (330), (7140) imply:
% 155.13/23.05  | | | | | | | | | | | | |   (7141)  all_14_2 = e2
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | SIMP: (7141) implies:
% 155.13/23.05  | | | | | | | | | | | | |   (7142)  all_14_2 = e2
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | REDUCE: (351), (7142) imply:
% 155.13/23.05  | | | | | | | | | | | | |   (7143)   ~ (all_52_3 = e2)
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | REDUCE: (370), (7142) imply:
% 155.13/23.05  | | | | | | | | | | | | |   (7144)   ~ (all_52_12 = e2)
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | REDUCE: (6665), (7142) imply:
% 155.13/23.05  | | | | | | | | | | | | |   (7145)   ~ (e3 = e2)
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | REDUCE: (51), (7142) imply:
% 155.13/23.05  | | | | | | | | | | | | |   (7146)  op(e0, e0) = e2
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (159), (163), (167), (168),
% 155.13/23.05  | | | | | | | | | | | | |            (169), (170), (199), (233), (234), (238), (268),
% 155.13/23.05  | | | | | | | | | | | | |            (352), (373), (6649), (6651), (6660), (6667),
% 155.13/23.05  | | | | | | | | | | | | |            (6677), (7143), (7144), (7146), (function-axioms)
% 155.13/23.05  | | | | | | | | | | | | |            are inconsistent by sub-proof #181.
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | |   (7147)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 155.13/23.05  | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | REF_CLOSE: (279), (374), (6662), (6669), (7147) are
% 155.13/23.05  | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 155.13/23.05  | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | |   (7148)  all_26_2 = e1
% 155.13/23.05  | | | | | | | | | | |   (7149)  ( ~ (all_26_0 = e0) & op(e1, e3) = all_26_0 &
% 155.13/23.05  | | | | | | | | | | |             $i(all_26_0)) | ( ~ (all_26_1 = e2) & op(e1, e1)
% 155.13/23.05  | | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | COMBINE_EQS: (307), (7148) imply:
% 155.13/23.05  | | | | | | | | | | |   (7150)  all_6_2 = e1
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | REDUCE: (338), (7150) imply:
% 155.13/23.05  | | | | | | | | | | |   (7151)   ~ (all_52_1 = e1)
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | REDUCE: (340), (7150) imply:
% 155.13/23.05  | | | | | | | | | | |   (7152)   ~ (all_52_2 = e1)
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | REDUCE: (342), (7150) imply:
% 155.13/23.05  | | | | | | | | | | |   (7153)   ~ (all_52_3 = e1)
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | REDUCE: (344), (7150) imply:
% 155.13/23.05  | | | | | | | | | | |   (7154)   ~ (all_52_4 = e1)
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | REDUCE: (346), (7150) imply:
% 155.13/23.05  | | | | | | | | | | |   (7155)   ~ (all_52_8 = e1)
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | REDUCE: (6662), (7150) imply:
% 155.13/23.05  | | | | | | | | | | |   (7156)   ~ (e2 = e1)
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | REDUCE: (39), (7150) imply:
% 155.13/23.05  | | | | | | | | | | |   (7157)  op(e3, e3) = e1
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | BETA: splitting (7149) gives:
% 155.13/23.05  | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | Case 1:
% 155.13/23.05  | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | |   (7158)   ~ (all_26_0 = e0) & op(e1, e3) = all_26_0 &
% 155.13/23.05  | | | | | | | | | | | |           $i(all_26_0)
% 155.13/23.05  | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | ALPHA: (7158) implies:
% 155.13/23.05  | | | | | | | | | | | |   (7159)   ~ (all_26_0 = e0)
% 155.13/23.05  | | | | | | | | | | | |   (7160)  op(e1, e3) = all_26_0
% 155.13/23.05  | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | BETA: splitting (231) gives:
% 155.13/23.05  | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | Case 1:
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | |   (7161)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 155.13/23.05  | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | BETA: splitting (7161) gives:
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | Case 1:
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | |   (7162)  all_56_0 = e1 & op(e3, e3) = e1
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | ALPHA: (7162) implies:
% 155.13/23.05  | | | | | | | | | | | | | |   (7163)  all_56_0 = e1
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (51), (73), (126), (128),
% 155.13/23.05  | | | | | | | | | | | | | |            (133), (134), (136), (141), (143), (144), (148),
% 155.13/23.05  | | | | | | | | | | | | | |            (149), (157), (158), (159), (163), (164), (165),
% 155.13/23.05  | | | | | | | | | | | | | |            (167), (168), (169), (170), (189), (192), (193),
% 155.13/23.05  | | | | | | | | | | | | | |            (195), (196), (199), (200), (203), (206), (210),
% 155.13/23.05  | | | | | | | | | | | | | |            (211), (212), (213), (214), (216), (223), (226),
% 155.13/23.05  | | | | | | | | | | | | | |            (228), (229), (230), (232), (233), (234), (236),
% 155.13/23.05  | | | | | | | | | | | | | |            (238), (239), (246), (249), (250), (258), (259),
% 155.13/23.05  | | | | | | | | | | | | | |            (268), (269), (272), (330), (349), (351), (352),
% 155.13/23.05  | | | | | | | | | | | | | |            (354), (358), (360), (362), (369), (370), (372),
% 155.13/23.05  | | | | | | | | | | | | | |            (373), (6649), (6651), (6653), (6659), (6660),
% 155.13/23.05  | | | | | | | | | | | | | |            (6663), (6665), (6667), (7151), (7152), (7153),
% 155.13/23.05  | | | | | | | | | | | | | |            (7154), (7157), (7159), (7160), (7163),
% 155.13/23.05  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.13/23.05  | | | | | | | | | | | | | |            #155.
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | |   (7164)  all_56_2 = e1 & op(e2, e3) = e1
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | ALPHA: (7164) implies:
% 155.13/23.05  | | | | | | | | | | | | | |   (7165)  all_56_2 = e1
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | Case 1:
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | |   (7166)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.13/23.05  | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | BETA: splitting (7166) gives:
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | Case 1:
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7167)  all_56_0 = e2 & op(e3, e3) = e2
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | ALPHA: (7167) implies:
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7168)  all_56_0 = e2
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7169)  op(e3, e3) = e2
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (73),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (126), (128), (133), (134), (136), (141), (143),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (144), (148), (149), (157), (158), (159), (163),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (189),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (192), (193), (195), (196), (199), (200), (203),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (206), (210), (211), (212), (213), (214), (216),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (223), (226), (228), (229), (230), (232), (233),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (234), (236), (238), (239), (246), (249), (250),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (258), (259), (268), (269), (272), (330), (349),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (351), (352), (354), (358), (360), (362), (369),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (370), (372), (373), (6649), (6651), (6653),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (6659), (6660), (6663), (6665), (6667), (7151),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (7152), (7153), (7154), (7155), (7157), (7159),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (7160), (7167), (7168), (7169), (function-axioms)
% 155.13/23.05  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #151.
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7170)  all_56_2 = e2 & op(e2, e3) = e2
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | ALPHA: (7170) implies:
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7171)  all_56_2 = e2
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7165), (7171) are inconsistent by sub-proof
% 155.13/23.05  | | | | | | | | | | | | | | | |            #600.
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | |   (7172)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.13/23.05  | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | BETA: splitting (7172) gives:
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | Case 1:
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7173)  all_56_6 = e2 & op(e1, e3) = e2
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6649), (7173), (function-axioms) are
% 155.13/23.05  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7174)  all_56_12 = e2 & op(e0, e3) = e2
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | ALPHA: (7174) implies:
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7175)  all_56_12 = e2
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7176)  op(e0, e3) = e2
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (159), (229), (235),
% 155.13/23.05  | | | | | | | | | | | | | | | |            (7157), (7165), (7175), (7176), (function-axioms)
% 155.13/23.05  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #481.
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | End of split
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | |   (7177)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 155.13/23.05  | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | BETA: splitting (7177) gives:
% 155.13/23.05  | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | Case 1:
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | |   (7178)  all_56_6 = e1 & op(e1, e3) = e1
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | ALPHA: (7178) implies:
% 155.13/23.05  | | | | | | | | | | | | | |   (7179)  op(e1, e3) = e1
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | REF_CLOSE: (163), (7152), (7179), (function-axioms) are
% 155.13/23.05  | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | Case 2:
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | |   (7180)  all_56_12 = e1 & op(e0, e3) = e1
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | ALPHA: (7180) implies:
% 155.13/23.05  | | | | | | | | | | | | | |   (7181)  all_56_12 = e1
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 155.13/23.05  | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | Case 1:
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | |   (7182)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.13/23.05  | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | BETA: splitting (7182) gives:
% 155.13/23.05  | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | Case 1:
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7183)  all_56_0 = e2 & op(e3, e3) = e2
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.05  | | | | | | | | | | | | | | | | ALPHA: (7183) implies:
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7184)  all_56_0 = e2
% 155.13/23.05  | | | | | | | | | | | | | | | |   (7185)  op(e3, e3) = e2
% 155.13/23.05  | | | | | | | | | | | | | | | | 
% 155.13/23.06  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (73),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (126), (128), (133), (134), (136), (141), (143),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (144), (148), (149), (157), (158), (159), (163),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (189),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (192), (193), (195), (196), (199), (200), (203),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (206), (210), (211), (212), (213), (214), (216),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (223), (226), (228), (229), (230), (232), (233),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (234), (236), (238), (239), (246), (249), (250),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (258), (259), (268), (269), (272), (330), (349),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (351), (352), (354), (358), (360), (362), (369),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (370), (372), (373), (6649), (6651), (6653),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (6659), (6660), (6663), (6665), (6667), (7151),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (7152), (7153), (7154), (7155), (7157), (7159),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (7160), (7183), (7184), (7185), (function-axioms)
% 155.25/23.06  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #151.
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | |   (7186)  all_56_2 = e2 & op(e2, e3) = e2
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | ALPHA: (7186) implies:
% 155.25/23.06  | | | | | | | | | | | | | | | |   (7187)  all_56_2 = e2
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (229), (235), (7157),
% 155.25/23.06  | | | | | | | | | | | | | | | |            (7181), (7187), (function-axioms) are inconsistent
% 155.25/23.06  | | | | | | | | | | | | | | | |            by sub-proof #496.
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | |   (7188)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.25/23.06  | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (6649), (7181), (7188),
% 155.25/23.06  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.06  | | | | | | | | | | | | | | |            #717.
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | |   (7189)   ~ (all_26_1 = e2) & op(e1, e1) = all_26_1 &
% 155.25/23.06  | | | | | | | | | | | |           $i(all_26_1)
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | ALPHA: (7189) implies:
% 155.25/23.06  | | | | | | | | | | | |   (7190)   ~ (all_26_1 = e2)
% 155.25/23.06  | | | | | | | | | | | |   (7191)  op(e1, e1) = all_26_1
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_26_1,
% 155.25/23.06  | | | | | | | | | | | |              e1, e1, simplifying with (6660), (7191) gives:
% 155.25/23.06  | | | | | | | | | | | |   (7192)  all_26_1 = e2
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | REDUCE: (7190), (7192) imply:
% 155.25/23.06  | | | | | | | | | | | |   (7193)  $false
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | CLOSE: (7193) is inconsistent.
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | |   (7194)  all_24_2 = e1
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | COMBINE_EQS: (318), (7194) imply:
% 155.25/23.06  | | | | | | | | | |   (7195)  all_4_2 = e1
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | REDUCE: (354), (7195) imply:
% 155.25/23.06  | | | | | | | | | |   (7196)   ~ (all_52_6 = e1)
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | REDUCE: (373), (7195) imply:
% 155.25/23.06  | | | | | | | | | |   (7197)   ~ (e3 = e1)
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | REDUCE: (36), (7195) imply:
% 155.25/23.06  | | | | | | | | | |   (7198)  op(e2, e2) = e1
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | BETA: splitting (70) gives:
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | |   (7199)   ~ (all_26_2 = e1)
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | REDUCE: (307), (7199) imply:
% 155.25/23.06  | | | | | | | | | | |   (7200)   ~ (all_6_2 = e1)
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (51), (73), (157), (158),
% 155.25/23.06  | | | | | | | | | | |            (159), (162), (163), (165), (168), (169), (170),
% 155.25/23.06  | | | | | | | | | | |            (189), (204), (233), (238), (239), (246), (279),
% 155.25/23.06  | | | | | | | | | | |            (330), (344), (346), (348), (351), (362), (369),
% 155.25/23.06  | | | | | | | | | | |            (374), (6649), (6652), (6660), (6662), (6663),
% 155.25/23.06  | | | | | | | | | | |            (6665), (7196), (7198), (7200), (function-axioms)
% 155.25/23.06  | | | | | | | | | | |            are inconsistent by sub-proof #741.
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | |   (7201)  all_26_2 = e1
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | COMBINE_EQS: (307), (7201) imply:
% 155.25/23.06  | | | | | | | | | | |   (7202)  all_6_2 = e1
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | SIMP: (7202) implies:
% 155.25/23.06  | | | | | | | | | | |   (7203)  all_6_2 = e1
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | REDUCE: (6662), (7203) imply:
% 155.25/23.06  | | | | | | | | | | |   (7204)   ~ (e2 = e1)
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | REDUCE: (39), (7203) imply:
% 155.25/23.06  | | | | | | | | | | |   (7205)  op(e3, e3) = e1
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (160), (165),
% 155.25/23.06  | | | | | | | | | | |            (169), (210), (221), (223), (224), (230), (234),
% 155.25/23.06  | | | | | | | | | | |            (236), (238), (6651), (6652), (6660), (7198),
% 155.25/23.06  | | | | | | | | | | |            (7205), (function-axioms) are inconsistent by
% 155.25/23.06  | | | | | | | | | | |            sub-proof #145.
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | 
% 155.25/23.06  | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | 
% 155.25/23.06  | | | | | | | | |   (7206)  all_18_2 = e3
% 155.25/23.06  | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | COMBINE_EQS: (301), (7206) imply:
% 155.25/23.06  | | | | | | | | |   (7207)  all_14_2 = e3
% 155.25/23.06  | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | SIMP: (7207) implies:
% 155.25/23.06  | | | | | | | | |   (7208)  all_14_2 = e3
% 155.25/23.06  | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | COMBINE_EQS: (299), (7208) imply:
% 155.25/23.06  | | | | | | | | |   (7209)  all_48_2 = e3
% 155.25/23.06  | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | REDUCE: (370), (7208) imply:
% 155.25/23.06  | | | | | | | | |   (7210)   ~ (all_52_12 = e3)
% 155.25/23.06  | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | REDUCE: (372), (7208) imply:
% 155.25/23.06  | | | | | | | | |   (7211)   ~ (all_52_14 = e3)
% 155.25/23.06  | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | REDUCE: (51), (7208) imply:
% 155.25/23.06  | | | | | | | | |   (7212)  op(e0, e0) = e3
% 155.25/23.06  | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | BETA: splitting (212) gives:
% 155.25/23.06  | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | |   (7213)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 155.25/23.06  | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | BETA: splitting (7213) gives:
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | |   (7214)  all_56_9 = e3 & op(e3, e0) = e3
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | ALPHA: (7214) implies:
% 155.25/23.06  | | | | | | | | | | |   (7215)  op(e3, e0) = e3
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | REF_CLOSE: (168), (7210), (7215), (function-axioms) are
% 155.25/23.06  | | | | | | | | | | |            inconsistent by sub-proof #976.
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | |   (7216)  all_56_10 = e3 & op(e2, e0) = e3
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | ALPHA: (7216) implies:
% 155.25/23.06  | | | | | | | | | | |   (7217)  all_56_10 = e3
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (210), (211),
% 155.25/23.06  | | | | | | | | | | |            (7212), (7217), (function-axioms) are inconsistent
% 155.25/23.06  | | | | | | | | | | |            by sub-proof #466.
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | |   (7218)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 155.25/23.06  | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | BETA: splitting (7218) gives:
% 155.25/23.06  | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | |   (7219)  all_56_11 = e3 & op(e1, e0) = e3
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | ALPHA: (7219) implies:
% 155.25/23.06  | | | | | | | | | | |   (7220)  op(e1, e0) = e3
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | REF_CLOSE: (160), (7211), (7220), (function-axioms) are
% 155.25/23.06  | | | | | | | | | | |            inconsistent by sub-proof #677.
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | |   (7221)  all_56_15 = e3 & op(e0, e0) = e3
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | ALPHA: (7221) implies:
% 155.25/23.06  | | | | | | | | | | |   (7222)  all_56_15 = e3
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | BETA: splitting (70) gives:
% 155.25/23.06  | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | |   (7223)   ~ (all_26_2 = e1)
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | REDUCE: (307), (7223) imply:
% 155.25/23.06  | | | | | | | | | | | |   (7224)   ~ (all_6_2 = e1)
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | BETA: splitting (204) gives:
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | |   (7225)  all_54_0 = e3
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | COMBINE_EQS: (279), (7225) imply:
% 155.25/23.06  | | | | | | | | | | | | |   (7226)  all_6_2 = e3
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | REDUCE: (340), (7226) imply:
% 155.25/23.06  | | | | | | | | | | | | |   (7227)   ~ (all_52_2 = e3)
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | REDUCE: (346), (7226) imply:
% 155.25/23.06  | | | | | | | | | | | | |   (7228)   ~ (all_52_8 = e3)
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | REDUCE: (39), (7226) imply:
% 155.25/23.06  | | | | | | | | | | | | |   (7229)  op(e3, e3) = e3
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | BETA: splitting (220) gives:
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | |   (7230)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 155.25/23.06  | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 155.25/23.06  | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | BETA: splitting (7230) gives:
% 155.25/23.06  | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | |   (7231)  all_56_4 = e3 & op(e3, e1) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | ALPHA: (7231) implies:
% 155.25/23.06  | | | | | | | | | | | | | | |   (7232)  op(e3, e1) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | REF_CLOSE: (169), (7228), (7232), (function-axioms) are
% 155.25/23.06  | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | |   (7233)  all_56_5 = e3 & op(e2, e1) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | ALPHA: (7233) implies:
% 155.25/23.06  | | | | | | | | | | | | | | |   (7234)  op(e2, e1) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | |   (7235)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 155.25/23.06  | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | BETA: splitting (7235) gives:
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | |   (7236)  all_56_6 = e3 & op(e1, e3) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7227), (7236), (function-axioms) are
% 155.25/23.06  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #681.
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | |   (7237)  all_56_7 = e3 & op(e1, e2) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | | ALPHA: (7237) implies:
% 155.25/23.06  | | | | | | | | | | | | | | | | |   (7238)  all_56_7 = e3
% 155.25/23.06  | | | | | | | | | | | | | | | | |   (7239)  op(e1, e2) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (51), (67), (113),
% 155.25/23.06  | | | | | | | | | | | | | | | | |            (123), (136), (143), (159), (160), (162), (163),
% 155.25/23.06  | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (199),
% 155.25/23.06  | | | | | | | | | | | | | | | | |            (206), (207), (209), (210), (211), (213), (214),
% 155.25/23.06  | | | | | | | | | | | | | | | | |            (216), (221), (223), (224), (225), (227), (229),
% 155.25/23.06  | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (236), (238),
% 155.25/23.06  | | | | | | | | | | | | | | | | |            (239), (268), (318), (349), (358), (360), (6648),
% 155.25/23.06  | | | | | | | | | | | | | | | | |            (6649), (6651), (6652), (6659), (6660), (7210),
% 155.25/23.06  | | | | | | | | | | | | | | | | |            (7212), (7222), (7229), (7234), (7238), (7239),
% 155.25/23.06  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.06  | | | | | | | | | | | | | | | | |            #137.
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | |   (7240)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 155.25/23.06  | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | BETA: splitting (7240) gives:
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | |   (7241)  all_56_8 = e3 & op(e1, e1) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | | ALPHA: (7241) implies:
% 155.25/23.06  | | | | | | | | | | | | | | | | |   (7242)  op(e1, e1) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6660), (7242), (function-axioms) are
% 155.25/23.06  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | |   (7243)  all_56_11 = e3 & op(e1, e0) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | | ALPHA: (7243) implies:
% 155.25/23.06  | | | | | | | | | | | | | | | | |   (7244)  op(e1, e0) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7211), (7244), (function-axioms) are
% 155.25/23.06  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #677.
% 155.25/23.06  | | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | |   (7245)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 155.25/23.06  | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 155.25/23.06  | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | BETA: splitting (7245) gives:
% 155.25/23.06  | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | Case 1:
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | |   (7246)  all_56_8 = e3 & op(e1, e1) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | ALPHA: (7246) implies:
% 155.25/23.06  | | | | | | | | | | | | | | |   (7247)  op(e1, e1) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | REF_CLOSE: (9), (6660), (7247), (function-axioms) are
% 155.25/23.06  | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | |   (7248)  all_56_14 = e3 & op(e0, e1) = e3
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | ALPHA: (7248) implies:
% 155.25/23.06  | | | | | | | | | | | | | | |   (7249)  all_56_14 = e3
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (206), (210),
% 155.25/23.06  | | | | | | | | | | | | | | |            (211), (217), (218), (224), (229), (231), (233),
% 155.25/23.06  | | | | | | | | | | | | | | |            (373), (6659), (7212), (7229), (7249),
% 155.25/23.06  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.06  | | | | | | | | | | | | | | |            #136.
% 155.25/23.06  | | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | |   (7250)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | | REF_CLOSE: (279), (374), (6662), (7224), (7250) are
% 155.25/23.06  | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 155.25/23.06  | | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | End of split
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | Case 2:
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | |   (7251)  all_26_2 = e1
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | COMBINE_EQS: (307), (7251) imply:
% 155.25/23.06  | | | | | | | | | | | |   (7252)  all_6_2 = e1
% 155.25/23.06  | | | | | | | | | | | | 
% 155.25/23.06  | | | | | | | | | | | | SIMP: (7252) implies:
% 155.25/23.07  | | | | | | | | | | | |   (7253)  all_6_2 = e1
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | REDUCE: (344), (7253) imply:
% 155.25/23.07  | | | | | | | | | | | |   (7254)   ~ (all_52_4 = e1)
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | REDUCE: (348), (7253) imply:
% 155.25/23.07  | | | | | | | | | | | |   (7255)   ~ (all_52_12 = e1)
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | REDUCE: (6662), (7253) imply:
% 155.25/23.07  | | | | | | | | | | | |   (7256)   ~ (e2 = e1)
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | REDUCE: (39), (7253) imply:
% 155.25/23.07  | | | | | | | | | | | |   (7257)  op(e3, e3) = e1
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | BETA: splitting (103) gives:
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | |   (7258)   ~ (all_48_2 = e3)
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | REDUCE: (7209), (7258) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7259)  $false
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | CLOSE: (7259) is inconsistent.
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | |   (7260)  ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 &
% 155.25/23.07  | | | | | | | | | | | | |             $i(all_48_0)) | ( ~ (all_48_1 = e1) & op(e3, e3)
% 155.25/23.07  | | | | | | | | | | | | |             = all_48_1 & $i(all_48_1))
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (133), (168), (170), (201),
% 155.25/23.07  | | | | | | | | | | | | |            (203), (238), (270), (272), (352), (6660), (7210),
% 155.25/23.07  | | | | | | | | | | | | |            (7212), (7254), (7255), (7257), (7260),
% 155.25/23.07  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.07  | | | | | | | | | | | | |            #415.
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | 
% 155.25/23.07  | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | 
% 155.25/23.07  | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | 
% 155.25/23.07  | | | | | | | |   (7261)  all_14_2 = e1
% 155.25/23.07  | | | | | | | | 
% 155.25/23.07  | | | | | | | | COMBINE_EQS: (327), (7261) imply:
% 155.25/23.07  | | | | | | | |   (7262)  all_16_2 = e1
% 155.25/23.07  | | | | | | | | 
% 155.25/23.07  | | | | | | | | REDUCE: (370), (7261) imply:
% 155.25/23.07  | | | | | | | |   (7263)   ~ (all_52_12 = e1)
% 155.25/23.07  | | | | | | | | 
% 155.25/23.07  | | | | | | | | REDUCE: (371), (7261) imply:
% 155.25/23.07  | | | | | | | |   (7264)   ~ (all_52_13 = e1)
% 155.25/23.07  | | | | | | | | 
% 155.25/23.07  | | | | | | | | REDUCE: (372), (7261) imply:
% 155.25/23.07  | | | | | | | |   (7265)   ~ (all_52_14 = e1)
% 155.25/23.07  | | | | | | | | 
% 155.25/23.07  | | | | | | | | REDUCE: (51), (7261) imply:
% 155.25/23.07  | | | | | | | |   (7266)  op(e0, e0) = e1
% 155.25/23.07  | | | | | | | | 
% 155.25/23.07  | | | | | | | | BETA: splitting (55) gives:
% 155.25/23.07  | | | | | | | | 
% 155.25/23.07  | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | 
% 155.25/23.07  | | | | | | | | |   (7267)   ~ (all_16_2 = e1)
% 155.25/23.07  | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | REDUCE: (7262), (7267) imply:
% 155.25/23.07  | | | | | | | | |   (7268)  $false
% 155.25/23.07  | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | CLOSE: (7268) is inconsistent.
% 155.25/23.07  | | | | | | | | | 
% 155.25/23.07  | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | 
% 155.25/23.07  | | | | | | | | |   (7269)  ( ~ (all_16_0 = e3) & op(e1, e0) = all_16_0 &
% 155.25/23.07  | | | | | | | | |             $i(all_16_0)) | ( ~ (all_16_1 = e2) & op(e1, e1) =
% 155.25/23.07  | | | | | | | | |             all_16_1 & $i(all_16_1))
% 155.25/23.07  | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | BETA: splitting (7269) gives:
% 155.25/23.07  | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | |   (7270)   ~ (all_16_0 = e3) & op(e1, e0) = all_16_0 &
% 155.25/23.07  | | | | | | | | | |           $i(all_16_0)
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | ALPHA: (7270) implies:
% 155.25/23.07  | | | | | | | | | |   (7271)   ~ (all_16_0 = e3)
% 155.25/23.07  | | | | | | | | | |   (7272)  op(e1, e0) = all_16_0
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 155.25/23.07  | | | | | | | | | |              all_16_0, e0, e1, simplifying with (160), (7272)
% 155.25/23.07  | | | | | | | | | |              gives:
% 155.25/23.07  | | | | | | | | | |   (7273)  all_52_14 = all_16_0
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | COMBINE_EQS: (250), (7273) imply:
% 155.25/23.07  | | | | | | | | | |   (7274)  all_54_11 = all_16_0
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | REDUCE: (141), (7273) imply:
% 155.25/23.07  | | | | | | | | | |   (7275)   ~ (all_52_2 = all_16_0)
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | REDUCE: (126), (7273) imply:
% 155.25/23.07  | | | | | | | | | |   (7276)   ~ (all_52_6 = all_16_0)
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | REDUCE: (112), (7273) imply:
% 155.25/23.07  | | | | | | | | | |   (7277)   ~ (all_52_12 = all_16_0)
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | REDUCE: (6653), (7273) imply:
% 155.25/23.07  | | | | | | | | | |   (7278)   ~ (all_16_0 = e2)
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | REDUCE: (7265), (7273) imply:
% 155.25/23.07  | | | | | | | | | |   (7279)   ~ (all_16_0 = e1)
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | BETA: splitting (193) gives:
% 155.25/23.07  | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | |   (7280)  all_54_11 = e3
% 155.25/23.07  | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | COMBINE_EQS: (7274), (7280) imply:
% 155.25/23.07  | | | | | | | | | | |   (7281)  all_16_0 = e3
% 155.25/23.07  | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | SIMP: (7281) implies:
% 155.25/23.07  | | | | | | | | | | |   (7282)  all_16_0 = e3
% 155.25/23.07  | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | REDUCE: (7271), (7282) imply:
% 155.25/23.07  | | | | | | | | | | |   (7283)  $false
% 155.25/23.07  | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | CLOSE: (7283) is inconsistent.
% 155.25/23.07  | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | |   (7284)   ~ (all_54_11 = e3)
% 155.25/23.07  | | | | | | | | | | |   (7285)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.25/23.07  | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | BETA: splitting (7285) gives:
% 155.25/23.07  | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | |   (7286)  all_54_11 = e2
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | COMBINE_EQS: (7274), (7286) imply:
% 155.25/23.07  | | | | | | | | | | | |   (7287)  all_16_0 = e2
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | SIMP: (7287) implies:
% 155.25/23.07  | | | | | | | | | | | |   (7288)  all_16_0 = e2
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | REDUCE: (7278), (7288) imply:
% 155.25/23.07  | | | | | | | | | | | |   (7289)  $false
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | CLOSE: (7289) is inconsistent.
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | |   (7290)   ~ (all_54_11 = e2)
% 155.25/23.07  | | | | | | | | | | | |   (7291)  all_54_11 = e1 | all_54_11 = e0
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | BETA: splitting (7291) gives:
% 155.25/23.07  | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | |   (7292)  all_54_11 = e1
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | COMBINE_EQS: (7274), (7292) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7293)  all_16_0 = e1
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | SIMP: (7293) implies:
% 155.25/23.07  | | | | | | | | | | | | |   (7294)  all_16_0 = e1
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | REDUCE: (7279), (7294) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7295)  $false
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | CLOSE: (7295) is inconsistent.
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | |   (7296)  all_54_11 = e0
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | COMBINE_EQS: (7274), (7296) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7297)  all_16_0 = e0
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | SIMP: (7297) implies:
% 155.25/23.07  | | | | | | | | | | | | |   (7298)  all_16_0 = e0
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | REDUCE: (7275), (7298) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7299)   ~ (all_52_2 = e0)
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | REDUCE: (7276), (7298) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7300)   ~ (all_52_6 = e0)
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | REDUCE: (7277), (7298) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7301)   ~ (all_52_12 = e0)
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | REDUCE: (7271), (7298) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7302)   ~ (e3 = e0)
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | REDUCE: (7278), (7298) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7303)   ~ (e2 = e0)
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | REDUCE: (7279), (7298) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7304)   ~ (e1 = e0)
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | REDUCE: (7272), (7298) imply:
% 155.25/23.07  | | | | | | | | | | | | |   (7305)  op(e1, e0) = e0
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | BETA: splitting (206) gives:
% 155.25/23.07  | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | |   (7306)  all_56_15 = e0 & op(e0, e0) = e0
% 155.25/23.07  | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | ALPHA: (7306) implies:
% 155.25/23.07  | | | | | | | | | | | | | |   (7307)  op(e0, e0) = e0
% 155.25/23.07  | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (7266), (7307), (function-axioms) are
% 155.25/23.07  | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 155.25/23.07  | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | |   (7308)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 155.25/23.07  | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 155.25/23.07  | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 155.25/23.07  | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 155.25/23.07  | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 155.25/23.07  | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | ALPHA: (7308) implies:
% 155.25/23.07  | | | | | | | | | | | | | |   (7309)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 155.25/23.07  | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 155.25/23.07  | | | | | | | | | | | | | |               e1) = e0)
% 155.25/23.07  | | | | | | | | | | | | | |   (7310)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 155.25/23.07  | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 155.25/23.07  | | | | | | | | | | | | | |               e0) = e0)
% 155.25/23.07  | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 155.25/23.07  | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | |   (7311)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 155.25/23.07  | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 155.25/23.07  | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | BETA: splitting (7311) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | |   (7312)  all_56_6 = e0 & op(e1, e3) = e0
% 155.25/23.07  | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | ALPHA: (7312) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | |   (7313)  all_56_6 = e0
% 155.25/23.07  | | | | | | | | | | | | | | | |   (7314)  op(e1, e3) = e0
% 155.25/23.07  | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | |   (7315)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 155.25/23.07  | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 155.25/23.07  | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | BETA: splitting (7315) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | |   (7316)  all_56_6 = e3 & op(e1, e3) = e3
% 155.25/23.07  | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | ALPHA: (7316) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | |   (7317)  op(e1, e3) = e3
% 155.25/23.07  | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7314), (7317), (function-axioms) are
% 155.25/23.07  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #913.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | |   (7318)  all_56_7 = e3 & op(e1, e2) = e3
% 155.25/23.07  | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | ALPHA: (7318) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | |   (7319)  all_56_7 = e3
% 155.25/23.07  | | | | | | | | | | | | | | | | | |   (7320)  op(e1, e2) = e3
% 155.25/23.07  | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | BETA: splitting (7310) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | |   (7321)  all_56_9 = e0 & op(e3, e0) = e0
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | ALPHA: (7321) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | |   (7322)  all_56_9 = e0
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |   (7323)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7323) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |   (7324)  all_56_9 = e2 & op(e3, e0) = e2
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7324) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |   (7325)  all_56_9 = e2
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7322), (7325) imply:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |   (7326)  e2 = e0
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (7326) imply:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |   (7327)  $false
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | CLOSE: (7327) is inconsistent.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |   (7328)  all_56_10 = e2 & op(e2, e0) = e2
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7328) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |   (7329)  all_56_10 = e2
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |   (7330)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7330) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |   (7331)  all_56_9 = e3 & op(e3, e0) = e3
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7331) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |   (7332)  all_56_9 = e3
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7322), (7332) imply:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |   (7333)  e3 = e0
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (7333) imply:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |   (7334)  $false
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7334) is inconsistent.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |   (7335)  all_56_10 = e3 & op(e2, e0) = e3
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7335) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |   (7336)  all_56_10 = e3
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7329), (7336) imply:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |   (7337)  e3 = e2
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (7337) imply:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |   (7338)  $false
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7338) is inconsistent.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |   (7339)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (7266), (7305), (7339),
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |            #294.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |   (7340)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (213), (214), (6659),
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |            (6660), (7266), (7319), (7320), (7340),
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |            #135.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | |   (7341)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 155.25/23.07  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (7341) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |   (7342)  all_56_10 = e0 & op(e2, e0) = e0
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | ALPHA: (7342) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |   (7343)  all_56_10 = e0
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |   (7344)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (7313), (7320), (7344),
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |            #134.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |   (7345)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7345) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |   (7346)  all_56_8 = e1 & op(e1, e1) = e1
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7346) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |   (7347)  op(e1, e1) = e1
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6660), (7347), (function-axioms) are
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |   (7348)  all_56_11 = e1 & op(e1, e0) = e1
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7348) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | |   (7349)  all_56_11 = e1
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |   (7350)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7350) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | |   (7351)  all_56_9 = e2 & op(e3, e0) = e2
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7351) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | |   (7352)  all_56_9 = e2
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (212), (7266), (7305),
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | |            (7310), (7349), (7352), (function-axioms) are
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #133.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | |   (7353)  all_56_10 = e2 & op(e2, e0) = e2
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7353) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | |   (7354)  all_56_10 = e2
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7343), (7354) are inconsistent by sub-proof
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | |            #755.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |   (7355)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (213), (214), (6659),
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |            (6660), (7266), (7319), (7320), (7355),
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | |            #135.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |   (7356)  all_56_11 = e0 & op(e1, e0) = e0
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | ALPHA: (7356) implies:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | |   (7357)  all_56_11 = e0
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |   (7358)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (7313), (7320), (7358),
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | |            #134.
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.07  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | |   (7359)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (6660), (7357), (7359),
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | |            #132.
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | End of split
% 155.25/23.08  | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | End of split
% 155.25/23.08  | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.08  | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | |   (7360)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 155.25/23.08  | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 155.25/23.08  | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (6660), (7305), (7360),
% 155.25/23.08  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.25/23.08  | | | | | | | | | | | | | | | | |            #313.
% 155.25/23.08  | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | End of split
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | Case 2:
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | |   (7361)  all_56_7 = e0 & op(e1, e2) = e0
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | ALPHA: (7361) implies:
% 155.25/23.08  | | | | | | | | | | | | | | | |   (7362)  all_56_7 = e0
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (214), (216), (6660),
% 155.25/23.08  | | | | | | | | | | | | | | | |            (7305), (7362), (function-axioms) are inconsistent
% 155.25/23.08  | | | | | | | | | | | | | | | |            by sub-proof #312.
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | End of split
% 155.25/23.08  | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | Case 2:
% 155.25/23.08  | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | |   (7363)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 155.25/23.08  | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 155.25/23.08  | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | BETA: splitting (7363) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | |   (7364)  all_56_8 = e0 & op(e1, e1) = e0
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | ALPHA: (7364) implies:
% 155.25/23.08  | | | | | | | | | | | | | | | |   (7365)  op(e1, e1) = e0
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6660), (7365), (function-axioms) are
% 155.25/23.08  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | Case 2:
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | |   (7366)  all_56_11 = e0 & op(e1, e0) = e0
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | ALPHA: (7366) implies:
% 155.25/23.08  | | | | | | | | | | | | | | | |   (7367)  all_56_11 = e0
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | |   (7368)   ~ (all_24_2 = e1)
% 155.25/23.08  | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | REDUCE: (318), (7368) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | |   (7369)   ~ (all_4_2 = e1)
% 155.25/23.08  | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | |   (7370)   ~ (all_26_2 = e1)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | REDUCE: (307), (7370) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | |   (7371)   ~ (all_6_2 = e1)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | |   (7372)  all_54_0 = e3
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (7372) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | |   (7373)  all_6_2 = e3
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | REDUCE: (340), (7373) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | |   (7374)   ~ (all_52_2 = e3)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | REDUCE: (346), (7373) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | |   (7375)   ~ (all_52_8 = e3)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | REDUCE: (348), (7373) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | |   (7376)   ~ (all_52_12 = e3)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (7373) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | |   (7377)  op(e3, e3) = e3
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | |   (7378)  all_54_3 = e3
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7376), (7378) are inconsistent by
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | |            sub-proof #310.
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | |   (7379)   ~ (all_54_3 = e3)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | |   (7380)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | |   (7381)  all_54_8 = e3
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7374), (7381) are inconsistent by
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | |            sub-proof #309.
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | |   (7382)   ~ (all_54_8 = e3)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | |   (7383)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7383) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | |   (7384)  all_54_8 = e2
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (6649), (7384) are inconsistent by
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #608.
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | |   (7385)   ~ (all_54_8 = e2)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | |   (7386)  all_54_8 = e1 | all_54_8 = e0
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7386) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | |   (7387)  all_54_8 = e1
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7387) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | |   (7388)  all_52_2 = e1
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7388) implies:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | |   (7389)  all_52_2 = e1
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (7389) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | |   (7390)   ~ (all_52_6 = e1)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7390) implies:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | |   (7391)   ~ (all_52_6 = e1)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7380) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | |   (7392)  all_54_3 = e2
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (7392) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | |   (7393)  all_52_12 = e2
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (7393) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | |   (7394)   ~ (all_52_13 = e2)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7394) implies:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | |   (7395)   ~ (all_52_13 = e2)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (7396)  all_54_9 = e3
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (7396) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (7397)  all_52_6 = e3
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7397) implies:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (7398)  all_52_6 = e3
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (7398) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (7399)   ~ (all_52_4 = e3)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (7398) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (7400)   ~ (all_4_2 = e3)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (7398) imply:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (7401)  op(e1, e2) = e3
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7402)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7402) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7403)  all_56_2 = e1 & op(e2, e3) = e1
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7403) implies:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7404)  all_56_2 = e1
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7405)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7405) gives:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7406)  all_56_0 = e2 & op(e3, e3) = e2
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7406) implies:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7407)  op(e3, e3) = e2
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7377), (7407), (function-axioms) are
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7408)  all_56_1 = e2 & op(e3, e2) = e2
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7408) implies:
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7409)  all_56_1 = e2
% 155.25/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7410)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7410) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7411)  all_56_0 = e2 & op(e3, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7411) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7412)  op(e3, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7377), (7412), (function-axioms) are
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7413)  all_56_2 = e2 & op(e2, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7413) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7414)  all_56_2 = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7404), (7414) imply:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7415)  e2 = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (7415) imply:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7416)  $false
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7416) is inconsistent.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7417)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7417) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7418)  all_56_6 = e2 & op(e1, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6649), (7418), (function-axioms) are
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7419)  all_56_12 = e2 & op(e0, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7419) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7420)  op(e0, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7421)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7421) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7422)  all_56_1 = e1 & op(e3, e2) = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7409), (7422) are inconsistent by sub-proof
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #911.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7423)  all_56_3 = e1 & op(e2, e2) = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7423) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7424)  op(e2, e2) = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (6652), (7404), (7424), (function-axioms)
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #355.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7425)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7425) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7426)  all_56_7 = e1 & op(e1, e2) = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7426) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7427)  op(e1, e2) = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7401), (7427), (function-axioms) are
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7428)  all_56_13 = e1 & op(e0, e2) = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7428) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7429)  all_56_13 = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (209), (229),
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (7266), (7309), (7377), (7420),
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7429), (function-axioms) are inconsistent by
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #129.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7430)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7430) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7431)  all_56_4 = e2 & op(e3, e1) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7431) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7432)  op(e3, e1) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6651), (7432), (function-axioms) are
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7433)  all_56_9 = e2 & op(e3, e0) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7433) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7434)  all_56_9 = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7435)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7435) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7436)  all_56_6 = e1 & op(e1, e3) = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7436) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7437)  all_56_6 = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7438)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7438) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7439)  all_56_0 = e2 & op(e3, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7439) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7440)  op(e3, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7377), (7440), (function-axioms) are
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7441)  all_56_2 = e2 & op(e2, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7441) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7442)  all_56_2 = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7404), (7442) are inconsistent by sub-proof
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #600.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7443)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7443) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7444)  all_56_6 = e2 & op(e1, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6649), (7444), (function-axioms) are
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7445)  all_56_12 = e2 & op(e0, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7445) implies:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7446)  op(e0, e3) = e2
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7447)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7447) gives:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7448)  all_56_1 = e1 & op(e3, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7448) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7449)  all_56_1 = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7450)  op(e3, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7451)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7451) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7452)  all_56_12 = e3 & op(e0, e3) = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7452) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7453)  all_56_12 = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7377), (7453), (function-axioms) are inconsistent
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7454)  all_56_13 = e3 & op(e0, e2) = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7454) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7455)  all_56_13 = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7456)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (214), (6660), (7367), (7377),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7401), (7437), (7449), (7456), (function-axioms)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #128.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7457)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7457) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7458)  all_56_4 = e0 & op(e3, e1) = e0
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7458) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7459)  all_56_4 = e0
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7460)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7460) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7461)  all_56_9 = e3 & op(e3, e0) = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7461) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7462)  all_56_9 = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7377), (7462), (function-axioms) are inconsistent
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #632.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7463)  all_56_10 = e3 & op(e2, e0) = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7463) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7464)  all_56_10 = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7465)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7465) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7466)  all_56_4 = e1 & op(e3, e1) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (232), (7377), (7434), (7449),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7459), (7466), (function-axioms) are inconsistent
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #127.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7467)  all_56_5 = e1 & op(e2, e1) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7467) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7468)  all_56_5 = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (51),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (113), (123), (125), (135), (136), (143),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (160), (162), (163), (164),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (169), (170), (191), (199),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (201), (204), (206), (207), (209), (210), (211),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (217), (218), (220),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (229), (230),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (236), (238), (239),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (248), (259), (268), (270), (279), (318), (340),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (346), (348), (349), (356), (358), (360), (373),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (6648), (6649), (6651), (6652), (6659),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6660), (6662), (7263), (7266), (7299), (7305),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7374), (7375), (7376), (7377), (7386), (7395),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7399), (7401), (7434), (7449), (7450), (7459),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7464), (7468), (function-axioms) are inconsistent
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #120.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7469)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7469) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7470)  all_56_8 = e1 & op(e1, e1) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7470) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7471)  op(e1, e1) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6660), (7471), (function-axioms) are
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7472)  all_56_14 = e1 & op(e0, e1) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7472) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7473)  all_56_14 = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (159), (208), (7266),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7309), (7455), (7473), (function-axioms) are
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #119.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7474)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (7266), (7305), (7474),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #294.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7475)  all_56_9 = e0 & op(e3, e0) = e0
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7475) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7476)  all_56_9 = e0
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7434), (7476) are inconsistent by sub-proof
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #316.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7477)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7477) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7478)  all_56_14 = e3 & op(e0, e1) = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7478) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7479)  all_56_14 = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7480)  op(e0, e1) = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (51),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (113), (123), (125), (135), (136), (143),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (160), (162), (163), (164),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (169), (170), (191), (199),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (201), (204), (206), (207), (209), (210), (211),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (217), (218), (220),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (229), (230),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (236), (238), (239),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (248), (259), (268), (270), (279), (318), (340),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (346), (348), (349), (356), (358), (360), (373),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (6648), (6649), (6651), (6652), (6659),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6660), (6662), (7263), (7266), (7299), (7305),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7374), (7375), (7376), (7377), (7386), (7395),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7399), (7401), (7450), (7479), (7480),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #121.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7481)  all_56_15 = e3 & op(e0, e0) = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7481) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7482)  op(e0, e0) = e3
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7266), (7482), (function-axioms) are
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7483)  all_56_3 = e1 & op(e2, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7483) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7484)  op(e2, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (6652), (7404), (7484), (function-axioms)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #355.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7485)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7485) gives:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7486)  all_56_7 = e1 & op(e1, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7486) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7487)  op(e1, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7401), (7487), (function-axioms) are
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7488)  all_56_13 = e1 & op(e0, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7488) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7489)  all_56_13 = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (209), (229),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (7266), (7309), (7377), (7446),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7489), (function-axioms) are inconsistent by
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #129.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7490)  all_56_7 = e1 & op(e1, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7490) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7491)  op(e1, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7401), (7491), (function-axioms) are
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7492)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (6660),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7266), (7305), (7310), (7434), (7492),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #118.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7493)  all_56_3 = e1 & op(e2, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7493) implies:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7494)  op(e2, e2) = e1
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (39), (51), (67), (113),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (136), (143), (159), (160), (162), (163),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (195),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (199), (201), (204), (206), (207), (209),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (212), (213), (214), (216), (217),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (223), (224), (225), (227),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (236),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (239), (258), (259), (268), (270), (279),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (318), (340), (346), (348), (349), (358), (360),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (374), (6648), (6649), (6650), (6651),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6659), (6660), (6662), (7263), (7266),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7299), (7300), (7305), (7391), (7494),
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #117.
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7495)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7495) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7496)  all_56_5 = e1 & op(e2, e1) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7496) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7497)  all_56_5 = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7498)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7498) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7499)  all_56_0 = e2 & op(e3, e3) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7499) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7500)  op(e3, e3) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7377), (7500), (function-axioms) are
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7501)  all_56_1 = e2 & op(e3, e2) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7501) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7502)  all_56_1 = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7503)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7503) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7504)  all_56_1 = e1 & op(e3, e2) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7502), (7504) are inconsistent by sub-proof
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #911.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7505)  all_56_3 = e1 & op(e2, e2) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7505) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7506)  op(e2, e2) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (39), (51), (67), (113),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (136), (143), (159), (160), (162), (163),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (195),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (199), (201), (204), (206), (207), (209),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (212), (213), (214), (216), (217),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (223), (224), (225), (227),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (236),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (239), (258), (259), (268), (270), (279),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (318), (340), (346), (348), (349), (358), (360),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (374), (6648), (6649), (6650), (6651),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6659), (6660), (6662), (7263), (7266),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7299), (7300), (7305), (7391), (7506),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #117.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7507)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7507) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7508)  all_56_7 = e1 & op(e1, e2) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7508) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7509)  op(e1, e2) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7401), (7509), (function-axioms) are
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7510)  all_56_13 = e1 & op(e0, e2) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7510) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7511)  all_56_13 = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7512)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (229), (231),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (373), (7377), (7512), (function-axioms)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #475.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7513)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7513) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7514)  all_56_5 = e3 & op(e2, e1) = e3
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7514) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7515)  all_56_5 = e3
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7497), (7515) are inconsistent by sub-proof
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #531.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7516)  all_56_10 = e3 & op(e2, e0) = e3
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7516) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7517)  all_56_10 = e3
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7518)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7518) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7519)  all_56_9 = e2 & op(e3, e0) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7519) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7520)  all_56_9 = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (159), (163),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (169), (208), (211), (213), (214), (216),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (220), (224), (229), (231), (233),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (6659), (6660), (7266), (7305), (7309),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7374), (7375), (7377), (7395), (7497), (7511),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7517), (7520), (function-axioms) are inconsistent
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #116.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7521)  all_56_10 = e2 & op(e2, e0) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7521) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7522)  op(e2, e0) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7395), (7522), (function-axioms) are
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7523)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7523) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7524)  all_56_11 = e2 & op(e1, e0) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (213), (214),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (6659), (7374), (7524), (function-axioms)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #115.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7525)  all_56_15 = e2 & op(e0, e0) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7525) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7526)  op(e0, e0) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7266), (7526), (function-axioms) are
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7527)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7527) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7528)  all_56_4 = e2 & op(e3, e1) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7528) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7529)  op(e3, e1) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6651), (7529), (function-axioms) are
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7530)  all_56_9 = e2 & op(e3, e0) = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7530) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7531)  all_56_9 = e2
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7532)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7532) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7533)  all_56_6 = e1 & op(e1, e3) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7533) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7534)  all_56_6 = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7535)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7535) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7536)  all_56_1 = e1 & op(e3, e2) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7536) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7537)  all_56_1 = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7538)  op(e3, e2) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7539)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (214), (6660), (7367), (7377),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7401), (7534), (7537), (7539), (function-axioms)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #128.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7540)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7540) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7541)  all_56_4 = e0 & op(e3, e1) = e0
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7541) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7542)  all_56_4 = e0
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7543)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (229), (231),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (373), (7377), (7543), (function-axioms)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #475.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7544)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7544) gives:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7545)  all_56_5 = e3 & op(e2, e1) = e3
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7545) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7546)  all_56_5 = e3
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7497), (7546) are inconsistent by sub-proof
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #531.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7547)  all_56_10 = e3 & op(e2, e0) = e3
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7547) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7548)  all_56_10 = e3
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (51),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (113), (123), (125), (135), (136), (143),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (160), (162), (163), (164),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (169), (170), (191), (199),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (201), (204), (206), (207), (209), (210), (211),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (217), (218), (220),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (229), (230),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (236), (238), (239),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (248), (259), (268), (270), (279), (318), (340),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (346), (348), (349), (356), (358), (360), (373),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (6648), (6649), (6651), (6652), (6659),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6660), (6662), (7263), (7266), (7299), (7305),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7374), (7375), (7376), (7377), (7386), (7395),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7399), (7401), (7497), (7531), (7537), (7538),
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7542), (7548), (function-axioms) are inconsistent
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #120.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7549)  all_56_9 = e0 & op(e3, e0) = e0
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7549) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7550)  all_56_9 = e0
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7531), (7550) are inconsistent by sub-proof
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #316.
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7551)  all_56_3 = e1 & op(e2, e2) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7551) implies:
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7552)  op(e2, e2) = e1
% 155.34/23.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (39), (51), (67), (113),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (136), (143), (159), (160), (162), (163),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (195),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (199), (201), (204), (206), (207), (209),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (212), (213), (214), (216), (217),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (223), (224), (225), (227),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (236),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (239), (258), (259), (268), (270), (279),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (318), (340), (346), (348), (349), (358), (360),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (374), (6648), (6649), (6650), (6651),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6659), (6660), (6662), (7263), (7266),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7299), (7300), (7305), (7391), (7552),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #117.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7553)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7553) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7554)  all_56_7 = e1 & op(e1, e2) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7554) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7555)  op(e1, e2) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7401), (7555), (function-axioms) are
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7556)  all_56_13 = e1 & op(e0, e2) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7556) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7557)  all_56_13 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7558)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (229), (231),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (373), (7377), (7558), (function-axioms)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #475.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7559)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7559) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7560)  all_56_5 = e3 & op(e2, e1) = e3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7560) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7561)  all_56_5 = e3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7497), (7561) are inconsistent by sub-proof
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #531.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7562)  all_56_10 = e3 & op(e2, e0) = e3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7562) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7563)  all_56_10 = e3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (159), (163),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (169), (208), (211), (213), (214), (216),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (220), (224), (229), (231), (233),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (6659), (6660), (7266), (7305), (7309),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7374), (7375), (7377), (7395), (7497), (7531),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7557), (7563), (function-axioms) are inconsistent
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #116.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7564)  all_56_7 = e1 & op(e1, e2) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7564) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7565)  op(e1, e2) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7401), (7565), (function-axioms) are
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7566)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (6660),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7266), (7305), (7310), (7531), (7566),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #118.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7567)  all_56_10 = e1 & op(e2, e0) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (230), (232),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (7266), (7305), (7377), (7567),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #293.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (7568)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (6650), (7300), (7391), (7568) are
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #673.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |   (7569)  all_54_3 = e1 | all_54_3 = e0
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7263), (7301), (7569) are inconsistent by
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #582.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | |   (7570)  all_54_8 = e0
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7299), (7570) are inconsistent by
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #613.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | |   (7571)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (374), (6662), (7371), (7571) are
% 155.34/23.11  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | |   (7572)  all_26_2 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (7572) imply:
% 155.34/23.11  | | | | | | | | | | | | | | | | | |   (7573)  all_6_2 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | SIMP: (7573) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | |   (7574)  all_6_2 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | REDUCE: (340), (7574) imply:
% 155.34/23.11  | | | | | | | | | | | | | | | | | |   (7575)   ~ (all_52_2 = e1)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | REDUCE: (346), (7574) imply:
% 155.34/23.11  | | | | | | | | | | | | | | | | | |   (7576)   ~ (all_52_8 = e1)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | REDUCE: (6662), (7574) imply:
% 155.34/23.11  | | | | | | | | | | | | | | | | | |   (7577)   ~ (e2 = e1)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | REDUCE: (39), (7574) imply:
% 155.34/23.11  | | | | | | | | | | | | | | | | | |   (7578)  op(e3, e3) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | |   (7579)  all_54_8 = e3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7579) imply:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | |   (7580)  all_52_2 = e3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | SIMP: (7580) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | |   (7581)  all_52_2 = e3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | REDUCE: (163), (7581) imply:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | |   (7582)  op(e1, e3) = e3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | |   (7583)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7583) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | |   (7584)  all_56_0 = e1 & op(e3, e3) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7584) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | |   (7585)  all_56_0 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | |   (7586)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7586) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | |   (7587)  all_56_6 = e1 & op(e1, e3) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7587) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | |   (7588)  op(e1, e3) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7575), (7588), (function-axioms) are
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | |   (7589)  all_56_7 = e1 & op(e1, e2) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7589) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | |   (7590)  all_56_7 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | |   (7591)  op(e1, e2) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |   (7592)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7592) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (7593)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7593) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (7594)  op(e3, e3) = e3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7578), (7594), (function-axioms) are
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (7595)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7595) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (7596)  op(e2, e2) = e2
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (7597)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (7598)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7597) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7599)  all_57_15 = e2 & op(e0, e0) = e2
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7599) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7600)  op(e0, e0) = e2
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7266), (7600), (function-axioms) are
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7601)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7601) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7602)   ~ (all_57_7 = e0)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7603)  op(e0, e2) = all_57_7
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7604)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7604) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7605)  all_56_2 = e1 & op(e2, e3) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (163), (229),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (6649), (7578), (7605),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #480.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7606)  all_56_3 = e1 & op(e2, e2) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7606) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7607)  op(e2, e2) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7596), (7607), (function-axioms) are
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7608)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7608) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7609)  all_56_5 = e1 & op(e2, e1) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7609) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7610)  all_56_5 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7611)  op(e2, e1) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (145),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (146), (148), (158), (159), (163), (164), (165),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (200), (210), (211), (224), (229), (233),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (269), (349), (373), (6649), (6652),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7264), (7266), (7305), (7310), (7367), (7369),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7575), (7578), (7582), (7585), (7591), (7596),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7598), (7602), (7603), (7610), (7611),
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #110.
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7612)  all_56_10 = e1 & op(e2, e0) = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7612) implies:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7613)  all_56_10 = e1
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7614)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7614) gives:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7615)  all_56_9 = e3 & op(e3, e0) = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7615) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7616)  all_56_9 = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7617)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7617) gives:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7618)  all_56_0 = e2 & op(e3, e3) = e2
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7618) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7619)  op(e3, e3) = e2
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7578), (7619), (function-axioms) are
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7620)  all_56_1 = e2 & op(e3, e2) = e2
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7620) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7621)  op(e3, e2) = e2
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7622)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7622) gives:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7623)  all_56_4 = e1 & op(e3, e1) = e1
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7576), (7623), (function-axioms) are
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #331.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7624)  all_56_5 = e1 & op(e2, e1) = e1
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7624) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7625)  all_56_5 = e1
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7626)  op(e2, e1) = e1
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (145),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (146), (148), (158), (159), (163), (164), (165),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (200), (210), (211), (224), (229), (233),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (269), (349), (373), (6649), (6652),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7264), (7266), (7305), (7310), (7367), (7369),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7575), (7578), (7582), (7585), (7591), (7596),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7598), (7602), (7603), (7625), (7626),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #110.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7627)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7627) gives:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7628)  all_56_8 = e1 & op(e1, e1) = e1
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7628) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7629)  op(e1, e1) = e1
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6660), (7629), (function-axioms) are
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7630)  all_56_14 = e1 & op(e0, e1) = e1
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7630) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7631)  all_56_14 = e1
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7632)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (373), (7621), (7632),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #432.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7633)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7633) gives:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7634)  all_56_7 = e3 & op(e1, e2) = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (163), (213), (214),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6660), (7575), (7582), (7634), (function-axioms)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #157.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7635)  all_56_13 = e3 & op(e0, e2) = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7635) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7636)  all_56_13 = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (159), (208), (7266),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7309), (7631), (7636), (function-axioms) are
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #119.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7637)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7637) gives:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7638)  all_56_4 = e2 & op(e3, e1) = e2
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7638) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7639)  op(e3, e1) = e2
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6651), (7639), (function-axioms) are
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7640)  all_56_9 = e2 & op(e3, e0) = e2
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7640) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7641)  all_56_9 = e2
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7616), (7641) are inconsistent by sub-proof
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #888.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7642)  all_56_10 = e3 & op(e2, e0) = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7642) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7643)  all_56_10 = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7613), (7643) are inconsistent by sub-proof
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #887.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7644)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7644) gives:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7645)  all_56_11 = e3 & op(e1, e0) = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7645) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7646)  all_56_11 = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (213), (6660), (7582), (7590),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7646), (function-axioms) are inconsistent by
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #156.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7647)  all_56_15 = e3 & op(e0, e0) = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7647) implies:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7648)  op(e0, e0) = e3
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7266), (7648), (function-axioms) are
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |   (7649)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (6660), (7266), (7649),
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | |            #748.
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | |   (7650)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | 
% 155.34/23.12  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (6660), (7367), (7650),
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | | |            #132.
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | |   (7651)  all_56_2 = e1 & op(e2, e3) = e1
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (163), (229),
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | |            (233), (235), (6649), (7578), (7651),
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | |            #480.
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | |   (7652)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | |            (235), (6649), (7575), (7578), (7652),
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | |            #479.
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | |   (7653)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (7653) gives:
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | |   (7654)  all_54_8 = e2
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (6649), (7654) are inconsistent by
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | |            sub-proof #608.
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | |   (7655)  all_54_8 = e1 | all_54_8 = e0
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7299), (7575), (7655) are inconsistent by
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | |            sub-proof #612.
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.12  | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | |   (7656)  all_24_2 = e1
% 155.45/23.12  | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (7656) imply:
% 155.45/23.12  | | | | | | | | | | | | | | | | |   (7657)  all_4_2 = e1
% 155.45/23.12  | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | REDUCE: (354), (7657) imply:
% 155.45/23.12  | | | | | | | | | | | | | | | | |   (7658)   ~ (all_52_6 = e1)
% 155.45/23.12  | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | REDUCE: (36), (7657) imply:
% 155.45/23.12  | | | | | | | | | | | | | | | | |   (7659)  op(e2, e2) = e1
% 155.45/23.12  | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (39), (51), (67), (113),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (123), (136), (143), (159), (160), (162), (163),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (195),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (196), (199), (201), (204), (206), (207), (209),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (210), (211), (212), (213), (214), (216), (217),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (218), (220), (221), (223), (224), (225), (227),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (236),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (238), (239), (258), (259), (268), (270), (279),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (318), (340), (346), (348), (349), (358), (360),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (373), (374), (6648), (6649), (6650), (6651),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (6652), (6659), (6660), (6662), (7263), (7266),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (7299), (7300), (7305), (7658), (7659),
% 155.45/23.12  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.45/23.12  | | | | | | | | | | | | | | | | |            #117.
% 155.45/23.12  | | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | Case 2:
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | |   (7660)   ~ (all_16_1 = e2) & op(e1, e1) = all_16_1 &
% 155.45/23.12  | | | | | | | | | |           $i(all_16_1)
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | ALPHA: (7660) implies:
% 155.45/23.12  | | | | | | | | | |   (7661)   ~ (all_16_1 = e2)
% 155.45/23.12  | | | | | | | | | |   (7662)  op(e1, e1) = all_16_1
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_16_1,
% 155.45/23.12  | | | | | | | | | |              e1, e1, simplifying with (6660), (7662) gives:
% 155.45/23.12  | | | | | | | | | |   (7663)  all_16_1 = e2
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | REDUCE: (7661), (7663) imply:
% 155.45/23.12  | | | | | | | | | |   (7664)  $false
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | CLOSE: (7664) is inconsistent.
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | | 
% 155.45/23.12  | | | | | | | | End of split
% 155.45/23.12  | | | | | | | | 
% 155.45/23.12  | | | | | | | End of split
% 155.45/23.12  | | | | | | | 
% 155.45/23.12  | | | | | | Case 2:
% 155.45/23.12  | | | | | | | 
% 155.45/23.12  | | | | | | |   (7665)  all_12_2 = e2
% 155.45/23.12  | | | | | | | 
% 155.45/23.12  | | | | | | | COMBINE_EQS: (324), (7665) imply:
% 155.45/23.12  | | | | | | |   (7666)  all_6_2 = e2
% 155.45/23.12  | | | | | | | 
% 155.45/23.12  | | | | | | | REDUCE: (338), (7666) imply:
% 155.45/23.12  | | | | | | |   (7667)   ~ (all_52_1 = e2)
% 155.45/23.12  | | | | | | | 
% 155.45/23.12  | | | | | | | REDUCE: (342), (7666) imply:
% 155.45/23.12  | | | | | | |   (7668)   ~ (all_52_3 = e2)
% 155.45/23.12  | | | | | | | 
% 155.45/23.12  | | | | | | | REDUCE: (348), (7666) imply:
% 155.45/23.12  | | | | | | |   (7669)   ~ (all_52_12 = e2)
% 155.45/23.12  | | | | | | | 
% 155.45/23.12  | | | | | | | BETA: splitting (233) gives:
% 155.45/23.12  | | | | | | | 
% 155.45/23.12  | | | | | | | Case 1:
% 155.45/23.12  | | | | | | | | 
% 155.45/23.12  | | | | | | | |   (7670)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 155.45/23.12  | | | | | | | |             op(e2, e3) = e2)
% 155.45/23.12  | | | | | | | | 
% 155.45/23.12  | | | | | | | | BETA: splitting (7670) gives:
% 155.45/23.12  | | | | | | | | 
% 155.45/23.12  | | | | | | | | Case 1:
% 155.45/23.12  | | | | | | | | | 
% 155.45/23.12  | | | | | | | | |   (7671)  all_56_0 = e2 & op(e3, e3) = e2
% 155.45/23.12  | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | ALPHA: (7671) implies:
% 155.45/23.12  | | | | | | | | |   (7672)  all_56_0 = e2
% 155.45/23.12  | | | | | | | | |   (7673)  op(e3, e3) = e2
% 155.45/23.12  | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | BETA: splitting (55) gives:
% 155.45/23.12  | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | Case 1:
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | |   (7674)   ~ (all_16_2 = e1)
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | REDUCE: (327), (7674) imply:
% 155.45/23.12  | | | | | | | | | |   (7675)   ~ (all_14_2 = e1)
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | BETA: splitting (58) gives:
% 155.45/23.12  | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | Case 1:
% 155.45/23.12  | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | |   (7676)   ~ (all_18_2 = e3)
% 155.45/23.12  | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | REDUCE: (301), (7676) imply:
% 155.45/23.12  | | | | | | | | | | |   (7677)   ~ (all_14_2 = e3)
% 155.45/23.12  | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | BETA: splitting (67) gives:
% 155.45/23.12  | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | Case 1:
% 155.45/23.12  | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | |   (7678)   ~ (all_24_2 = e1)
% 155.45/23.12  | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | REDUCE: (318), (7678) imply:
% 155.45/23.12  | | | | | | | | | | | |   (7679)   ~ (all_4_2 = e1)
% 155.45/23.12  | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | BETA: splitting (73) gives:
% 155.45/23.12  | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | Case 1:
% 155.45/23.12  | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | |   (7680)   ~ (all_28_2 = e2)
% 155.45/23.12  | | | | | | | | | | | | | 
% 155.45/23.12  | | | | | | | | | | | | | REDUCE: (330), (7680) imply:
% 155.45/23.12  | | | | | | | | | | | | |   (7681)   ~ (all_14_2 = e2)
% 155.45/23.12  | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | BETA: splitting (189) gives:
% 155.45/23.13  | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | |   (7682)  all_54_15 = e3
% 155.45/23.13  | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | REF_CLOSE: (246), (7677), (7682) are inconsistent by
% 155.45/23.13  | | | | | | | | | | | | | |            sub-proof #1010.
% 155.45/23.13  | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | Case 2:
% 155.45/23.13  | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | |   (7683)   ~ (all_54_15 = e3)
% 155.45/23.13  | | | | | | | | | | | | | |   (7684)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 155.45/23.13  | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 155.45/23.13  | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | |   (7685)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 155.45/23.13  | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 155.45/23.13  | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | BETA: splitting (7685) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | |   (7686)  all_56_9 = e2 & op(e3, e0) = e2
% 155.45/23.13  | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7669), (7686), (function-axioms) are
% 155.45/23.13  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #880.
% 155.45/23.13  | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | Case 2:
% 155.45/23.13  | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | |   (7687)  all_56_10 = e2 & op(e2, e0) = e2
% 155.45/23.13  | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | ALPHA: (7687) implies:
% 155.45/23.13  | | | | | | | | | | | | | | | |   (7688)  op(e2, e0) = e2
% 155.45/23.13  | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | BETA: splitting (7684) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | |   (7689)  all_54_15 = e2
% 155.45/23.13  | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7681), (7689) are inconsistent by
% 155.45/23.13  | | | | | | | | | | | | | | | | |            sub-proof #1009.
% 155.45/23.13  | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.13  | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | |   (7690)  all_54_15 = e1 | all_54_15 = e0
% 155.45/23.13  | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | BETA: splitting (7690) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7691)  all_54_15 = e1
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7675), (7691) are inconsistent by
% 155.45/23.13  | | | | | | | | | | | | | | | | | |            sub-proof #1008.
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7692)  all_54_15 = e0
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (7692) imply:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7693)  all_14_2 = e0
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | SIMP: (7693) implies:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7694)  all_14_2 = e0
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | REDUCE: (351), (7694) imply:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7695)   ~ (all_52_3 = e0)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | REDUCE: (362), (7694) imply:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7696)   ~ (all_52_7 = e0)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | REDUCE: (369), (7694) imply:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7697)   ~ (all_52_11 = e0)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | REDUCE: (371), (7694) imply:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7698)   ~ (all_52_13 = e0)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | REDUCE: (7677), (7694) imply:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7699)   ~ (e3 = e0)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | REDUCE: (7675), (7694) imply:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7700)   ~ (e1 = e0)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 155.45/23.13  | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (7688) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7701)  all_52_13 = e2
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | REDUCE: (360), (7701) imply:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7702)   ~ (all_4_2 = e2)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | SIMP: (7702) implies:
% 155.45/23.13  | | | | | | | | | | | | | | | | | |   (7703)   ~ (all_4_2 = e2)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | |   (7704)  all_54_5 = e3
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7704) imply:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | |   (7705)  all_4_2 = e3
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (7705) imply:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | |   (7706)  $false
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | CLOSE: (7706) is inconsistent.
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | |   (7707)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |   (7708)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7708) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |   (7709)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7709) implies:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |   (7710)  op(e3, e3) = e3
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7673), (7710), (function-axioms) are
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |   (7711)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7711) implies:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |   (7712)  op(e2, e2) = e2
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (268), (7679), (7703), (7707), (7712),
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |            #928.
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | End of split
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |   (7713)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7713) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |   (7714)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7714) implies:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |   (7715)  op(e1, e1) = e1
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6660), (7715), (function-axioms) are
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |   (7716)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7716) implies:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |   (7717)  op(e0, e0) = e0
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |   (7718)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11))
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7718) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | |   (7719)  all_57_12 = e0 & op(e2, e2) = e0
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7719) implies:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | |   (7720)  op(e2, e2) = e0
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |   (7721)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7721) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |   (7722)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7722) gives:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7723)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7667), (7723), (function-axioms) are
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (7724)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7724) gives:
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7725)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7667), (7725), (function-axioms) are
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7726)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7726) gives:
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7727)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7727) implies:
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7728)  op(e2, e3) = e2
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7667), (7728), (function-axioms) are
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7729)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.45/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7729) gives:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7730)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7730) implies:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7731)  op(e1, e1) = e3
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6660), (7731), (function-axioms) are
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7732)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7732) implies:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7733)  op(e2, e1) = e2
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7734)  op(e2, e2) = all_57_12
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (268), (6648), (6652), (7679),
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7703), (7707), (7733), (7734), (function-axioms)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #109.
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |   (7735)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7735) gives:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (7736)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (7673), (7717), (7720), (7736),
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |            #272.
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (7737)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7737) gives:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7738)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7738) gives:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7739)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7739) implies:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7740)  op(e1, e1) = e3
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6660), (7740), (function-axioms) are
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7741)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7741) implies:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7742)  op(e2, e2) = e1
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7720), (7742), (function-axioms) are
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7743)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (6660), (7717), (7743),
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            #108.
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |   (7744)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7744) gives:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |   (7745)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7745) gives:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7746)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7746) gives:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7747)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7673), (7720), (7747),
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            #271.
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7748)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7748) gives:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7749)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7749) implies:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7750)  op(e2, e1) = e2
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7751)  op(e2, e2) = all_57_12
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (268), (6648), (6652), (7679),
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7703), (7707), (7750), (7751), (function-axioms)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #109.
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7752)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7752) implies:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7753)  op(e0, e0) = e1
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (7717), (7753), (function-axioms) are
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7754)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7754) gives:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7755)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6660), (7720), (7755), (function-axioms) are
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #179.
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7756)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (7673), (7717), (7756),
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            #283.
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |   (7757)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7757) gives:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7758)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (7717), (7720), (7758),
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |            #918.
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7759)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7759) gives:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7760)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (7673), (7717), (7760),
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            #282.
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7761)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.49/23.15  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7761) gives:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7762)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7762) implies:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7763)  op(e2, e2) = e2
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7720), (7763), (function-axioms) are
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7764)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7764) gives:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7765)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7765) implies:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7766)  op(e1, e1) = e1
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6660), (7766), (function-axioms) are
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7767)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7767) implies:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7768)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7768) gives:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7769)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7769) gives:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7770)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7770) gives:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7771)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7771) implies:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7772)  op(e0, e3) = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7695), (7772), (function-axioms) are
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7773)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (6660), (7695), (7773),
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #745.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7774)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (159), (7673), (7695), (7696), (7774),
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #280.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7775)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7775) gives:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7776)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7776) gives:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7777)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7777) implies:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7778)  op(e1, e1) = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6660), (7778), (function-axioms) are
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7779)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (7673), (7696), (7779),
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #279.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7780)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7780) gives:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7781)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7781) gives:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7782)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e1) = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7782) implies:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7783)  op(e0, e1) = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7697), (7783), (function-axioms) are
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7784)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e1) = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7784) implies:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7785)  op(e1, e1) = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6660), (7785), (function-axioms) are
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7786)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7697), (7786), (function-axioms) are
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | |   (7787)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7787) implies:
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | |   (7788)   ~ (all_57_11 = e2)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | |   (7789)  op(e2, e0) = all_57_11
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7688), (7788), (7789), (function-axioms)
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #627.
% 155.49/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | Case 2:
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | |   (7790)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 155.49/23.17  | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | BETA: splitting (7790) gives:
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | Case 1:
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | |   (7791)  all_56_11 = e2 & op(e1, e0) = e2
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6653), (7791), (function-axioms) are
% 155.49/23.17  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #879.
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | Case 2:
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | |   (7792)  all_56_15 = e2 & op(e0, e0) = e2
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | ALPHA: (7792) implies:
% 155.49/23.17  | | | | | | | | | | | | | | | |   (7793)  op(e0, e0) = e2
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (7675), (7681), (7684), (7793),
% 155.49/23.17  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.17  | | | | | | | | | | | | | | | |            #798.
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | Case 2:
% 155.49/23.17  | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | |   (7794)  all_28_2 = e2
% 155.49/23.17  | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | COMBINE_EQS: (330), (7794) imply:
% 155.49/23.17  | | | | | | | | | | | | |   (7795)  all_14_2 = e2
% 155.49/23.17  | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | SIMP: (7795) implies:
% 155.49/23.17  | | | | | | | | | | | | |   (7796)  all_14_2 = e2
% 155.49/23.17  | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | REDUCE: (371), (7796) imply:
% 155.49/23.17  | | | | | | | | | | | | |   (7797)   ~ (all_52_13 = e2)
% 155.49/23.17  | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | REDUCE: (7677), (7796) imply:
% 155.49/23.17  | | | | | | | | | | | | |   (7798)   ~ (e3 = e2)
% 155.49/23.17  | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | REDUCE: (51), (7796) imply:
% 155.49/23.17  | | | | | | | | | | | | |   (7799)  op(e0, e0) = e2
% 155.49/23.17  | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.49/23.17  | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | Case 1:
% 155.49/23.17  | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | |   (7800)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.49/23.17  | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.49/23.17  | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.49/23.17  | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.49/23.17  | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.49/23.17  | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.49/23.17  | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.49/23.17  | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.49/23.17  | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.49/23.17  | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.49/23.17  | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.49/23.17  | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.49/23.17  | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.49/23.17  | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.49/23.17  | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.49/23.17  | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.49/23.17  | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | BETA: splitting (7800) gives:
% 155.49/23.17  | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | Case 1:
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | |   (7801)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.49/23.17  | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.49/23.17  | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.49/23.17  | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.49/23.17  | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.49/23.17  | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.49/23.17  | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.49/23.17  | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | ALPHA: (7801) implies:
% 155.49/23.17  | | | | | | | | | | | | | | |   (7802)  op(e3, e3) = e3
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (159), (163), (167), (168),
% 155.49/23.17  | | | | | | | | | | | | | | |            (169), (170), (199), (233), (234), (238), (268),
% 155.49/23.17  | | | | | | | | | | | | | | |            (352), (373), (6649), (6651), (6660), (7668),
% 155.49/23.17  | | | | | | | | | | | | | | |            (7669), (7679), (7799), (7802), (function-axioms)
% 155.49/23.17  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #181.
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | Case 2:
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | |   (7803)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.49/23.17  | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.49/23.17  | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.49/23.17  | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.49/23.17  | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.49/23.17  | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.49/23.17  | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.49/23.17  | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | ALPHA: (7803) implies:
% 155.49/23.17  | | | | | | | | | | | | | | |   (7804)  op(e2, e2) = e2
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.49/23.17  | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | Case 1:
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | |   (7805)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.49/23.17  | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.49/23.17  | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.49/23.17  | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.49/23.17  | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.49/23.17  | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.49/23.17  | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.49/23.17  | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.49/23.17  | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.49/23.17  | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.49/23.17  | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.49/23.17  | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.49/23.17  | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.49/23.17  | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.49/23.17  | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.49/23.17  | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.49/23.17  | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.49/23.17  | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.49/23.17  | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.17  | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.49/23.17  | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.49/23.17  | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.49/23.17  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.49/23.17  | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.49/23.17  | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.17  | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.49/23.17  | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.49/23.17  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.49/23.17  | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.17  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.17  | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.49/23.17  | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.49/23.17  | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.49/23.17  | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.49/23.17  | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.49/23.17  | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.17  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.49/23.17  | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.17  | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.49/23.17  | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.49/23.17  | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.49/23.17  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.49/23.17  | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.17  | | | | | | | | | | | | | | | |             e1)
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | BETA: splitting (7805) gives:
% 155.49/23.17  | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.17  | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | |   (7806)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.49/23.17  | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.49/23.17  | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.49/23.17  | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.49/23.17  | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.49/23.17  | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.49/23.17  | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.49/23.17  | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.49/23.17  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.49/23.17  | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.49/23.17  | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.49/23.17  | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.49/23.17  | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.49/23.17  | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.49/23.17  | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.17  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.49/23.17  | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.49/23.17  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.49/23.17  | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (167), (6652), (6660), (7667), (7806),
% 155.49/23.17  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.17  | | | | | | | | | | | | | | | | |            #114.
% 155.49/23.17  | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.17  | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | |   (7807)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.49/23.17  | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.17  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.49/23.17  | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.49/23.17  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.49/23.17  | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.17  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.17  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.49/23.17  | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.49/23.17  | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.49/23.17  | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.17  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.17  | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.49/23.17  | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.49/23.17  | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.49/23.17  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.49/23.17  | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.17  | | | | | | | | | | | | | | | | |             e1)
% 155.49/23.17  | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | BETA: splitting (7807) gives:
% 155.49/23.17  | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.17  | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | |   (7808)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.49/23.17  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.49/23.17  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.17  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.49/23.17  | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.49/23.17  | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.49/23.17  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.49/23.17  | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.17  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.17  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.49/23.17  | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | BETA: splitting (7808) gives:
% 155.49/23.17  | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |   (7809)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (7809) gives:
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |   (7810)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | ALPHA: (7810) implies:
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |   (7811)  op(e0, e0) = e3
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7799), (7811), (function-axioms) are
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |   (7812)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | ALPHA: (7812) implies:
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |   (7813)  op(e3, e3) = e3
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (159), (163), (167), (168),
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |            (169), (170), (199), (233), (234), (238), (268),
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |            (352), (373), (6649), (6651), (6660), (7668),
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |            (7669), (7679), (7799), (7813), (function-axioms)
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #181.
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |   (7814)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (7673), (7797), (7814),
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.17  | | | | | | | | | | | | | | | | | | |            #286.
% 155.49/23.17  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.17  | | | | | | | | | | | | | | | | | | 
% 155.49/23.17  | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.17  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | |   (7815)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.49/23.18  | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.49/23.18  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.49/23.18  | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             e1)
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | BETA: splitting (7815) gives:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |   (7816)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (6660), (7804), (7816),
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |            #113.
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |   (7817)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             e1)
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (6660), (7799), (7817),
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |            #107.
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | End of split
% 155.49/23.18  | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | End of split
% 155.49/23.18  | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | Case 2:
% 155.49/23.18  | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | |   (7818)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.18  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.49/23.18  | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.49/23.18  | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.49/23.18  | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.49/23.18  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.49/23.18  | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.49/23.18  | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.18  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.49/23.18  | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.18  | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.49/23.18  | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.49/23.18  | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.49/23.18  | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.49/23.18  | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.49/23.18  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.49/23.18  | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.49/23.18  | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.49/23.18  | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.49/23.18  | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.49/23.18  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.49/23.18  | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.49/23.18  | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.49/23.18  | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.49/23.18  | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.49/23.18  | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.49/23.18  | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.49/23.18  | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.49/23.18  | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.49/23.18  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.49/23.18  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.49/23.18  | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.49/23.18  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.49/23.18  | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.49/23.18  | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.49/23.18  | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.49/23.18  | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.49/23.18  | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.49/23.18  | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.49/23.18  | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.49/23.18  | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.18  | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.49/23.18  | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.49/23.18  | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.18  | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.49/23.18  | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.49/23.18  | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.18  | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.49/23.18  | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.49/23.18  | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.49/23.18  | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.49/23.18  | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.49/23.18  | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.49/23.18  | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.49/23.18  | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.49/23.18  | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.49/23.18  | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.49/23.18  | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.49/23.18  | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.49/23.18  | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.49/23.18  | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.49/23.18  | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.49/23.18  | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.49/23.18  | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.49/23.18  | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.18  | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.49/23.18  | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.49/23.18  | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.18  | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.49/23.18  | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.49/23.18  | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.49/23.18  | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.49/23.18  | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.49/23.18  | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.49/23.18  | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.49/23.18  | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | BETA: splitting (7818) gives:
% 155.49/23.18  | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.18  | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | |   (7819)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.49/23.18  | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.49/23.18  | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.49/23.18  | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.18  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.49/23.18  | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.49/23.18  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.49/23.18  | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.49/23.18  | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.49/23.18  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.18  | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.49/23.18  | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.49/23.18  | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.49/23.18  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.49/23.18  | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.49/23.18  | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.49/23.18  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.49/23.18  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.49/23.18  | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.49/23.18  | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.49/23.18  | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.49/23.18  | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.49/23.18  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.49/23.18  | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | BETA: splitting (7819) gives:
% 155.49/23.18  | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | |   (7820)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.49/23.18  | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.49/23.18  | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.49/23.18  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.49/23.18  | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.49/23.18  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | BETA: splitting (7820) gives:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |   (7821)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7673), (7804), (7821), (function-axioms) are
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #285.
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |   (7822)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (165), (6652), (7799), (7822),
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |            #106.
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | |   (7823)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.49/23.18  | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.49/23.18  | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.49/23.18  | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.49/23.18  | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | BETA: splitting (7823) gives:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |   (7824)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6660), (7797), (7824), (function-axioms)
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #198.
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |   (7825)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | BETA: splitting (7825) gives:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |   (7826)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | ALPHA: (7826) implies:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |   (7827)  op(e0, e0) = e3
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7799), (7827), (function-axioms) are
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |   (7828)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7828) gives:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |   (7829)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7829) implies:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |   (7830)  op(e3, e3) = e3
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (159), (163), (167), (168),
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |            (169), (170), (199), (233), (234), (238), (268),
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |            (352), (373), (6649), (6651), (6660), (7668),
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |            (7669), (7679), (7799), (7830), (function-axioms)
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #181.
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |   (7831)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7831) implies:
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |   (7832)  op(e3, e3) = e1
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7673), (7832), (function-axioms) are
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.18  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.18  | | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | | End of split
% 155.49/23.18  | | | | | | | | | | | | | | | | | 
% 155.49/23.18  | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.18  | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | |   (7833)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.49/23.19  | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.49/23.19  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.49/23.19  | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.49/23.19  | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.49/23.19  | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.49/23.19  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.49/23.19  | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.49/23.19  | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.49/23.19  | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.49/23.19  | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.49/23.19  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.49/23.19  | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.49/23.19  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.49/23.19  | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.49/23.19  | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.49/23.19  | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.49/23.19  | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.49/23.19  | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.19  | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.49/23.19  | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.49/23.19  | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | |                 e0)))
% 155.49/23.19  | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | BETA: splitting (7833) gives:
% 155.49/23.19  | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | |   (7834)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.49/23.19  | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.49/23.19  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.49/23.19  | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | BETA: splitting (7834) gives:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |   (7835)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6652), (7835), (function-axioms) are
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #871.
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |   (7836)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (7836) gives:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7837)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (7837) implies:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7838)  op(e2, e2) = e1
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7804), (7838), (function-axioms) are
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7839)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (7839) implies:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7840)  op(e0, e0) = e3
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7799), (7840), (function-axioms) are
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.19  | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | |   (7841)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.49/23.19  | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.49/23.19  | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.49/23.19  | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | BETA: splitting (7841) gives:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |   (7842)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (7842) gives:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7843)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (7843) implies:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7844)  op(e2, e0) = e2
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7797), (7844), (function-axioms) are
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7845)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (7845) implies:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7846)  op(e3, e3) = e3
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (159), (163), (167), (168),
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |            (169), (170), (199), (233), (234), (238), (268),
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |            (352), (373), (6649), (6651), (6660), (7668),
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |            (7669), (7679), (7799), (7846), (function-axioms)
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #181.
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |   (7847)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (7847) gives:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7848)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (7848) implies:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7849)  op(e2, e0) = e2
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7797), (7849), (function-axioms) are
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |   (7850)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7850) gives:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | |   (7851)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7851) implies:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | |   (7852)  op(e1, e1) = e1
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6660), (7852), (function-axioms) are
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.19  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |   (7853)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7853) implies:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |   (7854)  op(e0, e0) = all_57_15
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |   (7855)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (7799), (7854)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |              gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |   (7856)  all_57_15 = e2
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e2,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (7804) gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | |   (7857)  all_4_2 = e2
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7855) gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |   (7858)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7858) gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |   (7859)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7859) gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |   (7860)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e3) = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7860) implies:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |   (7861)  op(e3, e3) = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7673), (7861), (function-axioms) are
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |   (7862)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (6660), (7797), (7862),
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |            #169.
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |   (7863)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7863) gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |   (7864)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7856), (7864) are inconsistent by sub-proof
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |            #865.
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |   (7865)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (7673), (7797), (7865),
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |            #264.
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |   (7866)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7866) gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |   (7867)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7867) gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |   (7868)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7868) implies:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |   (7869)  op(e1, e1) = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6660), (7869), (function-axioms) are
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |   (7870)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7870) gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (7871)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7856), (7871) are inconsistent by sub-proof #863.
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (7872)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7872) implies:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (7873)  op(e3, e3) = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7673), (7873), (function-axioms) are
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |   (7874)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7874) gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |   (7875)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (6660), (7797), (7875),
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |            #164.
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |   (7876)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7876) gives:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (7877)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 & 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7877) implies:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (7878)  all_57_15 = e1
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7856), (7878) imply:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (7879)  e2 = e1
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7672), (7879) imply:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (7880)  all_56_0 = e1
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (159), (163), (167), (168), (169),
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (199), (233), (234), (238), (268), (352),
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (6649), (6651), (6660), (7668), (7669),
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |            (7679), (7799), (7880), (function-axioms) are
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #158.
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (7881)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = e0
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7856), (7881) are inconsistent by sub-proof
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | |            #861.
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | |   (7882)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.49/23.20  | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.49/23.20  | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.49/23.20  | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.49/23.20  | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.49/23.20  | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.49/23.20  | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.49/23.20  | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.49/23.20  | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.49/23.20  | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.49/23.20  | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.49/23.20  | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.49/23.20  | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.49/23.20  | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.49/23.20  | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.49/23.20  | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (6660), (7799), (7882),
% 155.49/23.20  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.20  | | | | | | | | | | | | | |            #780.
% 155.49/23.20  | | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | |   (7883)  all_24_2 = e1
% 155.49/23.20  | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | COMBINE_EQS: (318), (7883) imply:
% 155.49/23.20  | | | | | | | | | | | |   (7884)  all_4_2 = e1
% 155.49/23.20  | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | SIMP: (7884) implies:
% 155.49/23.20  | | | | | | | | | | | |   (7885)  all_4_2 = e1
% 155.49/23.20  | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | REDUCE: (36), (7885) imply:
% 155.49/23.20  | | | | | | | | | | | |   (7886)  op(e2, e2) = e1
% 155.49/23.20  | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (164), (165), (167), (223), (238),
% 155.49/23.20  | | | | | | | | | | | |            (6652), (6660), (7667), (7673), (7886),
% 155.49/23.20  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.20  | | | | | | | | | | | |            #253.
% 155.49/23.20  | | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | | End of split
% 155.49/23.20  | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | Case 2:
% 155.49/23.20  | | | | | | | | | | | 
% 155.49/23.20  | | | | | | | | | | |   (7887)  all_18_2 = e3
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | COMBINE_EQS: (301), (7887) imply:
% 155.49/23.21  | | | | | | | | | | |   (7888)  all_14_2 = e3
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | SIMP: (7888) implies:
% 155.49/23.21  | | | | | | | | | | |   (7889)  all_14_2 = e3
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | REDUCE: (51), (7889) imply:
% 155.49/23.21  | | | | | | | | | | |   (7890)  op(e0, e0) = e3
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | BETA: splitting (238) gives:
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | Case 1:
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | |   (7891)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.49/23.21  | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.49/23.21  | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.49/23.21  | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.49/23.21  | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.49/23.21  | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.49/23.21  | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.49/23.21  | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.49/23.21  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.49/23.21  | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.49/23.21  | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.49/23.21  | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.49/23.21  | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.49/23.21  | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.49/23.21  | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.49/23.21  | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | BETA: splitting (7891) gives:
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | Case 1:
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | |   (7892)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.49/23.21  | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.49/23.21  | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.49/23.21  | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.49/23.21  | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.49/23.21  | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.49/23.21  | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.49/23.21  | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | ALPHA: (7892) implies:
% 155.49/23.21  | | | | | | | | | | | | |   (7893)  op(e3, e3) = e3
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | REF_CLOSE: (9), (7673), (7893), (function-axioms) are
% 155.49/23.21  | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | |   (7894)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.49/23.21  | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.49/23.21  | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.49/23.21  | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.49/23.21  | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.49/23.21  | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.49/23.21  | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.49/23.21  | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | ALPHA: (7894) implies:
% 155.49/23.21  | | | | | | | | | | | | |   (7895)  op(e2, e2) = e2
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | REF_CLOSE: (9), (36), (160), (164), (168), (211), (360),
% 155.49/23.21  | | | | | | | | | | | | |            (6653), (7669), (7890), (7895), (function-axioms)
% 155.49/23.21  | | | | | | | | | | | | |            are inconsistent by sub-proof #877.
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | |   (7896)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.49/23.21  | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.49/23.21  | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.49/23.21  | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.49/23.21  | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.49/23.21  | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.49/23.21  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.49/23.21  | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.49/23.21  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.49/23.21  | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.49/23.21  | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.49/23.21  | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.49/23.21  | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.49/23.21  | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.49/23.21  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.49/23.21  | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | REF_CLOSE: (6), (7), (6660), (7890), (7896),
% 155.49/23.21  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.21  | | | | | | | | | | | |            #416.
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | |   (7897)  all_16_2 = e1
% 155.49/23.21  | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | COMBINE_EQS: (327), (7897) imply:
% 155.49/23.21  | | | | | | | | | |   (7898)  all_14_2 = e1
% 155.49/23.21  | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | SIMP: (7898) implies:
% 155.49/23.21  | | | | | | | | | |   (7899)  all_14_2 = e1
% 155.49/23.21  | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | REDUCE: (51), (7899) imply:
% 155.49/23.21  | | | | | | | | | |   (7900)  op(e0, e0) = e1
% 155.49/23.21  | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | BETA: splitting (211) gives:
% 155.49/23.21  | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | Case 1:
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | |   (7901)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 155.49/23.21  | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | BETA: splitting (7901) gives:
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | Case 1:
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | |   (7902)  all_56_9 = e2 & op(e3, e0) = e2
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | REF_CLOSE: (168), (7669), (7902), (function-axioms) are
% 155.49/23.21  | | | | | | | | | | | |            inconsistent by sub-proof #880.
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | |   (7903)  all_56_10 = e2 & op(e2, e0) = e2
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | ALPHA: (7903) implies:
% 155.49/23.21  | | | | | | | | | | | |   (7904)  op(e2, e0) = e2
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | Case 1:
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | |   (7905)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.49/23.21  | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.49/23.21  | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.49/23.21  | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.49/23.21  | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.49/23.21  | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.49/23.21  | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.49/23.21  | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.49/23.21  | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.49/23.21  | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.49/23.21  | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.49/23.21  | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.49/23.21  | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.49/23.21  | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.49/23.21  | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.49/23.21  | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | BETA: splitting (7905) gives:
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | Case 1:
% 155.49/23.21  | | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | |   (7906)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.49/23.21  | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.49/23.21  | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.49/23.21  | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.49/23.21  | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.49/23.21  | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.49/23.21  | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.49/23.21  | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.49/23.21  | | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | | ALPHA: (7906) implies:
% 155.49/23.21  | | | | | | | | | | | | | |   (7907)  op(e3, e3) = e3
% 155.49/23.21  | | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | | REF_CLOSE: (9), (7673), (7907), (function-axioms) are
% 155.49/23.21  | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 155.49/23.21  | | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | |   (7908)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.49/23.21  | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.49/23.21  | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.49/23.21  | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.49/23.21  | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.49/23.21  | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.49/23.21  | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.49/23.21  | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.49/23.21  | | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | | ALPHA: (7908) implies:
% 155.49/23.21  | | | | | | | | | | | | | |   (7909)  op(e2, e2) = e2
% 155.49/23.21  | | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (7904), (7909),
% 155.49/23.21  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.21  | | | | | | | | | | | | | |            #972.
% 155.49/23.21  | | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | |   (7910)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.49/23.21  | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.49/23.21  | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.49/23.21  | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.49/23.21  | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.49/23.21  | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.49/23.21  | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.49/23.21  | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.49/23.21  | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.49/23.21  | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.49/23.21  | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.49/23.21  | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.49/23.21  | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.49/23.21  | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.49/23.21  | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.49/23.21  | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (6660), (7900), (7910),
% 155.49/23.21  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.49/23.21  | | | | | | | | | | | | |            #748.
% 155.49/23.21  | | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | |   (7911)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 155.49/23.21  | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | BETA: splitting (7911) gives:
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | Case 1:
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | |   (7912)  all_56_11 = e2 & op(e1, e0) = e2
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | REF_CLOSE: (160), (6653), (7912), (function-axioms) are
% 155.49/23.21  | | | | | | | | | | | |            inconsistent by sub-proof #879.
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | |   (7913)  all_56_15 = e2 & op(e0, e0) = e2
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | ALPHA: (7913) implies:
% 155.49/23.21  | | | | | | | | | | | |   (7914)  op(e0, e0) = e2
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | | REF_CLOSE: (6), (7900), (7914), (function-axioms) are
% 155.49/23.21  | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.49/23.21  | | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | |   (7915)  all_56_2 = e2 & op(e2, e3) = e2
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | ALPHA: (7915) implies:
% 155.49/23.21  | | | | | | | | |   (7916)  op(e2, e3) = e2
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | REF_CLOSE: (167), (7667), (7916), (function-axioms) are
% 155.49/23.21  | | | | | | | | |            inconsistent by sub-proof #1007.
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | 
% 155.49/23.21  | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | 
% 155.49/23.21  | | | | | | | |   (7917)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 155.49/23.21  | | | | | | | |             op(e0, e3) = e2)
% 155.49/23.21  | | | | | | | | 
% 155.49/23.21  | | | | | | | | BETA: splitting (7917) gives:
% 155.49/23.21  | | | | | | | | 
% 155.49/23.21  | | | | | | | | Case 1:
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | |   (7918)  all_56_6 = e2 & op(e1, e3) = e2
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | REF_CLOSE: (163), (6649), (7918), (function-axioms) are
% 155.49/23.21  | | | | | | | | |            inconsistent by sub-proof #761.
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | Case 2:
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | |   (7919)  all_56_12 = e2 & op(e0, e3) = e2
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | | REF_CLOSE: (159), (7668), (7919), (function-axioms) are
% 155.49/23.21  | | | | | | | | |            inconsistent by sub-proof #858.
% 155.49/23.21  | | | | | | | | | 
% 155.49/23.21  | | | | | | | | End of split
% 155.49/23.21  | | | | | | | | 
% 155.49/23.21  | | | | | | | End of split
% 155.49/23.21  | | | | | | | 
% 155.49/23.21  | | | | | | End of split
% 155.49/23.21  | | | | | | 
% 155.49/23.21  | | | | | Case 2:
% 155.49/23.21  | | | | | | 
% 155.49/23.21  | | | | | |   (7920)  all_56_11 = e2 & op(e1, e0) = e2
% 155.49/23.21  | | | | | | 
% 155.49/23.21  | | | | | | REF_CLOSE: (160), (6653), (7920), (function-axioms) are inconsistent
% 155.49/23.21  | | | | | |            by sub-proof #879.
% 155.49/23.21  | | | | | | 
% 155.49/23.21  | | | | | End of split
% 155.49/23.21  | | | | | 
% 155.49/23.21  | | | | End of split
% 155.49/23.21  | | | | 
% 155.49/23.21  | | | End of split
% 155.49/23.21  | | | 
% 155.49/23.21  | | Case 2:
% 155.49/23.21  | | | 
% 155.49/23.21  | | |   (7921)  all_6_2 = e0
% 155.49/23.21  | | |   (7922)  ( ~ (all_6_0 = e1) & op(e0, e3) = all_6_0 & $i(all_6_0)) | ( ~
% 155.49/23.21  | | |             (all_6_1 = e2) & op(e0, e0) = all_6_1 & $i(all_6_1))
% 155.49/23.21  | | | 
% 155.49/23.21  | | | COMBINE_EQS: (329), (7921) imply:
% 155.49/23.21  | | |   (7923)  all_8_2 = e0
% 155.49/23.21  | | | 
% 155.49/23.21  | | | REDUCE: (338), (7921) imply:
% 155.49/23.21  | | |   (7924)   ~ (all_52_1 = e0)
% 155.49/23.21  | | | 
% 155.49/23.21  | | | REDUCE: (340), (7921) imply:
% 155.63/23.21  | | |   (7925)   ~ (all_52_2 = e0)
% 155.63/23.21  | | | 
% 155.63/23.21  | | | REDUCE: (342), (7921) imply:
% 155.63/23.21  | | |   (7926)   ~ (all_52_3 = e0)
% 155.63/23.21  | | | 
% 155.63/23.21  | | | REDUCE: (344), (7921) imply:
% 155.63/23.21  | | |   (7927)   ~ (all_52_4 = e0)
% 155.63/23.21  | | | 
% 155.63/23.21  | | | REDUCE: (346), (7921) imply:
% 155.63/23.21  | | |   (7928)   ~ (all_52_8 = e0)
% 155.63/23.21  | | | 
% 155.63/23.21  | | | REDUCE: (348), (7921) imply:
% 155.63/23.21  | | |   (7929)   ~ (all_52_12 = e0)
% 155.63/23.21  | | | 
% 155.63/23.21  | | | REDUCE: (39), (7921) imply:
% 155.63/23.21  | | |   (7930)  op(e3, e3) = e0
% 155.63/23.21  | | | 
% 155.63/23.21  | | | BETA: splitting (43) gives:
% 155.63/23.21  | | | 
% 155.63/23.21  | | | Case 1:
% 155.63/23.21  | | | | 
% 155.63/23.21  | | | |   (7931)   ~ (all_8_2 = e0)
% 155.63/23.21  | | | | 
% 155.63/23.21  | | | | REDUCE: (7923), (7931) imply:
% 155.63/23.21  | | | |   (7932)  $false
% 155.63/23.21  | | | | 
% 155.63/23.21  | | | | CLOSE: (7932) is inconsistent.
% 155.63/23.21  | | | | 
% 155.63/23.21  | | | Case 2:
% 155.63/23.21  | | | | 
% 155.63/23.21  | | | |   (7933)  ( ~ (all_8_0 = e2) & op(e0, e3) = all_8_0 & $i(all_8_0)) | ( ~
% 155.63/23.21  | | | |             (all_8_1 = e1) & op(e0, e0) = all_8_1 & $i(all_8_1))
% 155.63/23.21  | | | | 
% 155.63/23.21  | | | | BETA: splitting (46) gives:
% 155.63/23.21  | | | | 
% 155.63/23.21  | | | | Case 1:
% 155.63/23.21  | | | | | 
% 155.63/23.21  | | | | |   (7934)   ~ (all_10_2 = e2)
% 155.63/23.21  | | | | | 
% 155.63/23.21  | | | | | BETA: splitting (52) gives:
% 155.63/23.21  | | | | | 
% 155.63/23.21  | | | | | Case 1:
% 155.63/23.21  | | | | | | 
% 155.63/23.21  | | | | | |   (7935)   ~ (all_14_2 = e1)
% 155.63/23.21  | | | | | | 
% 155.63/23.21  | | | | | | BETA: splitting (58) gives:
% 155.63/23.21  | | | | | | 
% 155.63/23.21  | | | | | | Case 1:
% 155.63/23.21  | | | | | | | 
% 155.63/23.21  | | | | | | |   (7936)   ~ (all_18_2 = e3)
% 155.63/23.21  | | | | | | | 
% 155.63/23.21  | | | | | | | REDUCE: (301), (7936) imply:
% 155.63/23.21  | | | | | | |   (7937)   ~ (all_14_2 = e3)
% 155.63/23.21  | | | | | | | 
% 155.63/23.21  | | | | | | | BETA: splitting (61) gives:
% 155.63/23.21  | | | | | | | 
% 155.63/23.21  | | | | | | | Case 1:
% 155.63/23.21  | | | | | | | | 
% 155.63/23.21  | | | | | | | |   (7938)   ~ (all_20_2 = e3)
% 155.63/23.21  | | | | | | | | 
% 155.63/23.21  | | | | | | | | REDUCE: (325), (7938) imply:
% 155.63/23.21  | | | | | | | |   (7939)   ~ (all_10_2 = e3)
% 155.63/23.21  | | | | | | | | 
% 155.63/23.21  | | | | | | | | BETA: splitting (64) gives:
% 155.63/23.21  | | | | | | | | 
% 155.63/23.21  | | | | | | | | Case 1:
% 155.63/23.21  | | | | | | | | | 
% 155.63/23.21  | | | | | | | | |   (7940)   ~ (all_22_2 = e0)
% 155.63/23.21  | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | REDUCE: (251), (7940) imply:
% 155.63/23.21  | | | | | | | | |   (7941)   ~ (all_10_2 = e0)
% 155.63/23.21  | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | BETA: splitting (194) gives:
% 155.63/23.21  | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | Case 1:
% 155.63/23.21  | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | |   (7942)  all_54_10 = e3
% 155.63/23.21  | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | COMBINE_EQS: (336), (7942) imply:
% 155.63/23.21  | | | | | | | | | |   (7943)  all_10_2 = e3
% 155.63/23.21  | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | REDUCE: (7939), (7943) imply:
% 155.63/23.21  | | | | | | | | | |   (7944)  $false
% 155.63/23.21  | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | CLOSE: (7944) is inconsistent.
% 155.63/23.21  | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | Case 2:
% 155.63/23.21  | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | |   (7945)   ~ (all_54_10 = e3)
% 155.63/23.21  | | | | | | | | | |   (7946)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 155.63/23.21  | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | BETA: splitting (7946) gives:
% 155.63/23.21  | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | Case 1:
% 155.63/23.21  | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | |   (7947)  all_54_10 = e2
% 155.63/23.21  | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | COMBINE_EQS: (336), (7947) imply:
% 155.63/23.21  | | | | | | | | | | |   (7948)  all_10_2 = e2
% 155.63/23.21  | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | REDUCE: (7934), (7948) imply:
% 155.63/23.21  | | | | | | | | | | |   (7949)  $false
% 155.63/23.21  | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | CLOSE: (7949) is inconsistent.
% 155.63/23.21  | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | Case 2:
% 155.63/23.21  | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | |   (7950)   ~ (all_54_10 = e2)
% 155.63/23.21  | | | | | | | | | | |   (7951)  all_54_10 = e1 | all_54_10 = e0
% 155.63/23.21  | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | BETA: splitting (7951) gives:
% 155.63/23.21  | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | Case 1:
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | |   (7952)  all_54_10 = e1
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | COMBINE_EQS: (336), (7952) imply:
% 155.63/23.21  | | | | | | | | | | | |   (7953)  all_10_2 = e1
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | REDUCE: (350), (7953) imply:
% 155.63/23.21  | | | | | | | | | | | |   (7954)   ~ (all_52_2 = e1)
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | REDUCE: (361), (7953) imply:
% 155.63/23.21  | | | | | | | | | | | |   (7955)   ~ (all_52_6 = e1)
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | REDUCE: (363), (7953) imply:
% 155.63/23.21  | | | | | | | | | | | |   (7956)   ~ (all_52_8 = e1)
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | REDUCE: (364), (7953) imply:
% 155.63/23.21  | | | | | | | | | | | |   (7957)   ~ (all_52_9 = e1)
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | REDUCE: (366), (7953) imply:
% 155.63/23.21  | | | | | | | | | | | |   (7958)   ~ (all_52_11 = e1)
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | REDUCE: (368), (7953) imply:
% 155.63/23.21  | | | | | | | | | | | |   (7959)   ~ (all_52_14 = e1)
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | REDUCE: (7939), (7953) imply:
% 155.63/23.21  | | | | | | | | | | | |   (7960)   ~ (e3 = e1)
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | REDUCE: (7934), (7953) imply:
% 155.63/23.21  | | | | | | | | | | | |   (7961)   ~ (e2 = e1)
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | REDUCE: (45), (7953) imply:
% 155.63/23.21  | | | | | | | | | | | |   (7962)  op(e1, e1) = e1
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.21  | | | | | | | | | | | | BETA: splitting (67) gives:
% 155.63/23.21  | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | |   (7963)   ~ (all_24_2 = e1)
% 155.63/23.22  | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | REDUCE: (318), (7963) imply:
% 155.63/23.22  | | | | | | | | | | | | |   (7964)   ~ (all_4_2 = e1)
% 155.63/23.22  | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | BETA: splitting (73) gives:
% 155.63/23.22  | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | |   (7965)   ~ (all_28_2 = e2)
% 155.63/23.22  | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | REDUCE: (330), (7965) imply:
% 155.63/23.22  | | | | | | | | | | | | | |   (7966)   ~ (all_14_2 = e2)
% 155.63/23.22  | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 155.63/23.22  | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | |   (7967)  all_54_15 = e3
% 155.63/23.22  | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | REF_CLOSE: (246), (7937), (7967) are inconsistent by
% 155.63/23.22  | | | | | | | | | | | | | | |            sub-proof #1010.
% 155.63/23.22  | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | Case 2:
% 155.63/23.22  | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | |   (7968)   ~ (all_54_15 = e3)
% 155.63/23.22  | | | | | | | | | | | | | | |   (7969)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 155.63/23.22  | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | BETA: splitting (7969) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | |   (7970)  all_54_15 = e2
% 155.63/23.22  | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7966), (7970) are inconsistent by
% 155.63/23.22  | | | | | | | | | | | | | | | |            sub-proof #1009.
% 155.63/23.22  | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | Case 2:
% 155.63/23.22  | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | |   (7971)   ~ (all_54_15 = e2)
% 155.63/23.22  | | | | | | | | | | | | | | | |   (7972)  all_54_15 = e1 | all_54_15 = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | BETA: splitting (7972) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | |   (7973)  all_54_15 = e1
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7935), (7973) are inconsistent by
% 155.63/23.22  | | | | | | | | | | | | | | | | |            sub-proof #1008.
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | |   (7974)  all_54_15 = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (7974) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | |   (7975)  all_14_2 = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | SIMP: (7975) implies:
% 155.63/23.22  | | | | | | | | | | | | | | | | |   (7976)  all_14_2 = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | REDUCE: (369), (7976) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | |   (7977)   ~ (all_52_11 = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | REDUCE: (372), (7976) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | |   (7978)   ~ (all_52_14 = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | REDUCE: (7937), (7976) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | |   (7979)   ~ (e3 = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | REDUCE: (7935), (7976) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | |   (7980)   ~ (e1 = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | REDUCE: (51), (7976) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | |   (7981)  op(e0, e0) = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | |   (7982)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | BETA: splitting (7982) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | |   (7983)  all_56_6 = e0 & op(e1, e3) = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7925), (7983), (function-axioms) are
% 155.63/23.22  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #699.
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | |   (7984)  all_56_7 = e0 & op(e1, e2) = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | ALPHA: (7984) implies:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | |   (7985)  op(e1, e2) = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | |   (7986)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7986) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |   (7987)  all_56_4 = e0 & op(e3, e1) = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7928), (7987), (function-axioms) are
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #700.
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |   (7988)  all_56_5 = e0 & op(e2, e1) = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7988) implies:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |   (7989)  op(e2, e1) = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (7985) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |   (7990)  all_52_6 = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (7989) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |   (7991)  all_52_9 = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (7990) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |   (7992)   ~ (all_52_7 = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | SIMP: (7992) implies:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |   (7993)   ~ (all_52_7 = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (7991) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |   (7994)   ~ (all_52_11 = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (7991) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |   (7995)   ~ (all_4_2 = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | SIMP: (7995) implies:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | |   (7996)   ~ (all_4_2 = e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | |   (7997)  all_54_5 = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7997) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | |   (7998)  all_4_2 = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (7998) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | |   (7999)  $false
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7999) is inconsistent.
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | |   (8000)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8000) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | |   (8001)  all_54_5 = e2
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8001) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | |   (8002)  all_4_2 = e2
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (8002) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | |   (8003)   ~ (all_52_1 = e2)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (8002) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | |   (8004)   ~ (all_52_13 = e2)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (8002) imply:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | |   (8005)  op(e2, e2) = e2
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |   (8006)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8006) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (8007)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8007) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8008)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8003), (8008), (function-axioms) are
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8009)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8009) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8010)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8003), (8010), (function-axioms) are
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8011)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8011) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8012)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8012) implies:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8013)  op(e2, e3) = e2
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8003), (8013), (function-axioms) are
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8014)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8014) gives:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8015)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8015) implies:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8016)  op(e1, e1) = e3
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7962), (8016), (function-axioms) are
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8017)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8017) implies:
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8018)  op(e2, e1) = e2
% 155.63/23.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (8005), (8018),
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (8019)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8019) gives:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8020)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8020) gives:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8021)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (7981), (8021), (function-axioms) are
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #105.
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8022)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (7930), (8004), (8022),
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #104.
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8023)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8023) gives:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8024)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (7962), (8005), (8024),
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #992.
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8025)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (51), (163), (246), (7935), (7954), (7962),
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7972), (8025), (function-axioms) are inconsistent
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #255.
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |   (8026)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8026) gives:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (8027)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8027) gives:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8028)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8028) gives:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8029)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7930), (8005), (8029),
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #103.
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8030)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (246), (7935), (7962), (7972), (8030),
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #102.
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8031)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8031) gives:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8032)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (7955), (7962), (8032),
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8033)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (7930), (7981), (8033),
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #100.
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (8034)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8034) gives:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8035)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8035) gives:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8036)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8036) gives:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8037)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8037) implies:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8038)  op(e0, e0) = e2
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (7935), (7966), (7972), (8038),
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #799.
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8039)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8039) implies:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8040)  op(e2, e1) = e2
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (8005), (8040),
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8041)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (7981), (8005), (8041),
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #977.
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8042)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8042) gives:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8043)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8043) gives:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8044)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8044) implies:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8045)  op(e0, e0) = e2
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (7935), (7966), (7972), (8045),
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #799.
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8046)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8046) implies:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8047)  op(e3, e3) = e3
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8047), (function-axioms) are
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8048)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8048) gives:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8049)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8049) implies:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8050)  op(e2, e0) = e2
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8004), (8050), (function-axioms) are
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8051)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (160), (7926), (7959),
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7977), (7993), (8051), (function-axioms) are
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #96.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | |   (8052)  all_54_5 = e1 | all_54_5 = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7964), (7996), (8052) are inconsistent by
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |   (8053)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8053) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | |   (8054)  all_56_8 = e0 & op(e1, e1) = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8054) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | |   (8055)  op(e1, e1) = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7962), (8055), (function-axioms) are
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | |   (8056)  all_56_14 = e0 & op(e0, e1) = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8056) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | |   (8057)  op(e0, e1) = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7977), (8057), (function-axioms) are
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | |   (8058)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | BETA: splitting (8058) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | |   (8059)  all_56_8 = e0 & op(e1, e1) = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | ALPHA: (8059) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | |   (8060)  op(e1, e1) = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7962), (8060), (function-axioms) are
% 155.63/23.25  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | |   (8061)  all_56_11 = e0 & op(e1, e0) = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7978), (8061), (function-axioms) are
% 155.63/23.25  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #406.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | |   (8062)  all_28_2 = e2
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | COMBINE_EQS: (330), (8062) imply:
% 155.63/23.25  | | | | | | | | | | | | | |   (8063)  all_14_2 = e2
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | SIMP: (8063) implies:
% 155.63/23.25  | | | | | | | | | | | | | |   (8064)  all_14_2 = e2
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | REDUCE: (351), (8064) imply:
% 155.63/23.25  | | | | | | | | | | | | | |   (8065)   ~ (all_52_3 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | REDUCE: (362), (8064) imply:
% 155.63/23.25  | | | | | | | | | | | | | |   (8066)   ~ (all_52_7 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | REDUCE: (369), (8064) imply:
% 155.63/23.25  | | | | | | | | | | | | | |   (8067)   ~ (all_52_11 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | REDUCE: (371), (8064) imply:
% 155.63/23.25  | | | | | | | | | | | | | |   (8068)   ~ (all_52_13 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | REDUCE: (51), (8064) imply:
% 155.63/23.25  | | | | | | | | | | | | | |   (8069)  op(e0, e0) = e2
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | BETA: splitting (7922) gives:
% 155.63/23.25  | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | |   (8070)   ~ (all_6_0 = e1) & op(e0, e3) = all_6_0 &
% 155.63/23.25  | | | | | | | | | | | | | | |           $i(all_6_0)
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | ALPHA: (8070) implies:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8071)   ~ (all_6_0 = e1)
% 155.63/23.25  | | | | | | | | | | | | | | |   (8072)  op(e0, e3) = all_6_0
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 155.63/23.25  | | | | | | | | | | | | | | |              all_6_0, e3, e0, simplifying with (159), (8072)
% 155.63/23.25  | | | | | | | | | | | | | | |              gives:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8073)  all_52_3 = all_6_0
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | COMBINE_EQS: (249), (8073) imply:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8074)  all_54_12 = all_6_0
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | REDUCE: (148), (8073) imply:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8075)   ~ (all_52_1 = all_6_0)
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | REDUCE: (144), (8073) imply:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8076)   ~ (all_52_2 = all_6_0)
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | REDUCE: (140), (8073) imply:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8077)   ~ (all_52_7 = all_6_0)
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | SIMP: (8077) implies:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8078)   ~ (all_52_7 = all_6_0)
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | REDUCE: (139), (8073) imply:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8079)   ~ (all_52_11 = all_6_0)
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | SIMP: (8079) implies:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8080)   ~ (all_52_11 = all_6_0)
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | REDUCE: (8065), (8073) imply:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8081)   ~ (all_6_0 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | REDUCE: (7926), (8073) imply:
% 155.63/23.25  | | | | | | | | | | | | | | |   (8082)   ~ (all_6_0 = e0)
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | |   (8083)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 155.63/23.25  | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 155.63/23.25  | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | BETA: splitting (8083) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | |   (8084)  all_56_0 = e1 & op(e3, e3) = e1
% 155.63/23.25  | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | ALPHA: (8084) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | |   (8085)  op(e3, e3) = e1
% 155.63/23.25  | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7930), (8085), (function-axioms) are
% 155.63/23.25  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 155.63/23.25  | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | |   (8086)  all_56_2 = e1 & op(e2, e3) = e1
% 155.63/23.25  | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | ALPHA: (8086) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | |   (8087)  all_56_2 = e1
% 155.63/23.25  | | | | | | | | | | | | | | | | |   (8088)  op(e2, e3) = e1
% 155.63/23.25  | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | |   (8089)  all_54_12 = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8074), (8089) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | |   (8090)  all_6_0 = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | SIMP: (8090) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | |   (8091)  all_6_0 = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | REDUCE: (8075), (8091) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | |   (8092)   ~ (all_52_1 = e3)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | REDUCE: (8076), (8091) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | |   (8093)   ~ (all_52_2 = e3)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | REDUCE: (8078), (8091) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | |   (8094)   ~ (all_52_7 = e3)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | REDUCE: (8080), (8091) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | |   (8095)   ~ (all_52_11 = e3)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | |   (8096)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (8096) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |   (8097)  all_56_0 = e3 & op(e3, e3) = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | ALPHA: (8097) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |   (8098)  op(e3, e3) = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8098), (function-axioms) are
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |   (8099)  all_56_2 = e3 & op(e2, e3) = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | ALPHA: (8099) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |   (8100)  all_56_2 = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8087), (8100) are inconsistent by sub-proof
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |            #484.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | |   (8101)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (8101) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |   (8102)  all_56_6 = e3 & op(e1, e3) = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (8093), (8102), (function-axioms) are
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #681.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |   (8103)  all_56_12 = e3 & op(e0, e3) = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | ALPHA: (8103) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | |   (8104)  all_56_12 = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | |   (8105)  all_54_14 = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (8095), (8105) are inconsistent by
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | |            sub-proof #587.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | |   (8106)   ~ (all_54_14 = e3)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | |   (8107)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | |   (8108)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8108) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | |   (8109)  all_56_12 = e1 & op(e0, e3) = e1
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8104), (8109) are inconsistent by sub-proof
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | |            #736.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | |   (8110)  all_56_13 = e1 & op(e0, e2) = e1
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8110) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | |   (8111)  op(e0, e2) = e1
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | |   (8112)  all_54_8 = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8093), (8112) are inconsistent by
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #309.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | |   (8113)   ~ (all_54_8 = e3)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | |   (8114)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8114) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8115)  all_54_8 = e2
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8115) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8116)  all_52_2 = e2
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8116) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8117)  all_52_2 = e2
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (8117) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8118)   ~ (all_52_1 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (8117) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8119)   ~ (all_52_6 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8119) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8120)   ~ (all_52_6 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (8117) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8121)   ~ (all_52_14 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8121) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8122)   ~ (all_52_14 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8093), (8117) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8123)   ~ (e3 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8124)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8124) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8125)  all_56_6 = e2 & op(e1, e3) = e2
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8125) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8126)  all_56_6 = e2
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8107) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8127)  all_54_14 = e2
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (8067), (8127) are inconsistent by
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #95.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8128)   ~ (all_54_14 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8129)  all_54_14 = e1 | all_54_14 = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8129) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8130)  all_54_14 = e1
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (7958), (8130) are inconsistent by
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #586.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8131)  all_54_14 = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (8131) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8132)  all_52_11 = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8132) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8133)  all_52_11 = e0
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (8133) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8134)   ~ (all_52_7 = e0)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8095), (8133) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8135)   ~ (e3 = e0)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8067), (8133) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8136)   ~ (e2 = e0)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7958), (8133) imply:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8137)   ~ (e1 = e0)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8138)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8138) gives:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8139)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8139) implies:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8140)  op(e3, e3) = e3
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8104), (8140), (function-axioms) are inconsistent
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8141)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8141) implies:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8142)  op(e2, e2) = e2
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8143)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8143) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8144)  all_57_10 = e2 & op(e3, e3) = e2
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8144) implies:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8145)  op(e3, e3) = e2
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7930), (8145), (function-axioms) are
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8146)   ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8146) implies:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8147)   ~ (all_57_1 = e3)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8148)  op(e3, e2) = all_57_1
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8149)  all_54_4 = e3
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8092), (8149) are inconsistent by
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #931.
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8150)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8150) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8151)  all_54_4 = e2
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8118), (8151) are inconsistent by
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #519.
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8152)  all_54_4 = e1 | all_54_4 = e0
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8152) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e2,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (8142) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8153)  all_4_2 = e2
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1, e2, e3, simplifying with (170), (8148)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8154)  all_57_1 = all_52_4
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8147), (8154) imply:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8155)   ~ (all_52_4 = e3)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (8153) imply:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8156)   ~ (all_52_4 = e2)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (135), (191), (203), (248), (272), (7927), (8066),
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8094), (8134), (8155), (8156) are inconsistent by
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #94.
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8157)  all_54_4 = e0
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (7924), (8157) are inconsistent by
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #510.
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8158)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8158) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8159)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8159) implies:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8160)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8161)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8160) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8162)  all_57_15 = e1 & op(e0, e0) = e1
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8162) implies:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8163)  op(e0, e0) = e1
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8069), (8163), (function-axioms) are
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8164)   ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_8)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8164) implies:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8165)   ~ (all_57_8 = e0)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8166)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8166) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8167)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8167) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8168)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8088), (8168), (function-axioms) are
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #348.
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8169)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8169) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8170)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8088), (8170), (function-axioms) are
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #347.
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8171)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8171) gives:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8172)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8172) implies:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8173)  op(e2, e3) = e2
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8088), (8173), (function-axioms) are
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #428.
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8174)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7962), (8161), (8174), (function-axioms) are
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8175)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8175) gives:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8176)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8176) gives:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8177)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8177) gives:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8178)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8178) implies:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8179)  op(e0, e0) = e3
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8069), (8179), (function-axioms) are
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8180)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8180) implies:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8181)  op(e3, e3) = e3
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8104), (8181), (function-axioms) are inconsistent
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8182)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8182) gives:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8183)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8183) implies:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8184)  op(e2, e0) = e2
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8068), (8184), (function-axioms) are
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8185)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8185) implies:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8186)  op(e3, e3) = e1
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (233), (235),
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8087), (8088), (8126), (8186), (function-axioms)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #425.
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8187)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8187) gives:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8188)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (223), (224),
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7962), (8087), (8088), (8188), (function-axioms)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #93.
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8189)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (163), (7954), (7962), (8069), (8189),
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #874.
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.63/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8190)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8190) gives:
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8191)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8191) gives:
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8192)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8192) gives:
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8193)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8193) gives:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8194)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8194) implies:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8195)  op(e3, e3) = e1
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (233), (235),
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8087), (8088), (8126), (8195), (function-axioms)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #425.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8196)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8196) implies:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8197)  op(e2, e2) = e1
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (223), (224),
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8087), (8088), (8197), (function-axioms) are
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #259.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8198)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7962), (8069), (8198), (function-axioms) are
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8199)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8199) gives:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8200)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (7955), (7962), (8200),
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8201)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8201) gives:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8202)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8202) implies:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8203)  op(e0, e0) = e3
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8069), (8203), (function-axioms) are
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8204)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8204) gives:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8205)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8205) implies:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8206)  op(e3, e3) = e3
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8104), (8206), (function-axioms) are inconsistent
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8207)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8207) implies:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8208)  op(e3, e3) = e1
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (233), (235),
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8087), (8088), (8126), (8208), (function-axioms)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #425.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8209)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8209) gives:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8210)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8210) gives:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8211)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8211) gives:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8212)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8212) implies:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8213)  all_57_5 = e2
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8214)   ~ (all_57_12 = e1)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8215)  op(e2, e2) = all_57_12
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8161), (8213), (8214), (8215), (function-axioms)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #274.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8216)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8216) implies:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8217)  op(e2, e1) = e2
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8218)  op(e2, e2) = e2
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (8217), (8218),
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8219)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8219) gives:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8220)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8220) implies:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8221)  op(e2, e2) = e1
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (223), (224),
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8087), (8088), (8221), (function-axioms) are
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #259.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8222)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8222) implies:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8223)  op(e0, e0) = e3
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8069), (8223), (function-axioms) are
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8224)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8224) gives:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8225)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8225) gives:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8226)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8226) implies:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8227)  op(e2, e0) = e2
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8068), (8227), (function-axioms) are
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8228)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8228) implies:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8229)  op(e3, e3) = e3
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8104), (8229), (function-axioms) are inconsistent
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8230)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8230) gives:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8231)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8231) implies:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8232)  op(e2, e0) = e2
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8068), (8232), (function-axioms) are
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8233)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8233) gives:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8234)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8234) implies:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8235)  op(e1, e0) = e1
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7959), (8235), (function-axioms) are
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8236)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8236) implies:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8237)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8237) gives:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8238)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8238) gives:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8239)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (164), (7926), (7962), (8068), (8239),
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #92.
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8240)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8240) gives:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8241)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8241) implies:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8242)  op(e0, e3) = e0
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7926), (8242), (function-axioms) are
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8243)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8243) gives:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8244)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e2) = e0
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8244) implies:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8245)  op(e0, e2) = e0
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8111), (8245), (function-axioms) are
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #832.
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8246)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e2) = e0
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8246) implies:
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8247)  op(e2, e0) = e2
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8068), (8247), (function-axioms) are
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8248)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8248) gives:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8249)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8249) gives:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8250)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8250) implies:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8251)  op(e1, e1) = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7962), (8251), (function-axioms) are
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8252)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8252) gives:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8253)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8253) implies:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8254)  op(e0, e2) = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8111), (8254), (function-axioms) are
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #832.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8255)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8255) implies:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8256)  all_57_8 = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8165), (8256) imply:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8257)  $false
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8257) is inconsistent.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8258)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8258) gives:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8259)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (7962), (8068), (8259),
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #862.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8260)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7959), (8165), (8260), (function-axioms)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #807.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8261)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8261) implies:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8262)  op(e0, e0) = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8069), (8262), (function-axioms) are
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8263)  all_56_7 = e2 & op(e1, e2) = e2
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (8120), (8263), (function-axioms) are
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8264)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (7962), (8122), (8264),
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            #815.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (8265)  all_54_8 = e1 | all_54_8 = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7925), (7954), (8265) are inconsistent by
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #612.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | |   (8266)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8266) gives:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | |   (8267)  all_56_14 = e1 & op(e0, e1) = e1
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7958), (8267), (function-axioms) are
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #803.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | |   (8268)  all_56_15 = e1 & op(e0, e0) = e1
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8268) implies:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | |   (8269)  op(e0, e0) = e1
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8069), (8269), (function-axioms) are
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | |   (8270)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8071), (8074), (8081), (8082), (8270) are
% 155.71/23.30  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #91.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | |   (8271)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 155.71/23.30  | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 155.71/23.30  | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | BETA: splitting (8271) gives:
% 155.71/23.30  | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | |   (8272)  all_56_6 = e1 & op(e1, e3) = e1
% 155.71/23.30  | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | ALPHA: (8272) implies:
% 155.71/23.30  | | | | | | | | | | | | | | | | |   (8273)  op(e1, e3) = e1
% 155.71/23.30  | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7954), (8273), (function-axioms) are
% 155.71/23.30  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 155.71/23.30  | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | |   (8274)  all_56_12 = e1 & op(e0, e3) = e1
% 155.71/23.30  | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | ALPHA: (8274) implies:
% 155.71/23.30  | | | | | | | | | | | | | | | | |   (8275)  all_56_12 = e1
% 155.71/23.30  | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 155.71/23.30  | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | |   (8276)  all_54_12 = e3
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8074), (8276) imply:
% 155.71/23.30  | | | | | | | | | | | | | | | | | |   (8277)  all_6_0 = e3
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | SIMP: (8277) implies:
% 155.71/23.30  | | | | | | | | | | | | | | | | | |   (8278)  all_6_0 = e3
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | REDUCE: (8078), (8278) imply:
% 155.71/23.30  | | | | | | | | | | | | | | | | | |   (8279)   ~ (all_52_7 = e3)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | REDUCE: (8080), (8278) imply:
% 155.71/23.30  | | | | | | | | | | | | | | | | | |   (8280)   ~ (all_52_11 = e3)
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (209), (8069), (8275),
% 155.71/23.30  | | | | | | | | | | | | | | | | | |            (8279), (8280), (function-axioms) are inconsistent
% 155.71/23.30  | | | | | | | | | | | | | | | | | |            by sub-proof #90.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | |   (8281)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8071), (8074), (8081), (8082), (8281) are
% 155.71/23.30  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #91.
% 155.71/23.30  | | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | |   (8282)   ~ (all_6_1 = e2) & op(e0, e0) = all_6_1 &
% 155.71/23.30  | | | | | | | | | | | | | | |           $i(all_6_1)
% 155.71/23.30  | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | ALPHA: (8282) implies:
% 155.71/23.30  | | | | | | | | | | | | | | |   (8283)   ~ (all_6_1 = e2)
% 155.71/23.30  | | | | | | | | | | | | | | |   (8284)  op(e0, e0) = all_6_1
% 155.71/23.30  | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | | REF_CLOSE: (8069), (8283), (8284), (function-axioms) are
% 155.71/23.30  | | | | | | | | | | | | | | |            inconsistent by sub-proof #89.
% 155.71/23.30  | | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | |   (8285)  all_24_2 = e1
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | COMBINE_EQS: (318), (8285) imply:
% 155.71/23.30  | | | | | | | | | | | | |   (8286)  all_4_2 = e1
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | SIMP: (8286) implies:
% 155.71/23.30  | | | | | | | | | | | | |   (8287)  all_4_2 = e1
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | REDUCE: (36), (8287) imply:
% 155.71/23.30  | | | | | | | | | | | | |   (8288)  op(e2, e2) = e1
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (112), (144),
% 155.71/23.30  | | | | | | | | | | | | |            (157), (158), (159), (160), (162), (163), (168),
% 155.71/23.30  | | | | | | | | | | | | |            (169), (189), (221), (223), (224), (225), (227),
% 155.71/23.30  | | | | | | | | | | | | |            (228), (231), (232), (239), (246), (362), (369),
% 155.71/23.30  | | | | | | | | | | | | |            (370), (7922), (7926), (7929), (7930), (7937),
% 155.71/23.30  | | | | | | | | | | | | |            (7954), (7955), (7956), (7962), (8288),
% 155.71/23.30  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.30  | | | | | | | | | | | | |            #85.
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | |   (8289)  all_54_10 = e0
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | COMBINE_EQS: (336), (8289) imply:
% 155.71/23.30  | | | | | | | | | | | |   (8290)  all_10_2 = e0
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | REDUCE: (7941), (8290) imply:
% 155.71/23.30  | | | | | | | | | | | |   (8291)  $false
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | CLOSE: (8291) is inconsistent.
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | End of split
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | |   (8292)  all_22_2 = e0
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | COMBINE_EQS: (251), (8292) imply:
% 155.71/23.30  | | | | | | | | |   (8293)  all_10_2 = e0
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | SIMP: (8293) implies:
% 155.71/23.30  | | | | | | | | |   (8294)  all_10_2 = e0
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | REDUCE: (361), (8294) imply:
% 155.71/23.30  | | | | | | | | |   (8295)   ~ (all_52_6 = e0)
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | REDUCE: (364), (8294) imply:
% 155.71/23.30  | | | | | | | | |   (8296)   ~ (all_52_9 = e0)
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | REDUCE: (366), (8294) imply:
% 155.71/23.30  | | | | | | | | |   (8297)   ~ (all_52_11 = e0)
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | REDUCE: (368), (8294) imply:
% 155.71/23.30  | | | | | | | | |   (8298)   ~ (all_52_14 = e0)
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | REDUCE: (7939), (8294) imply:
% 155.71/23.30  | | | | | | | | |   (8299)   ~ (e3 = e0)
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | REDUCE: (7934), (8294) imply:
% 155.71/23.30  | | | | | | | | |   (8300)   ~ (e2 = e0)
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | REDUCE: (45), (8294) imply:
% 155.71/23.30  | | | | | | | | |   (8301)  op(e1, e1) = e0
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | BETA: splitting (67) gives:
% 155.71/23.30  | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | |   (8302)   ~ (all_24_2 = e1)
% 155.71/23.30  | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | REDUCE: (318), (8302) imply:
% 155.71/23.30  | | | | | | | | | |   (8303)   ~ (all_4_2 = e1)
% 155.71/23.30  | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | BETA: splitting (73) gives:
% 155.71/23.30  | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | |   (8304)   ~ (all_28_2 = e2)
% 155.71/23.30  | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | REDUCE: (330), (8304) imply:
% 155.71/23.30  | | | | | | | | | | |   (8305)   ~ (all_14_2 = e2)
% 155.71/23.30  | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | BETA: splitting (189) gives:
% 155.71/23.30  | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | |   (8306)  all_54_15 = e3
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | COMBINE_EQS: (246), (8306) imply:
% 155.71/23.30  | | | | | | | | | | | |   (8307)  all_14_2 = e3
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | REDUCE: (7937), (8307) imply:
% 155.71/23.30  | | | | | | | | | | | |   (8308)  $false
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | CLOSE: (8308) is inconsistent.
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | |   (8309)   ~ (all_54_15 = e3)
% 155.71/23.30  | | | | | | | | | | | |   (8310)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | BETA: splitting (8310) gives:
% 155.71/23.30  | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | |   (8311)  all_54_15 = e2
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | COMBINE_EQS: (246), (8311) imply:
% 155.71/23.30  | | | | | | | | | | | | |   (8312)  all_14_2 = e2
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | REDUCE: (8305), (8312) imply:
% 155.71/23.30  | | | | | | | | | | | | |   (8313)  $false
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | CLOSE: (8313) is inconsistent.
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | |   (8314)   ~ (all_54_15 = e2)
% 155.71/23.30  | | | | | | | | | | | | |   (8315)  all_54_15 = e1 | all_54_15 = e0
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | BETA: splitting (8315) gives:
% 155.71/23.30  | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | Case 1:
% 155.71/23.30  | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | |   (8316)  all_54_15 = e1
% 155.71/23.30  | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | COMBINE_EQS: (246), (8316) imply:
% 155.71/23.30  | | | | | | | | | | | | | |   (8317)  all_14_2 = e1
% 155.71/23.30  | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | REDUCE: (7935), (8317) imply:
% 155.71/23.30  | | | | | | | | | | | | | |   (8318)  $false
% 155.71/23.30  | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | | CLOSE: (8318) is inconsistent.
% 155.71/23.30  | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | Case 2:
% 155.71/23.30  | | | | | | | | | | | | | | 
% 155.71/23.30  | | | | | | | | | | | | | |   (8319)  all_54_15 = e0
% 155.71/23.30  | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | COMBINE_EQS: (246), (8319) imply:
% 155.71/23.31  | | | | | | | | | | | | | |   (8320)  all_14_2 = e0
% 155.71/23.31  | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | REDUCE: (362), (8320) imply:
% 155.71/23.31  | | | | | | | | | | | | | |   (8321)   ~ (all_52_7 = e0)
% 155.71/23.31  | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | REDUCE: (7935), (8320) imply:
% 155.71/23.31  | | | | | | | | | | | | | |   (8322)   ~ (e1 = e0)
% 155.71/23.31  | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | REDUCE: (51), (8320) imply:
% 155.71/23.31  | | | | | | | | | | | | | |   (8323)  op(e0, e0) = e0
% 155.71/23.31  | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 155.71/23.31  | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | Case 1:
% 155.71/23.31  | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | |   (8324)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 155.71/23.31  | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 155.71/23.31  | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | BETA: splitting (8324) gives:
% 155.71/23.31  | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | Case 1:
% 155.71/23.31  | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | |   (8325)  all_56_1 = e0 & op(e3, e2) = e0
% 155.71/23.31  | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | REF_CLOSE: (170), (7927), (8325), (function-axioms) are
% 155.71/23.31  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #84.
% 155.71/23.31  | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | Case 2:
% 155.71/23.31  | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | |   (8326)  all_56_3 = e0 & op(e2, e2) = e0
% 155.71/23.31  | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | ALPHA: (8326) implies:
% 155.71/23.31  | | | | | | | | | | | | | | | |   (8327)  op(e2, e2) = e0
% 155.71/23.31  | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.71/23.31  | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.31  | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | |   (8328)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.71/23.31  | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.71/23.31  | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.31  | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.71/23.31  | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.71/23.31  | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.71/23.31  | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.71/23.31  | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.71/23.31  | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.31  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.71/23.31  | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.71/23.31  | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.31  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.31  | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.71/23.31  | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.31  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.71/23.31  | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.71/23.31  | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.31  | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.31  | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.31  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.31  | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.31  | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.31  | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | BETA: splitting (8328) gives:
% 155.71/23.31  | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | |   (8329)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.71/23.31  | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.31  | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.71/23.31  | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.31  | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.71/23.31  | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.71/23.31  | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.71/23.31  | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | BETA: splitting (8329) gives:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |   (8330)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (8330) gives:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |   (8331)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8331) gives:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |   (8332)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8332) implies:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |   (8333)  op(e3, e3) = e2
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (135), (148), (157),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |            (158), (159), (163), (164), (165), (167), (168),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |            (169), (170), (199), (229), (230), (239), (268),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |            (352), (358), (360), (373), (7925), (7926),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |            (7928), (7929), (8297), (8301), (8303), (8323),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |            (8333), (function-axioms) are inconsistent by
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |            sub-proof #238.
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |   (8334)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8334) implies:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |   (8335)  op(e2, e2) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8327), (8335), (function-axioms) are
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |   (8336)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8301), (8327), (8336),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |            #367.
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |   (8337)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 155.71/23.31  | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (8337) gives:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |   (8338)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8323), (8327), (8338),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |            #826.
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |   (8339)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8339) gives:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |   (8340)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8340) implies:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |   (8341)  op(e2, e2) = e2
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8327), (8341), (function-axioms) are
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |   (8342)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8342) gives:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |   (8343)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8343) implies:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |   (8344)  op(e1, e1) = e3
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8301), (8344), (function-axioms) are
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |   (8345)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8345) implies:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |   (8346)  op(e3, e3) = e2
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (135), (148), (157),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |            (158), (159), (163), (164), (165), (167), (168),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (199), (229), (230), (239), (268),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |            (352), (358), (360), (373), (7925), (7926),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |            (7928), (7929), (8297), (8301), (8303), (8323),
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |            (8346), (function-axioms) are inconsistent by
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #238.
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.31  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.31  | | | | | | | | | | | | | | | | | | 
% 155.71/23.31  | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.31  | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | |   (8347)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.71/23.32  | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.71/23.32  | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | BETA: splitting (8347) gives:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |   (8348)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | BETA: splitting (8348) gives:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |   (8349)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8323), (8349), (function-axioms) are
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #105.
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |   (8350)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8350) gives:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |   (8351)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8351) implies:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |   (8352)  op(e3, e3) = e2
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (135), (148), (157),
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |            (158), (159), (163), (164), (165), (167), (168),
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |            (169), (170), (199), (229), (230), (239), (268),
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |            (352), (358), (360), (373), (7925), (7926),
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |            (7928), (7929), (8297), (8301), (8303), (8323),
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |            (8352), (function-axioms) are inconsistent by
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |            sub-proof #238.
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |   (8353)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8353) implies:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |   (8354)  op(e3, e3) = e1
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7930), (8354), (function-axioms) are
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |   (8355)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | BETA: splitting (8355) gives:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |   (8356)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8301), (8327), (8356),
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |            #366.
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |   (8357)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (51), (246), (7935), (8301), (8315),
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |            (8357), (function-axioms) are inconsistent by
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |            sub-proof #703.
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.32  | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | End of split
% 155.71/23.32  | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.32  | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | |   (8358)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.32  | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.32  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.32  | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.32  | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.32  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.32  | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.71/23.32  | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.71/23.32  | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.71/23.32  | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.71/23.32  | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.71/23.32  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.71/23.32  | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.71/23.32  | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.71/23.32  | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.32  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.71/23.32  | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.71/23.32  | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.71/23.32  | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.71/23.32  | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.32  | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.71/23.32  | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.71/23.32  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.71/23.32  | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.71/23.32  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.71/23.32  | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.71/23.32  | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.71/23.32  | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.71/23.32  | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.71/23.32  | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.32  | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.32  | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.32  | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.71/23.32  | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.71/23.32  | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.71/23.32  | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.71/23.32  | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.71/23.32  | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.71/23.32  | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.71/23.32  | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.71/23.32  | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | BETA: splitting (8358) gives:
% 155.71/23.32  | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | |   (8359)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.32  | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.71/23.32  | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.32  | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | BETA: splitting (8359) gives:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |   (8360)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | BETA: splitting (8360) gives:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |   (8361)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8361) gives:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |   (8362)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8362) implies:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |   (8363)  op(e3, e3) = e1
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7930), (8363), (function-axioms) are
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.32  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |   (8364)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8364) implies:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |   (8365)  op(e2, e2) = e1
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8327), (8365), (function-axioms) are
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |   (8366)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (51), (246), (7935), (8301), (8315), (8366),
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |            #702.
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |   (8367)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (8367) gives:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |   (8368)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8301), (8368), (function-axioms) are
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |   (8369)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (7930), (8323), (8369),
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |            #100.
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.33  | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | |   (8370)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.71/23.33  | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.71/23.33  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.71/23.33  | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.71/23.33  | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.33  | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | BETA: splitting (8370) gives:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |   (8371)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8323), (8327), (8371),
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |            #918.
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |   (8372)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (8372) gives:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |   (8373)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7930), (8323), (8373), (function-axioms) are
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #83.
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |   (8374)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8374) gives:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |   (8375)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8375) implies:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |   (8376)  op(e2, e2) = e2
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8327), (8376), (function-axioms) are
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |   (8377)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8377) gives:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | |   (8378)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8378) implies:
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | |   (8379)  op(e1, e1) = e1
% 155.71/23.33  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8301), (8379), (function-axioms) are
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |   (8380)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8380) implies:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |   (8381)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (7926), (8297), (8321),
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |            (8381), (function-axioms) are inconsistent by
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #97.
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | Case 2:
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | |   (8382)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 155.71/23.34  | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (8295), (8321), (8382),
% 155.71/23.34  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.34  | | | | | | | | | | | | | | |            #897.
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | End of split
% 155.71/23.34  | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | Case 2:
% 155.71/23.34  | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | |   (8383)  all_28_2 = e2
% 155.71/23.34  | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | COMBINE_EQS: (330), (8383) imply:
% 155.71/23.34  | | | | | | | | | | |   (8384)  all_14_2 = e2
% 155.71/23.34  | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | SIMP: (8384) implies:
% 155.71/23.34  | | | | | | | | | | |   (8385)  all_14_2 = e2
% 155.71/23.34  | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | REDUCE: (370), (8385) imply:
% 155.71/23.34  | | | | | | | | | | |   (8386)   ~ (all_52_12 = e2)
% 155.71/23.34  | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | REDUCE: (371), (8385) imply:
% 155.71/23.34  | | | | | | | | | | |   (8387)   ~ (all_52_13 = e2)
% 155.71/23.34  | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | REDUCE: (372), (8385) imply:
% 155.71/23.34  | | | | | | | | | | |   (8388)   ~ (all_52_14 = e2)
% 155.71/23.34  | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | REDUCE: (51), (8385) imply:
% 155.71/23.34  | | | | | | | | | | |   (8389)  op(e0, e0) = e2
% 155.71/23.34  | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | BETA: splitting (238) gives:
% 155.71/23.34  | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | Case 1:
% 155.71/23.34  | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | |   (8390)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.71/23.34  | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.71/23.34  | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.71/23.34  | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.71/23.34  | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.71/23.34  | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.71/23.34  | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.71/23.34  | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.71/23.34  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.71/23.34  | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.71/23.34  | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.71/23.34  | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.71/23.34  | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.71/23.34  | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.71/23.34  | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.71/23.34  | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.71/23.34  | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | BETA: splitting (8390) gives:
% 155.71/23.34  | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | Case 1:
% 155.71/23.34  | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | |   (8391)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.71/23.34  | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.71/23.34  | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.71/23.34  | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.71/23.34  | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.71/23.34  | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.71/23.34  | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.71/23.34  | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.71/23.34  | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | ALPHA: (8391) implies:
% 155.71/23.34  | | | | | | | | | | | | |   (8392)  op(e3, e3) = e3
% 155.71/23.34  | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8392), (function-axioms) are
% 155.71/23.34  | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.71/23.34  | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | Case 2:
% 155.71/23.34  | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | |   (8393)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.71/23.34  | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.71/23.34  | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.71/23.34  | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.71/23.34  | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.71/23.34  | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.71/23.34  | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.71/23.34  | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.71/23.34  | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | ALPHA: (8393) implies:
% 155.71/23.34  | | | | | | | | | | | | |   (8394)  op(e2, e2) = e2
% 155.71/23.34  | | | | | | | | | | | | |   (8395)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7
% 155.71/23.34  | | | | | | | | | | | | |               = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))
% 155.71/23.34  | | | | | | | | | | | | |   (8396)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 155.71/23.34  | | | | | | | | | | | | |               = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))
% 155.71/23.34  | | | | | | | | | | | | |   (8397)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1
% 155.71/23.34  | | | | | | | | | | | | |               = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))
% 155.71/23.34  | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | BETA: splitting (8396) gives:
% 155.71/23.34  | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | Case 1:
% 155.71/23.34  | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | |   (8398)  all_57_14 = e2 & op(e1, e1) = e2
% 155.71/23.34  | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | ALPHA: (8398) implies:
% 155.71/23.34  | | | | | | | | | | | | | |   (8399)  op(e1, e1) = e2
% 155.71/23.34  | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | REF_CLOSE: (5), (8301), (8399), (function-axioms) are
% 155.71/23.34  | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 155.71/23.34  | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | Case 2:
% 155.71/23.34  | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | |   (8400)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.71/23.34  | | | | | | | | | | | | | |           $i(all_57_3)
% 155.71/23.34  | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | ALPHA: (8400) implies:
% 155.71/23.34  | | | | | | | | | | | | | |   (8401)   ~ (all_57_3 = e1)
% 155.71/23.34  | | | | | | | | | | | | | |   (8402)  op(e1, e2) = all_57_3
% 155.71/23.34  | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 155.71/23.34  | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | Case 1:
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | |   (8403)  all_56_15 = e0 & op(e0, e0) = e0
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | ALPHA: (8403) implies:
% 155.71/23.34  | | | | | | | | | | | | | | |   (8404)  op(e0, e0) = e0
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | REF_CLOSE: (5), (8389), (8404), (function-axioms) are
% 155.71/23.34  | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | Case 2:
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | |   (8405)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 155.71/23.34  | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 155.71/23.34  | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 155.71/23.34  | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 155.71/23.34  | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | ALPHA: (8405) implies:
% 155.71/23.34  | | | | | | | | | | | | | | |   (8406)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 155.71/23.34  | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 155.71/23.34  | | | | | | | | | | | | | | |               e0) = e0)
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | BETA: splitting (8397) gives:
% 155.71/23.34  | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | Case 1:
% 155.71/23.34  | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | |   (8407)  all_57_10 = e2 & op(e3, e3) = e2
% 155.71/23.34  | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | ALPHA: (8407) implies:
% 155.71/23.34  | | | | | | | | | | | | | | | |   (8408)  op(e3, e3) = e2
% 155.71/23.34  | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7930), (8408), (function-axioms) are
% 155.71/23.34  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 155.71/23.34  | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | Case 2:
% 155.71/23.34  | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | |   (8409)   ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 155.71/23.34  | | | | | | | | | | | | | | | |           $i(all_57_1)
% 155.71/23.34  | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | ALPHA: (8409) implies:
% 155.71/23.34  | | | | | | | | | | | | | | | |   (8410)  op(e3, e2) = all_57_1
% 155.71/23.34  | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | BETA: splitting (8406) gives:
% 155.71/23.34  | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.34  | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | |   (8411)  all_56_9 = e0 & op(e3, e0) = e0
% 155.71/23.34  | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7929), (8411), (function-axioms) are
% 155.71/23.34  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #620.
% 155.71/23.34  | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.34  | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | |   (8412)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 155.71/23.34  | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 155.71/23.34  | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | BETA: splitting (8412) gives:
% 155.71/23.34  | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | |   (8413)  all_56_10 = e0 & op(e2, e0) = e0
% 155.71/23.34  | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | ALPHA: (8413) implies:
% 155.71/23.34  | | | | | | | | | | | | | | | | | |   (8414)  op(e2, e0) = e0
% 155.71/23.34  | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | |   (8415)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (8386), (8387), (8415),
% 155.71/23.34  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.34  | | | | | | | | | | | | | | | | | | |            #384.
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | |   (8416)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 155.71/23.34  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | BETA: splitting (8416) gives:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8417)  all_56_11 = e2 & op(e1, e0) = e2
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8388), (8417), (function-axioms) are
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #879.
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8418)  all_56_15 = e2 & op(e0, e0) = e2
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |              all_57_3, e2, e1, simplifying with (162), (8402)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |              gives:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8419)  all_57_3 = all_52_6
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (8414) gives:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8420)  all_52_13 = e0
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e2,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (36), (8394) gives:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8421)  all_4_2 = e2
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |              all_57_1, e2, e3, simplifying with (170), (8410)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |              gives:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8422)  all_57_1 = all_52_4
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (8401), (8419) imply:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8423)   ~ (all_52_6 = e1)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (8421) imply:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8424)   ~ (all_52_1 = e2)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (8421) imply:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8425)   ~ (all_52_6 = e2)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (8421) imply:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8426)   ~ (all_52_9 = e2)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (8421) imply:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | |   (8427)   ~ (e3 = e2)
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.34  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |   (8428)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8428) gives:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |   (8429)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (167), (8301), (8424), (8426), (8429),
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |            #379.
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |   (8430)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8430) gives:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |   (8431)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8431) gives:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |   (8432)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8432) gives:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8433)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8433) implies:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8434)  op(e0, e0) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (160), (164), (168), (211), (360),
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (8386), (8388), (8394), (8434), (function-axioms)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #877.
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8435)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8435) implies:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8436)  op(e3, e3) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8436), (function-axioms) are
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |   (8437)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (7930), (8387), (8437),
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |            #104.
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |   (8438)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8438) gives:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |   (8439)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8301), (8394), (8439),
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |            #705.
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |   (8440)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8440) gives:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8441)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8441) implies:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8442)  op(e0, e0) = e1
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8389), (8442), (function-axioms) are
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8443)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8301), (8443), (function-axioms) are
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #704.
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |   (8444)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.71/23.35  | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8444) gives:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |   (8445)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8445) gives:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |   (8446)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8446) gives:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |   (8447)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7930), (8394), (8447),
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |            #103.
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |   (8448)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8448) gives:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (8449)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8449) implies:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (8450)  op(e1, e1) = e2
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8301), (8450), (function-axioms) are
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (8451)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8451) implies:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (8452)  op(e0, e0) = e1
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8389), (8452), (function-axioms) are
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |   (8453)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8453) gives:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |   (8454)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8301), (8454), (function-axioms) are
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |   (8455)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8455) gives:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (8456)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8456) implies:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (8457)  op(e0, e0) = e3
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (160), (164), (168), (211), (360),
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (8386), (8388), (8394), (8457), (function-axioms)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #877.
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (8458)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (7930), (8458), (function-axioms) are
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #101.
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.36  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |   (8459)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8459) gives:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |   (8460)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (160), (164), (165), (168), (211),
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |            (360), (8386), (8388), (8394), (8426), (8460),
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |            #870.
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |   (8461)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8461) gives:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |   (8462)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8462) gives:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (8463)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8463) implies:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (8464)  op(e2, e0) = e2
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8387), (8464), (function-axioms) are
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (8465)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8465) implies:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (8466)  op(e3, e3) = e3
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8466), (function-axioms) are
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |   (8467)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8467) gives:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (8468)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8468) implies:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (8469)  op(e2, e0) = e2
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8387), (8469), (function-axioms) are
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (8470)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8470) gives:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8471)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8471) implies:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8472)  op(e1, e1) = e1
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8301), (8472), (function-axioms) are
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8473)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8473) implies:
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8474)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.71/23.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8475)  all_54_9 = e3
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (8475) imply:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8476)  all_52_6 = e3
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8476) implies:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8477)  all_52_6 = e3
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (8477) imply:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8478)   ~ (all_52_7 = e3)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8478) implies:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8479)   ~ (all_52_7 = e3)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8395) gives:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8480)  all_57_15 = e2 & op(e0, e0) = e2
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8480) implies:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8481)  all_57_15 = e2
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8474) gives:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8482)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8482) gives:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8483)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (164), (7926), (8387), (8483),
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #239.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8484)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8484) gives:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8485)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8485) implies:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8486)  op(e0, e3) = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7926), (8486), (function-axioms) are
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8487)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8487) gives:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8488)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e2) = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8488) implies:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8489)   ~ (all_57_15 = e2)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8481), (8489) imply:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8490)  $false
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8490) is inconsistent.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8491)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e2) = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8491) implies:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8492)  op(e2, e0) = e2
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8387), (8492), (function-axioms) are
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8493)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8493) gives:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8494)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8494) gives:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8495)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8495) implies:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8496)   ~ (all_57_15 = e2)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8481), (8496) imply:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8497)  $false
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8497) is inconsistent.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8498)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8498) gives:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8499)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8481), (8499) are inconsistent by sub-proof #863.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8500)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8500) implies:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8501)  op(e0, e1) = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (8297), (8501), (function-axioms) are
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8502)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8502) gives:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8503)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (164), (8297), (8387), (8503),
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #682.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8504)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (8297), (8504), (function-axioms) are
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8505)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8505) implies:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8506)   ~ (all_57_7 = e0)
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8507)  op(e0, e2) = all_57_7
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (135), (158), (170), (191), (203),
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (248), (272), (352), (356), (7927), (7930),
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8394), (8397), (8479), (8506), (8507),
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #82.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8508)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (8295), (8423), (8425), (8508) are
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #673.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | |   (8509)  all_56_11 = e0 & op(e1, e0) = e0
% 155.71/23.38  | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8298), (8509), (function-axioms) are
% 155.71/23.38  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #406.
% 155.71/23.38  | | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | |   (8510)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.71/23.38  | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.71/23.38  | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.71/23.38  | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.71/23.38  | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.71/23.38  | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.71/23.38  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.71/23.38  | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.71/23.38  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.71/23.38  | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.71/23.38  | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.71/23.38  | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.71/23.38  | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.71/23.38  | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.71/23.38  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.71/23.38  | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.71/23.38  | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | REF_CLOSE: (4), (5), (8301), (8389), (8510),
% 155.71/23.38  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.38  | | | | | | | | | | | |            #671.
% 155.71/23.38  | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | End of split
% 155.71/23.38  | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | |   (8511)  all_24_2 = e1
% 155.71/23.38  | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | COMBINE_EQS: (318), (8511) imply:
% 155.71/23.38  | | | | | | | | | |   (8512)  all_4_2 = e1
% 155.71/23.38  | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | REDUCE: (36), (8512) imply:
% 155.71/23.38  | | | | | | | | | |   (8513)  op(e2, e2) = e1
% 155.71/23.38  | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | BETA: splitting (238) gives:
% 155.71/23.38  | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | |   (8514)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.71/23.38  | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.71/23.38  | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.71/23.38  | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.71/23.38  | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.71/23.38  | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.71/23.38  | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.71/23.38  | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.71/23.38  | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.71/23.38  | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.71/23.38  | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.71/23.38  | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.71/23.38  | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.71/23.38  | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.71/23.38  | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.71/23.38  | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.71/23.38  | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | REF_CLOSE: (6), (7), (7930), (8513), (8514),
% 155.71/23.38  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.38  | | | | | | | | | | |            #81.
% 155.71/23.38  | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | |   (8515)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.71/23.38  | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.71/23.38  | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.71/23.38  | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.71/23.38  | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.71/23.38  | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.71/23.38  | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.71/23.38  | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.71/23.38  | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.71/23.38  | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.71/23.38  | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.71/23.38  | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.71/23.38  | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.71/23.38  | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.71/23.38  | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.71/23.38  | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.71/23.38  | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | BETA: splitting (8515) gives:
% 155.71/23.38  | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | Case 1:
% 155.71/23.38  | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | |   (8516)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.71/23.38  | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 155.71/23.38  | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.71/23.38  | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.71/23.38  | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.71/23.38  | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 155.71/23.38  | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 155.71/23.38  | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 155.71/23.38  | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | ALPHA: (8516) implies:
% 155.71/23.38  | | | | | | | | | | | |   (8517)  op(e1, e1) = e1
% 155.71/23.38  | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | | REF_CLOSE: (4), (8301), (8517), (function-axioms) are
% 155.71/23.38  | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.71/23.38  | | | | | | | | | | | | 
% 155.71/23.38  | | | | | | | | | | | Case 2:
% 155.71/23.38  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | |   (8518)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.71/23.39  | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 155.71/23.39  | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.71/23.39  | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.71/23.39  | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.71/23.39  | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.71/23.39  | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.71/23.39  | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | ALPHA: (8518) implies:
% 155.71/23.39  | | | | | | | | | | | |   (8519)  op(e0, e0) = e0
% 155.71/23.39  | | | | | | | | | | | |   (8520)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.71/23.39  | | | | | | | | | | | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.71/23.39  | | | | | | | | | | | |             $i(all_57_11))
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | BETA: splitting (8520) gives:
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | |   (8521)  all_57_12 = e0 & op(e2, e2) = e0
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | ALPHA: (8521) implies:
% 155.71/23.39  | | | | | | | | | | | | |   (8522)  op(e2, e2) = e0
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | REF_CLOSE: (4), (8513), (8522), (function-axioms) are
% 155.71/23.39  | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | |   (8523)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.71/23.39  | | | | | | | | | | | | |           $i(all_57_11)
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | ALPHA: (8523) implies:
% 155.71/23.39  | | | | | | | | | | | | |   (8524)  op(e2, e0) = all_57_11
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | BETA: splitting (221) gives:
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | |   (8525)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 155.71/23.39  | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | BETA: splitting (8525) gives:
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | |   (8526)  all_56_2 = e0 & op(e2, e3) = e0
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | REF_CLOSE: (167), (7924), (8526), (function-axioms) are
% 155.71/23.39  | | | | | | | | | | | | | | |            inconsistent by sub-proof #80.
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | |   (8527)  all_56_3 = e0 & op(e2, e2) = e0
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | ALPHA: (8527) implies:
% 155.71/23.39  | | | | | | | | | | | | | | |   (8528)  op(e2, e2) = e0
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | REF_CLOSE: (4), (8513), (8528), (function-axioms) are
% 155.71/23.39  | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | End of split
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | |   (8529)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 155.71/23.39  | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | REF_CLOSE: (51), (164), (165), (371), (8296), (8519), (8524),
% 155.71/23.39  | | | | | | | | | | | | | |            (8529), (function-axioms) are inconsistent by
% 155.71/23.39  | | | | | | | | | | | | | |            sub-proof #78.
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | End of split
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | End of split
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | End of split
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | End of split
% 155.71/23.39  | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | End of split
% 155.71/23.39  | | | | | | | | | 
% 155.71/23.39  | | | | | | | | End of split
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | |   (8530)  all_20_2 = e3
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | COMBINE_EQS: (325), (8530) imply:
% 155.71/23.39  | | | | | | | |   (8531)  all_10_2 = e3
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | SIMP: (8531) implies:
% 155.71/23.39  | | | | | | | |   (8532)  all_10_2 = e3
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | COMBINE_EQS: (331), (8532) imply:
% 155.71/23.39  | | | | | | | |   (8533)  all_30_2 = e3
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | REDUCE: (350), (8532) imply:
% 155.71/23.39  | | | | | | | |   (8534)   ~ (all_52_2 = e3)
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | REDUCE: (361), (8532) imply:
% 155.71/23.39  | | | | | | | |   (8535)   ~ (all_52_6 = e3)
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | REDUCE: (363), (8532) imply:
% 155.71/23.39  | | | | | | | |   (8536)   ~ (all_52_8 = e3)
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | REDUCE: (364), (8532) imply:
% 155.71/23.39  | | | | | | | |   (8537)   ~ (all_52_9 = e3)
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | REDUCE: (366), (8532) imply:
% 155.71/23.39  | | | | | | | |   (8538)   ~ (all_52_11 = e3)
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | REDUCE: (368), (8532) imply:
% 155.71/23.39  | | | | | | | |   (8539)   ~ (all_52_14 = e3)
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | BETA: splitting (76) gives:
% 155.71/23.39  | | | | | | | | 
% 155.71/23.39  | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | 
% 155.71/23.39  | | | | | | | | |   (8540)   ~ (all_30_2 = e3)
% 155.71/23.39  | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | REDUCE: (8533), (8540) imply:
% 155.71/23.39  | | | | | | | | |   (8541)  $false
% 155.71/23.39  | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | CLOSE: (8541) is inconsistent.
% 155.71/23.39  | | | | | | | | | 
% 155.71/23.39  | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | 
% 155.71/23.39  | | | | | | | | |   (8542)  ( ~ (all_30_0 = e2) & op(e3, e1) = all_30_0 &
% 155.71/23.39  | | | | | | | | |             $i(all_30_0)) | ( ~ (all_30_1 = e0) & op(e3, e3) =
% 155.71/23.39  | | | | | | | | |             all_30_1 & $i(all_30_1))
% 155.71/23.39  | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | BETA: splitting (216) gives:
% 155.71/23.39  | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | |   (8543)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 155.71/23.39  | | | | | | | | | |             & op(e1, e2) = e3)
% 155.71/23.39  | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | BETA: splitting (8543) gives:
% 155.71/23.39  | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | |   (8544)  all_56_6 = e3 & op(e1, e3) = e3
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | REF_CLOSE: (163), (8534), (8544), (function-axioms) are
% 155.71/23.39  | | | | | | | | | | |            inconsistent by sub-proof #681.
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | |   (8545)  all_56_7 = e3 & op(e1, e2) = e3
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | REF_CLOSE: (162), (8535), (8545), (function-axioms) are
% 155.71/23.39  | | | | | | | | | | |            inconsistent by sub-proof #388.
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | End of split
% 155.71/23.39  | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | |   (8546)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 155.71/23.39  | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 155.71/23.39  | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | BETA: splitting (8546) gives:
% 155.71/23.39  | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | |   (8547)  all_56_8 = e3 & op(e1, e1) = e3
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | ALPHA: (8547) implies:
% 155.71/23.39  | | | | | | | | | | |   (8548)  all_56_8 = e3
% 155.71/23.39  | | | | | | | | | | |   (8549)  op(e1, e1) = e3
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | BETA: splitting (8542) gives:
% 155.71/23.39  | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | |   (8550)   ~ (all_30_0 = e2) & op(e3, e1) = all_30_0 &
% 155.71/23.39  | | | | | | | | | | | |           $i(all_30_0)
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | ALPHA: (8550) implies:
% 155.71/23.39  | | | | | | | | | | | |   (8551)   ~ (all_30_0 = e2)
% 155.71/23.39  | | | | | | | | | | | |   (8552)  op(e3, e1) = all_30_0
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 155.71/23.39  | | | | | | | | | | | |              all_30_0, e1, e3, simplifying with (169), (8552)
% 155.71/23.39  | | | | | | | | | | | |              gives:
% 155.71/23.39  | | | | | | | | | | | |   (8553)  all_52_8 = all_30_0
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | COMBINE_EQS: (271), (8553) imply:
% 155.71/23.39  | | | | | | | | | | | |   (8554)  all_54_2 = all_30_0
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | REDUCE: (123), (8553) imply:
% 155.71/23.39  | | | | | | | | | | | |   (8555)   ~ (all_52_9 = all_30_0)
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | SIMP: (8555) implies:
% 155.71/23.39  | | | | | | | | | | | |   (8556)   ~ (all_52_9 = all_30_0)
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | REDUCE: (121), (8553) imply:
% 155.71/23.39  | | | | | | | | | | | |   (8557)   ~ (all_52_11 = all_30_0)
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | SIMP: (8557) implies:
% 155.71/23.39  | | | | | | | | | | | |   (8558)   ~ (all_52_11 = all_30_0)
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | REDUCE: (120), (8553) imply:
% 155.71/23.39  | | | | | | | | | | | |   (8559)   ~ (all_52_12 = all_30_0)
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | SIMP: (8559) implies:
% 155.71/23.39  | | | | | | | | | | | |   (8560)   ~ (all_52_12 = all_30_0)
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | REDUCE: (8536), (8553) imply:
% 155.71/23.39  | | | | | | | | | | | |   (8561)   ~ (all_30_0 = e3)
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | REDUCE: (7928), (8553) imply:
% 155.71/23.39  | | | | | | | | | | | |   (8562)   ~ (all_30_0 = e0)
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | BETA: splitting (202) gives:
% 155.71/23.39  | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | |   (8563)  all_54_2 = e3
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | COMBINE_EQS: (8554), (8563) imply:
% 155.71/23.39  | | | | | | | | | | | | |   (8564)  all_30_0 = e3
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | REDUCE: (8561), (8564) imply:
% 155.71/23.39  | | | | | | | | | | | | |   (8565)  $false
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | CLOSE: (8565) is inconsistent.
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | |   (8566)   ~ (all_54_2 = e3)
% 155.71/23.39  | | | | | | | | | | | | |   (8567)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | BETA: splitting (8567) gives:
% 155.71/23.39  | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | |   (8568)  all_54_2 = e2
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | COMBINE_EQS: (8554), (8568) imply:
% 155.71/23.39  | | | | | | | | | | | | | |   (8569)  all_30_0 = e2
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | REDUCE: (8551), (8569) imply:
% 155.71/23.39  | | | | | | | | | | | | | |   (8570)  $false
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | CLOSE: (8570) is inconsistent.
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | |   (8571)   ~ (all_54_2 = e2)
% 155.71/23.39  | | | | | | | | | | | | | |   (8572)  all_54_2 = e1 | all_54_2 = e0
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | BETA: splitting (8572) gives:
% 155.71/23.39  | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | |   (8573)  all_54_2 = e1
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | COMBINE_EQS: (8554), (8573) imply:
% 155.71/23.39  | | | | | | | | | | | | | | |   (8574)  all_30_0 = e1
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | REDUCE: (8556), (8574) imply:
% 155.71/23.39  | | | | | | | | | | | | | | |   (8575)   ~ (all_52_9 = e1)
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | REDUCE: (8558), (8574) imply:
% 155.71/23.39  | | | | | | | | | | | | | | |   (8576)   ~ (all_52_11 = e1)
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | REDUCE: (8560), (8574) imply:
% 155.71/23.39  | | | | | | | | | | | | | | |   (8577)   ~ (all_52_12 = e1)
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | REDUCE: (8561), (8574) imply:
% 155.71/23.39  | | | | | | | | | | | | | | |   (8578)   ~ (e3 = e1)
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | REDUCE: (8551), (8574) imply:
% 155.71/23.39  | | | | | | | | | | | | | | |   (8579)   ~ (e2 = e1)
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | |   (8580)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 155.71/23.39  | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 155.71/23.39  | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | BETA: splitting (8580) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | |   (8581)  all_56_4 = e1 & op(e3, e1) = e1
% 155.71/23.39  | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | ALPHA: (8581) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | |   (8582)  all_56_4 = e1
% 155.71/23.39  | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | |   (8583)   ~ (all_24_2 = e1)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | REDUCE: (318), (8583) imply:
% 155.71/23.39  | | | | | | | | | | | | | | | | | |   (8584)   ~ (all_4_2 = e1)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | |   (8585)   ~ (all_28_2 = e2)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | REDUCE: (330), (8585) imply:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | |   (8586)   ~ (all_14_2 = e2)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | |   (8587)  all_54_15 = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7937), (8587) are inconsistent by
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | |            sub-proof #1010.
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | |   (8588)   ~ (all_54_15 = e3)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | |   (8589)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8589) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | |   (8590)  all_54_15 = e2
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (8586), (8590) are inconsistent by
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1009.
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | |   (8591)   ~ (all_54_15 = e2)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | |   (8592)  all_54_15 = e1 | all_54_15 = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8592) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |   (8593)  all_54_15 = e1
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7935), (8593) are inconsistent by
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1008.
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |   (8594)  all_54_15 = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (8594) imply:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |   (8595)  all_14_2 = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | SIMP: (8595) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |   (8596)  all_14_2 = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (8596) imply:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |   (8597)   ~ (all_52_7 = e0)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (8596) imply:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |   (8598)   ~ (all_52_11 = e0)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (8596) imply:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |   (8599)   ~ (all_52_14 = e0)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7937), (8596) imply:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |   (8600)   ~ (e3 = e0)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8586), (8596) imply:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |   (8601)   ~ (e2 = e0)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7935), (8596) imply:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | |   (8602)   ~ (e1 = e0)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | |   (8603)  all_56_15 = e0 & op(e0, e0) = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8603) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | |   (8604)  all_56_15 = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | |   (8605)  op(e0, e0) = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | |   (8606)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8606) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (8607)  all_56_6 = e0 & op(e1, e3) = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7925), (8607), (function-axioms) are
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #699.
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (8608)  all_56_7 = e0 & op(e1, e2) = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8608) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (8609)  all_56_7 = e0
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8610)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8610) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8611)  all_56_1 = e1 & op(e3, e2) = e1
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8611) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8612)  all_56_1 = e1
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8613)  op(e3, e2) = e1
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8614)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (118), (121), (165), (190), (247), (271),
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7928), (8538), (8572), (8582), (8598), (8614),
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #77.
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8615)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8615) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8616)  all_56_8 = e2 & op(e1, e1) = e2
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8616) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8617)  op(e1, e1) = e2
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8549), (8617), (function-axioms) are
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8618)  all_56_14 = e2 & op(e0, e1) = e2
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8618) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8619)  all_56_14 = e2
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8620)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8620) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8621)  all_56_0 = e3 & op(e3, e3) = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8621) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8622)  op(e3, e3) = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8622), (function-axioms) are
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8623)  all_56_1 = e3 & op(e3, e2) = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8623) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8624)  op(e3, e2) = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8613), (8624), (function-axioms) are
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #345.
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8625)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8625) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8626)  all_56_4 = e3 & op(e3, e1) = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8626) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8627)  op(e3, e1) = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8536), (8627), (function-axioms) are
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8628)  all_56_9 = e3 & op(e3, e0) = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8628) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8629)  all_56_9 = e3
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8630)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8630) gives:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8631)  all_56_0 = e2 & op(e3, e3) = e2
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8631) implies:
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8632)  op(e3, e3) = e2
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (157), (165), (218), (230),
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8549), (8575), (8576), (8612), (8629), (8632),
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #229.
% 155.71/23.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8633)  all_56_1 = e2 & op(e3, e2) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8633) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8634)  all_56_1 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8612), (8634) are inconsistent by sub-proof
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #680.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8635)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8635) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8636)  all_56_4 = e2 & op(e3, e1) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8582), (8636) are inconsistent by sub-proof
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #317.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8637)  all_56_9 = e2 & op(e3, e0) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8637) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8638)  all_56_9 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8629), (8638) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8639)  e3 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8548), (8639) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8640)  all_56_8 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (217), (218),
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (8536), (8619), (8640), (function-axioms)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #178.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8641)  all_56_3 = e1 & op(e2, e2) = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8641) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8642)  op(e2, e2) = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (8584), (8642),
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #690.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8643)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8643) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8644)  all_56_7 = e1 & op(e1, e2) = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8644) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8645)  all_56_7 = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8609), (8645) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8646)  e1 = e0
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8646) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8647)  e1 = e0
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8582), (8647) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8648)  all_56_4 = e0
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (157), (165), (218), (8549), (8575),
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8576), (8648), (function-axioms) are inconsistent
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #230.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8649)  all_56_13 = e1 & op(e0, e2) = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8649) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8650)  all_56_13 = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8651)  op(e0, e2) = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8652)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8652) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8653)  all_56_1 = e3 & op(e3, e2) = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8653) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8654)  all_56_1 = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8655)  op(e3, e2) = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8656)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8656) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8657)  all_56_0 = e2 & op(e3, e3) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8657) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8658)  op(e3, e3) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7930), (8658), (function-axioms) are
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8659)  all_56_1 = e2 & op(e3, e2) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8659) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8660)  op(e3, e2) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8655), (8660), (function-axioms) are
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #433.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8661)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8661) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8662)  all_56_4 = e2 & op(e3, e1) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8582), (8662) are inconsistent by sub-proof
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #317.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8663)  all_56_9 = e2 & op(e3, e0) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8663) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8664)  all_56_9 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8665)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8665) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8666)  all_56_9 = e3 & op(e3, e0) = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8666) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8667)  all_56_9 = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8664), (8667) are inconsistent by sub-proof
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #888.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8668)  all_56_10 = e3 & op(e2, e0) = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8668) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8669)  all_56_10 = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8670)  all_54_14 = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (8538), (8670) are inconsistent by
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #587.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8671)   ~ (all_54_14 = e3)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8672)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8672) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8673)  all_54_14 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (8673) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8674)  all_52_11 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8674) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8675)  all_52_11 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (8675) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8676)   ~ (all_52_9 = e2)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8538), (8675) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8677)   ~ (e3 = e2)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8678)  all_54_6 = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (8537), (8678) are inconsistent by
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #518.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8679)   ~ (all_54_6 = e3)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8680)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8680) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8681)  all_54_6 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (8681) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8682)  all_52_9 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8682) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8683)  all_52_9 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8676), (8683) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8684)  $false
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8684) is inconsistent.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8685)  all_54_6 = e1 | all_54_6 = e0
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8686)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (118), (121), (165), (190), (247), (271),
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7928), (8538), (8572), (8582), (8598), (8686),
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #77.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8687)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8687) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8688)  all_56_8 = e2 & op(e1, e1) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8688) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8689)  op(e1, e1) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8549), (8689), (function-axioms) are
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8690)  all_56_14 = e2 & op(e0, e1) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8690) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8691)  all_56_14 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8692)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8692) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8693)  all_56_2 = e1 & op(e2, e3) = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8693) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8694)  all_56_2 = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8695)  op(e2, e3) = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8685) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8696)  all_54_6 = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (8696) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8697)  all_52_9 = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8697) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8698)  all_52_9 = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8575), (8698) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8699)  $false
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8699) is inconsistent.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8700)  all_54_6 = e0
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (8700) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8701)  all_52_9 = e0
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8701) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8702)  all_52_9 = e0
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (8702) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8703)   ~ (all_4_2 = e0)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8703) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8704)   ~ (all_4_2 = e0)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8705)  all_54_5 = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (373), (8705) are inconsistent by sub-proof
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #930.
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8706)   ~ (all_54_5 = e3)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8707)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8707) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8708)  all_54_5 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8708) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8709)  all_4_2 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8709) implies:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8710)  all_4_2 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (8710) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8711)   ~ (all_52_1 = e2)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (8710) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8712)   ~ (all_52_13 = e2)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (8710) imply:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8713)  op(e2, e2) = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8714)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8714) gives:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8715)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8715) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8716)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8711), (8716), (function-axioms) are
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8717)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8717) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8718)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8711), (8718), (function-axioms) are
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8719)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8719) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8720)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8720) implies:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8721)  op(e2, e3) = e2
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8711), (8721), (function-axioms) are
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8722)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8722) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8723)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8723) implies:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8724)  op(e1, e3) = e1
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (133), (141), (163), (170), (193), (201),
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (250), (270), (272), (7929), (8539),
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8577), (8599), (8655), (8724), (function-axioms)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #76.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8725)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8725) implies:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8726)  op(e2, e1) = e2
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (121), (165), (190), (247), (271), (7928),
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8538), (8572), (8598), (8726), (function-axioms)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #583.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8727)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8727) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8728)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8728) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8729)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8729) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8730)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8730) implies:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8731)  op(e0, e0) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8605), (8731), (function-axioms) are
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8732)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8732) implies:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8733)  op(e3, e3) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (8582), (8654), (8664),
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8733), (function-axioms) are inconsistent by
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #949.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8734)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8734) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8735)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8735) implies:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8736)  op(e2, e0) = e2
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8712), (8736), (function-axioms) are
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8737)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8737) implies:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8738)  op(e3, e3) = e1
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (8534), (8694), (8695), (8738),
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #75.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8739)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8739) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8740)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (8536), (8713), (8740),
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #565.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8741)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8741) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8742)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8742) implies:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8743)  op(e0, e0) = e1
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (7935), (8592), (8743),
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #790.
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8744)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8744) gives:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8745)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8745) implies:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8746)  op(e1, e3) = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (133), (141), (163), (170), (193), (201),
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (250), (270), (272), (7929), (8539),
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8577), (8599), (8655), (8746), (function-axioms)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #76.
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8747)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8747) implies:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8748)  op(e1, e1) = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8549), (8748), (function-axioms) are
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8749)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8749) gives:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8750)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8750) gives:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8751)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8751) gives:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8752)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8752) gives:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8753)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8753) implies:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8754)  op(e3, e3) = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (8534), (8694), (8695), (8754),
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #75.
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8755)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8755) implies:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8756)  op(e2, e2) = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8713), (8756), (function-axioms) are
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8757)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (51), (246), (7935), (8549), (8592), (8757),
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #577.
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8758)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8758) gives:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8759)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (8549), (8759), (function-axioms) are
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #644.
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8760)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8760) gives:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8761)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8761) implies:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8762)  op(e0, e0) = e3
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8605), (8762), (function-axioms) are
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8763)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8763) gives:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8764)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8764) implies:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8765)  op(e3, e3) = e3
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (8582), (8654), (8664),
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8765), (function-axioms) are inconsistent by
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #949.
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8766)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8766) implies:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8767)  op(e3, e3) = e1
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (8534), (8694), (8695), (8767),
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #75.
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8768)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8768) gives:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8769)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8769) gives:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8770)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8770) gives:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8771)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8771) implies:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8772)  op(e0, e0) = e2
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (207), (209),
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8651), (8691), (8772), (function-axioms) are
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #74.
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8773)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8773) implies:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8774)  op(e2, e1) = e2
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (121), (165), (190), (247), (271), (7928),
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8538), (8572), (8598), (8774), (function-axioms)
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #583.
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8775)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8605), (8713), (8775),
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #977.
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8776)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8776) gives:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8777)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8777) gives:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8778)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8778) implies:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8779)  op(e0, e0) = e2
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (207), (209),
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8651), (8691), (8779), (function-axioms) are
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #74.
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8780)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8780) implies:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8781)  op(e3, e3) = e3
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (8582), (8654), (8664),
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8781), (function-axioms) are inconsistent by
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #949.
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8782)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8782) gives:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8783)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8783) implies:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8784)  op(e2, e0) = e2
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8712), (8784), (function-axioms) are
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8785)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8785) gives:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8786)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8786) implies:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8787)  op(e1, e1) = e1
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8549), (8787), (function-axioms) are
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8788)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8788) implies:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8789)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8790)  all_54_1 = e3
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (8790) imply:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8791)  all_52_4 = e3
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8791) implies:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8792)  all_52_4 = e3
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (8792) imply:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8793)   ~ (all_52_12 = e3)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8793) implies:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8794)   ~ (all_52_12 = e3)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8789) gives:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8795)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8795) gives:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8796)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (164), (7926), (8549), (8712), (8796),
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #642.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8797)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (164), (168), (7926), (8712), (8794),
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8797), (function-axioms) are inconsistent by
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #73.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8798)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8798) gives:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8799)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (157), (8549), (8598), (8651), (8799),
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #72.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8800)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (164), (8549), (8598), (8712), (8800),
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #639.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8801)   ~ (all_54_1 = e3)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (272), (8801) imply:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8802)   ~ (all_52_4 = e3)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (8655), (8802), (function-axioms) are
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8803)  all_54_5 = e1 | all_54_5 = e0
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (8584), (8704), (8803) are inconsistent by
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8804)  all_56_3 = e1 & op(e2, e2) = e1
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8804) implies:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8805)  op(e2, e2) = e1
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (199), (268), (373), (8584), (8805),
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #690.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8806)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8806) gives:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8807)  all_56_5 = e1 & op(e2, e1) = e1
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8575), (8807), (function-axioms) are
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8808)  all_56_10 = e1 & op(e2, e0) = e1
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8669), (8808) are inconsistent by sub-proof
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #556.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8809)  all_54_14 = e1 | all_54_14 = e0
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (8576), (8598), (8809) are inconsistent by
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #585.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8810)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (8539), (8605), (8810),
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #622.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8811)  all_56_3 = e3 & op(e2, e2) = e3
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8811) implies:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8812)  op(e2, e2) = e3
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (8812), (function-axioms) are
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #711.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8813)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (8535), (8650), (8813),
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | |   (8814)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (210), (211), (212),
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | |            (8549), (8604), (8605), (8814), (function-axioms)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #216.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | |   (8815)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8815) implies:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | |   (8816)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (7926), (8597), (8598),
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | |            (8816), (function-axioms) are inconsistent by
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #881.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | |   (8817)  all_28_2 = e2
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (8817) imply:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | |   (8818)  all_14_2 = e2
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | SIMP: (8818) implies:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | |   (8819)  all_14_2 = e2
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | REDUCE: (369), (8819) imply:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | |   (8820)   ~ (all_52_11 = e2)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | REDUCE: (7937), (8819) imply:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | |   (8821)   ~ (e3 = e2)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | REDUCE: (51), (8819) imply:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | |   (8822)  op(e0, e0) = e2
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | |   (8823)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8823) gives:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | |   (8824)  all_56_4 = e2 & op(e3, e1) = e2
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8582), (8824) are inconsistent by sub-proof
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | |            #317.
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | |   (8825)  all_56_5 = e2 & op(e2, e1) = e2
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8825) implies:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | |   (8826)  op(e2, e1) = e2
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.44  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |   (8827)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8827) gives:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |   (8828)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8828) implies:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |   (8829)  op(e3, e3) = e3
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8829), (function-axioms) are
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |   (8830)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8830) implies:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |   (8831)  op(e2, e2) = e2
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (8826), (8831),
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |   (8832)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (8549), (8822), (8832),
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | |            #508.
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | |   (8833)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (8549), (8820), (8833),
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | |            #210.
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | |   (8834)  all_24_2 = e1
% 155.71/23.45  | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (8834) imply:
% 155.71/23.45  | | | | | | | | | | | | | | | | | |   (8835)  all_4_2 = e1
% 155.71/23.45  | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | SIMP: (8835) implies:
% 155.71/23.45  | | | | | | | | | | | | | | | | | |   (8836)  all_4_2 = e1
% 155.71/23.45  | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | REDUCE: (360), (8836) imply:
% 155.71/23.45  | | | | | | | | | | | | | | | | | |   (8837)   ~ (all_52_13 = e1)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | REDUCE: (36), (8836) imply:
% 155.71/23.45  | | | | | | | | | | | | | | | | | |   (8838)  op(e2, e2) = e1
% 155.71/23.45  | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |   (8839)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (7930), (8838), (8839),
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |            #81.
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |   (8840)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (51), (160), (164), (168), (210),
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |            (8549), (8577), (8837), (8840), (function-axioms)
% 155.71/23.45  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #209.
% 155.71/23.45  | | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | |   (8841)  all_56_5 = e1 & op(e2, e1) = e1
% 155.71/23.45  | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8575), (8841), (function-axioms) are
% 155.71/23.45  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 155.71/23.45  | | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | |   (8842)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 155.71/23.45  | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (8549), (8576), (8842),
% 155.71/23.45  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.71/23.45  | | | | | | | | | | | | | | | |            #231.
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | |   (8843)  all_54_2 = e0
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | COMBINE_EQS: (8554), (8843) imply:
% 155.71/23.45  | | | | | | | | | | | | | | |   (8844)  all_30_0 = e0
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | REDUCE: (8562), (8844) imply:
% 155.71/23.45  | | | | | | | | | | | | | | |   (8845)  $false
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | CLOSE: (8845) is inconsistent.
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | |   (8846)   ~ (all_30_1 = e0) & op(e3, e3) = all_30_1 &
% 155.71/23.45  | | | | | | | | | | | |           $i(all_30_1)
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | ALPHA: (8846) implies:
% 155.71/23.45  | | | | | | | | | | | |   (8847)   ~ (all_30_1 = e0)
% 155.71/23.45  | | | | | | | | | | | |   (8848)  op(e3, e3) = all_30_1
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_30_1,
% 155.71/23.45  | | | | | | | | | | | |              e3, e3, simplifying with (7930), (8848) gives:
% 155.71/23.45  | | | | | | | | | | | |   (8849)  all_30_1 = e0
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | REDUCE: (8847), (8849) imply:
% 155.71/23.45  | | | | | | | | | | | |   (8850)  $false
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | CLOSE: (8850) is inconsistent.
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | |   (8851)  all_56_11 = e3 & op(e1, e0) = e3
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | ALPHA: (8851) implies:
% 155.71/23.45  | | | | | | | | | | |   (8852)  op(e1, e0) = e3
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | REF_CLOSE: (160), (8539), (8852), (function-axioms) are
% 155.71/23.45  | | | | | | | | | | |            inconsistent by sub-proof #677.
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | | 
% 155.71/23.45  | | | | | | | | End of split
% 155.71/23.45  | | | | | | | | 
% 155.71/23.45  | | | | | | | End of split
% 155.71/23.45  | | | | | | | 
% 155.71/23.45  | | | | | | Case 2:
% 155.71/23.45  | | | | | | | 
% 155.71/23.45  | | | | | | |   (8853)  all_18_2 = e3
% 155.71/23.45  | | | | | | | 
% 155.71/23.45  | | | | | | | COMBINE_EQS: (301), (8853) imply:
% 155.71/23.45  | | | | | | |   (8854)  all_14_2 = e3
% 155.71/23.45  | | | | | | | 
% 155.71/23.45  | | | | | | | SIMP: (8854) implies:
% 155.71/23.45  | | | | | | |   (8855)  all_14_2 = e3
% 155.71/23.45  | | | | | | | 
% 155.71/23.45  | | | | | | | REDUCE: (362), (8855) imply:
% 155.71/23.45  | | | | | | |   (8856)   ~ (all_52_7 = e3)
% 155.71/23.45  | | | | | | | 
% 155.71/23.45  | | | | | | | REDUCE: (369), (8855) imply:
% 155.71/23.45  | | | | | | |   (8857)   ~ (all_52_11 = e3)
% 155.71/23.45  | | | | | | | 
% 155.71/23.45  | | | | | | | REDUCE: (370), (8855) imply:
% 155.71/23.45  | | | | | | |   (8858)   ~ (all_52_12 = e3)
% 155.71/23.45  | | | | | | | 
% 155.71/23.45  | | | | | | | REDUCE: (51), (8855) imply:
% 155.71/23.45  | | | | | | |   (8859)  op(e0, e0) = e3
% 155.71/23.45  | | | | | | | 
% 155.71/23.45  | | | | | | | BETA: splitting (64) gives:
% 155.71/23.45  | | | | | | | 
% 155.71/23.45  | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | 
% 155.71/23.45  | | | | | | | |   (8860)   ~ (all_22_2 = e0)
% 155.71/23.45  | | | | | | | | 
% 155.71/23.45  | | | | | | | | REDUCE: (251), (8860) imply:
% 155.71/23.45  | | | | | | | |   (8861)   ~ (all_10_2 = e0)
% 155.71/23.45  | | | | | | | | 
% 155.71/23.45  | | | | | | | | BETA: splitting (61) gives:
% 155.71/23.45  | | | | | | | | 
% 155.71/23.45  | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | 
% 155.71/23.45  | | | | | | | | |   (8862)   ~ (all_20_2 = e3)
% 155.71/23.45  | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | REDUCE: (325), (8862) imply:
% 155.71/23.45  | | | | | | | | |   (8863)   ~ (all_10_2 = e3)
% 155.71/23.45  | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | BETA: splitting (194) gives:
% 155.71/23.45  | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | |   (8864)  all_54_10 = e3
% 155.71/23.45  | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | REF_CLOSE: (336), (8863), (8864) are inconsistent by
% 155.71/23.45  | | | | | | | | | |            sub-proof #361.
% 155.71/23.45  | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | |   (8865)   ~ (all_54_10 = e3)
% 155.71/23.45  | | | | | | | | | |   (8866)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 155.71/23.45  | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | BETA: splitting (8866) gives:
% 155.71/23.45  | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | |   (8867)  all_54_10 = e2
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | REF_CLOSE: (336), (7934), (8867) are inconsistent by
% 155.71/23.45  | | | | | | | | | | |            sub-proof #360.
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | |   (8868)   ~ (all_54_10 = e2)
% 155.71/23.45  | | | | | | | | | | |   (8869)  all_54_10 = e1 | all_54_10 = e0
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | BETA: splitting (8869) gives:
% 155.71/23.45  | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | |   (8870)  all_54_10 = e1
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | COMBINE_EQS: (336), (8870) imply:
% 155.71/23.45  | | | | | | | | | | | |   (8871)  all_10_2 = e1
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | SIMP: (8871) implies:
% 155.71/23.45  | | | | | | | | | | | |   (8872)  all_10_2 = e1
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | REDUCE: (350), (8872) imply:
% 155.71/23.45  | | | | | | | | | | | |   (8873)   ~ (all_52_2 = e1)
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | REDUCE: (361), (8872) imply:
% 155.71/23.45  | | | | | | | | | | | |   (8874)   ~ (all_52_6 = e1)
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | REDUCE: (366), (8872) imply:
% 155.71/23.45  | | | | | | | | | | | |   (8875)   ~ (all_52_11 = e1)
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | REDUCE: (368), (8872) imply:
% 155.71/23.45  | | | | | | | | | | | |   (8876)   ~ (all_52_14 = e1)
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | REDUCE: (8863), (8872) imply:
% 155.71/23.45  | | | | | | | | | | | |   (8877)   ~ (e3 = e1)
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | REDUCE: (7934), (8872) imply:
% 155.71/23.45  | | | | | | | | | | | |   (8878)   ~ (e2 = e1)
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | REDUCE: (45), (8872) imply:
% 155.71/23.45  | | | | | | | | | | | |   (8879)  op(e1, e1) = e1
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | BETA: splitting (67) gives:
% 155.71/23.45  | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | |   (8880)   ~ (all_24_2 = e1)
% 155.71/23.45  | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | REDUCE: (318), (8880) imply:
% 155.71/23.45  | | | | | | | | | | | | |   (8881)   ~ (all_4_2 = e1)
% 155.71/23.45  | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | BETA: splitting (79) gives:
% 155.71/23.45  | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | |   (8882)   ~ (all_32_2 = e0)
% 155.71/23.45  | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | REDUCE: (314), (8882) imply:
% 155.71/23.45  | | | | | | | | | | | | | |   (8883)   ~ (all_4_2 = e0)
% 155.71/23.45  | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 155.71/23.45  | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | |   (8884)  all_54_5 = e3
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8884) imply:
% 155.71/23.45  | | | | | | | | | | | | | | |   (8885)  all_4_2 = e3
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | REDUCE: (373), (8885) imply:
% 155.71/23.45  | | | | | | | | | | | | | | |   (8886)  $false
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | CLOSE: (8886) is inconsistent.
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | Case 2:
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | |   (8887)   ~ (all_54_5 = e3)
% 155.71/23.45  | | | | | | | | | | | | | | |   (8888)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | BETA: splitting (8888) gives:
% 155.71/23.45  | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | |   (8889)  all_54_5 = e2
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8889) imply:
% 155.71/23.45  | | | | | | | | | | | | | | | |   (8890)  all_4_2 = e2
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | REDUCE: (349), (8890) imply:
% 155.71/23.45  | | | | | | | | | | | | | | | |   (8891)   ~ (all_52_1 = e2)
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | REDUCE: (358), (8890) imply:
% 155.71/23.45  | | | | | | | | | | | | | | | |   (8892)   ~ (all_52_9 = e2)
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | REDUCE: (360), (8890) imply:
% 155.71/23.45  | | | | | | | | | | | | | | | |   (8893)   ~ (all_52_13 = e2)
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | REDUCE: (373), (8890) imply:
% 155.71/23.45  | | | | | | | | | | | | | | | |   (8894)   ~ (e3 = e2)
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | REDUCE: (36), (8890) imply:
% 155.71/23.45  | | | | | | | | | | | | | | | |   (8895)  op(e2, e2) = e2
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.71/23.45  | | | | | | | | | | | | | | | | 
% 155.71/23.45  | | | | | | | | | | | | | | | | Case 1:
% 155.71/23.45  | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | |   (8896)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.83/23.46  | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.83/23.46  | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e1)
% 155.83/23.46  | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | BETA: splitting (8896) gives:
% 155.83/23.46  | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | |   (8897)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.83/23.46  | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (167), (8879), (8891), (8892), (8897),
% 155.83/23.46  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.83/23.46  | | | | | | | | | | | | | | | | | |            #1000.
% 155.83/23.46  | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | |   (8898)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | |             e1)
% 155.83/23.46  | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | BETA: splitting (8898) gives:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |   (8899)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | BETA: splitting (8899) gives:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |   (8900)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8900) gives:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | |   (8901)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8901) implies:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | |   (8902)  op(e0, e3) = e0
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7926), (8902), (function-axioms) are
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | |   (8903)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8903) implies:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | |   (8904)  op(e3, e3) = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8904), (function-axioms) are
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |   (8905)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (7930), (8893), (8905),
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |            #104.
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |   (8906)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | |             e1)
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | BETA: splitting (8906) gives:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |   (8907)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (8879), (8895), (8907),
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |            #992.
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |   (8908)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |             e1)
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (8859), (8873), (8879), (8908),
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | |            #420.
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.46  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.46  | | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | End of split
% 155.83/23.46  | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.46  | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | |   (8909)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.83/23.46  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.83/23.46  | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.83/23.46  | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.83/23.46  | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.83/23.46  | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.83/23.46  | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.83/23.46  | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.83/23.46  | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.83/23.46  | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.83/23.46  | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.83/23.46  | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.83/23.46  | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.83/23.46  | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.83/23.46  | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.83/23.46  | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.83/23.46  | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.83/23.46  | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.83/23.46  | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.83/23.46  | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | BETA: splitting (8909) gives:
% 155.83/23.46  | | | | | | | | | | | | | | | | | 
% 155.83/23.46  | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.46  | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | |   (8910)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.83/23.47  | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | BETA: splitting (8910) gives:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |   (8911)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (8911) gives:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |   (8912)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7930), (8895), (8912),
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |            #103.
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |   (8913)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (8859), (8879), (8913),
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |            #453.
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |   (8914)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (8914) gives:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |   (8915)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (8874), (8879), (8915),
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |            #983.
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |   (8916)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8916) gives:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |   (8917)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8917) implies:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |   (8918)  op(e0, e3) = e0
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7926), (8918), (function-axioms) are
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |   (8919)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (7930), (8919), (function-axioms) are
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #101.
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.47  | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | |   (8920)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.83/23.47  | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | |                 e0)))
% 155.83/23.47  | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | BETA: splitting (8920) gives:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |   (8921)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (8921) gives:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |   (8922)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (8859), (8892), (8922),
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |            #412.
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |   (8923)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8923) gives:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |   (8924)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8924) implies:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |   (8925)  op(e2, e2) = e1
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8895), (8925), (function-axioms) are
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |   (8926)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8926) implies:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |   (8927)  op(e0, e3) = e0
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7926), (8927), (function-axioms) are
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.47  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |   (8928)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.83/23.47  | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.83/23.48  | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | BETA: splitting (8928) gives:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |   (8929)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8929) gives:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |   (8930)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8930) implies:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |   (8931)  op(e0, e0) = e2
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8859), (8931), (function-axioms) are
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |   (8932)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8932) implies:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |   (8933)  op(e3, e3) = e3
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8933), (function-axioms) are
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | End of split
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |   (8934)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8934) gives:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |   (8935)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8935) implies:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |   (8936)  op(e2, e0) = e2
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8893), (8936), (function-axioms) are
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |   (8937)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.83/23.48  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8937) gives:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |   (8938)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8938) implies:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |   (8939)  op(e1, e0) = e1
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8876), (8939), (function-axioms) are
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |   (8940)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8940) implies:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |   (8941)  op(e0, e0) = all_57_15
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |   (8942)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (8859), (8941)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | |   (8943)  all_57_15 = e3
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8942) gives:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |   (8944)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8944) gives:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |   (8945)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (164), (7926), (8879), (8893), (8945),
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |            #92.
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |   (8946)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (164), (168), (7926), (8858), (8893),
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |            (8946), (function-axioms) are inconsistent by
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #73.
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |   (8947)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8947) gives:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |   (8948)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8948) gives:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (8949)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8949) implies:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (8950)  op(e1, e1) = e0
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8879), (8950), (function-axioms) are
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (8951)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8951) gives:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8952)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8943), (8952) are inconsistent by sub-proof
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            #449.
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8953)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8953) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8954)  op(e3, e0) = e3
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8858), (8954), (function-axioms) are
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |   (8955)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8955) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (8956)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (8879), (8893), (8956),
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |            #862.
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (8957)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (8876), (8943), (8957),
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | |            #446.
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | |   (8958)  all_54_5 = e1 | all_54_5 = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | REF_CLOSE: (268), (8881), (8883), (8958) are inconsistent by
% 155.92/23.49  | | | | | | | | | | | | | | | |            sub-proof #962.
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | |   (8959)  all_32_2 = e0
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | COMBINE_EQS: (314), (8959) imply:
% 155.92/23.49  | | | | | | | | | | | | | |   (8960)  all_4_2 = e0
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | REDUCE: (358), (8960) imply:
% 155.92/23.49  | | | | | | | | | | | | | |   (8961)   ~ (all_52_9 = e0)
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | REDUCE: (373), (8960) imply:
% 155.92/23.49  | | | | | | | | | | | | | |   (8962)   ~ (e3 = e0)
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | REDUCE: (8881), (8960) imply:
% 155.92/23.49  | | | | | | | | | | | | | |   (8963)   ~ (e1 = e0)
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | REDUCE: (36), (8960) imply:
% 155.92/23.49  | | | | | | | | | | | | | |   (8964)  op(e2, e2) = e0
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | |   (8965)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 155.92/23.49  | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | BETA: splitting (8965) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | |   (8966)  all_56_4 = e0 & op(e3, e1) = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7928), (8966), (function-axioms) are
% 155.92/23.49  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #700.
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | |   (8967)  all_56_5 = e0 & op(e2, e1) = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | ALPHA: (8967) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | |   (8968)  op(e2, e1) = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8961), (8968), (function-axioms) are
% 155.92/23.49  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #79.
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | |   (8969)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 155.92/23.49  | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | BETA: splitting (8969) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | |   (8970)  all_56_8 = e0 & op(e1, e1) = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | ALPHA: (8970) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | |   (8971)  op(e1, e1) = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8879), (8971), (function-axioms) are
% 155.92/23.49  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | |   (8972)  all_56_14 = e0 & op(e0, e1) = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | ALPHA: (8972) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | |   (8973)  op(e0, e1) = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | |   (8974)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.92/23.49  | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.92/23.49  | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.92/23.49  | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | BETA: splitting (8974) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | |   (8975)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | ALPHA: (8975) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | | | |   (8976)  op(e3, e3) = e3
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (8976), (function-axioms) are
% 155.92/23.49  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | |   (8977)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | ALPHA: (8977) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | | | |   (8978)  op(e2, e2) = e2
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8964), (8978), (function-axioms) are
% 155.92/23.49  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | |   (8979)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.92/23.49  | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.92/23.49  | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.92/23.49  | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.92/23.49  | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.92/23.49  | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.92/23.49  | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | BETA: splitting (8979) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | |   (8980)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | ALPHA: (8980) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | | | |   (8981)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 155.92/23.49  | | | | | | | | | | | | | | | | | |   (8982)  (all_57_10 = e1 & op(e3, e3) = e1) | ( ~ (all_57_4
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | BETA: splitting (8981) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | |   (8983)  all_57_15 = e1 & op(e0, e0) = e1
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | ALPHA: (8983) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | |   (8984)  op(e0, e0) = e1
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8859), (8984), (function-axioms) are
% 155.92/23.49  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | |   (8985)   ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | | |           $i(all_57_8)
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | ALPHA: (8985) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | |   (8986)  op(e0, e1) = all_57_8
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | BETA: splitting (8982) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | |   (8987)  all_57_10 = e1 & op(e3, e3) = e1
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | ALPHA: (8987) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | |   (8988)  op(e3, e3) = e1
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7930), (8988), (function-axioms) are
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_57_8,
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (8973), (8986) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | |   (8989)  all_57_8 = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8859), (8981), (8989), (function-axioms) are
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #430.
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | |   (8990)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.92/23.49  | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.92/23.49  | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.92/23.49  | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | ALPHA: (8990) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | | | |   (8991)  op(e0, e0) = e0
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8859), (8991), (function-axioms) are
% 155.92/23.49  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | End of split
% 155.92/23.49  | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | |   (8992)  all_24_2 = e1
% 155.92/23.49  | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | COMBINE_EQS: (318), (8992) imply:
% 155.92/23.49  | | | | | | | | | | | | |   (8993)  all_4_2 = e1
% 155.92/23.49  | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | SIMP: (8993) implies:
% 155.92/23.49  | | | | | | | | | | | | |   (8994)  all_4_2 = e1
% 155.92/23.49  | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | REDUCE: (356), (8994) imply:
% 155.92/23.49  | | | | | | | | | | | | |   (8995)   ~ (all_52_7 = e1)
% 155.92/23.49  | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | REDUCE: (36), (8994) imply:
% 155.92/23.49  | | | | | | | | | | | | |   (8996)  op(e2, e2) = e1
% 155.92/23.49  | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.92/23.49  | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | |   (8997)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.92/23.49  | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.92/23.49  | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.92/23.49  | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.92/23.49  | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.92/23.49  | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.92/23.49  | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.92/23.49  | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.92/23.49  | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.92/23.49  | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (7930), (8996), (8997),
% 155.92/23.49  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.49  | | | | | | | | | | | | | |            #81.
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | Case 2:
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | |   (8998)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.92/23.49  | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.92/23.49  | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.92/23.49  | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.92/23.49  | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.92/23.49  | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.92/23.49  | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.92/23.49  | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.92/23.49  | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.92/23.49  | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.92/23.49  | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.92/23.49  | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.92/23.49  | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | BETA: splitting (8998) gives:
% 155.92/23.49  | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | |   (8999)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.92/23.49  | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 155.92/23.49  | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.92/23.49  | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.92/23.49  | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.92/23.49  | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 155.92/23.49  | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 155.92/23.49  | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | ALPHA: (8999) implies:
% 155.92/23.49  | | | | | | | | | | | | | | |   (9000)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 155.92/23.49  | | | | | | | | | | | | | | |               = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | |   (9001)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 155.92/23.49  | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | BETA: splitting (9001) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | |   (9002)  all_56_12 = e1 & op(e0, e3) = e1
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | ALPHA: (9002) implies:
% 155.92/23.49  | | | | | | | | | | | | | | | | |   (9003)  all_56_12 = e1
% 155.92/23.49  | | | | | | | | | | | | | | | | |   (9004)  op(e0, e3) = e1
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.92/23.49  | | | | | | | | | | | | | | | | | 
% 155.92/23.49  | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.49  | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | |   (9005)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | |             e1)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | BETA: splitting (9005) gives:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |   (9006)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | BETA: splitting (9006) gives:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |   (9007)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9007) gives:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |   (9008)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (7930), (8996), (9008),
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |            #88.
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |   (9009)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (8879), (8996), (9009),
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |            #800.
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |   (9010)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9010) gives:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |   (9011)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9011) gives:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |   (9012)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |           = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9012) implies:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |   (9013)  op(e0, e0) = e2
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (209), (8856), (8857),
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |            (9003), (9013), (function-axioms) are inconsistent
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #90.
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |   (9014)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9014) implies:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |   (9015)  op(e3, e0) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8858), (9015), (function-axioms) are
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |   (9016)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (8879), (8996), (9016),
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |            #793.
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |   (9017)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | |             e1)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | BETA: splitting (9017) gives:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |   (9018)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9018) gives:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |   (9019)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9019) gives:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |   (9020)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9020) implies:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |   (9021)  op(e0, e3) = e0
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9004), (9021), (function-axioms) are
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |   (9022)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9022) implies:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |   (9023)  op(e3, e3) = e3
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (9023), (function-axioms) are
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |   (9024)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7930), (9024), (function-axioms) are
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #87.
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.50  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |   (9025)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             e1)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9025) gives:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |   (9026)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (8873), (8879), (9026),
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |            #791.
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |   (9027)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (8859), (8873), (8879), (9027),
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |            #420.
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.51  | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | |   (9028)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.92/23.51  | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.92/23.51  | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.92/23.51  | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | BETA: splitting (9028) gives:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |   (9029)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | BETA: splitting (9029) gives:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |   (9030)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9030) gives:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |   (9031)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (7930), (8874), (9031),
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |            #86.
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |   (9032)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (8859), (8879), (9032),
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |            #453.
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |   (9033)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9033) gives:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |   (9034)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (8874), (8879), (9034),
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |            #983.
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |   (9035)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9035) gives:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |   (9036)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9036) implies:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |   (9037)  op(e0, e3) = e0
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9004), (9037), (function-axioms) are
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |   (9038)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (7930), (9038), (function-axioms) are
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #101.
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.51  | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.51  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |   (9039)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (9039) gives:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |   (9040)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9040) gives:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |   (9041)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9041) gives:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9042)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9042) implies:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9043)  op(e0, e0) = e2
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (209), (8856), (8857),
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |            (9003), (9043), (function-axioms) are inconsistent
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #90.
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9044)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9044) implies:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9045)  op(e2, e2) = e2
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8996), (9045), (function-axioms) are
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |   (9046)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (8876), (9004), (9046),
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | |            #393.
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | End of split
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | Case 2:
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | | 
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |   (9047)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.92/23.52  | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9047) gives:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |   (9048)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9048) gives:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9049)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9049) implies:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9050)  op(e0, e0) = e2
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (209), (8856), (8857),
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |            (9003), (9050), (function-axioms) are inconsistent
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #90.
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9051)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9051) implies:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9052)  op(e3, e3) = e3
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (9052), (function-axioms) are
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |   (9053)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9053) gives:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9054)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9054) implies:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9055)  op(e2, e2) = e2
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8996), (9055), (function-axioms) are
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |   (9056)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9056) gives:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | |   (9057)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9057) implies:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | |   (9058)  op(e1, e0) = e1
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8876), (9058), (function-axioms) are
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |   (9059)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9059) implies:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |   (9060)  op(e0, e0) = all_57_15
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |   (9061)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9061) gives:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |   (9062)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9062) gives:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (9063)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8879), (9004), (9063), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #251.
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (9064)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9064) gives:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9065)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9065) implies:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9066)  op(e0, e3) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9004), (9066), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9067)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9067) gives:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9068)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e2) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9068) implies:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9069)  op(e3, e0) = e3
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8858), (9069), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9070)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e2) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9070) implies:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9071)  op(e2, e2) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8996), (9071), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |   (9072)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9072) gives:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (9073)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9073) gives:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9074)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9074) implies:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9075)  op(e1, e1) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8879), (9075), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9076)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9076) gives:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9077)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9077) implies:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9078)  all_57_15 = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9060), (9078) imply:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9079)  op(e0, e0) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8859), (9079), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9080)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9080) implies:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9081)  all_57_8 = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8859), (9000), (9081), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #430.
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (9082)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9082) gives:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9083)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9083) gives:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9084)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e1) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9084) implies:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9085)  all_57_8 = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8859), (9000), (9085), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #430.
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9086)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e1) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9086) implies:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9087)  op(e1, e1) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8879), (9087), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9088)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8859), (9000), (9088), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #205.
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | |   (9089)  all_56_13 = e1 & op(e0, e2) = e1
% 155.96/23.53  | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8995), (9089), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #712.
% 155.96/23.53  | | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | |   (9090)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 155.96/23.53  | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 155.96/23.53  | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (8859), (8875), (9090),
% 155.96/23.53  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.96/23.53  | | | | | | | | | | | | | | | |            #431.
% 155.96/23.53  | | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | |   (9091)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.96/23.53  | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 155.96/23.53  | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.96/23.53  | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.96/23.53  | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.96/23.53  | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.96/23.53  | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 155.96/23.53  | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | ALPHA: (9091) implies:
% 155.96/23.53  | | | | | | | | | | | | | | |   (9092)  op(e0, e0) = e0
% 155.96/23.53  | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | | REF_CLOSE: (7), (8859), (9092), (function-axioms) are
% 155.96/23.53  | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 155.96/23.53  | | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | |   (9093)  all_54_10 = e0
% 155.96/23.53  | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | | REF_CLOSE: (336), (8861), (9093) are inconsistent by
% 155.96/23.53  | | | | | | | | | | | |            sub-proof #329.
% 155.96/23.53  | | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | | 
% 155.96/23.53  | | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | | 
% 155.96/23.53  | | | | | | | | |   (9094)  all_20_2 = e3
% 155.96/23.53  | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | COMBINE_EQS: (325), (9094) imply:
% 155.96/23.53  | | | | | | | | |   (9095)  all_10_2 = e3
% 155.96/23.53  | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | REDUCE: (45), (9095) imply:
% 155.96/23.53  | | | | | | | | |   (9096)  op(e1, e1) = e3
% 155.96/23.53  | | | | | | | | | 
% 155.96/23.53  | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (36), (135), (158), (170),
% 155.96/23.53  | | | | | | | | |            (191), (203), (238), (248), (272), (352), (356),
% 155.96/23.53  | | | | | | | | |            (7927), (7930), (8856), (8859), (9096),
% 155.96/23.53  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.96/23.53  | | | | | | | | |            #70.
% 155.96/23.53  | | | | | | | | | 
% 155.96/23.53  | | | | | | | | End of split
% 155.96/23.53  | | | | | | | | 
% 155.96/23.53  | | | | | | | Case 2:
% 155.96/23.53  | | | | | | | | 
% 155.96/23.53  | | | | | | | |   (9097)  all_22_2 = e0
% 155.96/23.53  | | | | | | | |   (9098)  ( ~ (all_22_0 = e2) & op(e0, e1) = all_22_0 &
% 155.96/23.53  | | | | | | | |             $i(all_22_0)) | ( ~ (all_22_1 = e3) & op(e0, e0) =
% 155.96/23.53  | | | | | | | |             all_22_1 & $i(all_22_1))
% 155.96/23.53  | | | | | | | | 
% 155.96/23.53  | | | | | | | | COMBINE_EQS: (251), (9097) imply:
% 155.96/23.53  | | | | | | | |   (9099)  all_10_2 = e0
% 155.96/23.53  | | | | | | | | 
% 155.96/23.53  | | | | | | | | SIMP: (9099) implies:
% 155.96/23.53  | | | | | | | |   (9100)  all_10_2 = e0
% 155.96/23.54  | | | | | | | | 
% 155.96/23.54  | | | | | | | | REDUCE: (366), (9100) imply:
% 155.96/23.54  | | | | | | | |   (9101)   ~ (all_52_11 = e0)
% 155.96/23.54  | | | | | | | | 
% 155.96/23.54  | | | | | | | | REDUCE: (45), (9100) imply:
% 155.96/23.54  | | | | | | | |   (9102)  op(e1, e1) = e0
% 155.96/23.54  | | | | | | | | 
% 155.96/23.54  | | | | | | | | BETA: splitting (238) gives:
% 155.96/23.54  | | | | | | | | 
% 155.96/23.54  | | | | | | | | Case 1:
% 155.96/23.54  | | | | | | | | | 
% 155.96/23.54  | | | | | | | | |   (9103)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3
% 155.96/23.54  | | | | | | | | |                 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.96/23.54  | | | | | | | | |                 op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.96/23.54  | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.96/23.54  | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.96/23.54  | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.96/23.54  | | | | | | | | |                 = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.96/23.54  | | | | | | | | |                 all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 &
% 155.96/23.54  | | | | | | | | |             op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 155.96/23.54  | | | | | | | | |                 e2) | ( ~ (all_57_1 = e3) & op(e3, e2) =
% 155.96/23.54  | | | | | | | | |                 all_57_1 & $i(all_57_1))) & ((all_57_14 = e2 &
% 155.96/23.54  | | | | | | | | |                 op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 155.96/23.54  | | | | | | | | |                 op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 155.96/23.54  | | | | | | | | |             ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~
% 155.96/23.54  | | | | | | | | |                 (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 155.96/23.54  | | | | | | | | |                 $i(all_57_7))))
% 155.96/23.54  | | | | | | | | | 
% 155.96/23.54  | | | | | | | | | BETA: splitting (9103) gives:
% 155.96/23.54  | | | | | | | | | 
% 155.96/23.54  | | | | | | | | | Case 1:
% 155.96/23.54  | | | | | | | | | | 
% 155.96/23.54  | | | | | | | | | |   (9104)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.96/23.54  | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.96/23.54  | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.96/23.54  | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.96/23.54  | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.96/23.54  | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.96/23.54  | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.96/23.54  | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.96/23.54  | | | | | | | | | | 
% 155.96/23.54  | | | | | | | | | | ALPHA: (9104) implies:
% 155.96/23.54  | | | | | | | | | |   (9105)  op(e3, e3) = e3
% 155.96/23.54  | | | | | | | | | | 
% 155.96/23.54  | | | | | | | | | | REF_CLOSE: (7), (7930), (9105), (function-axioms) are
% 155.96/23.54  | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.96/23.54  | | | | | | | | | | 
% 155.96/23.54  | | | | | | | | | Case 2:
% 155.96/23.54  | | | | | | | | | | 
% 155.96/23.54  | | | | | | | | | |   (9106)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.96/23.54  | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.96/23.54  | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.96/23.54  | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.96/23.54  | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.96/23.54  | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.96/23.54  | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.96/23.54  | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.96/23.54  | | | | | | | | | | 
% 155.96/23.54  | | | | | | | | | | REF_CLOSE: (9), (36), (125), (157), (158), (190), (191),
% 155.96/23.54  | | | | | | | | | |            (247), (248), (356), (8856), (8857), (8859),
% 155.96/23.54  | | | | | | | | | |            (9098), (9101), (9106), (function-axioms) are
% 155.96/23.54  | | | | | | | | | |            inconsistent by sub-proof #204.
% 155.96/23.54  | | | | | | | | | | 
% 155.96/23.54  | | | | | | | | | End of split
% 155.96/23.54  | | | | | | | | | 
% 155.96/23.54  | | | | | | | | Case 2:
% 155.96/23.54  | | | | | | | | | 
% 155.96/23.54  | | | | | | | | |   (9107)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1
% 155.96/23.54  | | | | | | | | |                 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 155.96/23.54  | | | | | | | | |                 op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.96/23.54  | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.96/23.54  | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.96/23.54  | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 155.96/23.54  | | | | | | | | |                 = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 155.96/23.54  | | | | | | | | |                 all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 &
% 155.96/23.54  | | | | | | | | |             op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 155.96/23.54  | | | | | | | | |                 e0) | ( ~ (all_57_9 = e3) & op(e3, e0) =
% 155.96/23.54  | | | | | | | | |                 all_57_9 & $i(all_57_9))) & ((all_57_12 = e0 &
% 155.96/23.54  | | | | | | | | |                 op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 155.96/23.54  | | | | | | | | |                 op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 155.96/23.54  | | | | | | | | |             ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~
% 155.96/23.54  | | | | | | | | |                 (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 155.96/23.54  | | | | | | | | |                 $i(all_57_13))))
% 155.96/23.54  | | | | | | | | | 
% 155.96/23.54  | | | | | | | | | REF_CLOSE: (4), (7), (8859), (9102), (9107), (function-axioms)
% 155.96/23.54  | | | | | | | | |            are inconsistent by sub-proof #411.
% 155.96/23.54  | | | | | | | | | 
% 155.96/23.54  | | | | | | | | End of split
% 155.96/23.54  | | | | | | | | 
% 155.96/23.54  | | | | | | | End of split
% 155.96/23.54  | | | | | | | 
% 155.96/23.54  | | | | | | End of split
% 155.96/23.54  | | | | | | 
% 155.96/23.54  | | | | | Case 2:
% 155.96/23.54  | | | | | | 
% 155.96/23.54  | | | | | |   (9108)  all_14_2 = e1
% 155.96/23.54  | | | | | | 
% 155.96/23.54  | | | | | | REDUCE: (351), (9108) imply:
% 155.96/23.54  | | | | | |   (9109)   ~ (all_52_3 = e1)
% 155.96/23.54  | | | | | | 
% 155.96/23.54  | | | | | | REDUCE: (362), (9108) imply:
% 155.96/23.54  | | | | | |   (9110)   ~ (all_52_7 = e1)
% 155.96/23.54  | | | | | | 
% 155.96/23.54  | | | | | | REDUCE: (370), (9108) imply:
% 155.96/23.54  | | | | | |   (9111)   ~ (all_52_12 = e1)
% 155.96/23.54  | | | | | | 
% 155.96/23.54  | | | | | | REDUCE: (371), (9108) imply:
% 155.96/23.54  | | | | | |   (9112)   ~ (all_52_13 = e1)
% 155.96/23.54  | | | | | | 
% 155.96/23.54  | | | | | | REDUCE: (51), (9108) imply:
% 155.96/23.54  | | | | | |   (9113)  op(e0, e0) = e1
% 155.96/23.54  | | | | | | 
% 155.96/23.54  | | | | | | BETA: splitting (7933) gives:
% 155.96/23.54  | | | | | | 
% 155.96/23.54  | | | | | | Case 1:
% 155.96/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | |   (9114)   ~ (all_8_0 = e2) & op(e0, e3) = all_8_0 & $i(all_8_0)
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | ALPHA: (9114) implies:
% 155.98/23.54  | | | | | | |   (9115)   ~ (all_8_0 = e2)
% 155.98/23.54  | | | | | | |   (9116)  op(e0, e3) = all_8_0
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 155.98/23.54  | | | | | | |              all_8_0, e3, e0, simplifying with (159), (9116)
% 155.98/23.54  | | | | | | |              gives:
% 155.98/23.54  | | | | | | |   (9117)  all_52_3 = all_8_0
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | COMBINE_EQS: (249), (9117) imply:
% 155.98/23.54  | | | | | | |   (9118)  all_54_12 = all_8_0
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | REDUCE: (148), (9117) imply:
% 155.98/23.54  | | | | | | |   (9119)   ~ (all_52_1 = all_8_0)
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | REDUCE: (144), (9117) imply:
% 155.98/23.54  | | | | | | |   (9120)   ~ (all_52_2 = all_8_0)
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | REDUCE: (140), (9117) imply:
% 155.98/23.54  | | | | | | |   (9121)   ~ (all_52_7 = all_8_0)
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | SIMP: (9121) implies:
% 155.98/23.54  | | | | | | |   (9122)   ~ (all_52_7 = all_8_0)
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | REDUCE: (139), (9117) imply:
% 155.98/23.54  | | | | | | |   (9123)   ~ (all_52_11 = all_8_0)
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | SIMP: (9123) implies:
% 155.98/23.54  | | | | | | |   (9124)   ~ (all_52_11 = all_8_0)
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | REDUCE: (9109), (9117) imply:
% 155.98/23.54  | | | | | | |   (9125)   ~ (all_8_0 = e1)
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | REDUCE: (7926), (9117) imply:
% 155.98/23.54  | | | | | | |   (9126)   ~ (all_8_0 = e0)
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | BETA: splitting (192) gives:
% 155.98/23.54  | | | | | | | 
% 155.98/23.54  | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | 
% 155.98/23.54  | | | | | | | |   (9127)  all_54_12 = e3
% 155.98/23.54  | | | | | | | | 
% 155.98/23.54  | | | | | | | | COMBINE_EQS: (9118), (9127) imply:
% 155.98/23.54  | | | | | | | |   (9128)  all_8_0 = e3
% 155.98/23.54  | | | | | | | | 
% 155.98/23.54  | | | | | | | | SIMP: (9128) implies:
% 155.98/23.54  | | | | | | | |   (9129)  all_8_0 = e3
% 155.98/23.54  | | | | | | | | 
% 155.98/23.54  | | | | | | | | REDUCE: (9119), (9129) imply:
% 155.98/23.54  | | | | | | | |   (9130)   ~ (all_52_1 = e3)
% 155.98/23.54  | | | | | | | | 
% 155.98/23.54  | | | | | | | | REDUCE: (9120), (9129) imply:
% 155.98/23.54  | | | | | | | |   (9131)   ~ (all_52_2 = e3)
% 155.98/23.54  | | | | | | | | 
% 155.98/23.54  | | | | | | | | REDUCE: (9122), (9129) imply:
% 155.98/23.54  | | | | | | | |   (9132)   ~ (all_52_7 = e3)
% 155.98/23.54  | | | | | | | | 
% 155.98/23.54  | | | | | | | | REDUCE: (9124), (9129) imply:
% 155.98/23.54  | | | | | | | |   (9133)   ~ (all_52_11 = e3)
% 155.98/23.54  | | | | | | | | 
% 155.98/23.54  | | | | | | | | BETA: splitting (235) gives:
% 155.98/23.54  | | | | | | | | 
% 155.98/23.54  | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | 
% 155.98/23.54  | | | | | | | | |   (9134)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 &
% 155.98/23.54  | | | | | | | | |             op(e2, e3) = e3)
% 155.98/23.54  | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | BETA: splitting (9134) gives:
% 155.98/23.54  | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | |   (9135)  all_56_0 = e3 & op(e3, e3) = e3
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | ALPHA: (9135) implies:
% 155.98/23.54  | | | | | | | | | |   (9136)  op(e3, e3) = e3
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | REF_CLOSE: (7), (7930), (9136), (function-axioms) are
% 155.98/23.54  | | | | | | | | | |            inconsistent by sub-proof #971.
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | |   (9137)  all_56_2 = e3 & op(e2, e3) = e3
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | ALPHA: (9137) implies:
% 155.98/23.54  | | | | | | | | | |   (9138)  all_56_2 = e3
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | BETA: splitting (233) gives:
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | |   (9139)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.98/23.54  | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | BETA: splitting (9139) gives:
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | |   (9140)  all_56_0 = e2 & op(e3, e3) = e2
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | ALPHA: (9140) implies:
% 155.98/23.54  | | | | | | | | | | | |   (9141)  op(e3, e3) = e2
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | REF_CLOSE: (5), (7930), (9141), (function-axioms) are
% 155.98/23.54  | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | |   (9142)  all_56_2 = e2 & op(e2, e3) = e2
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | REF_CLOSE: (9), (9138), (9142) are inconsistent by sub-proof
% 155.98/23.54  | | | | | | | | | | | |            #778.
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | End of split
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | |   (9143)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.98/23.54  | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | BETA: splitting (9143) gives:
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | |   (9144)  all_56_6 = e2 & op(e1, e3) = e2
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | ALPHA: (9144) implies:
% 155.98/23.54  | | | | | | | | | | | |   (9145)  all_56_6 = e2
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (159), (231), (7930), (9109),
% 155.98/23.54  | | | | | | | | | | | |            (9138), (9145), (function-axioms) are inconsistent
% 155.98/23.54  | | | | | | | | | | | |            by sub-proof #69.
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | |   (9146)  all_56_12 = e2 & op(e0, e3) = e2
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | ALPHA: (9146) implies:
% 155.98/23.54  | | | | | | | | | | | |   (9147)  all_56_12 = e2
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (209), (9113), (9132),
% 155.98/23.54  | | | | | | | | | | | |            (9133), (9147), (function-axioms) are inconsistent
% 155.98/23.54  | | | | | | | | | | | |            by sub-proof #68.
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | End of split
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | End of split
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | End of split
% 155.98/23.54  | | | | | | | | | 
% 155.98/23.54  | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | 
% 155.98/23.54  | | | | | | | | |   (9148)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3
% 155.98/23.54  | | | | | | | | |             & op(e0, e3) = e3)
% 155.98/23.54  | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | BETA: splitting (9148) gives:
% 155.98/23.54  | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | |   (9149)  all_56_6 = e3 & op(e1, e3) = e3
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | REF_CLOSE: (163), (9131), (9149), (function-axioms) are
% 155.98/23.54  | | | | | | | | | |            inconsistent by sub-proof #681.
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | |   (9150)  all_56_12 = e3 & op(e0, e3) = e3
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | ALPHA: (9150) implies:
% 155.98/23.54  | | | | | | | | | |   (9151)  all_56_12 = e3
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | BETA: splitting (61) gives:
% 155.98/23.54  | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | |   (9152)   ~ (all_20_2 = e3)
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | REDUCE: (325), (9152) imply:
% 155.98/23.54  | | | | | | | | | | |   (9153)   ~ (all_10_2 = e3)
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | BETA: splitting (64) gives:
% 155.98/23.54  | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | |   (9154)   ~ (all_22_2 = e0)
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | REDUCE: (251), (9154) imply:
% 155.98/23.54  | | | | | | | | | | | |   (9155)   ~ (all_10_2 = e0)
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | BETA: splitting (194) gives:
% 155.98/23.54  | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | |   (9156)  all_54_10 = e3
% 155.98/23.54  | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | REF_CLOSE: (336), (9153), (9156) are inconsistent by
% 155.98/23.54  | | | | | | | | | | | | |            sub-proof #361.
% 155.98/23.54  | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | |   (9157)   ~ (all_54_10 = e3)
% 155.98/23.54  | | | | | | | | | | | | |   (9158)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 155.98/23.54  | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | BETA: splitting (9158) gives:
% 155.98/23.54  | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | |   (9159)  all_54_10 = e2
% 155.98/23.54  | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | REF_CLOSE: (336), (7934), (9159) are inconsistent by
% 155.98/23.54  | | | | | | | | | | | | | |            sub-proof #360.
% 155.98/23.54  | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | |   (9160)  all_54_10 = e1 | all_54_10 = e0
% 155.98/23.54  | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | BETA: splitting (9160) gives:
% 155.98/23.54  | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | |   (9161)  all_54_10 = e1
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | COMBINE_EQS: (336), (9161) imply:
% 155.98/23.54  | | | | | | | | | | | | | | |   (9162)  all_10_2 = e1
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | SIMP: (9162) implies:
% 155.98/23.54  | | | | | | | | | | | | | | |   (9163)  all_10_2 = e1
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | REDUCE: (350), (9163) imply:
% 155.98/23.54  | | | | | | | | | | | | | | |   (9164)   ~ (all_52_2 = e1)
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | REDUCE: (361), (9163) imply:
% 155.98/23.54  | | | | | | | | | | | | | | |   (9165)   ~ (all_52_6 = e1)
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | REDUCE: (363), (9163) imply:
% 155.98/23.54  | | | | | | | | | | | | | | |   (9166)   ~ (all_52_8 = e1)
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | REDUCE: (366), (9163) imply:
% 155.98/23.54  | | | | | | | | | | | | | | |   (9167)   ~ (all_52_11 = e1)
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | REDUCE: (368), (9163) imply:
% 155.98/23.54  | | | | | | | | | | | | | | |   (9168)   ~ (all_52_14 = e1)
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | REDUCE: (9153), (9163) imply:
% 155.98/23.54  | | | | | | | | | | | | | | |   (9169)   ~ (e3 = e1)
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | REDUCE: (45), (9163) imply:
% 155.98/23.54  | | | | | | | | | | | | | | |   (9170)  op(e1, e1) = e1
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 155.98/23.54  | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | |   (9171)  all_54_8 = e3
% 155.98/23.54  | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9171) imply:
% 155.98/23.54  | | | | | | | | | | | | | | | |   (9172)  all_52_2 = e3
% 155.98/23.54  | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | REDUCE: (9131), (9172) imply:
% 155.98/23.54  | | | | | | | | | | | | | | | |   (9173)  $false
% 155.98/23.54  | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | CLOSE: (9173) is inconsistent.
% 155.98/23.54  | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | |   (9174)   ~ (all_54_8 = e3)
% 155.98/23.54  | | | | | | | | | | | | | | | |   (9175)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.98/23.54  | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | BETA: splitting (9175) gives:
% 155.98/23.54  | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | |   (9176)  all_54_8 = e2
% 155.98/23.54  | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9176) imply:
% 155.98/23.54  | | | | | | | | | | | | | | | | |   (9177)  all_52_2 = e2
% 155.98/23.54  | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | REDUCE: (149), (9177) imply:
% 155.98/23.54  | | | | | | | | | | | | | | | | |   (9178)   ~ (all_52_1 = e2)
% 155.98/23.54  | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | REDUCE: (143), (9177) imply:
% 155.98/23.54  | | | | | | | | | | | | | | | | |   (9179)   ~ (all_52_6 = e2)
% 155.98/23.54  | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | SIMP: (9179) implies:
% 155.98/23.54  | | | | | | | | | | | | | | | | |   (9180)   ~ (all_52_6 = e2)
% 155.98/23.54  | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | REDUCE: (141), (9177) imply:
% 155.98/23.54  | | | | | | | | | | | | | | | | |   (9181)   ~ (all_52_14 = e2)
% 155.98/23.54  | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | SIMP: (9181) implies:
% 155.98/23.54  | | | | | | | | | | | | | | | | |   (9182)   ~ (all_52_14 = e2)
% 155.98/23.54  | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | REDUCE: (9131), (9177) imply:
% 155.98/23.54  | | | | | | | | | | | | | | | | |   (9183)   ~ (e3 = e2)
% 155.98/23.54  | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 155.98/23.54  | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | |   (9184)  all_54_4 = e3
% 155.98/23.54  | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (9130), (9184) are inconsistent by
% 155.98/23.54  | | | | | | | | | | | | | | | | | |            sub-proof #931.
% 155.98/23.54  | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | |   (9185)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 155.98/23.54  | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | |   (9186)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 155.98/23.54  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (7930), (9178), (9186),
% 155.98/23.54  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.54  | | | | | | | | | | | | | | | | | | |            #67.
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | |   (9187)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 155.98/23.54  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (9187) gives:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | |   (9188)  all_56_6 = e2 & op(e1, e3) = e2
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | ALPHA: (9188) implies:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | |   (9189)  all_56_6 = e2
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | |   (9190)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9190) gives:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | |   (9191)  all_56_0 = e1 & op(e3, e3) = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9191) implies:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | |   (9192)  op(e3, e3) = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7930), (9192), (function-axioms) are
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | |   (9193)  all_56_1 = e1 & op(e3, e2) = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9193) implies:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | |   (9194)  all_56_1 = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | |   (9195)  op(e3, e2) = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | |   (9196)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9196) gives:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | |   (9197)  all_56_0 = e1 & op(e3, e3) = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9197) implies:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | |   (9198)  op(e3, e3) = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7930), (9198), (function-axioms) are
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | |   (9199)  all_56_2 = e1 & op(e2, e3) = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9199) implies:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | |   (9200)  all_56_2 = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | |   (9201)  op(e2, e3) = e1
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (9202)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9202) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9203)  all_56_1 = e3 & op(e3, e2) = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9203) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9204)  op(e3, e2) = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9195), (9204), (function-axioms) are
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #345.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9205)  all_56_3 = e3 & op(e2, e2) = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9205) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9206)  op(e2, e2) = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (9206), (function-axioms) are
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #711.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (9207)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9207) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9208)  all_56_7 = e3 & op(e1, e2) = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9208) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9209)  all_56_7 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9210)  op(e1, e2) = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9211)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9211) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9212)  all_56_6 = e0 & op(e1, e3) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7925), (9212), (function-axioms) are
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #699.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9213)  all_56_7 = e0 & op(e1, e2) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9209), (9213) are inconsistent by sub-proof
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #909.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9214)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9214) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9215)  all_56_8 = e0 & op(e1, e1) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9215) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9216)  op(e1, e1) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9170), (9216), (function-axioms) are
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9217)  all_56_11 = e0 & op(e1, e0) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9217) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9218)  op(e1, e0) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (9218) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9219)  all_52_14 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (9210) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9220)  all_52_6 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1,
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (9195) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9221)  all_52_4 = e1
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (9221) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9222)   ~ (all_52_7 = e1)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (9221) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9223)   ~ (all_4_2 = e1)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9223) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9224)   ~ (all_4_2 = e1)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (9220) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9225)   ~ (all_52_7 = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (9220) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9226)   ~ (all_4_2 = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (9219) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9227)   ~ (all_52_13 = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9182), (9219) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9228)   ~ (e2 = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9168), (9219) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9229)   ~ (e1 = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9230)   ~ (all_32_2 = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (9230) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9231)   ~ (all_4_2 = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9232)  all_54_5 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (373), (9232) are inconsistent by sub-proof
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #930.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9233)   ~ (all_54_5 = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9234)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9235)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9235) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9236)  all_56_2 = e0 & op(e2, e3) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7924), (9236), (function-axioms) are
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #80.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9237)  all_56_3 = e0 & op(e2, e2) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9237) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9238)  op(e2, e2) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9234) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9239)  all_54_5 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (9239) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9240)  all_4_2 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9240) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9241)  all_4_2 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (9241) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9242)  op(e2, e2) = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9238), (9242), (function-axioms) are
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9243)  all_54_5 = e1 | all_54_5 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (9224), (9231), (9243) are inconsistent by
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9244)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9244) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9245)  all_56_5 = e0 & op(e2, e1) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9245) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9246)  all_56_5 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9247)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (36), (159), (231), (373), (7930),
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9109), (9189), (9247), (function-axioms) are
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #66.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9248)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9248) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9249)  all_56_5 = e3 & op(e2, e1) = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9249) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9250)  all_56_5 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9246), (9250) are inconsistent by sub-proof
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #591.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9251)  all_56_10 = e3 & op(e2, e0) = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9251) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9252)  all_56_10 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9253)  op(e2, e0) = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9254)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9254) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9255)  all_56_1 = e0 & op(e3, e2) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (7927), (9255), (function-axioms) are
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #84.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9256)  all_56_3 = e0 & op(e2, e2) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9256) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9257)  op(e2, e2) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (222), (223), (9246),
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9252), (9253), (9257), (function-axioms) are
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #552.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9258)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9258) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9259)  all_56_7 = e0 & op(e1, e2) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9209), (9259) are inconsistent by sub-proof
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #909.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9260)  all_56_13 = e0 & op(e0, e2) = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9260) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9261)  all_56_13 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9262)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9262) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9263)  all_56_4 = e3 & op(e3, e1) = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9263) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9264)  all_56_4 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9265)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9265) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9266)  all_56_0 = e2 & op(e3, e3) = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9266) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9267)  op(e3, e3) = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7930), (9267), (function-axioms) are
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9268)  all_56_1 = e2 & op(e3, e2) = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9268) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9269)  all_56_1 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9194), (9269) are inconsistent by sub-proof
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #680.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9270)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9270) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9271)  all_56_4 = e2 & op(e3, e1) = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9271) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9272)  all_56_4 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9264), (9272) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9273)  e3 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9151), (9273) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9274)  all_56_12 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (209), (9113), (9132),
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9133), (9274), (function-axioms) are inconsistent
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #68.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9275)  all_56_9 = e2 & op(e3, e0) = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9275) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9276)  all_56_9 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9234) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9277)  all_54_5 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (9277) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9278)  all_4_2 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9278) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9279)  all_4_2 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (9279) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9280)   ~ (all_52_7 = e2)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (9279) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9281)   ~ (all_52_13 = e2)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (9279) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9282)  op(e2, e2) = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9283)  all_54_13 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (9132), (9283) are inconsistent by
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #385.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9284)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9284) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9285)  all_54_13 = e2
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (9280), (9285) are inconsistent by
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #505.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9286)   ~ (all_54_13 = e2)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9287)  all_54_13 = e1 | all_54_13 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9287) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9288)  all_54_13 = e1
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (9110), (9288) are inconsistent by
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #504.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9289)  all_54_13 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (9289) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9290)  all_52_7 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9290) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9291)  all_52_7 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (9291) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9292)   ~ (all_52_11 = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9292) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9293)   ~ (all_52_11 = e0)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9294)  all_54_14 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (9133), (9294) are inconsistent by
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #587.
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9295)   ~ (all_54_14 = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9296)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9297)  all_54_7 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (9297) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9298)  all_52_13 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9298) implies:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9299)  all_52_13 = e3
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (9299) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9300)   ~ (all_52_9 = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (9299) imply:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9301)   ~ (all_52_12 = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9302)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9302) gives:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9303)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.98/23.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9303) implies:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9304)  op(e3, e3) = e3
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (157), (165),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (206), (209), (210), (211), (224), (225),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (229), (231), (233), (268), (373),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9133), (9209), (9210), (9224), (9300), (9304),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #464.
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9305)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9305) implies:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9306)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9307)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (135), (140), (158), (159), (170),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (192), (203), (248), (249), (272), (352),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (356), (7926), (7927), (7930), (9109), (9113),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9115), (9116), (9282), (9306), (9307),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #64.
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9308)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9308) gives:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9309)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9309) implies:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9310)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9311)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9311) gives:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9312)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9312) gives:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9313)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (268), (269), (349), (373),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9185), (9224), (9282), (9313), (function-axioms)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #381.
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9314)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9314) gives:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9315)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (268), (269), (349), (373),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9185), (9224), (9282), (9315), (function-axioms)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #380.
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9316)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9316) gives:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9317)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9317) implies:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9318)  op(e2, e3) = e2
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (167), (199), (268), (269), (349), (373),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9185), (9224), (9282), (9318), (function-axioms)
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #926.
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9319)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (9168), (9209), (9210), (9310), (9319),
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #63.
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9320)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9320) gives:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9321)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9321) gives:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9322)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9322) gives:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9323)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9323) implies:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9324)  op(e0, e0) = e3
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (210), (211),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9252), (9324), (function-axioms) are inconsistent
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #466.
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9325)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9325) implies:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9326)  op(e3, e3) = e3
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (157), (165),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (206), (209), (210), (211), (224), (225),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (229), (231), (233), (268), (373),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9133), (9209), (9210), (9224), (9300), (9326),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #464.
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9327)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9327) gives:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9328)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9328) implies:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9329)  op(e2, e0) = e2
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9281), (9329), (function-axioms) are
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9330)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9330) implies:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9331)  op(e3, e3) = e1
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (9194), (9264), (9276),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9331), (function-axioms) are inconsistent by
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #62.
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9332)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9332) gives:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9333)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9333) gives:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9334)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9334) implies:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9335)  op(e1, e1) = e3
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (9168), (9209), (9210), (9335),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #457.
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9336)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9336) implies:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9337)  op(e2, e2) = e1
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (118), (165), (190), (221), (223),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (247), (9133), (9167), (9200), (9293),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9337), (function-axioms) are inconsistent by
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #61.
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9338)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9338) gives:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9339)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9339) implies:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9340)  op(e0, e1) = e0
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9293), (9340), (function-axioms) are
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9341)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (163), (213),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (9164), (9168), (9209), (9210),
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9341), (function-axioms) are inconsistent by
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #455.
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9342)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9342) gives:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9343)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9343) gives:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9344)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9344) gives:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9345)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9345) gives:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9346)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9346) implies:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9347)  op(e3, e3) = e1
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (9194), (9264), (9276),
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9347), (function-axioms) are inconsistent by
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #62.
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9348)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9348) implies:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9349)  op(e2, e2) = e1
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (118), (165), (190), (221), (223),
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (247), (9133), (9167), (9200), (9293),
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9349), (function-axioms) are inconsistent by
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #61.
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9350)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9350) gives:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9351)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9351) implies:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9352)  op(e1, e1) = e2
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9170), (9352), (function-axioms) are
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9353)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9353) implies:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9354)  op(e0, e1) = e0
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9293), (9354), (function-axioms) are
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9355)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9355) gives:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9356)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9170), (9210), (9356),
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #60.
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9357)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9357) gives:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9358)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9358) implies:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9359)  op(e0, e0) = e3
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (210), (211),
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9252), (9359), (function-axioms) are inconsistent
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #466.
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9360)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9360) gives:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9361)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9361) implies:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9362)  op(e3, e3) = e3
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (157), (165),
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (206), (209), (210), (211), (224), (225),
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (229), (231), (233), (268), (373),
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9133), (9209), (9210), (9224), (9300), (9362),
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #464.
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9363)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9363) implies:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9364)  op(e3, e3) = e1
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (9194), (9264), (9276),
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9364), (function-axioms) are inconsistent by
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #62.
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9365)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9365) gives:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9366)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9366) gives:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9367)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9367) gives:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9368)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9368) implies:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9369)  op(e0, e0) = e2
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9113), (9369), (function-axioms) are
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9370)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9370) implies:
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9371)  op(e2, e1) = e2
% 155.98/23.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (165), (247), (9167), (9293), (9296),
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9371), (function-axioms) are inconsistent by
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #584.
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9372)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9372) gives:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9373)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9373) implies:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9374)  op(e2, e2) = e1
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (118), (165), (190), (221), (223),
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (247), (9133), (9167), (9200), (9293),
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9374), (function-axioms) are inconsistent by
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #61.
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9375)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9375) implies:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9376)  op(e0, e0) = e3
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (210), (211),
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9252), (9376), (function-axioms) are inconsistent
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #466.
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9377)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9377) gives:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9378)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9378) gives:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9379)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9379) implies:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9380)  op(e0, e0) = e2
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9113), (9380), (function-axioms) are
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9381)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9381) implies:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9382)  op(e3, e3) = e3
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (157), (165),
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (206), (209), (210), (211), (224), (225),
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (229), (231), (233), (268), (373),
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9133), (9209), (9210), (9224), (9300), (9382),
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #464.
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9383)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9383) gives:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9384)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9384) implies:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9385)  op(e2, e0) = e2
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9281), (9385), (function-axioms) are
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9386)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9386) gives:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9387)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9387) implies:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9388)  op(e1, e0) = e1
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9218), (9388), (function-axioms) are
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #545.
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9389)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9389) implies:
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9390)  op(e0, e0) = all_57_15
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9391)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.98/23.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9391) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9392)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9392) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9393)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (164), (7926), (9170), (9281), (9393),
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #92.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9394)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (164), (168), (7926), (9281), (9301),
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9394), (function-axioms) are inconsistent by
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #73.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9395)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9395) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9396)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9396) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9397)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9397) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9398)  op(e1, e1) = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9170), (9398), (function-axioms) are
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9399)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9399) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9400)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9400) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9401)  all_57_15 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9390), (9401) imply:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9402)  op(e0, e0) = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (9113), (9402), (function-axioms) are
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9403)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9403) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9404)  op(e0, e1) = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9293), (9404), (function-axioms) are
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9405)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9405) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9406)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (9170), (9281), (9406),
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #862.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9407)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9293), (9407), (function-axioms) are
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9408)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9408) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9409)  op(e0, e0) = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (9113), (9409), (function-axioms) are
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9410)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (9112), (9227), (9281), (9410) are
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #235.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9411)  all_54_5 = e1 | all_54_5 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (9224), (9231), (9411) are inconsistent by
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9412)  all_56_5 = e3 & op(e2, e1) = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9412) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9413)  all_56_5 = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9246), (9413) are inconsistent by sub-proof
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #591.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9414)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9414) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9415)  all_56_8 = e3 & op(e1, e1) = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9415) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9416)  op(e1, e1) = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (9168), (9209), (9210), (9416),
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #457.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9417)  all_56_14 = e3 & op(e0, e1) = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9417) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9418)  all_56_14 = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9419)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9419) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9420)  all_56_12 = e2 & op(e0, e3) = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9420) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9421)  all_56_12 = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9151), (9421) are inconsistent by sub-proof
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #616.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9422)  all_56_13 = e2 & op(e0, e2) = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9422) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9423)  all_56_13 = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9261), (9423) imply:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9424)  e2 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (9424) imply:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9425)  $false
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9425) is inconsistent.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9426)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9426) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9427)  all_56_14 = e2 & op(e0, e1) = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9427) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9428)  all_56_14 = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9418), (9428) are inconsistent by sub-proof
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #723.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9429)  all_56_15 = e2 & op(e0, e0) = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9429) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9430)  op(e0, e0) = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9113), (9430), (function-axioms) are
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9431)  all_56_10 = e0 & op(e2, e0) = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9431) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9432)  all_56_10 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9433)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (36), (159), (231), (373), (7930),
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9109), (9189), (9433), (function-axioms) are
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #66.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9434)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9434) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9435)  all_56_5 = e3 & op(e2, e1) = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9435) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9436)  op(e2, e1) = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9234) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9437)  all_54_5 = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (9437) imply:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9438)  all_4_2 = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9438) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9439)  all_4_2 = e2
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (9439) imply:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9440)   ~ (all_52_13 = e2)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9441)  all_54_7 = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (9441) imply:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9442)  all_52_13 = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9442) implies:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9443)  all_52_13 = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (9443) imply:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9444)   ~ (all_52_9 = e3)
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9436), (9444), (function-axioms) are
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #763.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9445)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (9112), (9227), (9440), (9445) are
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #235.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9446)  all_54_5 = e1 | all_54_5 = e0
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (9224), (9231), (9446) are inconsistent by
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9447)  all_56_10 = e3 & op(e2, e0) = e3
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9432), (9447) are inconsistent by sub-proof
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #261.
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9448)  all_32_2 = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (9448) imply:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9449)  all_4_2 = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (9449) imply:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9450)   ~ (all_52_7 = e0)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (9449) imply:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9451)   ~ (e3 = e0)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (9449) imply:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9452)  op(e2, e2) = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9453)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9194), (9452), (9453),
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #192.
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9454)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9454) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9455)  all_56_7 = e2 & op(e1, e2) = e2
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (9180), (9455), (function-axioms) are
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9456)  all_56_13 = e2 & op(e0, e2) = e2
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9456) implies:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9457)  all_56_13 = e2
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9458)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9458) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9459)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9459) implies:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9460)  op(e3, e3) = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (209), (229),
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (9113), (9133), (9189), (9457), (9460),
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #59.
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9461)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9461) implies:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9462)  op(e2, e2) = e2
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9452), (9462), (function-axioms) are
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9463)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9463) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9464)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9464) implies:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9465)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9466)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9467)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9467) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9468)  all_56_4 = e0 & op(e3, e1) = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7928), (9468), (function-axioms) are
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #700.
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9469)  all_56_5 = e0 & op(e2, e1) = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9469) implies:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9470)  all_56_5 = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9471)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9471) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9472)  all_56_2 = e3 & op(e2, e3) = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9472) implies:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9473)  all_56_2 = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (159), (231), (7930), (9109),
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9189), (9473), (function-axioms) are inconsistent
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #69.
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9474)  all_56_3 = e3 & op(e2, e2) = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9474) implies:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9475)  op(e2, e2) = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9452), (9475), (function-axioms) are
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9476)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (222), (223),
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9452), (9470), (9476), (function-axioms) are
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9477)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9477) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9478)  all_56_8 = e0 & op(e1, e1) = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9478) implies:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9479)  op(e1, e1) = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9170), (9479), (function-axioms) are
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9480)  all_56_14 = e0 & op(e0, e1) = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9480) implies:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9481)  all_56_14 = e0
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9482)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9482) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9483)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9483) gives:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9484)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9178), (9484), (function-axioms) are
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 155.98/23.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9485)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9485) gives:
% 155.98/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9486)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9178), (9486), (function-axioms) are
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9487)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9487) gives:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9488)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9488) implies:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9489)  op(e2, e3) = e2
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9178), (9489), (function-axioms) are
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9490)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (9168), (9209), (9210), (9466), (9490),
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #63.
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9491)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9491) gives:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9492)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9492) gives:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9493)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9493) gives:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9494)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9494) implies:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9495)  op(e0, e0) = e3
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (207), (9151), (9457), (9481),
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9495), (function-axioms) are inconsistent by
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #58.
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9496)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e2) = e3
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9496) implies:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9497)  op(e3, e3) = e3
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (209), (229),
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (9113), (9133), (9189), (9457), (9497),
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #59.
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9498)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9498) gives:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9499)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9499) implies:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9500)  op(e3, e3) = e2
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7930), (9500), (function-axioms) are
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9501)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9501) implies:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9502)  op(e3, e3) = e1
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (9131), (9200), (9201), (9502),
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #75.
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9503)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9503) gives:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9504)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (213), (214),
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (9168), (9209), (9210), (9452), (9504),
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #444.
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9505)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9505) gives:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9506)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9506) implies:
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9507)  op(e1, e3) = e1
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9164), (9507), (function-axioms) are
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9508)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (163), (213),
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (9164), (9168), (9209), (9210),
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9508), (function-axioms) are inconsistent by
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #455.
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9509)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9509) gives:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9510)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9510) gives:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9511)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9511) gives:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9512)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9512) gives:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9513)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9513) implies:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9514)  op(e3, e3) = e1
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (9131), (9200), (9201), (9514),
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #75.
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9515)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9515) implies:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9516)  op(e2, e2) = e1
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9452), (9516), (function-axioms) are
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9517)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9517) gives:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9518)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9518) implies:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9519)  op(e1, e1) = e2
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9170), (9519), (function-axioms) are
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9520)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9520) implies:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9521)  op(e1, e2) = e1
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9210), (9521), (function-axioms) are
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9522)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9522) gives:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9523)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9170), (9210), (9523),
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #60.
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9524)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9524) gives:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9525)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9525) implies:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9526)  op(e0, e0) = e3
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (207), (9151), (9457), (9481),
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9526), (function-axioms) are inconsistent by
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #58.
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9527)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9527) gives:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9528)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9528) implies:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9529)  op(e3, e3) = e3
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (209), (229),
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (9113), (9133), (9189), (9457), (9529),
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #59.
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9530)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9530) implies:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9531)  op(e3, e3) = e1
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (9131), (9200), (9201), (9531),
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #75.
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9532)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.05/23.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9532) gives:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9533)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9533) gives:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9534)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9113), (9452), (9534),
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #343.
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9535)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9535) gives:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9536)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9536) implies:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9537)  op(e2, e2) = e1
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9452), (9537), (function-axioms) are
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9538)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9538) implies:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9539)  op(e0, e0) = e3
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (207), (9151), (9457), (9481),
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9539), (function-axioms) are inconsistent by
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #58.
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9540)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9540) gives:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9541)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9541) gives:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9542)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9542) implies:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9543)  op(e0, e0) = e2
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9113), (9543), (function-axioms) are
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9544)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9544) implies:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9545)  op(e3, e3) = e3
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (209), (229),
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (9113), (9133), (9189), (9457), (9545),
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #59.
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9546)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9546) gives:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9547)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9547) implies:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9548)  op(e2, e2) = e2
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9452), (9548), (function-axioms) are
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #942.
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9549)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9549) gives:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9550)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9550) implies:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9551)  op(e1, e0) = e1
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9218), (9551), (function-axioms) are
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #545.
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9552)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9552) implies:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9553)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9465) gives:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9554)  all_57_15 = e1 & op(e0, e0) = e1
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9554) implies:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9555)  all_57_15 = e1
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (158), (159), (226),
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (7926), (9170), (9194), (9209), (9210),
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9450), (9452), (9553), (9555),
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #57.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9556)   ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_8)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9556) implies:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9557)   ~ (all_57_8 = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9553) gives:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9558)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9558) gives:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9559)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (7926), (9170), (9559),
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #821.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9560)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (159), (7926), (9450), (9560),
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #98.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9561)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9561) gives:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9562)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9562) gives:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9563)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e1 & op(e0, e2) = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9563) implies:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9564)  op(e1, e1) = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9170), (9564), (function-axioms) are
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9565)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9565) gives:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9566)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e2) = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9566) implies:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9567)  op(e0, e2) = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9450), (9567), (function-axioms) are
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9568)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e1) = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9568) implies:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9569)  all_57_8 = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9557), (9569) imply:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9570)  $false
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9570) is inconsistent.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9571)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9571) gives:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9572)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9170), (9557), (9572), (function-axioms) are
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #808.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9573)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9573) gives:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9574)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 & 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9574) implies:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9575)  all_57_15 = e1
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (158), (159), (226),
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (7926), (9170), (9194), (9209), (9210),
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9450), (9452), (9553), (9575),
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #57.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9576)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9576) implies:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9577)  all_57_8 = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9557), (9577) imply:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9578)  $false
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9578) is inconsistent.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9579)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9579) implies:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9580)  op(e0, e0) = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (9113), (9580), (function-axioms) are
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9581)  all_56_13 = e3 & op(e0, e2) = e3
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9132), (9581), (function-axioms) are
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | |   (9582)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (9109), (9164), (9582),
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | |            #202.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | |   (9583)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9583) gives:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | |   (9584)  all_56_4 = e1 & op(e3, e1) = e1
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9166), (9584), (function-axioms) are
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #331.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | |   (9585)  all_56_9 = e1 & op(e3, e0) = e1
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9111), (9585), (function-axioms) are
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #851.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | |   (9586)  all_56_12 = e2 & op(e0, e3) = e2
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | ALPHA: (9586) implies:
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | |   (9587)  all_56_12 = e2
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (209), (9113), (9132),
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | |            (9133), (9587), (function-axioms) are inconsistent
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | |            by sub-proof #68.
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | |   (9588)  all_54_8 = e1 | all_54_8 = e0
% 156.05/23.65  | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7925), (9164), (9588) are inconsistent by
% 156.05/23.65  | | | | | | | | | | | | | | | | |            sub-proof #612.
% 156.05/23.65  | | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | |   (9589)  all_54_10 = e0
% 156.05/23.65  | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | | REF_CLOSE: (336), (9155), (9589) are inconsistent by
% 156.05/23.65  | | | | | | | | | | | | | | |            sub-proof #329.
% 156.05/23.65  | | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | |   (9590)  all_22_2 = e0
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | COMBINE_EQS: (251), (9590) imply:
% 156.05/23.65  | | | | | | | | | | | |   (9591)  all_10_2 = e0
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | SIMP: (9591) implies:
% 156.05/23.65  | | | | | | | | | | | |   (9592)  all_10_2 = e0
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | REDUCE: (361), (9592) imply:
% 156.05/23.65  | | | | | | | | | | | |   (9593)   ~ (all_52_6 = e0)
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | REDUCE: (9153), (9592) imply:
% 156.05/23.65  | | | | | | | | | | | |   (9594)   ~ (e3 = e0)
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | REDUCE: (7934), (9592) imply:
% 156.05/23.65  | | | | | | | | | | | |   (9595)   ~ (e2 = e0)
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | REDUCE: (45), (9592) imply:
% 156.05/23.65  | | | | | | | | | | | |   (9596)  op(e1, e1) = e0
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (128),
% 156.05/23.65  | | | | | | | | | | | |            (158), (162), (191), (195), (229), (231), (233),
% 156.05/23.65  | | | | | | | | | | | |            (238), (248), (258), (354), (356), (9110), (9113),
% 156.05/23.65  | | | | | | | | | | | |            (9151), (9593), (9596), (function-axioms) are
% 156.05/23.65  | | | | | | | | | | | |            inconsistent by sub-proof #56.
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | End of split
% 156.05/23.65  | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | Case 2:
% 156.05/23.65  | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | |   (9597)  all_20_2 = e3
% 156.05/23.65  | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | COMBINE_EQS: (325), (9597) imply:
% 156.05/23.65  | | | | | | | | | | |   (9598)  all_10_2 = e3
% 156.05/23.65  | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | SIMP: (9598) implies:
% 156.05/23.65  | | | | | | | | | | |   (9599)  all_10_2 = e3
% 156.05/23.65  | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | REDUCE: (45), (9599) imply:
% 156.05/23.65  | | | | | | | | | | |   (9600)  op(e1, e1) = e3
% 156.05/23.65  | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | BETA: splitting (238) gives:
% 156.05/23.65  | | | | | | | | | | | 
% 156.05/23.65  | | | | | | | | | | | Case 1:
% 156.05/23.65  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | |   (9601)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.05/23.66  | | | | | | | | | | | |                 e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 156.05/23.66  | | | | | | | | | | | |                 & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.05/23.66  | | | | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.05/23.66  | | | | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.05/23.66  | | | | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 156.05/23.66  | | | | | | | | | | | |                   e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 156.05/23.66  | | | | | | | | | | | |                   e3) = all_57_6 & $i(all_57_6)))) |
% 156.05/23.66  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.05/23.66  | | | | | | | | | | | |                 e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 156.05/23.66  | | | | | | | | | | | |                 & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.05/23.66  | | | | | | | | | | | |             ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.05/23.66  | | | | | | | | | | | |                 (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.05/23.66  | | | | | | | | | | | |                 $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 156.05/23.66  | | | | | | | | | | | |                   e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 156.05/23.66  | | | | | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | BETA: splitting (9601) gives:
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | |   (9602)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.05/23.66  | | | | | | | | | | | | |               e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 156.05/23.66  | | | | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.05/23.66  | | | | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.05/23.66  | | | | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.05/23.66  | | | | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 156.05/23.66  | | | | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 156.05/23.66  | | | | | | | | | | | | |               all_57_6 & $i(all_57_6)))
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | ALPHA: (9602) implies:
% 156.05/23.66  | | | | | | | | | | | | |   (9603)  op(e3, e3) = e3
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 156.05/23.66  | | | | | | | | | | | | |            (9151), (9603), (function-axioms) are inconsistent
% 156.05/23.66  | | | | | | | | | | | | |            by sub-proof #729.
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | Case 2:
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | |   (9604)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.05/23.66  | | | | | | | | | | | | |               e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 156.05/23.66  | | | | | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.05/23.66  | | | | | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.05/23.66  | | | | | | | | | | | | |               (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.05/23.66  | | | | | | | | | | | | |               $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 156.05/23.66  | | | | | | | | | | | | |               = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 156.05/23.66  | | | | | | | | | | | | |               all_57_7 & $i(all_57_7)))
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | ALPHA: (9604) implies:
% 156.05/23.66  | | | | | | | | | | | | |   (9605)  op(e2, e2) = e2
% 156.05/23.66  | | | | | | | | | | | | |   (9606)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7
% 156.05/23.66  | | | | | | | | | | | | |               = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))
% 156.05/23.66  | | | | | | | | | | | | |   (9607)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1
% 156.05/23.66  | | | | | | | | | | | | |               = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (135), (140), (158), (159), (170),
% 156.05/23.66  | | | | | | | | | | | | |            (191), (192), (203), (248), (249), (272), (352),
% 156.05/23.66  | | | | | | | | | | | | |            (356), (7926), (7927), (7930), (9109), (9113),
% 156.05/23.66  | | | | | | | | | | | | |            (9115), (9116), (9605), (9606), (9607),
% 156.05/23.66  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.66  | | | | | | | | | | | | |            #64.
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | End of split
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | Case 2:
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | |   (9608)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 156.05/23.66  | | | | | | | | | | | |                 e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 156.05/23.66  | | | | | | | | | | | |                 & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.05/23.66  | | | | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.05/23.66  | | | | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.05/23.66  | | | | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 156.05/23.66  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 156.05/23.66  | | | | | | | | | | | |                   e1) = all_57_8 & $i(all_57_8)))) |
% 156.05/23.66  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.05/23.66  | | | | | | | | | | | |                 e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 156.05/23.66  | | | | | | | | | | | |                 & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.05/23.66  | | | | | | | | | | | |             ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.05/23.66  | | | | | | | | | | | |                 (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.05/23.66  | | | | | | | | | | | |                 $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.05/23.66  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.05/23.66  | | | | | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (9113), (9600), (9608),
% 156.05/23.66  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.66  | | | | | | | | | | | |            #297.
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | End of split
% 156.05/23.66  | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | End of split
% 156.05/23.66  | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | End of split
% 156.05/23.66  | | | | | | | | | 
% 156.05/23.66  | | | | | | | | End of split
% 156.05/23.66  | | | | | | | | 
% 156.05/23.66  | | | | | | | Case 2:
% 156.05/23.66  | | | | | | | | 
% 156.05/23.66  | | | | | | | |   (9609)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.05/23.66  | | | | | | | | 
% 156.05/23.66  | | | | | | | | REF_CLOSE: (249), (7926), (9109), (9115), (9118), (9609) are
% 156.05/23.66  | | | | | | | |            inconsistent by sub-proof #65.
% 156.05/23.66  | | | | | | | | 
% 156.05/23.66  | | | | | | | End of split
% 156.05/23.66  | | | | | | | 
% 156.05/23.66  | | | | | | Case 2:
% 156.05/23.66  | | | | | | | 
% 156.05/23.66  | | | | | | |   (9610)   ~ (all_8_1 = e1) & op(e0, e0) = all_8_1 & $i(all_8_1)
% 156.05/23.66  | | | | | | | 
% 156.05/23.66  | | | | | | | REF_CLOSE: (9113), (9610), (function-axioms) are inconsistent by
% 156.05/23.66  | | | | | | |            sub-proof #55.
% 156.05/23.66  | | | | | | | 
% 156.05/23.66  | | | | | | End of split
% 156.05/23.66  | | | | | | 
% 156.05/23.66  | | | | | End of split
% 156.05/23.66  | | | | | 
% 156.05/23.66  | | | | Case 2:
% 156.05/23.66  | | | | | 
% 156.05/23.66  | | | | |   (9611)  all_10_2 = e2
% 156.05/23.66  | | | | | 
% 156.05/23.66  | | | | | REDUCE: (350), (9611) imply:
% 156.05/23.66  | | | | |   (9612)   ~ (all_52_2 = e2)
% 156.05/23.66  | | | | | 
% 156.05/23.66  | | | | | REDUCE: (363), (9611) imply:
% 156.05/23.66  | | | | |   (9613)   ~ (all_52_8 = e2)
% 156.05/23.66  | | | | | 
% 156.05/23.66  | | | | | REDUCE: (364), (9611) imply:
% 156.05/23.66  | | | | |   (9614)   ~ (all_52_9 = e2)
% 156.05/23.66  | | | | | 
% 156.05/23.66  | | | | | REDUCE: (45), (9611) imply:
% 156.05/23.66  | | | | |   (9615)  op(e1, e1) = e2
% 156.05/23.66  | | | | | 
% 156.05/23.66  | | | | | BETA: splitting (52) gives:
% 156.05/23.66  | | | | | 
% 156.05/23.66  | | | | | Case 1:
% 156.05/23.66  | | | | | | 
% 156.05/23.66  | | | | | |   (9616)   ~ (all_14_2 = e1)
% 156.05/23.66  | | | | | | 
% 156.05/23.66  | | | | | | BETA: splitting (58) gives:
% 156.05/23.66  | | | | | | 
% 156.05/23.66  | | | | | | Case 1:
% 156.05/23.66  | | | | | | | 
% 156.05/23.66  | | | | | | |   (9617)   ~ (all_18_2 = e3)
% 156.05/23.66  | | | | | | | 
% 156.05/23.66  | | | | | | | REDUCE: (301), (9617) imply:
% 156.05/23.66  | | | | | | |   (9618)   ~ (all_14_2 = e3)
% 156.05/23.66  | | | | | | | 
% 156.05/23.66  | | | | | | | BETA: splitting (67) gives:
% 156.05/23.66  | | | | | | | 
% 156.05/23.66  | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | 
% 156.05/23.66  | | | | | | | |   (9619)   ~ (all_24_2 = e1)
% 156.05/23.66  | | | | | | | | 
% 156.05/23.66  | | | | | | | | REDUCE: (318), (9619) imply:
% 156.05/23.66  | | | | | | | |   (9620)   ~ (all_4_2 = e1)
% 156.05/23.66  | | | | | | | | 
% 156.05/23.66  | | | | | | | | BETA: splitting (73) gives:
% 156.05/23.66  | | | | | | | | 
% 156.05/23.66  | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | 
% 156.05/23.66  | | | | | | | | |   (9621)   ~ (all_28_2 = e2)
% 156.05/23.66  | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | REDUCE: (330), (9621) imply:
% 156.05/23.66  | | | | | | | | |   (9622)   ~ (all_14_2 = e2)
% 156.05/23.66  | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | BETA: splitting (189) gives:
% 156.05/23.66  | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | |   (9623)  all_54_15 = e3
% 156.05/23.66  | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | COMBINE_EQS: (246), (9623) imply:
% 156.05/23.66  | | | | | | | | | |   (9624)  all_14_2 = e3
% 156.05/23.66  | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | REDUCE: (9618), (9624) imply:
% 156.05/23.66  | | | | | | | | | |   (9625)  $false
% 156.05/23.66  | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | CLOSE: (9625) is inconsistent.
% 156.05/23.66  | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | Case 2:
% 156.05/23.66  | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | |   (9626)   ~ (all_54_15 = e3)
% 156.05/23.66  | | | | | | | | | |   (9627)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.05/23.66  | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | BETA: splitting (9627) gives:
% 156.05/23.66  | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | |   (9628)  all_54_15 = e2
% 156.05/23.66  | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | COMBINE_EQS: (246), (9628) imply:
% 156.05/23.66  | | | | | | | | | | |   (9629)  all_14_2 = e2
% 156.05/23.66  | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | REDUCE: (9622), (9629) imply:
% 156.05/23.66  | | | | | | | | | | |   (9630)  $false
% 156.05/23.66  | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | CLOSE: (9630) is inconsistent.
% 156.05/23.66  | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | Case 2:
% 156.05/23.66  | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | |   (9631)   ~ (all_54_15 = e2)
% 156.05/23.66  | | | | | | | | | | |   (9632)  all_54_15 = e1 | all_54_15 = e0
% 156.05/23.66  | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | BETA: splitting (9632) gives:
% 156.05/23.66  | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | |   (9633)  all_54_15 = e1
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | COMBINE_EQS: (246), (9633) imply:
% 156.05/23.66  | | | | | | | | | | | |   (9634)  all_14_2 = e1
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | REDUCE: (9616), (9634) imply:
% 156.05/23.66  | | | | | | | | | | | |   (9635)  $false
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | CLOSE: (9635) is inconsistent.
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | Case 2:
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | |   (9636)  all_54_15 = e0
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | COMBINE_EQS: (246), (9636) imply:
% 156.05/23.66  | | | | | | | | | | | |   (9637)  all_14_2 = e0
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | REDUCE: (362), (9637) imply:
% 156.05/23.66  | | | | | | | | | | | |   (9638)   ~ (all_52_7 = e0)
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | REDUCE: (369), (9637) imply:
% 156.05/23.66  | | | | | | | | | | | |   (9639)   ~ (all_52_11 = e0)
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | REDUCE: (9618), (9637) imply:
% 156.05/23.66  | | | | | | | | | | | |   (9640)   ~ (e3 = e0)
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | REDUCE: (9622), (9637) imply:
% 156.05/23.66  | | | | | | | | | | | |   (9641)   ~ (e2 = e0)
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | REDUCE: (9616), (9637) imply:
% 156.05/23.66  | | | | | | | | | | | |   (9642)   ~ (e1 = e0)
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | BETA: splitting (206) gives:
% 156.05/23.66  | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | |   (9643)  all_56_15 = e0 & op(e0, e0) = e0
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | ALPHA: (9643) implies:
% 156.05/23.66  | | | | | | | | | | | | |   (9644)  all_56_15 = e0
% 156.05/23.66  | | | | | | | | | | | | |   (9645)  op(e0, e0) = e0
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | BETA: splitting (213) gives:
% 156.05/23.66  | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | |   (9646)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 156.05/23.66  | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 156.05/23.66  | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | BETA: splitting (9646) gives:
% 156.05/23.66  | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | |   (9647)  all_56_6 = e0 & op(e1, e3) = e0
% 156.05/23.66  | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | REF_CLOSE: (163), (7925), (9647), (function-axioms) are
% 156.05/23.66  | | | | | | | | | | | | | | |            inconsistent by sub-proof #699.
% 156.05/23.66  | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | Case 2:
% 156.05/23.66  | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | |   (9648)  all_56_7 = e0 & op(e1, e2) = e0
% 156.05/23.66  | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | ALPHA: (9648) implies:
% 156.05/23.66  | | | | | | | | | | | | | | |   (9649)  op(e1, e2) = e0
% 156.05/23.66  | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 156.05/23.66  | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | |   (9650)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 156.05/23.66  | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 156.05/23.66  | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | BETA: splitting (9650) gives:
% 156.05/23.66  | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | |   (9651)  all_56_4 = e0 & op(e3, e1) = e0
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7928), (9651), (function-axioms) are
% 156.05/23.66  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #700.
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | |   (9652)  all_56_5 = e0 & op(e2, e1) = e0
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | ALPHA: (9652) implies:
% 156.05/23.66  | | | | | | | | | | | | | | | | |   (9653)  op(e2, e1) = e0
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 156.05/23.66  | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (9649) gives:
% 156.05/23.66  | | | | | | | | | | | | | | | | |   (9654)  all_52_6 = e0
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 156.05/23.66  | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (9653) gives:
% 156.05/23.66  | | | | | | | | | | | | | | | | |   (9655)  all_52_9 = e0
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | REDUCE: (128), (9654) imply:
% 156.05/23.66  | | | | | | | | | | | | | | | | |   (9656)   ~ (all_52_7 = e0)
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | REDUCE: (118), (9655) imply:
% 156.05/23.66  | | | | | | | | | | | | | | | | |   (9657)   ~ (all_52_11 = e0)
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | REDUCE: (358), (9655) imply:
% 156.05/23.66  | | | | | | | | | | | | | | | | |   (9658)   ~ (all_4_2 = e0)
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | SIMP: (9658) implies:
% 156.05/23.66  | | | | | | | | | | | | | | | | |   (9659)   ~ (all_4_2 = e0)
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 156.05/23.66  | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.66  | | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | |   (9660)  all_54_5 = e3
% 156.05/23.66  | | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (9660) imply:
% 156.05/23.66  | | | | | | | | | | | | | | | | | |   (9661)  all_4_2 = e3
% 156.05/23.66  | | | | | | | | | | | | | | | | | | 
% 156.05/23.66  | | | | | | | | | | | | | | | | | | REDUCE: (373), (9661) imply:
% 156.05/23.67  | | | | | | | | | | | | | | | | | |   (9662)  $false
% 156.05/23.67  | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | CLOSE: (9662) is inconsistent.
% 156.05/23.67  | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | |   (9663)   ~ (all_54_5 = e3)
% 156.05/23.67  | | | | | | | | | | | | | | | | | |   (9664)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 156.05/23.67  | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | BETA: splitting (9664) gives:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | |   (9665)  all_54_5 = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (9665) imply:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | |   (9666)  all_4_2 = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | REDUCE: (349), (9666) imply:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | |   (9667)   ~ (all_52_1 = e2)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | REDUCE: (360), (9666) imply:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | |   (9668)   ~ (all_52_13 = e2)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (9666) imply:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | |   (9669)   ~ (e3 = e2)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (9666) imply:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | |   (9670)  op(e2, e2) = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | |   (9671)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (7930), (9667), (9671),
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | |            #67.
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | |   (9672)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9672) gives:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | |   (9673)  all_56_6 = e2 & op(e1, e3) = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9612), (9673), (function-axioms) are
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | |   (9674)  all_56_12 = e2 & op(e0, e3) = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9674) implies:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | |   (9675)  op(e0, e3) = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |   (9676)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | |             e1)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9676) gives:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |   (9677)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9677) gives:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |   (9678)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9667), (9678), (function-axioms) are
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |   (9679)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_12))
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9679) gives:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (9680)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9667), (9680), (function-axioms) are
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (9681)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9681) gives:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9682)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9682) implies:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9683)  op(e2, e3) = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9667), (9683), (function-axioms) are
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9684)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9684) gives:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9685)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9685) implies:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9686)  op(e1, e1) = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9615), (9686), (function-axioms) are
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9687)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9687) implies:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9688)  op(e2, e1) = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (9670), (9688),
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |   (9689)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.05/23.67  | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9689) gives:
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |   (9690)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9690) gives:
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (9691)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3)
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (9645), (9691), (function-axioms) are
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #105.
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (9692)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (7930), (9668), (9692),
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |            #104.
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |   (9693)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9693) gives:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (9694)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9694) gives:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9695)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9695) implies:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9696)  op(e1, e1) = e3
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9615), (9696), (function-axioms) are
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9697)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9697) implies:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9698)  op(e2, e2) = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (268), (9620), (9664), (9698),
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            #691.
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (9699)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             e1)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (9615), (9645), (9699),
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |            #108.
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |   (9700)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9700) gives:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |   (9701)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9701) gives:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |   (9702)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9702) gives:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (9703)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9703) gives:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9704)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9704) implies:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9705)  op(e3, e3) = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7930), (9705), (function-axioms) are
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9706)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9706) implies:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9707)  op(e2, e2) = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (268), (9620), (9664), (9707),
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            #691.
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (9708)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9708) gives:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9709)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9709) implies:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9710)  op(e2, e1) = e2
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (9670), (9710),
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9711)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9711) implies:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9712)  op(e0, e0) = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (9645), (9712), (function-axioms) are
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |   (9713)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9713) gives:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (9714)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1)
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9615), (9668), (9714), (function-axioms)
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #198.
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (9715)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (7930), (9645), (9715),
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |            #100.
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |   (9716)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9716) gives:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |   (9717)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9717) gives:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (9718)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2)
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9718) gives:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9719)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9719) implies:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9720)  op(e0, e0) = e2
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9645), (9720), (function-axioms) are
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9721)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e1) = e2
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9721) implies:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9722)  op(e2, e1) = e2
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (9670), (9722),
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (9723)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (268), (9620), (9645), (9664), (9723),
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |            #221.
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |   (9724)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9724) gives:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (9725)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3)
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7930), (9645), (9725), (function-axioms) are
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #83.
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (9726)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9726) gives:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9727)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9727) implies:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9728)  op(e2, e0) = e2
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9668), (9728), (function-axioms) are
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9729)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0)))
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9729) gives:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9730)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9730) implies:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9731)  op(e1, e1) = e1
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9615), (9731), (function-axioms) are
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9732)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0))
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9732) implies:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9733)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9733) gives:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9734)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9734) gives:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9735)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (164), (9615), (9668), (9675), (9735),
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #168.
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9736)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9736) gives:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9737)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9737) implies:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9738)  op(e0, e3) = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (9675), (9738), (function-axioms) are
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #689.
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9739)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9739) gives:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9740)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e2) = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9740) implies:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9741)  op(e0, e2) = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9638), (9741), (function-axioms) are
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9742)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e2) = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9742) implies:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9743)  op(e2, e0) = e2
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9668), (9743), (function-axioms) are
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9744)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (158), (164), (9615), (9638), (9639),
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9668), (9744), (function-axioms) are inconsistent
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #163.
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | |   (9745)  all_54_5 = e1 | all_54_5 = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (9620), (9659), (9745) are inconsistent by
% 156.11/23.70  | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 156.11/23.70  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | |   (9746)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 156.11/23.70  | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 156.11/23.70  | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | BETA: splitting (9746) gives:
% 156.11/23.70  | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | |   (9747)  all_56_8 = e0 & op(e1, e1) = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | ALPHA: (9747) implies:
% 156.11/23.70  | | | | | | | | | | | | | | | | |   (9748)  op(e1, e1) = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9615), (9748), (function-axioms) are
% 156.11/23.70  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 156.11/23.70  | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | |   (9749)  all_56_14 = e0 & op(e0, e1) = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | ALPHA: (9749) implies:
% 156.11/23.70  | | | | | | | | | | | | | | | | |   (9750)  op(e0, e1) = e0
% 156.11/23.70  | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9639), (9750), (function-axioms) are
% 156.11/23.70  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 156.11/23.70  | | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | |   (9751)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 156.11/23.70  | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 156.11/23.70  | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (210), (211), (212),
% 156.11/23.70  | | | | | | | | | | | | | |            (9615), (9644), (9645), (9751), (function-axioms)
% 156.11/23.70  | | | | | | | | | | | | | |            are inconsistent by sub-proof #159.
% 156.11/23.70  | | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | |   (9752)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 156.11/23.70  | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 156.11/23.70  | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 156.11/23.70  | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 156.11/23.70  | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | ALPHA: (9752) implies:
% 156.11/23.70  | | | | | | | | | | | | |   (9753)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 156.11/23.70  | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 156.11/23.70  | | | | | | | | | | | | |               e1) = e0)
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (7926), (9638), (9639),
% 156.11/23.70  | | | | | | | | | | | | |            (9753), (function-axioms) are inconsistent by
% 156.11/23.70  | | | | | | | | | | | | |            sub-proof #881.
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.70  | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.70  | | | | | | | | |   (9754)  all_28_2 = e2
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | COMBINE_EQS: (330), (9754) imply:
% 156.11/23.70  | | | | | | | | |   (9755)  all_14_2 = e2
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | SIMP: (9755) implies:
% 156.11/23.70  | | | | | | | | |   (9756)  all_14_2 = e2
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | REDUCE: (351), (9756) imply:
% 156.11/23.70  | | | | | | | | |   (9757)   ~ (all_52_3 = e2)
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | REDUCE: (370), (9756) imply:
% 156.11/23.70  | | | | | | | | |   (9758)   ~ (all_52_12 = e2)
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | REDUCE: (51), (9756) imply:
% 156.11/23.70  | | | | | | | | |   (9759)  op(e0, e0) = e2
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | BETA: splitting (233) gives:
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | |   (9760)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 156.11/23.70  | | | | | | | | | |             & op(e2, e3) = e2)
% 156.11/23.70  | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | BETA: splitting (9760) gives:
% 156.11/23.70  | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | |   (9761)  all_56_0 = e2 & op(e3, e3) = e2
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | ALPHA: (9761) implies:
% 156.11/23.70  | | | | | | | | | | |   (9762)  op(e3, e3) = e2
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | REF_CLOSE: (5), (7930), (9762), (function-axioms) are
% 156.11/23.70  | | | | | | | | | | |            inconsistent by sub-proof #281.
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | |   (9763)  all_56_2 = e2 & op(e2, e3) = e2
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | ALPHA: (9763) implies:
% 156.11/23.70  | | | | | | | | | | |   (9764)  op(e2, e3) = e2
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | BETA: splitting (234) gives:
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | |   (9765)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 156.11/23.70  | | | | | | | | | | | |             & op(e3, e2) = e2)
% 156.11/23.70  | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | BETA: splitting (9765) gives:
% 156.11/23.70  | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | |   (9766)  all_56_0 = e2 & op(e3, e3) = e2
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | ALPHA: (9766) implies:
% 156.11/23.70  | | | | | | | | | | | | |   (9767)  op(e3, e3) = e2
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | REF_CLOSE: (5), (7930), (9767), (function-axioms) are
% 156.11/23.70  | | | | | | | | | | | | |            inconsistent by sub-proof #281.
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | |   (9768)  all_56_1 = e2 & op(e3, e2) = e2
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | ALPHA: (9768) implies:
% 156.11/23.70  | | | | | | | | | | | | |   (9769)  op(e3, e2) = e2
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (167), (170), (199), (238), (268),
% 156.11/23.70  | | | | | | | | | | | | |            (352), (373), (9615), (9620), (9759), (9764),
% 156.11/23.70  | | | | | | | | | | | | |            (9769), (function-axioms) are inconsistent by
% 156.11/23.70  | | | | | | | | | | | | |            sub-proof #182.
% 156.11/23.70  | | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | |   (9770)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 156.11/23.70  | | | | | | | | | | | |             & op(e3, e0) = e2)
% 156.11/23.70  | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | | REF_CLOSE: (168), (169), (9613), (9758), (9770),
% 156.11/23.70  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.70  | | | | | | | | | | | |            #511.
% 156.11/23.70  | | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | |   (9771)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 156.11/23.70  | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 156.11/23.70  | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | BETA: splitting (9771) gives:
% 156.11/23.70  | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | |   (9772)  all_56_6 = e2 & op(e1, e3) = e2
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | REF_CLOSE: (163), (9612), (9772), (function-axioms) are
% 156.11/23.70  | | | | | | | | | | |            inconsistent by sub-proof #761.
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | |   (9773)  all_56_12 = e2 & op(e0, e3) = e2
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | | REF_CLOSE: (159), (9757), (9773), (function-axioms) are
% 156.11/23.70  | | | | | | | | | | |            inconsistent by sub-proof #858.
% 156.11/23.70  | | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | | 
% 156.11/23.70  | | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.70  | | | | | | | | End of split
% 156.11/23.70  | | | | | | | | 
% 156.11/23.70  | | | | | | | Case 2:
% 156.11/23.70  | | | | | | | | 
% 156.11/23.70  | | | | | | | |   (9774)  all_24_2 = e1
% 156.11/23.70  | | | | | | | | 
% 156.11/23.70  | | | | | | | | COMBINE_EQS: (318), (9774) imply:
% 156.11/23.70  | | | | | | | |   (9775)  all_4_2 = e1
% 156.11/23.70  | | | | | | | | 
% 156.11/23.70  | | | | | | | | REDUCE: (354), (9775) imply:
% 156.11/23.70  | | | | | | | |   (9776)   ~ (all_52_6 = e1)
% 156.11/23.70  | | | | | | | | 
% 156.11/23.70  | | | | | | | | REDUCE: (360), (9775) imply:
% 156.11/23.70  | | | | | | | |   (9777)   ~ (all_52_13 = e1)
% 156.11/23.70  | | | | | | | | 
% 156.11/23.70  | | | | | | | | REDUCE: (373), (9775) imply:
% 156.11/23.70  | | | | | | | |   (9778)   ~ (e3 = e1)
% 156.11/23.70  | | | | | | | | 
% 156.11/23.70  | | | | | | | | REDUCE: (36), (9775) imply:
% 156.11/23.70  | | | | | | | |   (9779)  op(e2, e2) = e1
% 156.11/23.70  | | | | | | | | 
% 156.11/23.70  | | | | | | | | BETA: splitting (238) gives:
% 156.11/23.70  | | | | | | | | 
% 156.11/23.70  | | | | | | | | Case 1:
% 156.11/23.70  | | | | | | | | | 
% 156.11/23.71  | | | | | | | | |   (9780)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3
% 156.11/23.71  | | | | | | | | |                 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 156.11/23.71  | | | | | | | | |                 op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.11/23.71  | | | | | | | | |             ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.11/23.71  | | | | | | | | |                 (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.11/23.71  | | | | | | | | |                 $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 156.11/23.71  | | | | | | | | |                 = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 156.11/23.71  | | | | | | | | |                 all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 &
% 156.11/23.71  | | | | | | | | |             op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 156.11/23.71  | | | | | | | | |                 e2) | ( ~ (all_57_1 = e3) & op(e3, e2) =
% 156.11/23.71  | | | | | | | | |                 all_57_1 & $i(all_57_1))) & ((all_57_14 = e2 &
% 156.11/23.71  | | | | | | | | |                 op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 156.11/23.71  | | | | | | | | |                 op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 156.11/23.71  | | | | | | | | |             ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~
% 156.11/23.71  | | | | | | | | |                 (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 156.11/23.71  | | | | | | | | |                 $i(all_57_7))))
% 156.11/23.71  | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | REF_CLOSE: (6), (7), (7930), (9779), (9780), (function-axioms)
% 156.11/23.71  | | | | | | | | |            are inconsistent by sub-proof #81.
% 156.11/23.71  | | | | | | | | | 
% 156.11/23.71  | | | | | | | | Case 2:
% 156.11/23.71  | | | | | | | | | 
% 156.11/23.71  | | | | | | | | |   (9781)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1
% 156.11/23.71  | | | | | | | | |                 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 156.11/23.71  | | | | | | | | |                 op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.11/23.71  | | | | | | | | |             ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.11/23.71  | | | | | | | | |                 (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.11/23.71  | | | | | | | | |                 $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 156.11/23.71  | | | | | | | | |                 = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 156.11/23.71  | | | | | | | | |                 all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 &
% 156.11/23.71  | | | | | | | | |             op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 156.11/23.71  | | | | | | | | |                 e0) | ( ~ (all_57_9 = e3) & op(e3, e0) =
% 156.11/23.71  | | | | | | | | |                 all_57_9 & $i(all_57_9))) & ((all_57_12 = e0 &
% 156.11/23.71  | | | | | | | | |                 op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 156.11/23.71  | | | | | | | | |                 op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 156.11/23.71  | | | | | | | | |             ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~
% 156.11/23.71  | | | | | | | | |                 (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 156.11/23.71  | | | | | | | | |                 $i(all_57_13))))
% 156.11/23.71  | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | BETA: splitting (9781) gives:
% 156.11/23.71  | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | Case 1:
% 156.11/23.71  | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | |   (9782)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 156.11/23.71  | | | | | | | | | |               e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 156.11/23.71  | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.11/23.71  | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.11/23.71  | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.11/23.71  | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 156.11/23.71  | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 156.11/23.71  | | | | | | | | | |               all_57_8 & $i(all_57_8)))
% 156.11/23.71  | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | ALPHA: (9782) implies:
% 156.11/23.71  | | | | | | | | | |   (9783)  op(e1, e1) = e1
% 156.11/23.71  | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | REF_CLOSE: (6), (9615), (9783), (function-axioms) are
% 156.11/23.71  | | | | | | | | | |            inconsistent by sub-proof #986.
% 156.11/23.71  | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | Case 2:
% 156.11/23.71  | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | |   (9784)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.11/23.71  | | | | | | | | | |               e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 156.11/23.71  | | | | | | | | | |               op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.11/23.71  | | | | | | | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.11/23.71  | | | | | | | | | |               (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.11/23.71  | | | | | | | | | |               $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.11/23.71  | | | | | | | | | |                 e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.11/23.71  | | | | | | | | | |                 e0) = all_57_13 & $i(all_57_13)))
% 156.11/23.71  | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | ALPHA: (9784) implies:
% 156.11/23.71  | | | | | | | | | |   (9785)  all_57_15 = e0
% 156.11/23.71  | | | | | | | | | |   (9786)  op(e0, e0) = e0
% 156.11/23.71  | | | | | | | | | |   (9787)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.11/23.71  | | | | | | | | | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.11/23.71  | | | | | | | | | |             $i(all_57_11))
% 156.11/23.71  | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | BETA: splitting (9787) gives:
% 156.11/23.71  | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | Case 1:
% 156.11/23.71  | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | |   (9788)  all_57_12 = e0 & op(e2, e2) = e0
% 156.11/23.71  | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | ALPHA: (9788) implies:
% 156.11/23.71  | | | | | | | | | | |   (9789)  op(e2, e2) = e0
% 156.11/23.71  | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | REF_CLOSE: (4), (9779), (9789), (function-axioms) are
% 156.11/23.71  | | | | | | | | | | |            inconsistent by sub-proof #960.
% 156.11/23.71  | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | Case 2:
% 156.11/23.71  | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | |   (9790)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.11/23.71  | | | | | | | | | | |           $i(all_57_11)
% 156.11/23.71  | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | ALPHA: (9790) implies:
% 156.11/23.71  | | | | | | | | | | |   (9791)   ~ (all_57_11 = e2)
% 156.11/23.71  | | | | | | | | | | |   (9792)  op(e2, e0) = all_57_11
% 156.11/23.71  | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | BETA: splitting (239) gives:
% 156.11/23.71  | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | Case 1:
% 156.11/23.71  | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | |   (9793)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.11/23.71  | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.11/23.71  | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.11/23.71  | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.11/23.71  | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.11/23.71  | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.11/23.71  | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.11/23.71  | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.11/23.71  | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.11/23.71  | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.11/23.71  | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.11/23.71  | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.71  | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.11/23.71  | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.11/23.71  | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.11/23.71  | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.11/23.71  | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.11/23.71  | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.11/23.71  | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.11/23.71  | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.11/23.71  | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.11/23.71  | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.11/23.71  | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.11/23.71  | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.71  | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.71  | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.11/23.71  | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.11/23.71  | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 156.11/23.71  | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.11/23.71  | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.71  | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.71  | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.11/23.71  | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.11/23.71  | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.11/23.71  | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.11/23.71  | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.11/23.71  | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.71  | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.11/23.71  | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.71  | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.11/23.71  | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.11/23.71  | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.11/23.71  | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.11/23.71  | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.11/23.71  | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.11/23.71  | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.11/23.71  | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.11/23.71  | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.71  | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.11/23.71  | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.71  | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.11/23.71  | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.11/23.71  | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.11/23.71  | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.11/23.71  | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.11/23.71  | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.71  | | | | | | | | | | | |             e1)
% 156.11/23.71  | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | BETA: splitting (9793) gives:
% 156.11/23.71  | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | Case 1:
% 156.11/23.71  | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | |   (9794)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.11/23.71  | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.11/23.71  | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.11/23.71  | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.11/23.71  | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.11/23.71  | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.11/23.71  | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.11/23.71  | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.11/23.71  | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.11/23.71  | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.11/23.71  | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.11/23.71  | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.71  | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.11/23.71  | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.11/23.71  | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.11/23.71  | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.11/23.71  | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.11/23.71  | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.11/23.71  | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.11/23.71  | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.11/23.71  | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.11/23.71  | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.11/23.71  | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.11/23.71  | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.71  | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.71  | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.11/23.71  | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.11/23.71  | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.11/23.71  | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | BETA: splitting (9794) gives:
% 156.11/23.71  | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | Case 1:
% 156.11/23.71  | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | |   (9795)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.11/23.71  | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.11/23.71  | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.11/23.71  | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.11/23.71  | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.11/23.71  | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.11/23.71  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.11/23.71  | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.11/23.71  | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.11/23.71  | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.11/23.71  | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.11/23.71  | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.71  | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 156.11/23.71  | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | BETA: splitting (9795) gives:
% 156.11/23.71  | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | Case 1:
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | |   (9796)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.11/23.71  | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.11/23.71  | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.11/23.71  | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.11/23.71  | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.11/23.71  | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.11/23.71  | | | | | | | | | | | | | | |             $i(all_57_10))
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (7930), (9779), (9796),
% 156.11/23.71  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.71  | | | | | | | | | | | | | | |            #88.
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | Case 2:
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | |   (9797)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 156.11/23.71  | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.11/23.71  | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 156.11/23.71  | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.11/23.71  | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.11/23.71  | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.11/23.71  | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.11/23.71  | | | | | | | | | | | | | | |             $i(all_57_10))
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (9776), (9779), (9797),
% 156.11/23.71  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.71  | | | | | | | | | | | | | | |            #751.
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | End of split
% 156.11/23.71  | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | Case 2:
% 156.11/23.71  | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | |   (9798)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.11/23.71  | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.11/23.71  | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.11/23.71  | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.11/23.71  | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.11/23.71  | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.11/23.71  | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.11/23.71  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 156.11/23.71  | | | | | | | | | | | | | |             &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | | | |             e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 156.11/23.71  | | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 156.11/23.71  | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 156.11/23.71  | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 156.11/23.71  | | | | | | | | | | | | | |             e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 156.11/23.71  | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.11/23.71  | | | | | | | | | | | | | |             = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 156.11/23.71  | | | | | | | | | | | | | |             & $i(all_57_12))
% 156.11/23.71  | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | BETA: splitting (9798) gives:
% 156.11/23.71  | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | Case 1:
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | |   (9799)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.11/23.71  | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.11/23.71  | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.11/23.71  | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.11/23.71  | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.11/23.71  | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.11/23.71  | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.11/23.71  | | | | | | | | | | | | | | |             $i(all_57_10))
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | BETA: splitting (9799) gives:
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | Case 1:
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | |   (9800)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.11/23.71  | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 156.11/23.71  | | | | | | | | | | | | | | | |           = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.11/23.71  | | | | | | | | | | | | | | | |           $i(all_57_12)
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | | ALPHA: (9800) implies:
% 156.11/23.71  | | | | | | | | | | | | | | | |   (9801)  op(e0, e0) = e2
% 156.11/23.71  | | | | | | | | | | | | | | | |   (9802)  op(e2, e3) = e2
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (238), (9615), (9779), (9801),
% 156.11/23.71  | | | | | | | | | | | | | | | |            (9802), (function-axioms) are inconsistent by
% 156.11/23.71  | | | | | | | | | | | | | | | |            sub-proof #779.
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | Case 2:
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | |   (9803)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 156.11/23.71  | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.11/23.71  | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | | ALPHA: (9803) implies:
% 156.11/23.71  | | | | | | | | | | | | | | | |   (9804)  op(e2, e2) = e3
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9779), (9804), (function-axioms) are
% 156.11/23.71  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | End of split
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | Case 2:
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | |   (9805)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.11/23.71  | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.11/23.71  | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.11/23.71  | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.71  | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.71  | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.11/23.71  | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.11/23.71  | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.11/23.71  | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | BETA: splitting (9805) gives:
% 156.11/23.71  | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | Case 1:
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | |   (9806)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.11/23.71  | | | | | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | | ALPHA: (9806) implies:
% 156.11/23.71  | | | | | | | | | | | | | | | |   (9807)  op(e2, e2) = e2
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9779), (9807), (function-axioms) are
% 156.11/23.71  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | Case 2:
% 156.11/23.71  | | | | | | | | | | | | | | | | 
% 156.11/23.71  | | | | | | | | | | | | | | | |   (9808)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.11/23.71  | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.71  | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.71  | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.11/23.72  | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.11/23.72  | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.11/23.72  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | BETA: splitting (9808) gives:
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.72  | | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | |   (9809)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.11/23.72  | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.72  | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.11/23.72  | | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | | ALPHA: (9809) implies:
% 156.11/23.72  | | | | | | | | | | | | | | | | |   (9810)  op(e1, e1) = e3
% 156.11/23.72  | | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9615), (9810), (function-axioms) are
% 156.11/23.72  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 156.11/23.72  | | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.72  | | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | |   (9811)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 156.11/23.72  | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.11/23.72  | | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 156.11/23.72  | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 156.11/23.72  | | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | | ALPHA: (9811) implies:
% 156.11/23.72  | | | | | | | | | | | | | | | | |   (9812)   ~ (all_57_12 = e1)
% 156.11/23.72  | | | | | | | | | | | | | | | | |   (9813)  op(e2, e2) = all_57_12
% 156.11/23.72  | | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (9779), (9812), (9813), (function-axioms) are
% 156.11/23.72  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #795.
% 156.11/23.72  | | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | End of split
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | End of split
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | End of split
% 156.11/23.72  | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | End of split
% 156.11/23.72  | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | Case 2:
% 156.11/23.72  | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | |   (9814)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.11/23.72  | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.72  | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.72  | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.11/23.72  | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.11/23.72  | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.11/23.72  | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.11/23.72  | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.11/23.72  | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.11/23.72  | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.72  | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.11/23.72  | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.11/23.72  | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.11/23.72  | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.11/23.72  | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.11/23.72  | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.11/23.72  | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.11/23.72  | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.11/23.72  | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.11/23.72  | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.72  | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.11/23.72  | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.72  | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.11/23.72  | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.11/23.72  | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.11/23.72  | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.11/23.72  | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.11/23.72  | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | | |             e1)
% 156.11/23.72  | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | BETA: splitting (9814) gives:
% 156.11/23.72  | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | Case 1:
% 156.11/23.72  | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | |   (9815)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.11/23.72  | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.72  | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.72  | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.11/23.72  | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.11/23.72  | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.11/23.72  | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.11/23.72  | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.11/23.72  | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.11/23.72  | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.72  | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.11/23.72  | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14))
% 156.11/23.72  | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | BETA: splitting (9815) gives:
% 156.11/23.72  | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | Case 1:
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | |   (9816)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.11/23.72  | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.11/23.72  | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.72  | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.11/23.72  | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.11/23.72  | | | | | | | | | | | | | | |               e2) = e3)
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (9786), (9816), (function-axioms) are
% 156.11/23.72  | | | | | | | | | | | | | | |            inconsistent by sub-proof #105.
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | Case 2:
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | |   (9817)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 156.11/23.72  | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 156.11/23.72  | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 156.11/23.72  | | | | | | | | | | | | | | |             = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 156.11/23.72  | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 156.11/23.72  | | | | | | | | | | | | | | |               e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.11/23.72  | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.72  | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | BETA: splitting (9817) gives:
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | Case 1:
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | |   (9818)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 156.11/23.72  | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 156.11/23.72  | | | | | | | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.11/23.72  | | | | | | | | | | | | | | | |           $i(all_57_12)
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | ALPHA: (9818) implies:
% 156.11/23.72  | | | | | | | | | | | | | | | |   (9819)  op(e2, e0) = e2
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9791), (9792), (9819), (function-axioms)
% 156.11/23.72  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #627.
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | Case 2:
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | |   (9820)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.72  | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 156.11/23.72  | | | | | | | | | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.72  | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | ALPHA: (9820) implies:
% 156.11/23.72  | | | | | | | | | | | | | | | |   (9821)  op(e3, e3) = e1
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (160), (165),
% 156.11/23.72  | | | | | | | | | | | | | | | |            (169), (210), (221), (223), (224), (230), (234),
% 156.11/23.72  | | | | | | | | | | | | | | | |            (236), (238), (9613), (9614), (9615), (9779),
% 156.11/23.72  | | | | | | | | | | | | | | | |            (9821), (function-axioms) are inconsistent by
% 156.11/23.72  | | | | | | | | | | | | | | | |            sub-proof #145.
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | End of split
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | End of split
% 156.11/23.72  | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | Case 2:
% 156.11/23.72  | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | |   (9822)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.11/23.72  | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.72  | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.11/23.72  | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.11/23.72  | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.11/23.72  | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.11/23.72  | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.72  | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.11/23.72  | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.72  | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.11/23.72  | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.11/23.72  | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.11/23.72  | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.11/23.72  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.11/23.72  | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | | | |             e1)
% 156.11/23.72  | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | BETA: splitting (9822) gives:
% 156.11/23.72  | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | Case 1:
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | |   (9823)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.11/23.72  | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.72  | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.11/23.72  | | | | | | | | | | | | | | |             = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.11/23.72  | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.11/23.72  | | | | | | | | | | | | | | |             e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | BETA: splitting (9823) gives:
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | Case 1:
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | |   (9824)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.11/23.72  | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.72  | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | ALPHA: (9824) implies:
% 156.11/23.72  | | | | | | | | | | | | | | | |   (9825)  op(e1, e1) = e3
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9615), (9825), (function-axioms) are
% 156.11/23.72  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | Case 2:
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | |   (9826)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.11/23.72  | | | | | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 156.11/23.72  | | | | | | | | | | | | | | | |           = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.72  | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | ALPHA: (9826) implies:
% 156.11/23.72  | | | | | | | | | | | | | | | |   (9827)  op(e2, e1) = e2
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9614), (9827), (function-axioms) are
% 156.11/23.72  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 156.11/23.72  | | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | End of split
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | Case 2:
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | |   (9828)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.72  | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.11/23.72  | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.72  | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.11/23.72  | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.11/23.72  | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.11/23.72  | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.11/23.72  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.11/23.72  | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | | | | |             e1)
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (9615), (9786), (9828),
% 156.11/23.72  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.72  | | | | | | | | | | | | | | |            #108.
% 156.11/23.72  | | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | | End of split
% 156.11/23.72  | | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | | End of split
% 156.11/23.72  | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | End of split
% 156.11/23.72  | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | Case 2:
% 156.11/23.72  | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | |   (9829)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.72  | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.11/23.72  | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.72  | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.11/23.72  | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.11/23.72  | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.72  | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.11/23.72  | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.11/23.72  | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.11/23.72  | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.11/23.72  | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.72  | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.11/23.72  | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.72  | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.72  | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.11/23.72  | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.11/23.72  | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.11/23.72  | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.11/23.72  | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.11/23.72  | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.11/23.72  | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.11/23.72  | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.11/23.72  | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.11/23.72  | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.11/23.72  | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.11/23.72  | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.11/23.72  | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.11/23.72  | | | | | | | | | | | |             $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 156.11/23.72  | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.11/23.72  | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 156.11/23.72  | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.11/23.72  | | | | | | | | | | | |           (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.11/23.72  | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 156.11/23.72  | | | | | | | | | | | |             e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 156.11/23.72  | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.11/23.72  | | | | | | | | | | | |             = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.11/23.72  | | | | | | | | | | | |             & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 156.11/23.72  | | | | | | | | | | | |             e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 156.11/23.72  | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 156.11/23.72  | | | | | | | | | | | |             op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.11/23.72  | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 156.11/23.72  | | | | | | | | | | | |             & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 156.11/23.72  | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 156.11/23.72  | | | | | | | | | | | |             = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.11/23.72  | | | | | | | | | | | |           (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.11/23.72  | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 156.11/23.72  | | | | | | | | | | | |             = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 156.11/23.72  | | | | | | | | | | | |               e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 156.11/23.72  | | | | | | | | | | | |             & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 156.11/23.72  | | | | | | | | | | | |             e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 156.11/23.72  | | | | | | | | | | | |             & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 156.11/23.72  | | | | | | | | | | | |                 e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.72  | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.11/23.72  | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 156.11/23.72  | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.72  | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.11/23.72  | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.11/23.72  | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.72  | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.11/23.72  | | | | | | | | | | | |                   e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 156.11/23.72  | | | | | | | | | | | |                 e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 156.11/23.72  | | | | | | | | | | | |               (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 156.11/23.72  | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 156.11/23.72  | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e2) = e0) |
% 156.11/23.72  | | | | | | | | | | | |               (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 156.11/23.72  | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 156.11/23.72  | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e2) = e0) |
% 156.11/23.72  | | | | | | | | | | | |               (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 156.11/23.72  | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 156.11/23.72  | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e2) = e0) |
% 156.11/23.72  | | | | | | | | | | | |               (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 156.11/23.72  | | | | | | | | | | | |                 & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.11/23.72  | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.11/23.72  | | | | | | | | | | | |                 (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.11/23.72  | | | | | | | | | | | |                   e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 156.11/23.72  | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.72  | | | | | | | | | | | |                 (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.11/23.72  | | | | | | | | | | | |                   e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 156.11/23.72  | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.72  | | | | | | | | | | | |                 (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.11/23.72  | | | | | | | | | | | |                   e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 156.11/23.72  | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 156.11/23.72  | | | | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.11/23.72  | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.11/23.72  | | | | | | | | | | | |                 $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 156.11/23.72  | | | | | | | | | | | |                 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 156.11/23.72  | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | BETA: splitting (9829) gives:
% 156.11/23.72  | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | Case 1:
% 156.11/23.72  | | | | | | | | | | | | | 
% 156.11/23.72  | | | | | | | | | | | | |   (9830)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.72  | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.11/23.73  | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.73  | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.11/23.73  | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.11/23.73  | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.73  | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.11/23.73  | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.11/23.73  | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.11/23.73  | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.11/23.73  | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.73  | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.11/23.73  | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.73  | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.73  | | | | | | | | | | | | |             all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.11/23.73  | | | | | | | | | | | | |               = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.11/23.73  | | | | | | | | | | | | |             e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.11/23.73  | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.11/23.73  | | | | | | | | | | | | |             &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | |             e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.11/23.73  | | | | | | | | | | | | |             = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.11/23.73  | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.11/23.73  | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.11/23.73  | | | | | | | | | | | | |             e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.11/23.73  | | | | | | | | | | | | |             = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.11/23.73  | | | | | | | | | | | | |             all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.11/23.73  | | | | | | | | | | | | |               = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.11/23.73  | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.11/23.73  | | | | | | | | | | | | |             $i(all_57_14))
% 156.11/23.73  | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | BETA: splitting (9830) gives:
% 156.11/23.73  | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | Case 1:
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | |   (9831)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.73  | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.11/23.73  | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.73  | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.11/23.73  | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.11/23.73  | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.73  | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.11/23.73  | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.11/23.73  | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.11/23.73  | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.11/23.73  | | | | | | | | | | | | | |           (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.73  | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.11/23.73  | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.11/23.73  | | | | | | | | | | | | | |             = e1 & $i(all_57_14))
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | BETA: splitting (9831) gives:
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | Case 1:
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | |   (9832)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.11/23.73  | | | | | | | | | | | | | | |             ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.11/23.73  | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.11/23.73  | | | | | | | | | | | | | | |             all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.11/23.73  | | | | | | | | | | | | | | |               e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.11/23.73  | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.73  | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (160), (165),
% 156.11/23.73  | | | | | | | | | | | | | | |            (169), (210), (221), (223), (224), (230), (234),
% 156.11/23.73  | | | | | | | | | | | | | | |            (236), (238), (9613), (9614), (9615), (9779),
% 156.11/23.73  | | | | | | | | | | | | | | |            (9832), (function-axioms) are inconsistent by
% 156.11/23.73  | | | | | | | | | | | | | | |            sub-proof #138.
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | |   (9833)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.11/23.73  | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.73  | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 156.11/23.73  | | | | | | | | | | | | | | |             = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 156.11/23.73  | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.11/23.73  | | | | | | | | | | | | | | |             op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.11/23.73  | | | | | | | | | | | | | | |             $i(all_57_14))
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | BETA: splitting (9833) gives:
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | Case 1:
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9834)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.11/23.73  | | | | | | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.73  | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | ALPHA: (9834) implies:
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9835)   ~ (all_57_12 = e1)
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9836)  op(e2, e2) = all_57_12
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | REF_CLOSE: (9779), (9835), (9836), (function-axioms) are
% 156.11/23.73  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #795.
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9837)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.11/23.73  | | | | | | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 156.11/23.73  | | | | | | | | | | | | | | | |           = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.11/23.73  | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | ALPHA: (9837) implies:
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9838)  op(e0, e0) = e1
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (9786), (9838), (function-axioms) are
% 156.11/23.73  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | End of split
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | End of split
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | |   (9839)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.11/23.73  | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.11/23.73  | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.11/23.73  | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.11/23.73  | | | | | | | | | | | | | |               e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 156.11/23.73  | | | | | | | | | | | | | |             all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 156.11/23.73  | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 156.11/23.73  | | | | | | | | | | | | | |             = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 156.11/23.73  | | | | | | | | | | | | | |           (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.11/23.73  | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.11/23.73  | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.11/23.73  | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.11/23.73  | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.11/23.73  | | | | | | | | | | | | | |             & $i(all_57_14))
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | BETA: splitting (9839) gives:
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | Case 1:
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | |   (9840)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.11/23.73  | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.11/23.73  | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.11/23.73  | | | | | | | | | | | | | | |             = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.11/23.73  | | | | | | | | | | | | | | |               e1) = e1)
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | BETA: splitting (9840) gives:
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | Case 1:
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9841)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 156.11/23.73  | | | | | | | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.11/23.73  | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | | | | |           e2 & $i(all_57_12)
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | ALPHA: (9841) implies:
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9842)  op(e2, e0) = e2
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9791), (9792), (9842), (function-axioms)
% 156.11/23.73  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #627.
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9843)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) &
% 156.11/23.73  | | | | | | | | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = e1
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | ALPHA: (9843) implies:
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9844)  op(e1, e1) = e1
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9615), (9844), (function-axioms) are
% 156.11/23.73  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | End of split
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | |   (9845)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.11/23.73  | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.73  | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.73  | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 156.11/23.73  | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 156.11/23.73  | | | | | | | | | | | | | | |               e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 156.11/23.73  | | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 156.11/23.73  | | | | | | | | | | | | | | |               e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | BETA: splitting (9845) gives:
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | Case 1:
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9846)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.11/23.73  | | | | | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.11/23.73  | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.73  | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | ALPHA: (9846) implies:
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9847)  op(e0, e0) = e3
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9786), (9847), (function-axioms) are
% 156.11/23.73  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9848)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.11/23.73  | | | | | | | | | | | | | | | |             op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.11/23.73  | | | | | | | | | | | | | | | |             e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.11/23.73  | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.11/23.73  | | | | | | | | | | | | | | | |             = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.11/23.73  | | | | | | | | | | | | | | | |             & $i(all_57_14))
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | BETA: splitting (9848) gives:
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.73  | | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | |   (9849)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.11/23.73  | | | | | | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3
% 156.11/23.73  | | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | | ALPHA: (9849) implies:
% 156.11/23.73  | | | | | | | | | | | | | | | | |   (9850)  op(e3, e3) = e3
% 156.11/23.73  | | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7930), (9850), (function-axioms) are
% 156.11/23.73  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 156.11/23.73  | | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | |   (9851)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 156.11/23.73  | | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.11/23.73  | | | | | | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.11/23.73  | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.11/23.73  | | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | | ALPHA: (9851) implies:
% 156.11/23.73  | | | | | | | | | | | | | | | | |   (9852)  op(e3, e3) = e1
% 156.11/23.73  | | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (160), (165),
% 156.11/23.73  | | | | | | | | | | | | | | | | |            (169), (210), (221), (223), (224), (230), (234),
% 156.11/23.73  | | | | | | | | | | | | | | | | |            (236), (238), (9613), (9614), (9615), (9779),
% 156.11/23.73  | | | | | | | | | | | | | | | | |            (9852), (function-axioms) are inconsistent by
% 156.11/23.73  | | | | | | | | | | | | | | | | |            sub-proof #145.
% 156.11/23.73  | | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | End of split
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | End of split
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | End of split
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | End of split
% 156.11/23.73  | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | |   (9853)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.11/23.73  | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.73  | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.73  | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.11/23.73  | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.11/23.73  | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.11/23.73  | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.11/23.73  | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.11/23.73  | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.11/23.73  | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.11/23.73  | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.73  | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 156.11/23.73  | | | | | | | | | | | | |             = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 156.11/23.73  | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.11/23.73  | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.11/23.73  | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 156.11/23.73  | | | | | | | | | | | | |             &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 156.11/23.73  | | | | | | | | | | | | |             e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 156.11/23.73  | | | | | | | | | | | | |               = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 156.11/23.73  | | | | | | | | | | | | |           (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.11/23.73  | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.11/23.73  | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.11/23.73  | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.11/23.73  | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.73  | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.73  | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.73  | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.11/23.73  | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.73  | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.73  | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.11/23.73  | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.73  | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.11/23.73  | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.11/23.73  | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.73  | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.11/23.73  | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.11/23.73  | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.73  | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.11/23.73  | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.11/23.73  | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.73  | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.11/23.73  | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.11/23.73  | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.11/23.73  | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.11/23.73  | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.11/23.73  | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.11/23.73  | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.11/23.73  | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.11/23.73  | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.11/23.73  | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.11/23.73  | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.11/23.73  | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.11/23.73  | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.11/23.73  | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.11/23.73  | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.11/23.73  | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.11/23.73  | | | | | | | | | | | | |                 e0)))
% 156.11/23.73  | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | BETA: splitting (9853) gives:
% 156.11/23.73  | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | Case 1:
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | |   (9854)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.11/23.73  | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.73  | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.73  | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.11/23.73  | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.11/23.73  | | | | | | | | | | | | | |               e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.11/23.73  | | | | | | | | | | | | | |             all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.11/23.73  | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.11/23.73  | | | | | | | | | | | | | |             all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.11/23.73  | | | | | | | | | | | | | |           (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.11/23.73  | | | | | | | | | | | | | |             ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.11/23.73  | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.73  | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | BETA: splitting (9854) gives:
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | Case 1:
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | |   (9855)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.11/23.73  | | | | | | | | | | | | | | |             ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.11/23.73  | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.73  | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.11/23.73  | | | | | | | | | | | | | | |             = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.11/23.73  | | | | | | | | | | | | | | |               e1) = e2)
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | REF_CLOSE: (5), (9779), (9786), (9855), (function-axioms) are
% 156.11/23.73  | | | | | | | | | | | | | | |            inconsistent by sub-proof #576.
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | |   (9856)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 156.11/23.73  | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 156.11/23.73  | | | | | | | | | | | | | | |               e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 156.11/23.73  | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 156.11/23.73  | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 156.11/23.73  | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.11/23.73  | | | | | | | | | | | | | | |             & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.11/23.73  | | | | | | | | | | | | | | |             $i(all_57_10))
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | BETA: splitting (9856) gives:
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | Case 1:
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9857)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 156.11/23.73  | | | | | | | | | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.11/23.73  | | | | | | | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.11/23.73  | | | | | | | | | | | | | | | |           $i(all_57_14)
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | ALPHA: (9857) implies:
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9858)  op(e2, e1) = e2
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9614), (9858), (function-axioms) are
% 156.11/23.73  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9859)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.11/23.73  | | | | | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.11/23.73  | | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.11/23.73  | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | ALPHA: (9859) implies:
% 156.11/23.73  | | | | | | | | | | | | | | | |   (9860)  op(e0, e0) = e3
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9786), (9860), (function-axioms) are
% 156.11/23.73  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 156.11/23.73  | | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | | End of split
% 156.11/23.73  | | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | | End of split
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.73  | | | | | | | | | | | | | Case 2:
% 156.11/23.73  | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | |   (9861)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.11/23.74  | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.11/23.74  | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.74  | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.11/23.74  | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.11/23.74  | | | | | | | | | | | | | |               e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 156.11/23.74  | | | | | | | | | | | | | |              ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 156.11/23.74  | | | | | | | | | | | | | |             e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 156.11/23.74  | | | | | | | | | | | | | |               = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 156.11/23.74  | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.11/23.74  | | | | | | | | | | | | | |             ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.11/23.74  | | | | | | | | | | | | | |                 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 156.11/23.74  | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e3) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 156.11/23.74  | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 156.11/23.74  | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e3) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 156.11/23.74  | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 156.11/23.74  | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e3) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | |               (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 156.11/23.74  | | | | | | | | | | | | | |                 & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.11/23.74  | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 156.11/23.74  | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 156.11/23.74  | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 156.11/23.74  | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | |                 (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.11/23.74  | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 156.11/23.74  | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | |                   e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 156.11/23.74  | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.74  | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 156.11/23.74  | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.74  | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.11/23.74  | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.74  | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | |                   e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.11/23.74  | | | | | | | | | | | | | |                 e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.11/23.74  | | | | | | | | | | | | | |                 op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.11/23.74  | | | | | | | | | | | | | |                 op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 156.11/23.74  | | | | | | | | | | | | | |                 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.11/23.74  | | | | | | | | | | | | | |                 op(e0, e1) = e0)))
% 156.11/23.74  | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | BETA: splitting (9861) gives:
% 156.11/23.74  | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | Case 1:
% 156.11/23.74  | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | |   (9862)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.11/23.74  | | | | | | | | | | | | | | |              ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.11/23.74  | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.11/23.74  | | | | | | | | | | | | | | |             e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.11/23.74  | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.11/23.74  | | | | | | | | | | | | | | |               e0) = e3)
% 156.11/23.74  | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7930), (9786), (9862), (function-axioms) are
% 156.11/23.74  | | | | | | | | | | | | | | |            inconsistent by sub-proof #83.
% 156.11/23.74  | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | Case 2:
% 156.11/23.74  | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | |   (9863)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.11/23.74  | | | | | | | | | | | | | | |             op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 156.11/23.74  | | | | | | | | | | | | | | |             = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 156.11/23.74  | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 156.11/23.74  | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.74  | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.11/23.74  | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.11/23.74  | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.11/23.74  | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.74  | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.74  | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.74  | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.11/23.74  | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.11/23.74  | | | | | | | | | | | | | | |                 e0)))
% 156.11/23.74  | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | BETA: splitting (9863) gives:
% 156.11/23.74  | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | Case 1:
% 156.11/23.74  | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | |   (9864)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.11/23.74  | | | | | | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2
% 156.11/23.74  | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | ALPHA: (9864) implies:
% 156.11/23.74  | | | | | | | | | | | | | | | |   (9865)  op(e2, e2) = e2
% 156.11/23.74  | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9779), (9865), (function-axioms) are
% 156.11/23.74  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #993.
% 156.11/23.74  | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | Case 2:
% 156.11/23.74  | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | |   (9866)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.11/23.74  | | | | | | | | | | | | | | | |             op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.11/23.74  | | | | | | | | | | | | | | | |             = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | |                 all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.74  | | | | | | | | | | | | | | | |                   e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.11/23.74  | | | | | | | | | | | | | | | |                   e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.11/23.74  | | | | | | | | | | | | | | | |                   e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | | | |                   e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.11/23.74  | | | | | | | | | | | | | | | |                 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.74  | | | | | | | | | | | | | | | |                 op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.74  | | | | | | | | | | | | | | | |                 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.74  | | | | | | | | | | | | | | | |                 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | | | |                   e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | |                 op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | |                 op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | |                 op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.11/23.74  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | |                 all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.11/23.74  | | | | | | | | | | | | | | | |                 e0)))
% 156.11/23.74  | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | BETA: splitting (9866) gives:
% 156.11/23.74  | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.74  | | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | |   (9867)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.11/23.74  | | | | | | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1
% 156.11/23.74  | | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | | ALPHA: (9867) implies:
% 156.11/23.74  | | | | | | | | | | | | | | | | |   (9868)  op(e1, e1) = e1
% 156.11/23.74  | | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9615), (9868), (function-axioms) are
% 156.11/23.74  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 156.11/23.74  | | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.74  | | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | |   (9869)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.11/23.74  | | | | | | | | | | | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.11/23.74  | | | | | | | | | | | | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.11/23.74  | | | | | | | | | | | | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.11/23.74  | | | | | | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.11/23.74  | | | | | | | | | | | | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 156.11/23.74  | | | | | | | | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.74  | | | | | | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 156.11/23.74  | | | | | | | | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 156.11/23.74  | | | | | | | | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e0))
% 156.11/23.74  | | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | | ALPHA: (9869) implies:
% 156.11/23.74  | | | | | | | | | | | | | | | | |   (9870)  op(e0, e0) = all_57_15
% 156.11/23.74  | | | | | | | | | | | | | | | | |   (9871)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.11/23.74  | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.11/23.74  | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.11/23.74  | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.11/23.74  | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.11/23.74  | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.11/23.74  | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 156.11/23.74  | | | | | | | | | | | | | | | | |           | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.11/23.74  | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.11/23.74  | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 156.11/23.74  | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 156.11/23.74  | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.11/23.74  | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 156.11/23.74  | | | | | | | | | | | | | | | | |               = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 156.11/23.74  | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 156.11/23.74  | | | | | | | | | | | | | | | | |           (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.11/23.74  | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 156.11/23.74  | | | | | | | | | | | | | | | | | 
% 156.11/23.74  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e0,
% 156.11/23.74  | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (51), (9786) gives:
% 156.11/23.74  | | | | | | | | | | | | | | | | |   (9872)  all_14_2 = e0
% 156.11/23.74  | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 156.11/23.75  | | | | | | | | | | | | | | | | |              all_57_11, e0, e2, simplifying with (164), (9792)
% 156.11/23.75  | | | | | | | | | | | | | | | | |              gives:
% 156.11/23.75  | | | | | | | | | | | | | | | | |   (9873)  all_57_11 = all_52_13
% 156.11/23.75  | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | REDUCE: (9791), (9873) imply:
% 156.11/23.75  | | | | | | | | | | | | | | | | |   (9874)   ~ (all_52_13 = e2)
% 156.11/23.75  | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | REDUCE: (362), (9872) imply:
% 156.11/23.75  | | | | | | | | | | | | | | | | |   (9875)   ~ (all_52_7 = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | REDUCE: (369), (9872) imply:
% 156.11/23.75  | | | | | | | | | | | | | | | | |   (9876)   ~ (all_52_11 = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | REDUCE: (371), (9872) imply:
% 156.11/23.75  | | | | | | | | | | | | | | | | |   (9877)   ~ (all_52_13 = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 156.11/23.75  | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | |   (9878)  all_54_7 = e3
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (9878) imply:
% 156.11/23.75  | | | | | | | | | | | | | | | | | |   (9879)  all_52_13 = e3
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | SIMP: (9879) implies:
% 156.11/23.75  | | | | | | | | | | | | | | | | | |   (9880)  all_52_13 = e3
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | REDUCE: (113), (9880) imply:
% 156.11/23.75  | | | | | | | | | | | | | | | | | |   (9881)   ~ (all_52_12 = e3)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | REDUCE: (164), (9880) imply:
% 156.11/23.75  | | | | | | | | | | | | | | | | | |   (9882)  op(e2, e0) = e3
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | BETA: splitting (9871) gives:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |   (9883)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |               e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | BETA: splitting (9883) gives:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |   (9884)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (159), (7926), (9615), (9882), (9884),
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |            #112.
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |   (9885)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9885) gives:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |   (9886)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = e0
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9886) implies:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |   (9887)  op(e0, e3) = e0
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7926), (9887), (function-axioms) are
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |   (9888)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9888) gives:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | |   (9889)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e0, e2) = e0
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9889) implies:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | |   (9890)  op(e3, e0) = e3
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9881), (9890), (function-axioms) are
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | |   (9891)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | |           = e2 & op(e0, e2) = e0
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9891) implies:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | |   (9892)  op(e2, e0) = e2
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9882), (9892), (function-axioms) are
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #580.
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |   (9893)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | BETA: splitting (9893) gives:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |   (9894)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |           | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |               e0) = e3 & op(e0, e1) = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (158), (9615), (9875), (9876), (9894),
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |            #165.
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |   (9895)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | |             = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9895) gives:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |   (9896)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (9615), (9882), (9896),
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |            #111.
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |   (9897)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |             &  ~ (e1 = e0) & op(e0, e1) = e0)
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9876), (9897), (function-axioms) are
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | Case 2:
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | |   (9898)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (9777), (9874), (9877), (9898) are
% 156.11/23.75  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #235.
% 156.11/23.75  | | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | | 
% 156.11/23.75  | | | | | | | | End of split
% 156.11/23.75  | | | | | | | | 
% 156.11/23.75  | | | | | | | End of split
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | Case 2:
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | |   (9899)  all_18_2 = e3
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | | COMBINE_EQS: (301), (9899) imply:
% 156.11/23.75  | | | | | | |   (9900)  all_14_2 = e3
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | | REDUCE: (362), (9900) imply:
% 156.11/23.75  | | | | | | |   (9901)   ~ (all_52_7 = e3)
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | | REDUCE: (51), (9900) imply:
% 156.11/23.75  | | | | | | |   (9902)  op(e0, e0) = e3
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | | BETA: splitting (238) gives:
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | | Case 1:
% 156.11/23.75  | | | | | | | | 
% 156.11/23.75  | | | | | | | |   (9903)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 &
% 156.11/23.75  | | | | | | | |                 op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2,
% 156.11/23.75  | | | | | | | |                   e3) = all_57_0 & $i(all_57_0))) & ((all_57_14
% 156.11/23.75  | | | | | | | |                 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) &
% 156.11/23.75  | | | | | | | |                 op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 156.11/23.75  | | | | | | | |             ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 156.11/23.75  | | | | | | | |                   = e0) & op(e0, e3) = all_57_6 &
% 156.11/23.75  | | | | | | | |                 $i(all_57_6)))) | (all_57_12 = e2 & op(e2, e2) =
% 156.11/23.75  | | | | | | | |             e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 156.11/23.75  | | | | | | | |                 (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 156.11/23.75  | | | | | | | |                 $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) =
% 156.11/23.75  | | | | | | | |                 e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 156.11/23.75  | | | | | | | |                 all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 &
% 156.11/23.75  | | | | | | | |                 op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 156.11/23.75  | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 156.11/23.75  | | | | | | | | 
% 156.11/23.75  | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (135), (158), (170), (191),
% 156.11/23.75  | | | | | | | |            (203), (248), (272), (352), (356), (7927), (7930),
% 156.11/23.75  | | | | | | | |            (9901), (9902), (9903), (function-axioms) are
% 156.11/23.75  | | | | | | | |            inconsistent by sub-proof #71.
% 156.11/23.75  | | | | | | | | 
% 156.11/23.75  | | | | | | | Case 2:
% 156.11/23.75  | | | | | | | | 
% 156.11/23.75  | | | | | | | |   (9904)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 &
% 156.11/23.75  | | | | | | | |                 op(e3, e3) = e1) | ( ~ (all_57_4 = e3) & op(e3,
% 156.11/23.75  | | | | | | | |                   e1) = all_57_4 & $i(all_57_4))) & ((all_57_12
% 156.11/23.75  | | | | | | | |                 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) &
% 156.11/23.75  | | | | | | | |                 op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 156.11/23.75  | | | | | | | |             ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 156.11/23.75  | | | | | | | |                   = e0) & op(e0, e1) = all_57_8 &
% 156.11/23.75  | | | | | | | |                 $i(all_57_8)))) | (all_57_15 = e0 & op(e0, e0) =
% 156.11/23.75  | | | | | | | |             e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 156.11/23.75  | | | | | | | |                 (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 156.11/23.75  | | | | | | | |                 $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) =
% 156.11/23.75  | | | | | | | |                 e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 156.11/23.75  | | | | | | | |                 all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 &
% 156.11/23.75  | | | | | | | |                 op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.11/23.75  | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 156.11/23.75  | | | | | | | | 
% 156.11/23.75  | | | | | | | | REF_CLOSE: (6), (7), (9615), (9902), (9904), (function-axioms)
% 156.11/23.75  | | | | | | | |            are inconsistent by sub-proof #416.
% 156.11/23.75  | | | | | | | | 
% 156.11/23.75  | | | | | | | End of split
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | End of split
% 156.11/23.75  | | | | | | 
% 156.11/23.75  | | | | | Case 2:
% 156.11/23.75  | | | | | | 
% 156.11/23.75  | | | | | |   (9905)  all_14_2 = e1
% 156.11/23.75  | | | | | | 
% 156.11/23.75  | | | | | | REDUCE: (351), (9905) imply:
% 156.11/23.75  | | | | | |   (9906)   ~ (all_52_3 = e1)
% 156.11/23.75  | | | | | | 
% 156.11/23.75  | | | | | | REDUCE: (51), (9905) imply:
% 156.11/23.75  | | | | | |   (9907)  op(e0, e0) = e1
% 156.11/23.75  | | | | | | 
% 156.11/23.75  | | | | | | BETA: splitting (7933) gives:
% 156.11/23.75  | | | | | | 
% 156.11/23.75  | | | | | | Case 1:
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | |   (9908)   ~ (all_8_0 = e2) & op(e0, e3) = all_8_0 & $i(all_8_0)
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | | ALPHA: (9908) implies:
% 156.11/23.75  | | | | | | |   (9909)   ~ (all_8_0 = e2)
% 156.11/23.75  | | | | | | |   (9910)  op(e0, e3) = all_8_0
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | | BETA: splitting (238) gives:
% 156.11/23.75  | | | | | | | 
% 156.11/23.75  | | | | | | | Case 1:
% 156.11/23.75  | | | | | | | | 
% 156.11/23.75  | | | | | | | |   (9911)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 &
% 156.11/23.75  | | | | | | | |                 op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2,
% 156.11/23.75  | | | | | | | |                   e3) = all_57_0 & $i(all_57_0))) & ((all_57_14
% 156.11/23.75  | | | | | | | |                 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) &
% 156.11/23.75  | | | | | | | |                 op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 156.11/23.75  | | | | | | | |             ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 156.11/23.75  | | | | | | | |                   = e0) & op(e0, e3) = all_57_6 &
% 156.11/23.75  | | | | | | | |                 $i(all_57_6)))) | (all_57_12 = e2 & op(e2, e2) =
% 156.11/23.75  | | | | | | | |             e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 156.11/23.75  | | | | | | | |                 (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 156.11/23.75  | | | | | | | |                 $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) =
% 156.11/23.75  | | | | | | | |                 e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 156.11/23.75  | | | | | | | |                 all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 &
% 156.11/23.75  | | | | | | | |                 op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 156.11/23.75  | | | | | | | |                   e2) = all_57_7 & $i(all_57_7))))
% 156.11/23.75  | | | | | | | | 
% 156.11/23.75  | | | | | | | | BETA: splitting (9911) gives:
% 156.11/23.75  | | | | | | | | 
% 156.11/23.75  | | | | | | | | Case 1:
% 156.11/23.75  | | | | | | | | | 
% 156.11/23.75  | | | | | | | | |   (9912)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3
% 156.11/23.75  | | | | | | | | |               & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 156.11/23.75  | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.11/23.75  | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2
% 156.11/23.75  | | | | | | | | |                 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)))
% 156.11/23.75  | | | | | | | | |           & ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~
% 156.11/23.75  | | | | | | | | |               (all_57_6 = e0) & op(e0, e3) = all_57_6 &
% 156.11/23.75  | | | | | | | | |               $i(all_57_6)))
% 156.11/23.75  | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | ALPHA: (9912) implies:
% 156.11/23.75  | | | | | | | | |   (9913)  op(e3, e3) = e3
% 156.11/23.75  | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | REF_CLOSE: (7), (7930), (9913), (function-axioms) are
% 156.11/23.75  | | | | | | | | |            inconsistent by sub-proof #971.
% 156.11/23.75  | | | | | | | | | 
% 156.11/23.75  | | | | | | | | Case 2:
% 156.11/23.75  | | | | | | | | | 
% 156.11/23.75  | | | | | | | | |   (9914)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2
% 156.11/23.75  | | | | | | | | |               & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 156.11/23.75  | | | | | | | | |               op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.11/23.75  | | | | | | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3
% 156.11/23.75  | | | | | | | | |                 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3)))
% 156.11/23.75  | | | | | | | | |           & ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~
% 156.11/23.75  | | | | | | | | |               (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 156.11/23.75  | | | | | | | | |               $i(all_57_7)))
% 156.11/23.75  | | | | | | | | | 
% 156.11/23.75  | | | | | | | | | ALPHA: (9914) implies:
% 156.11/23.75  | | | | | | | | |   (9915)  op(e2, e2) = e2
% 156.11/23.75  | | | | | | | | |   (9916)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 =
% 156.11/23.75  | | | | | | | | |               e0) & op(e0, e2) = all_57_7 & $i(all_57_7))
% 156.11/23.75  | | | | | | | | |   (9917)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 156.11/23.75  | | | | | | | | |               e3) & op(e3, e2) = all_57_1 & $i(all_57_1))
% 156.11/23.75  | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | REF_CLOSE: (5), (6), (36), (135), (140), (158), (159), (170),
% 156.21/23.76  | | | | | | | | |            (191), (192), (203), (248), (249), (272), (352),
% 156.21/23.76  | | | | | | | | |            (356), (7926), (7927), (7930), (9906), (9907),
% 156.21/23.76  | | | | | | | | |            (9909), (9910), (9915), (9916), (9917),
% 156.21/23.76  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.21/23.76  | | | | | | | | |            #64.
% 156.21/23.76  | | | | | | | | | 
% 156.21/23.76  | | | | | | | | End of split
% 156.21/23.76  | | | | | | | | 
% 156.21/23.76  | | | | | | | Case 2:
% 156.21/23.76  | | | | | | | | 
% 156.21/23.76  | | | | | | | |   (9918)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 &
% 156.21/23.76  | | | | | | | |                 op(e3, e3) = e1) | ( ~ (all_57_4 = e3) & op(e3,
% 156.21/23.76  | | | | | | | |                   e1) = all_57_4 & $i(all_57_4))) & ((all_57_12
% 156.21/23.76  | | | | | | | |                 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) &
% 156.21/23.76  | | | | | | | |                 op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 156.21/23.76  | | | | | | | |             ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 156.21/23.76  | | | | | | | |                   = e0) & op(e0, e1) = all_57_8 &
% 156.21/23.76  | | | | | | | |                 $i(all_57_8)))) | (all_57_15 = e0 & op(e0, e0) =
% 156.21/23.76  | | | | | | | |             e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 156.21/23.76  | | | | | | | |                 (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 156.21/23.76  | | | | | | | |                 $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) =
% 156.21/23.76  | | | | | | | |                 e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 156.21/23.76  | | | | | | | |                 all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 &
% 156.21/23.76  | | | | | | | |                 op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.21/23.76  | | | | | | | |                   e0) = all_57_13 & $i(all_57_13))))
% 156.21/23.76  | | | | | | | | 
% 156.21/23.76  | | | | | | | | REF_CLOSE: (4), (6), (51), (9615), (9907), (9918),
% 156.21/23.76  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #748.
% 156.21/23.76  | | | | | | | | 
% 156.21/23.76  | | | | | | | End of split
% 156.21/23.76  | | | | | | | 
% 156.21/23.76  | | | | | | Case 2:
% 156.21/23.76  | | | | | | | 
% 156.21/23.76  | | | | | | |   (9919)   ~ (all_8_1 = e1) & op(e0, e0) = all_8_1 & $i(all_8_1)
% 156.21/23.76  | | | | | | | 
% 156.21/23.76  | | | | | | | REF_CLOSE: (9907), (9919), (function-axioms) are inconsistent by
% 156.21/23.76  | | | | | | |            sub-proof #55.
% 156.21/23.76  | | | | | | | 
% 156.21/23.76  | | | | | | End of split
% 156.21/23.76  | | | | | | 
% 156.21/23.76  | | | | | End of split
% 156.21/23.76  | | | | | 
% 156.21/23.76  | | | | End of split
% 156.21/23.76  | | | | 
% 156.21/23.76  | | | End of split
% 156.21/23.76  | | | 
% 156.21/23.76  | | End of split
% 156.21/23.76  | | 
% 156.21/23.76  | Case 2:
% 156.21/23.76  | | 
% 156.21/23.76  | |   (9920)  all_4_2 = e3
% 156.21/23.76  | |   (9921)  ( ~ (all_4_0 = e0) & op(e3, e2) = all_4_0 & $i(all_4_0)) | ( ~
% 156.21/23.76  | |             (all_4_1 = e1) & op(e3, e3) = all_4_1 & $i(all_4_1))
% 156.21/23.76  | | 
% 156.21/23.76  | | COMBINE_EQS: (305), (9920) imply:
% 156.21/23.76  | |   (9922)  all_40_2 = e3
% 156.21/23.76  | | 
% 156.21/23.76  | | REDUCE: (349), (9920) imply:
% 156.21/23.76  | |   (9923)   ~ (all_52_1 = e3)
% 156.21/23.76  | | 
% 156.21/23.76  | | REDUCE: (352), (9920) imply:
% 156.21/23.76  | |   (9924)   ~ (all_52_4 = e3)
% 156.21/23.76  | | 
% 156.21/23.76  | | REDUCE: (354), (9920) imply:
% 156.21/23.76  | |   (9925)   ~ (all_52_6 = e3)
% 156.21/23.76  | | 
% 156.21/23.76  | | REDUCE: (356), (9920) imply:
% 156.21/23.76  | |   (9926)   ~ (all_52_7 = e3)
% 156.21/23.76  | | 
% 156.21/23.76  | | REDUCE: (358), (9920) imply:
% 156.21/23.76  | |   (9927)   ~ (all_52_9 = e3)
% 156.21/23.76  | | 
% 156.21/23.76  | | REDUCE: (360), (9920) imply:
% 156.21/23.76  | |   (9928)   ~ (all_52_13 = e3)
% 156.21/23.76  | | 
% 156.21/23.76  | | REDUCE: (36), (9920) imply:
% 156.21/23.76  | |   (9929)  op(e2, e2) = e3
% 156.21/23.76  | | 
% 156.21/23.76  | | BETA: splitting (40) gives:
% 156.21/23.76  | | 
% 156.21/23.76  | | Case 1:
% 156.21/23.76  | | | 
% 156.21/23.76  | | |   (9930)   ~ (all_6_2 = e0)
% 156.21/23.76  | | | 
% 156.21/23.76  | | | BETA: splitting (46) gives:
% 156.21/23.76  | | | 
% 156.21/23.76  | | | Case 1:
% 156.21/23.76  | | | | 
% 156.21/23.76  | | | |   (9931)   ~ (all_10_2 = e2)
% 156.21/23.76  | | | | 
% 156.21/23.76  | | | | BETA: splitting (49) gives:
% 156.21/23.76  | | | | 
% 156.21/23.76  | | | | Case 1:
% 156.21/23.76  | | | | | 
% 156.21/23.76  | | | | |   (9932)   ~ (all_12_2 = e2)
% 156.21/23.76  | | | | | 
% 156.21/23.76  | | | | | REDUCE: (324), (9932) imply:
% 156.21/23.76  | | | | |   (9933)   ~ (all_6_2 = e2)
% 156.21/23.76  | | | | | 
% 156.21/23.76  | | | | | BETA: splitting (52) gives:
% 156.21/23.76  | | | | | 
% 156.21/23.76  | | | | | Case 1:
% 156.21/23.76  | | | | | | 
% 156.21/23.76  | | | | | |   (9934)   ~ (all_14_2 = e1)
% 156.21/23.76  | | | | | | 
% 156.21/23.76  | | | | | | BETA: splitting (58) gives:
% 156.21/23.76  | | | | | | 
% 156.21/23.76  | | | | | | Case 1:
% 156.21/23.76  | | | | | | | 
% 156.21/23.76  | | | | | | |   (9935)   ~ (all_18_2 = e3)
% 156.21/23.76  | | | | | | | 
% 156.21/23.76  | | | | | | | REDUCE: (301), (9935) imply:
% 156.21/23.76  | | | | | | |   (9936)   ~ (all_14_2 = e3)
% 156.21/23.76  | | | | | | | 
% 156.21/23.76  | | | | | | | BETA: splitting (61) gives:
% 156.21/23.76  | | | | | | | 
% 156.21/23.76  | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | 
% 156.21/23.76  | | | | | | | |   (9937)   ~ (all_20_2 = e3)
% 156.21/23.76  | | | | | | | | 
% 156.21/23.76  | | | | | | | | REDUCE: (325), (9937) imply:
% 156.21/23.76  | | | | | | | |   (9938)   ~ (all_10_2 = e3)
% 156.21/23.76  | | | | | | | | 
% 156.21/23.76  | | | | | | | | BETA: splitting (64) gives:
% 156.21/23.76  | | | | | | | | 
% 156.21/23.76  | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | 
% 156.21/23.76  | | | | | | | | |   (9939)   ~ (all_22_2 = e0)
% 156.21/23.76  | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | REDUCE: (251), (9939) imply:
% 156.21/23.76  | | | | | | | | |   (9940)   ~ (all_10_2 = e0)
% 156.21/23.76  | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | BETA: splitting (194) gives:
% 156.21/23.76  | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | |   (9941)  all_54_10 = e3
% 156.21/23.76  | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | COMBINE_EQS: (336), (9941) imply:
% 156.21/23.76  | | | | | | | | | |   (9942)  all_10_2 = e3
% 156.21/23.76  | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | REDUCE: (9938), (9942) imply:
% 156.21/23.76  | | | | | | | | | |   (9943)  $false
% 156.21/23.76  | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | CLOSE: (9943) is inconsistent.
% 156.21/23.76  | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | Case 2:
% 156.21/23.76  | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | |   (9944)   ~ (all_54_10 = e3)
% 156.21/23.76  | | | | | | | | | |   (9945)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.21/23.76  | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | BETA: splitting (9945) gives:
% 156.21/23.76  | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | |   (9946)  all_54_10 = e2
% 156.21/23.76  | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | COMBINE_EQS: (336), (9946) imply:
% 156.21/23.76  | | | | | | | | | | |   (9947)  all_10_2 = e2
% 156.21/23.76  | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | REDUCE: (9931), (9947) imply:
% 156.21/23.76  | | | | | | | | | | |   (9948)  $false
% 156.21/23.76  | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | CLOSE: (9948) is inconsistent.
% 156.21/23.76  | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | Case 2:
% 156.21/23.76  | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | |   (9949)   ~ (all_54_10 = e2)
% 156.21/23.76  | | | | | | | | | | |   (9950)  all_54_10 = e1 | all_54_10 = e0
% 156.21/23.76  | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | BETA: splitting (9950) gives:
% 156.21/23.76  | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | |   (9951)  all_54_10 = e1
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | COMBINE_EQS: (336), (9951) imply:
% 156.21/23.76  | | | | | | | | | | | |   (9952)  all_10_2 = e1
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | REDUCE: (350), (9952) imply:
% 156.21/23.76  | | | | | | | | | | | |   (9953)   ~ (all_52_2 = e1)
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | REDUCE: (361), (9952) imply:
% 156.21/23.76  | | | | | | | | | | | |   (9954)   ~ (all_52_6 = e1)
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | REDUCE: (364), (9952) imply:
% 156.21/23.76  | | | | | | | | | | | |   (9955)   ~ (all_52_9 = e1)
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | REDUCE: (366), (9952) imply:
% 156.21/23.76  | | | | | | | | | | | |   (9956)   ~ (all_52_11 = e1)
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | REDUCE: (368), (9952) imply:
% 156.21/23.76  | | | | | | | | | | | |   (9957)   ~ (all_52_14 = e1)
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | REDUCE: (9938), (9952) imply:
% 156.21/23.76  | | | | | | | | | | | |   (9958)   ~ (e3 = e1)
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | REDUCE: (9931), (9952) imply:
% 156.21/23.76  | | | | | | | | | | | |   (9959)   ~ (e2 = e1)
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | REDUCE: (45), (9952) imply:
% 156.21/23.76  | | | | | | | | | | | |   (9960)  op(e1, e1) = e1
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | BETA: splitting (73) gives:
% 156.21/23.76  | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | |   (9961)   ~ (all_28_2 = e2)
% 156.21/23.76  | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | REDUCE: (330), (9961) imply:
% 156.21/23.76  | | | | | | | | | | | | |   (9962)   ~ (all_14_2 = e2)
% 156.21/23.76  | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | BETA: splitting (189) gives:
% 156.21/23.76  | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | |   (9963)  all_54_15 = e3
% 156.21/23.76  | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | COMBINE_EQS: (246), (9963) imply:
% 156.21/23.76  | | | | | | | | | | | | | |   (9964)  all_14_2 = e3
% 156.21/23.76  | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | REDUCE: (9936), (9964) imply:
% 156.21/23.76  | | | | | | | | | | | | | |   (9965)  $false
% 156.21/23.76  | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | CLOSE: (9965) is inconsistent.
% 156.21/23.76  | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | Case 2:
% 156.21/23.76  | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | |   (9966)   ~ (all_54_15 = e3)
% 156.21/23.76  | | | | | | | | | | | | | |   (9967)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.21/23.76  | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | BETA: splitting (9967) gives:
% 156.21/23.76  | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | |   (9968)  all_54_15 = e2
% 156.21/23.76  | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | COMBINE_EQS: (246), (9968) imply:
% 156.21/23.76  | | | | | | | | | | | | | | |   (9969)  all_14_2 = e2
% 156.21/23.76  | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | REDUCE: (9962), (9969) imply:
% 156.21/23.76  | | | | | | | | | | | | | | |   (9970)  $false
% 156.21/23.76  | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | CLOSE: (9970) is inconsistent.
% 156.21/23.76  | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | Case 2:
% 156.21/23.76  | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | |   (9971)   ~ (all_54_15 = e2)
% 156.21/23.76  | | | | | | | | | | | | | | |   (9972)  all_54_15 = e1 | all_54_15 = e0
% 156.21/23.76  | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | BETA: splitting (9972) gives:
% 156.21/23.76  | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9973)  all_54_15 = e1
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (9973) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9974)  all_14_2 = e1
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | REDUCE: (9934), (9974) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9975)  $false
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | CLOSE: (9975) is inconsistent.
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | Case 2:
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9976)  all_54_15 = e0
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (9976) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9977)  all_14_2 = e0
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | REDUCE: (351), (9977) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9978)   ~ (all_52_3 = e0)
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | REDUCE: (362), (9977) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9979)   ~ (all_52_7 = e0)
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | REDUCE: (369), (9977) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9980)   ~ (all_52_11 = e0)
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | REDUCE: (9936), (9977) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9981)   ~ (e3 = e0)
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | REDUCE: (9962), (9977) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9982)   ~ (e2 = e0)
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | REDUCE: (9934), (9977) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9983)   ~ (e1 = e0)
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | REDUCE: (51), (9977) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | |   (9984)  op(e0, e0) = e0
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 156.21/23.76  | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | |   (9985)   ~ (all_26_2 = e1)
% 156.21/23.76  | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | REDUCE: (307), (9985) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | | |   (9986)   ~ (all_6_2 = e1)
% 156.21/23.76  | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 156.21/23.76  | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | |   (9987)  all_54_0 = e3
% 156.21/23.76  | | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (9987) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | | | |   (9988)  all_6_2 = e3
% 156.21/23.76  | | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | REDUCE: (346), (9988) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | | | |   (9989)   ~ (all_52_8 = e3)
% 156.21/23.76  | | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | REDUCE: (348), (9988) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | | | |   (9990)   ~ (all_52_12 = e3)
% 156.21/23.76  | | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | REDUCE: (39), (9988) imply:
% 156.21/23.76  | | | | | | | | | | | | | | | | | |   (9991)  op(e3, e3) = e3
% 156.21/23.76  | | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 156.21/23.76  | | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |   (9992)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |           (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |           (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |               e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.76  | | | | | | | | | | | | | | | | | | |             e1)
% 156.21/23.76  | | | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (9992) gives:
% 156.21/23.76  | | | | | | | | | | | | | | | | | | | 
% 156.21/23.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.76  | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |   (9993)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |               e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9993) gives:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |   (9994)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |               e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |             = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |           (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |             e3 & $i(all_57_10))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9994) gives:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |   (9995)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |               e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |               e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9995) gives:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (9996)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |           = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9996) implies:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (9997)  op(e3, e3) = e2
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9991), (9997), (function-axioms) are
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (9998)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |           e3 & $i(all_57_10)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9998) implies:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (9999)  op(e3, e2) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (9924), (9999), (function-axioms) are
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |   (10000)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10000) gives:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (10001)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10001) implies:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (10002)  op(e1, e1) = e2
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9960), (10002), (function-axioms) are
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (10003)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10003) implies:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (10004)  op(e3, e1) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9989), (10004), (function-axioms) are
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |   (10005)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_12))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10005) gives:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |   (10006)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (9984), (9990), (10006),
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |            #932.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |   (10007)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10007) gives:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (10008)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10008) implies:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (10009)  op(e2, e2) = e2
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10009), (function-axioms) are
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |   (10010)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9960), (9991), (10010),
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | |            #924.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | End of split
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |   (10011)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | |              e1)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10011) gives:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |   (10012)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10012) gives:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |   (10013)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |                e2) = e3)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (9924), (9984), (10013),
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |            #997.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |   (10014)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |                e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9991), (10014), (function-axioms) are
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |   (10015)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10015) gives:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |   (10016)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (9960), (10016), (function-axioms)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #53.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |   (10017)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (163), (9953), (9960), (9984),
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |            (10017), (function-axioms) are inconsistent by
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #988.
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | End of split
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | End of split
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | 
% 156.21/23.77  | | | | | | | | | | | | | | | | | | Case 2:
% 156.21/23.77  | | | | | | | | | | | | | | | | | | | 
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |   (10018)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 156.21/23.78  | | | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 156.21/23.78  | | | | | | | | | | | | | | | | | | | 
% 156.21/23.78  | | | | | | | | | | | | | | | | | | | BETA: splitting (10018) gives:
% 156.21/23.78  | | | | | | | | | | | | | | | | | | | 
% 156.21/23.78  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.21/23.78  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |   (10019)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10019) gives:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |   (10020)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14))
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10020) gives:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |   (10021)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (9991), (10021), (function-axioms)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #52.
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |   (10022)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (9960), (9984), (10022),
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            #985.
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |   (10023)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |                e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10023) gives:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |   (10024)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (9954), (9960), (10024),
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            #983.
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |   (10025)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |                e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |                e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (169), (9984), (9989), (9991), (10025),
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            #980.
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |   (10026)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10026) gives:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |   (10027)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10027) gives:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |   (10028)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |                e1) = e2)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (9929), (9984), (10028),
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            #51.
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |   (10029)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9929), (9984), (10029),
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | |            #50.
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.78  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |   (10030)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10030) gives:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |   (10031)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (9984), (9990), (10031),
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |            #975.
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |   (10032)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10032) gives:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |   (10033)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10033) implies:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |   (10034)  op(e2, e2) = e2
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10034), (function-axioms) are
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |   (10035)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (160), (9957), (9978),
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |            (9979), (9980), (10035), (function-axioms) are
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #96.
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.79  | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | |   (10036)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.26/23.79  | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (9930), (9933), (9986), (10036) are
% 156.26/23.79  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 156.26/23.79  | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | End of split
% 156.26/23.79  | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.79  | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | |   (10037)  all_26_2 = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (10037) imply:
% 156.26/23.79  | | | | | | | | | | | | | | | | |   (10038)  all_6_2 = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | REDUCE: (342), (10038) imply:
% 156.26/23.79  | | | | | | | | | | | | | | | | |   (10039)   ~ (all_52_3 = e1)
% 156.26/23.79  | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | REDUCE: (348), (10038) imply:
% 156.26/23.79  | | | | | | | | | | | | | | | | |   (10040)   ~ (all_52_12 = e1)
% 156.26/23.79  | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | REDUCE: (39), (10038) imply:
% 156.26/23.79  | | | | | | | | | | | | | | | | |   (10041)  op(e3, e3) = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 156.26/23.79  | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | |   (10042)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | BETA: splitting (10042) gives:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | |   (10043)  all_56_12 = e1 & op(e0, e3) = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (10039), (10043), (function-axioms) are
% 156.26/23.79  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #852.
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | |   (10044)  all_56_13 = e1 & op(e0, e2) = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | ALPHA: (10044) implies:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | |   (10045)  op(e0, e2) = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | |   (10046)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10046) gives:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |   (10047)  all_56_9 = e1 & op(e3, e0) = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10040), (10047), (function-axioms) are
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #851.
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |   (10048)  all_56_10 = e1 & op(e2, e0) = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10048) implies:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | |   (10049)  op(e2, e0) = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |   (10050)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10050) gives:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |   (10051)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10051) gives:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |   (10052)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10052) gives:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (10053)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10053) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10054)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10054) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10055)  op(e3, e3) = e2
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10041), (10055), (function-axioms) are
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10056)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 & 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10056) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10057)  op(e3, e2) = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (9924), (10057), (function-axioms) are
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (10058)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10058) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10059)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10059) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10060)  op(e1, e1) = e2
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9960), (10060), (function-axioms) are
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10061)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10061) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10062)   ~ (all_57_10 = e1)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10063)  op(e3, e3) = all_57_10
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (10041),
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |              (10063) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10064)  all_57_10 = e1
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10062), (10064) imply:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10065)  $false
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10065) is inconsistent.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |   (10066)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_12))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10066) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (10067)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10067) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10068)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10068) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10069)  op(e0, e0) = e2
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9984), (10069), (function-axioms) are
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10070)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10070) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10071)  op(e2, e3) = e2
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10072)  op(e3, e0) = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10073)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9929), (10041), (10073),
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #49.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10074)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10074) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10075)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_8 & $i(all_57_8)))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10075) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10076)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10077)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10077) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10078)  all_57_12 = e1 & op(e2, e2) = e1
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10078) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10079)  op(e2, e2) = e1
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (10079), (function-axioms) are
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10080)   ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10080) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10081)  op(e2, e1) = all_57_5
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10076) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10082)  all_57_15 = e1 & op(e0, e0) = e1
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10082) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10083)  op(e0, e0) = e1
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (9984), (10083), (function-axioms) are
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10084)   ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_8)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10084) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10085)  op(e0, e1) = all_57_8
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_8, e1, e0, simplifying with (157), (10085)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10086)  all_57_8 = all_52_11
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e1,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (10045) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10087)  all_52_7 = e1
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (164), (10049) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10088)  all_52_13 = e1
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5, e1, e2, simplifying with (165), (10081)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10089)  all_57_5 = all_52_9
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (10071) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10090)  all_52_1 = e2
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (168), (10072) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10091)  all_52_12 = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (10090) imply:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10092)   ~ (all_52_3 = e2)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10092) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10093)   ~ (all_52_3 = e2)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (10091) imply:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10094)   ~ (all_52_8 = e3)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10095)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (9927), (10094), (10095),
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #48.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10096)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10096) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10097)  all_56_8 = e3 & op(e1, e1) = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10097) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10098)  op(e1, e1) = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9960), (10098), (function-axioms) are
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10099)  all_56_14 = e3 & op(e0, e1) = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10099) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10100)  op(e0, e1) = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10101)  all_54_12 = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (10101) imply:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10102)  all_52_3 = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10102) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10103)  all_52_3 = e3
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (10103) imply:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10104)   ~ (all_52_11 = e3)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10104) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10105)   ~ (all_52_11 = e3)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (10100), (10105), (function-axioms) are
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #720.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10106)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10106) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10107)  all_54_12 = e2
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (10093), (10107) are inconsistent by
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #696.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10108)  all_54_12 = e1 | all_54_12 = e0
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (9978), (10039), (10108) are inconsistent
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #619.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10109)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13)))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10109) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10110)  (all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10110) gives:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10111)  all_57_10 = e0 & op(e3, e3) = e0
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10111) implies:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10112)  op(e3, e3) = e0
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10041), (10112), (function-axioms) are
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10113)   ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_9)
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10072), (10113), (function-axioms) are
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #47.
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.80  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (10114)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10114) gives:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10115)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10115) implies:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10116)  op(e2, e2) = e2
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10116), (function-axioms) are
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10117)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9960), (10041), (10117),
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            #825.
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |   (10118)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10118) gives:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |   (10119)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10119) gives:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (10120)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9984), (10041), (10120),
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |            #850.
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (10121)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (9953), (10049), (10121),
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |            #812.
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |   (10122)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10122) gives:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (10123)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (9960), (10123), (function-axioms)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #53.
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (10124)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (51), (163), (9953), (9960), (9984),
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |            (10124), (function-axioms) are inconsistent by
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #988.
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |   (10125)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10125) gives:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |   (10126)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10126) gives:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |   (10127)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14))
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10127) gives:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (10128)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10128) gives:
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10129)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10129) implies:
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10130)  op(e1, e2) = e1
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (9954), (10130), (function-axioms) are
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #984.
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10131)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10131) implies:
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10132)  op(e2, e2) = e1
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (10132), (function-axioms) are
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (10133)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (9960), (9984), (10133),
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |            #985.
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |   (10134)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (160), (162), (9954), (9957), (9960),
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |            (9984), (10041), (10134), (function-axioms) are
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #838.
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.26/23.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |   (10135)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10135) gives:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |   (10136)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10136) gives:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (10137)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2)
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (9929), (9984), (10137),
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |            #51.
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (10138)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9929), (9984), (10138),
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |            #50.
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |   (10139)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10139) gives:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (10140)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9984), (10041), (10140),
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |            #836.
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (10141)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10141) gives:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10142)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10142) implies:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10143)  op(e2, e2) = e2
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10143), (function-axioms) are
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10144)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10144) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10145)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10145) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10146)  op(e1, e0) = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (9957), (10146), (function-axioms) are
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10147)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0))
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10147) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10148)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (159), (9960), (9978), (9980),
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10041), (10045), (10148), (function-axioms) are
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #819.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | |   (10149)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10149) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | |   (10150)  all_56_11 = e1 & op(e1, e0) = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10150) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | |   (10151)  op(e1, e0) = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (9957), (10151), (function-axioms) are
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | |   (10152)  all_56_15 = e1 & op(e0, e0) = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10152) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | |   (10153)  op(e0, e0) = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (9984), (10153), (function-axioms) are
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | |   (10154)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (157), (9956), (9984), (10154),
% 156.38/23.83  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.38/23.83  | | | | | | | | | | | | | | | | | |            #215.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | End of split
% 156.38/23.83  | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | |   (10155)  all_28_2 = e2
% 156.38/23.83  | | | | | | | | | | | | |   (10156)  ( ~ (all_28_0 = e1) & op(e2, e0) = all_28_0 &
% 156.38/23.83  | | | | | | | | | | | | |              $i(all_28_0)) | ( ~ (all_28_1 = e3) & op(e2, e2)
% 156.38/23.83  | | | | | | | | | | | | |              = all_28_1 & $i(all_28_1))
% 156.38/23.83  | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | COMBINE_EQS: (330), (10155) imply:
% 156.38/23.83  | | | | | | | | | | | | |   (10157)  all_14_2 = e2
% 156.38/23.83  | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | REDUCE: (351), (10157) imply:
% 156.38/23.83  | | | | | | | | | | | | |   (10158)   ~ (all_52_3 = e2)
% 156.38/23.83  | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | REDUCE: (370), (10157) imply:
% 156.38/23.83  | | | | | | | | | | | | |   (10159)   ~ (all_52_12 = e2)
% 156.38/23.83  | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | REDUCE: (371), (10157) imply:
% 156.38/23.83  | | | | | | | | | | | | |   (10160)   ~ (all_52_13 = e2)
% 156.38/23.83  | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | REDUCE: (372), (10157) imply:
% 156.38/23.83  | | | | | | | | | | | | |   (10161)   ~ (all_52_14 = e2)
% 156.38/23.83  | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | REDUCE: (51), (10157) imply:
% 156.38/23.83  | | | | | | | | | | | | |   (10162)  op(e0, e0) = e2
% 156.38/23.83  | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | BETA: splitting (10156) gives:
% 156.38/23.83  | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | |   (10163)   ~ (all_28_0 = e1) & op(e2, e0) = all_28_0 &
% 156.38/23.83  | | | | | | | | | | | | | |            $i(all_28_0)
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | ALPHA: (10163) implies:
% 156.38/23.83  | | | | | | | | | | | | | |   (10164)   ~ (all_28_0 = e1)
% 156.38/23.83  | | | | | | | | | | | | | |   (10165)  op(e2, e0) = all_28_0
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 156.38/23.83  | | | | | | | | | | | | | |              all_28_0, e0, e2, simplifying with (164), (10165)
% 156.38/23.83  | | | | | | | | | | | | | |              gives:
% 156.38/23.83  | | | | | | | | | | | | | |   (10166)  all_52_13 = all_28_0
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | COMBINE_EQS: (260), (10166) imply:
% 156.38/23.83  | | | | | | | | | | | | | |   (10167)  all_54_7 = all_28_0
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | REDUCE: (145), (10166) imply:
% 156.38/23.83  | | | | | | | | | | | | | |   (10168)   ~ (all_52_1 = all_28_0)
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | REDUCE: (117), (10166) imply:
% 156.38/23.83  | | | | | | | | | | | | | |   (10169)   ~ (all_52_9 = all_28_0)
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | REDUCE: (113), (10166) imply:
% 156.38/23.83  | | | | | | | | | | | | | |   (10170)   ~ (all_52_12 = all_28_0)
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | REDUCE: (110), (10166) imply:
% 156.38/23.83  | | | | | | | | | | | | | |   (10171)   ~ (all_52_14 = all_28_0)
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | SIMP: (10171) implies:
% 156.38/23.83  | | | | | | | | | | | | | |   (10172)   ~ (all_52_14 = all_28_0)
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | REDUCE: (9928), (10166) imply:
% 156.38/23.83  | | | | | | | | | | | | | |   (10173)   ~ (all_28_0 = e3)
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | REDUCE: (10160), (10166) imply:
% 156.38/23.83  | | | | | | | | | | | | | |   (10174)   ~ (all_28_0 = e2)
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 156.38/23.83  | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | |   (10175)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 156.38/23.83  | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 156.38/23.83  | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | BETA: splitting (10175) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | |   (10176)  all_56_2 = e1 & op(e2, e3) = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | ALPHA: (10176) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | |   (10177)  all_56_2 = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | |   (10178)  all_54_7 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | COMBINE_EQS: (10167), (10178) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | |   (10179)  all_28_0 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | REDUCE: (10173), (10179) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | |   (10180)  $false
% 156.38/23.83  | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | CLOSE: (10180) is inconsistent.
% 156.38/23.83  | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | |   (10181)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | BETA: splitting (10181) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | |   (10182)  all_54_7 = e2
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10167), (10182) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | |   (10183)  all_28_0 = e2
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | REDUCE: (10174), (10183) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | |   (10184)  $false
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | CLOSE: (10184) is inconsistent.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | |   (10185)   ~ (all_54_7 = e2)
% 156.38/23.83  | | | | | | | | | | | | | | | | | |   (10186)  all_54_7 = e1 | all_54_7 = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | BETA: splitting (10186) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10187)  all_54_7 = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10167), (10187) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10188)  all_28_0 = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | REDUCE: (10164), (10188) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10189)  $false
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | CLOSE: (10189) is inconsistent.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10190)  all_54_7 = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10167), (10190) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10191)  all_28_0 = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | REDUCE: (10168), (10191) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10192)   ~ (all_52_1 = e0)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | REDUCE: (10169), (10191) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10193)   ~ (all_52_9 = e0)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | REDUCE: (10170), (10191) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10194)   ~ (all_52_12 = e0)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | REDUCE: (10172), (10191) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10195)   ~ (all_52_14 = e0)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | REDUCE: (10174), (10191) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10196)   ~ (e2 = e0)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | REDUCE: (10164), (10191) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | |   (10197)   ~ (e1 = e0)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | |   (10198)  all_54_11 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (10198) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | |   (10199)  all_52_14 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | SIMP: (10199) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | |   (10200)  all_52_14 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (10200) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | |   (10201)   ~ (all_52_12 = e3)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (10200) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | |   (10202)  op(e1, e0) = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | |   (10203)  all_54_6 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (10203) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | |   (10204)  all_52_9 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | REDUCE: (9927), (10204) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | |   (10205)  $false
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | CLOSE: (10205) is inconsistent.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | |   (10206)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | |   (10207)  all_54_3 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10207) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | |   (10208)  all_52_12 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10201), (10208) imply:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | |   (10209)  $false
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10209) is inconsistent.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | |   (10210)   ~ (all_54_3 = e3)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | |   (10211)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | |   (10212)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10212) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | |   (10213)  all_56_9 = e3 & op(e3, e0) = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10213) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | |   (10214)  op(e3, e0) = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10201), (10214), (function-axioms) are
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | |   (10215)  all_56_10 = e3 & op(e2, e0) = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10215) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | |   (10216)  all_56_10 = e3
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (10217)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10217) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10218)  all_56_9 = e1 & op(e3, e0) = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10218) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10219)  all_56_9 = e1
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10220)  all_56_15 = e0 & op(e0, e0) = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10220) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10221)  op(e0, e0) = e0
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10162), (10221), (function-axioms) are
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10222)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10222) implies:
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10223)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 156.38/23.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10223) gives:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10224)  all_56_9 = e0 & op(e3, e0) = e0
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10224) implies:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10225)  all_56_9 = e0
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10219), (10225) are inconsistent by
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #756.
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10226)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10226) gives:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10227)  all_56_10 = e0 & op(e2, e0) = e0
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10216), (10227) are inconsistent by
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #551.
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10228)  all_56_11 = e0 & op(e1, e0) = e0
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10228) implies:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10229)  op(e1, e0) = e0
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10202), (10229), (function-axioms) are
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #314.
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10230)  all_56_10 = e1 & op(e2, e0) = e1
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10164), (10165), (10230), (function-axioms) are
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #46.
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (10231)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (9957), (10162), (10231),
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | |            #45.
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | |   (10232)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10232) gives:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | |   (10233)  all_56_11 = e3 & op(e1, e0) = e3
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10233) implies:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | |   (10234)  all_56_11 = e3
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (10235)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10235) gives:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10236)  all_56_9 = e1 & op(e3, e0) = e1
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10236) implies:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10237)  all_56_9 = e1
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10211) gives:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10238)  all_54_3 = e2
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10238) imply:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10239)  all_52_12 = e2
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10239) implies:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10240)  all_52_12 = e2
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10159), (10240) imply:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10241)  $false
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10241) is inconsistent.
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10242)   ~ (all_54_3 = e2)
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10243)  all_54_3 = e1 | all_54_3 = e0
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10244)  all_56_15 = e0 & op(e0, e0) = e0
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10244) implies:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10245)  op(e0, e0) = e0
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10162), (10245), (function-axioms) are
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10246)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10246) implies:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10247)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10247) gives:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.38/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10248)  all_56_9 = e0 & op(e3, e0) = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10194), (10248), (function-axioms) are
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #620.
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10249)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10249) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10250)  all_56_10 = e0 & op(e2, e0) = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10250) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10251)  all_56_10 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10243) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10252)  all_54_3 = e1
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10252) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10253)  all_52_12 = e1
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10253) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10254)  all_52_12 = e1
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (10254) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10255)   ~ (all_6_2 = e1)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10255) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10256)   ~ (all_6_2 = e1)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (10254) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10257)  op(e3, e0) = e1
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10206) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10258)  all_54_6 = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (10258) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10259)  all_52_9 = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (10259) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10260)   ~ (all_52_1 = e2)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (10259) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10261)   ~ (all_52_8 = e2)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (10259) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10262)  op(e2, e1) = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10263)  all_54_4 = e3
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10263) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10264)  all_52_1 = e3
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9923), (10264) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10265)  $false
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10265) is inconsistent.
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10266)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10267)  all_54_0 = e3
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (10267) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10268)  all_6_2 = e3
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10268) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10269)  all_6_2 = e3
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (342), (10269) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10270)   ~ (all_52_3 = e3)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (10269) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10271)   ~ (all_52_8 = e3)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (10269) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10272)  op(e3, e3) = e3
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10273)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10273) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10274)  all_56_0 = e2 & op(e3, e3) = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10274) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10275)  op(e3, e3) = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (51),
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (58), (61), (64), (73), (123), (157), (158),
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (189), (194), (202), (214),
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (225), (227), (228), (230),
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (234), (236), (238), (239), (246), (251),
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (271), (301), (325), (330), (336), (350), (351),
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (358), (361), (362), (363), (364), (368), (369),
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (370), (371), (9924), (9929), (9931), (10260),
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10261), (10275), (function-axioms) are
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #34.
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10276)  all_56_1 = e2 & op(e3, e2) = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10276) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10277)  all_56_1 = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10278)  op(e3, e2) = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10266) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10279)  all_54_4 = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10279) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10280)  all_52_1 = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10260), (10280) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10281)  $false
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10281) is inconsistent.
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10282)   ~ (all_54_4 = e2)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10283)  all_54_4 = e1 | all_54_4 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10284)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (10272), (10277), (10284),
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #634.
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10285)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10285) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10286)  all_56_4 = e0 & op(e3, e1) = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10286) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10287)  all_56_4 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10283) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10288)  all_54_4 = e1
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10288) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10289)  all_52_1 = e1
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10289) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10290)  all_52_1 = e1
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (10290) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10291)   ~ (all_52_2 = e1)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (10290) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10292)   ~ (all_52_3 = e1)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10292) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10293)   ~ (all_52_3 = e1)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (10290) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10294)  op(e2, e3) = e1
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10295)  all_54_12 = e3
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (10270), (10295) are inconsistent by
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #697.
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10296)   ~ (all_54_12 = e3)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10297)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10297) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10298)  all_54_12 = e2
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (10158), (10298) are inconsistent by
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #696.
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10299)   ~ (all_54_12 = e2)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10300)  all_54_12 = e1 | all_54_12 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10300) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10301)  all_54_12 = e1
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (10293), (10301) are inconsistent by
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #695.
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10302)  all_54_12 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (10302) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10303)  all_52_3 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10303) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10304)  all_52_3 = e0
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (10304) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10305)   ~ (all_52_7 = e0)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10305) implies:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10306)   ~ (all_52_7 = e0)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10270), (10304) imply:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10307)   ~ (e3 = e0)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10308)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.44/23.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10308) gives:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10309)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10309) gives:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10310)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10260), (10310), (function-axioms) are
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1005.
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10311)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_12))
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10311) gives:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10312)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10260), (10312), (function-axioms) are
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10313)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10313) gives:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10314)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10314) implies:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10315)  op(e2, e3) = e2
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10260), (10315), (function-axioms) are
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10316)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10316) gives:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10317)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10317) implies:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10318)  op(e1, e1) = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (157), (165), (218), (9955), (9956),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10287), (10318), (function-axioms) are
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10319)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10319) implies:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10320)  op(e3, e3) = e2
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (51),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (58), (61), (64), (73), (123), (157), (158),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (189), (194), (202), (214),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (225), (227), (228), (230),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (234), (236), (238), (239), (246), (251),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (271), (301), (325), (330), (336), (350), (351),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (358), (361), (362), (363), (364), (368), (369),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (370), (371), (9924), (9929), (9931), (10260),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10261), (10320), (function-axioms) are
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #34.
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10321)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10321) gives:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10322)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10322) gives:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10323)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10162), (10278), (10323), (function-axioms)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #33.
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10324)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10324) gives:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10325)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10325) implies:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10326)  op(e2, e0) = e2
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (10160), (10326), (function-axioms) are
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10327)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10327) implies:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10328)  op(e3, e3) = e1
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (230), (234),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (10237), (10261), (10328),
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #147.
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10329)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10329) gives:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10330)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10330) gives:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10331)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10331) implies:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10332)  op(e1, e1) = e3
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (157), (165), (218), (9955), (9956),
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10287), (10332), (function-axioms) are
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10333)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10333) implies:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10334)  op(e2, e2) = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (223), (224),
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10177), (10251), (10294), (10334),
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #260.
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10335)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10335) gives:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10336)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10336) implies:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10337)  op(e0, e0) = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10162), (10337), (function-axioms) are
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10338)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10338) gives:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10339)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10339) implies:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10340)  op(e1, e1) = e3
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (157), (165), (218), (9955), (9956),
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10287), (10340), (function-axioms) are
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10341)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10341) implies:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10342)  op(e1, e3) = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9953), (10342), (function-axioms) are
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #990.
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10343)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10343) gives:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10344)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10344) gives:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10345)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14))
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10345) gives:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10346)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10346) gives:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10347)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10347) implies:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10348)  op(e3, e3) = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (230), (234),
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (10237), (10261), (10348),
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #147.
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10349)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10349) implies:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10350)  op(e2, e2) = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (223), (224),
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10177), (10251), (10294), (10350),
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #260.
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10351)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9960), (10162), (10351), (function-axioms)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #873.
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10352)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10352) gives:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10353)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (9954), (9960), (10353),
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10354)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10354) gives:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10355)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10355) implies:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10356)  op(e0, e0) = e3
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10162), (10356), (function-axioms) are
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10357)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10357) gives:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10358)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10358) implies:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10359)  op(e3, e1) = e3
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10271), (10359), (function-axioms) are
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10360)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10360) implies:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10361)  op(e3, e3) = e1
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (230), (234),
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (10237), (10261), (10361),
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #147.
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10362)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10362) gives:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10363)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10363) gives:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10364)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10364) gives:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10365)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10365) implies:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10366)  op(e0, e2) = e0
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10306), (10366), (function-axioms) are
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10367)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10367) implies:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10368)  op(e2, e2) = e2
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (10262), (10368),
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10369)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10369) gives:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10370)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10370) implies:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10371)  op(e2, e2) = e1
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (223), (224),
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10177), (10251), (10294), (10371),
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #260.
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10372)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10372) implies:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10373)  op(e0, e0) = e3
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10162), (10373), (function-axioms) are
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10374)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10374) gives:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10375)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (10160), (10257), (10375),
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #715.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10376)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10376) gives:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10377)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10377) implies:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10378)  op(e2, e2) = e2
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (165), (358), (10262), (10378),
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10379)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10379) gives:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10380)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10380) implies:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10381)  op(e1, e0) = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (9957), (10381), (function-axioms) are
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10382)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0))
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10382) implies:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10383)  op(e0, e0) = all_57_15
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10384)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (159), (160), (164), (167),
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (9957), (9960), (10158), (10160), (10162),
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10260), (10272), (10383), (10384),
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #857.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10385)  all_54_4 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (10192), (10385) are inconsistent by
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #510.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10386)  all_56_9 = e0 & op(e3, e0) = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10386) implies:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10387)  all_56_9 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10235) gives:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10237), (10387) imply:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10388)  e1 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (10388) imply:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10389)  $false
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10389) is inconsistent.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10390)  all_56_10 = e1 & op(e2, e0) = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10251), (10390) are inconsistent by
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #434.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10391)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10391) gives:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10392)  all_56_11 = e1 & op(e1, e0) = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10392) implies:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10393)  all_56_11 = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10234), (10393) imply:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10394)  e3 = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10394) implies:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10395)  e3 = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (10395) imply:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10396)  $false
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10396) is inconsistent.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10397)  all_56_15 = e1 & op(e0, e0) = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10397) implies:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10398)  op(e0, e0) = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10162), (10398), (function-axioms) are
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10399)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (10159), (10261), (10399),
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #511.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10400)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (9930), (9933), (10256), (10400) are
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10401)  all_54_6 = e1 | all_54_6 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10401) gives:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10402)  all_54_6 = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (10402) imply:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10403)  all_52_9 = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9955), (10403) imply:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10404)  $false
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10404) is inconsistent.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10405)  all_54_6 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (10405) imply:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10406)  all_52_9 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10193), (10406) imply:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10407)  $false
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10407) is inconsistent.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10408)  all_54_3 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10408) imply:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10409)  all_52_12 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10409) implies:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10410)  all_52_12 = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10194), (10410) imply:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10411)  $false
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10411) is inconsistent.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10412)  all_56_11 = e0 & op(e1, e0) = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10412) implies:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10413)  op(e1, e0) = e0
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10202), (10413), (function-axioms) are
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #314.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10414)  all_56_10 = e1 & op(e2, e0) = e1
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10164), (10165), (10414), (function-axioms) are
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #46.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (10415)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (9957), (10162), (10415),
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | |            #45.
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | | |   (10416)  all_56_15 = e3 & op(e0, e0) = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10416) implies:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | | |   (10417)  op(e0, e0) = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10162), (10417), (function-axioms) are
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |   (10418)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10418) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |   (10419)  all_54_11 = e2
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (10161), (10419) are inconsistent by
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |            sub-proof #588.
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |   (10420)  all_54_11 = e1 | all_54_11 = e0
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (9957), (10195), (10420) are inconsistent
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #623.
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | |   (10421)  all_56_3 = e1 & op(e2, e2) = e1
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | ALPHA: (10421) implies:
% 156.44/23.89  | | | | | | | | | | | | | | | |   (10422)  op(e2, e2) = e1
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (10422), (function-axioms) are
% 156.44/23.89  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | |   (10423)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 156.44/23.89  | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 156.44/23.89  | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | BETA: splitting (10423) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | |   (10424)  all_56_5 = e1 & op(e2, e1) = e1
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9955), (10424), (function-axioms) are
% 156.44/23.89  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | |   (10425)  all_56_10 = e1 & op(e2, e0) = e1
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | REF_CLOSE: (10164), (10165), (10425), (function-axioms) are
% 156.44/23.89  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #46.
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | |   (10426)   ~ (all_28_1 = e3) & op(e2, e2) = all_28_1 &
% 156.44/23.89  | | | | | | | | | | | | | |            $i(all_28_1)
% 156.44/23.89  | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | ALPHA: (10426) implies:
% 156.44/23.89  | | | | | | | | | | | | | |   (10427)   ~ (all_28_1 = e3)
% 156.44/23.89  | | | | | | | | | | | | | |   (10428)  op(e2, e2) = all_28_1
% 156.44/23.89  | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 156.44/23.89  | | | | | | | | | | | | | |              e2, e2, simplifying with (9929), (10428) gives:
% 156.44/23.89  | | | | | | | | | | | | | |   (10429)  all_28_1 = e3
% 156.44/23.89  | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | REDUCE: (10427), (10429) imply:
% 156.44/23.89  | | | | | | | | | | | | | |   (10430)  $false
% 156.44/23.89  | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | CLOSE: (10430) is inconsistent.
% 156.44/23.89  | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | |   (10431)  all_54_10 = e0
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | COMBINE_EQS: (336), (10431) imply:
% 156.44/23.89  | | | | | | | | | | | |   (10432)  all_10_2 = e0
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | REDUCE: (9940), (10432) imply:
% 156.44/23.89  | | | | | | | | | | | |   (10433)  $false
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | CLOSE: (10433) is inconsistent.
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | End of split
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | |   (10434)  all_22_2 = e0
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | COMBINE_EQS: (251), (10434) imply:
% 156.44/23.89  | | | | | | | | |   (10435)  all_10_2 = e0
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | COMBINE_EQS: (333), (10435) imply:
% 156.44/23.89  | | | | | | | | |   (10436)  all_38_2 = e0
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | REDUCE: (361), (10435) imply:
% 156.44/23.89  | | | | | | | | |   (10437)   ~ (all_52_6 = e0)
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | REDUCE: (364), (10435) imply:
% 156.44/23.89  | | | | | | | | |   (10438)   ~ (all_52_9 = e0)
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | REDUCE: (366), (10435) imply:
% 156.44/23.89  | | | | | | | | |   (10439)   ~ (all_52_11 = e0)
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | REDUCE: (9931), (10435) imply:
% 156.44/23.89  | | | | | | | | |   (10440)   ~ (e2 = e0)
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | REDUCE: (45), (10435) imply:
% 156.44/23.89  | | | | | | | | |   (10441)  op(e1, e1) = e0
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | BETA: splitting (73) gives:
% 156.44/23.89  | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | |   (10442)   ~ (all_28_2 = e2)
% 156.44/23.89  | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | REDUCE: (330), (10442) imply:
% 156.44/23.89  | | | | | | | | | |   (10443)   ~ (all_14_2 = e2)
% 156.44/23.89  | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | BETA: splitting (189) gives:
% 156.44/23.89  | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | |   (10444)  all_54_15 = e3
% 156.44/23.89  | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | REF_CLOSE: (246), (9936), (10444) are inconsistent by
% 156.44/23.89  | | | | | | | | | | |            sub-proof #1010.
% 156.44/23.89  | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | |   (10445)   ~ (all_54_15 = e3)
% 156.44/23.89  | | | | | | | | | | |   (10446)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.44/23.89  | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | BETA: splitting (10446) gives:
% 156.44/23.89  | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | |   (10447)  all_54_15 = e2
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | REF_CLOSE: (246), (10443), (10447) are inconsistent by
% 156.44/23.89  | | | | | | | | | | | |            sub-proof #1009.
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | |   (10448)   ~ (all_54_15 = e2)
% 156.44/23.89  | | | | | | | | | | | |   (10449)  all_54_15 = e1 | all_54_15 = e0
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | BETA: splitting (10449) gives:
% 156.44/23.89  | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | |   (10450)  all_54_15 = e1
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | REF_CLOSE: (246), (9934), (10450) are inconsistent by
% 156.44/23.89  | | | | | | | | | | | | |            sub-proof #1008.
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | |   (10451)  all_54_15 = e0
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | COMBINE_EQS: (246), (10451) imply:
% 156.44/23.89  | | | | | | | | | | | | |   (10452)  all_14_2 = e0
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | SIMP: (10452) implies:
% 156.44/23.89  | | | | | | | | | | | | |   (10453)  all_14_2 = e0
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | REDUCE: (362), (10453) imply:
% 156.44/23.89  | | | | | | | | | | | | |   (10454)   ~ (all_52_7 = e0)
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | REDUCE: (371), (10453) imply:
% 156.44/23.89  | | | | | | | | | | | | |   (10455)   ~ (all_52_13 = e0)
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | REDUCE: (9936), (10453) imply:
% 156.44/23.89  | | | | | | | | | | | | |   (10456)   ~ (e3 = e0)
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | REDUCE: (9934), (10453) imply:
% 156.44/23.89  | | | | | | | | | | | | |   (10457)   ~ (e1 = e0)
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | REDUCE: (51), (10453) imply:
% 156.44/23.89  | | | | | | | | | | | | |   (10458)  op(e0, e0) = e0
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | BETA: splitting (221) gives:
% 156.44/23.89  | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | |   (10459)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 156.44/23.89  | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 156.44/23.89  | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | BETA: splitting (10459) gives:
% 156.44/23.89  | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | |   (10460)  all_56_2 = e0 & op(e2, e3) = e0
% 156.44/23.89  | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | ALPHA: (10460) implies:
% 156.44/23.89  | | | | | | | | | | | | | | |   (10461)  op(e2, e3) = e0
% 156.44/23.89  | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | |   (10462)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 156.44/23.89  | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | BETA: splitting (10462) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | |   (10463)  all_56_1 = e0 & op(e3, e2) = e0
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | ALPHA: (10463) implies:
% 156.44/23.89  | | | | | | | | | | | | | | | | |   (10464)  all_56_1 = e0
% 156.44/23.89  | | | | | | | | | | | | | | | | |   (10465)  op(e3, e2) = e0
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 156.44/23.89  | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (10461) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | |   (10466)  all_52_1 = e0
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 156.44/23.89  | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (10465) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | |   (10467)  all_52_4 = e0
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | REDUCE: (148), (10466) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | |   (10468)   ~ (all_52_3 = e0)
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | SIMP: (10468) implies:
% 156.44/23.89  | | | | | | | | | | | | | | | | |   (10469)   ~ (all_52_3 = e0)
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | REDUCE: (135), (10467) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | |   (10470)   ~ (all_52_7 = e0)
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | REDUCE: (344), (10467) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | |   (10471)   ~ (all_6_2 = e0)
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | BETA: splitting (9921) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10472)   ~ (all_4_0 = e0) & op(e3, e2) = all_4_0 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | |            $i(all_4_0)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | ALPHA: (10472) implies:
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10473)   ~ (all_4_0 = e0)
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10474)  op(e3, e2) = all_4_0
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0,
% 156.44/23.89  | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (10465), (10474) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10475)  all_4_0 = e0
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | REDUCE: (10473), (10475) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10476)  $false
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | CLOSE: (10476) is inconsistent.
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10477)   ~ (all_4_1 = e1) & op(e3, e3) = all_4_1 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | ALPHA: (10477) implies:
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10478)   ~ (all_4_1 = e1)
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10479)  op(e3, e3) = all_4_1
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 156.44/23.89  | | | | | | | | | | | | | | | | | |              all_4_1, e3, e3, simplifying with (39), (10479)
% 156.44/23.89  | | | | | | | | | | | | | | | | | |              gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10480)  all_6_2 = all_4_1
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (10480) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10481)  all_54_0 = all_4_1
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | REDUCE: (346), (10480) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10482)   ~ (all_52_8 = all_4_1)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | REDUCE: (348), (10480) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10483)   ~ (all_52_12 = all_4_1)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | REDUCE: (9933), (10480) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10484)   ~ (all_4_1 = e2)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | REDUCE: (9930), (10480) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | | |   (10485)   ~ (all_4_1 = e0)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | |   (10486)  all_54_0 = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10481), (10486) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | |   (10487)  all_4_1 = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | REDUCE: (10482), (10487) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | |   (10488)   ~ (all_52_8 = e3)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | REDUCE: (10483), (10487) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | |   (10489)   ~ (all_52_12 = e3)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | REDUCE: (10479), (10487) imply:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | |   (10490)  op(e3, e3) = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |   (10491)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | |              e1)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10491) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |   (10492)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10492) gives:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.89  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |   (10493)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10461), (10493), (function-axioms) are
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #242.
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |   (10494)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_12))
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10494) gives:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |   (10495)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10461), (10495), (function-axioms) are
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #241.
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |   (10496)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10496) gives:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |   (10497)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10497) implies:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |   (10498)  op(e2, e3) = e2
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10461), (10498), (function-axioms) are
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #709.
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |   (10499)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10499) gives:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (10500)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10500) implies:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (10501)  op(e1, e1) = e3
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10441), (10501), (function-axioms) are
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (10502)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10502) implies:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (10503)  op(e3, e3) = e2
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (168), (169), (236), (10464), (10488),
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (10489), (10503), (function-axioms) are
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #212.
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |   (10504)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10504) gives:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |   (10505)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10505) gives:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |   (10506)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (9924), (10458), (10506),
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |            #997.
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |   (10507)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |                e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10507) gives:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |   (10508)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10508) implies:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |   (10509)  op(e3, e3) = e2
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (168), (169), (236), (10464), (10488),
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            (10489), (10509), (function-axioms) are
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #212.
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |   (10510)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10510) implies:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |   (10511)  op(e3, e3) = e1
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10490), (10511), (function-axioms) are
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |   (10512)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10512) gives:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |   (10513)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9929), (10441), (10513),
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |            #41.
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |   (10514)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (51), (10441), (10458), (10514),
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | |            #240.
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.90  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |   (10515)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10515) gives:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |   (10516)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10516) gives:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |   (10517)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10517) gives:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |   (10518)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (10490), (10518), (function-axioms)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #52.
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |   (10519)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (51), (10441), (10458), (10519),
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |            #491.
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |   (10520)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10520) gives:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |   (10521)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10441), (10521), (function-axioms) are
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |   (10522)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |                e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (169), (10458), (10488), (10490),
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |            (10522), (function-axioms) are inconsistent by
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #980.
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |   (10523)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10523) gives:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |   (10524)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10524) gives:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |   (10525)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (9929), (10458), (10525),
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |            #51.
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |   (10526)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9929), (10458), (10526),
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | |            #50.
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |   (10527)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10527) gives:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.44/23.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | |   (10528)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (10458), (10489), (10528),
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | |            #975.
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.44/23.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |   (10529)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10529) gives:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |   (10530)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10530) implies:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |   (10531)  op(e2, e2) = e2
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10531), (function-axioms) are
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |   (10532)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10532) gives:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (10533)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10533) implies:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (10534)  op(e1, e1) = e1
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10441), (10534), (function-axioms) are
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (10535)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e0))
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10535) implies:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (10536)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (10439), (10454), (10469),
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |            (10536), (function-axioms) are inconsistent by
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #97.
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | |   (10537)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | BETA: splitting (10537) gives:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | |   (10538)  all_54_0 = e2
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10481), (10538) imply:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | |   (10539)  all_4_1 = e2
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (10484), (10539) imply:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | |   (10540)  $false
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | CLOSE: (10540) is inconsistent.
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | |   (10541)  all_54_0 = e1 | all_54_0 = e0
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10541) gives:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | |   (10542)  all_54_0 = e1
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10481), (10542) imply:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | |   (10543)  all_4_1 = e1
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | REDUCE: (10478), (10543) imply:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | |   (10544)  $false
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | CLOSE: (10544) is inconsistent.
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | |   (10545)  all_54_0 = e0
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10481), (10545) imply:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | |   (10546)  all_4_1 = e0
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | REDUCE: (10485), (10546) imply:
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | |   (10547)  $false
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | CLOSE: (10547) is inconsistent.
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | |   (10548)  all_56_3 = e0 & op(e2, e2) = e0
% 156.75/23.92  | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | ALPHA: (10548) implies:
% 156.75/23.92  | | | | | | | | | | | | | | | | |   (10549)  op(e2, e2) = e0
% 156.75/23.92  | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (10549), (function-axioms) are
% 156.75/23.92  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 156.75/23.92  | | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | |   (10550)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 156.75/23.92  | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 156.75/23.92  | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (10437), (10454), (10550),
% 156.75/23.92  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/23.92  | | | | | | | | | | | | | | | |            #897.
% 156.75/23.92  | | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | |   (10551)  all_56_3 = e0 & op(e2, e2) = e0
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | ALPHA: (10551) implies:
% 156.75/23.92  | | | | | | | | | | | | | | |   (10552)  op(e2, e2) = e0
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (10552), (function-axioms) are
% 156.75/23.92  | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | |   (10553)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 156.75/23.92  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 156.75/23.92  | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | BETA: splitting (10553) gives:
% 156.75/23.92  | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | Case 1:
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | |   (10554)  all_56_5 = e0 & op(e2, e1) = e0
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | ALPHA: (10554) implies:
% 156.75/23.92  | | | | | | | | | | | | | | |   (10555)  op(e2, e1) = e0
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | REF_CLOSE: (165), (10438), (10555), (function-axioms) are
% 156.75/23.92  | | | | | | | | | | | | | | |            inconsistent by sub-proof #79.
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | |   (10556)  all_56_10 = e0 & op(e2, e0) = e0
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | ALPHA: (10556) implies:
% 156.75/23.92  | | | | | | | | | | | | | | |   (10557)  op(e2, e0) = e0
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 156.75/23.92  | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (10557) gives:
% 156.75/23.92  | | | | | | | | | | | | | | |   (10558)  all_52_13 = e0
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | REDUCE: (10455), (10558) imply:
% 156.75/23.92  | | | | | | | | | | | | | | |   (10559)  $false
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | | CLOSE: (10559) is inconsistent.
% 156.75/23.92  | | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | End of split
% 156.75/23.92  | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | |   (10560)  all_28_2 = e2
% 156.75/23.92  | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | COMBINE_EQS: (330), (10560) imply:
% 156.75/23.92  | | | | | | | | | |   (10561)  all_14_2 = e2
% 156.75/23.92  | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | REDUCE: (369), (10561) imply:
% 156.75/23.92  | | | | | | | | | |   (10562)   ~ (all_52_11 = e2)
% 156.75/23.92  | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | REDUCE: (9936), (10561) imply:
% 156.75/23.92  | | | | | | | | | |   (10563)   ~ (e3 = e2)
% 156.75/23.92  | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | REDUCE: (51), (10561) imply:
% 156.75/23.92  | | | | | | | | | |   (10564)  op(e0, e0) = e2
% 156.75/23.92  | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | BETA: splitting (88) gives:
% 156.75/23.92  | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | Case 1:
% 156.75/23.92  | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | |   (10565)   ~ (all_38_2 = e0)
% 156.75/23.92  | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | REDUCE: (10436), (10565) imply:
% 156.75/23.92  | | | | | | | | | | |   (10566)  $false
% 156.75/23.92  | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | CLOSE: (10566) is inconsistent.
% 156.75/23.92  | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | Case 2:
% 156.75/23.92  | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | |   (10567)  ( ~ (all_38_0 = e3) & op(e0, e1) = all_38_0 &
% 156.75/23.92  | | | | | | | | | | |              $i(all_38_0)) | ( ~ (all_38_1 = e2) & op(e0, e0)
% 156.75/23.92  | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 156.75/23.92  | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | BETA: splitting (10567) gives:
% 156.75/23.92  | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | Case 1:
% 156.75/23.92  | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | |   (10568)   ~ (all_38_0 = e3) & op(e0, e1) = all_38_0 &
% 156.75/23.92  | | | | | | | | | | | |            $i(all_38_0)
% 156.75/23.92  | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | ALPHA: (10568) implies:
% 156.75/23.92  | | | | | | | | | | | |   (10569)   ~ (all_38_0 = e3)
% 156.75/23.92  | | | | | | | | | | | |   (10570)  op(e0, e1) = all_38_0
% 156.75/23.92  | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | BETA: splitting (238) gives:
% 156.75/23.92  | | | | | | | | | | | | 
% 156.75/23.92  | | | | | | | | | | | | Case 1:
% 156.75/23.92  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | |   (10571)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.75/23.93  | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 156.75/23.93  | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.75/23.93  | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.75/23.93  | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.75/23.93  | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 156.75/23.93  | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 156.75/23.93  | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 156.75/23.93  | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.75/23.93  | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 156.75/23.93  | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.75/23.93  | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.75/23.93  | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.75/23.93  | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 156.75/23.93  | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 156.75/23.93  | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | BETA: splitting (10571) gives:
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | |   (10572)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.75/23.93  | | | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 156.75/23.93  | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.75/23.93  | | | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.75/23.93  | | | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.75/23.93  | | | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 156.75/23.93  | | | | | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 156.75/23.93  | | | | | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 156.75/23.93  | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | ALPHA: (10572) implies:
% 156.75/23.93  | | | | | | | | | | | | | |   (10573)  op(e3, e3) = e3
% 156.75/23.93  | | | | | | | | | | | | | |   (10574)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 156.75/23.93  | | | | | | | | | | | | | |                = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 156.75/23.93  | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | BETA: splitting (10574) gives:
% 156.75/23.93  | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | |   (10575)  all_57_15 = e3 & op(e0, e0) = e3
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | ALPHA: (10575) implies:
% 156.75/23.93  | | | | | | | | | | | | | | |   (10576)  op(e0, e0) = e3
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | REF_CLOSE: (9), (10564), (10576), (function-axioms) are
% 156.75/23.93  | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | |   (10577)   ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 &
% 156.75/23.93  | | | | | | | | | | | | | | |            $i(all_57_6)
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | ALPHA: (10577) implies:
% 156.75/23.93  | | | | | | | | | | | | | | |   (10578)  op(e0, e3) = all_57_6
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 156.75/23.93  | | | | | | | | | | | | | | |              all_38_0, e1, e0, simplifying with (157), (10570)
% 156.75/23.93  | | | | | | | | | | | | | | |              gives:
% 156.75/23.93  | | | | | | | | | | | | | | |   (10579)  all_52_11 = all_38_0
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 156.75/23.93  | | | | | | | | | | | | | | |              all_57_6, e3, e0, simplifying with (159), (10578)
% 156.75/23.93  | | | | | | | | | | | | | | |              gives:
% 156.75/23.93  | | | | | | | | | | | | | | |   (10580)  all_57_6 = all_52_3
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e3,
% 156.75/23.93  | | | | | | | | | | | | | | |              e3, e3, simplifying with (39), (10573) gives:
% 156.75/23.93  | | | | | | | | | | | | | | |   (10581)  all_6_2 = e3
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | COMBINE_EQS: (247), (10579) imply:
% 156.75/23.93  | | | | | | | | | | | | | | |   (10582)  all_54_14 = all_38_0
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | REDUCE: (139), (10579) imply:
% 156.75/23.93  | | | | | | | | | | | | | | |   (10583)   ~ (all_52_3 = all_38_0)
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | REDUCE: (125), (10579) imply:
% 156.75/23.93  | | | | | | | | | | | | | | |   (10584)   ~ (all_52_7 = all_38_0)
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | REDUCE: (10562), (10579) imply:
% 156.75/23.93  | | | | | | | | | | | | | | |   (10585)   ~ (all_38_0 = e2)
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | REDUCE: (10439), (10579) imply:
% 156.75/23.93  | | | | | | | | | | | | | | |   (10586)   ~ (all_38_0 = e0)
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | |   (10587)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 156.75/23.93  | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 156.75/23.93  | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | BETA: splitting (10587) gives:
% 156.75/23.93  | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | |   (10588)  all_56_12 = e3 & op(e0, e3) = e3
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | | ALPHA: (10588) implies:
% 156.75/23.93  | | | | | | | | | | | | | | | | |   (10589)  all_56_12 = e3
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 156.75/23.93  | | | | | | | | | | | | | | | | |            (10573), (10589), (function-axioms) are
% 156.75/23.93  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #729.
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | |   (10590)  all_56_13 = e3 & op(e0, e2) = e3
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9926), (10590), (function-axioms) are
% 156.75/23.93  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | |   (10591)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 156.75/23.93  | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 156.75/23.93  | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | BETA: splitting (10591) gives:
% 156.75/23.93  | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | |   (10592)  all_56_14 = e3 & op(e0, e1) = e3
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | | ALPHA: (10592) implies:
% 156.75/23.93  | | | | | | | | | | | | | | | | |   (10593)  all_56_14 = e3
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (159), (190), (207), (10564), (10569),
% 156.75/23.93  | | | | | | | | | | | | | | | | |            (10582), (10583), (10584), (10585), (10586),
% 156.75/23.93  | | | | | | | | | | | | | | | | |            (10593), (function-axioms) are inconsistent by
% 156.75/23.93  | | | | | | | | | | | | | | | | |            sub-proof #665.
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | |   (10594)  all_56_15 = e3 & op(e0, e0) = e3
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | | ALPHA: (10594) implies:
% 156.75/23.93  | | | | | | | | | | | | | | | | |   (10595)  op(e0, e0) = e3
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10564), (10595), (function-axioms) are
% 156.75/23.93  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 156.75/23.93  | | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | |   (10596)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.75/23.93  | | | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 156.75/23.93  | | | | | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.75/23.93  | | | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.75/23.93  | | | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.75/23.93  | | | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 156.75/23.93  | | | | | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 156.75/23.93  | | | | | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 156.75/23.93  | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | ALPHA: (10596) implies:
% 156.75/23.93  | | | | | | | | | | | | | |   (10597)  op(e2, e2) = e2
% 156.75/23.93  | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10597), (function-axioms) are
% 156.75/23.93  | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/23.93  | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | |   (10598)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 156.75/23.93  | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 156.75/23.93  | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.75/23.93  | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.75/23.93  | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.75/23.93  | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 156.75/23.93  | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 156.75/23.93  | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 156.75/23.93  | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.75/23.93  | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 156.75/23.93  | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.75/23.93  | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.75/23.93  | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.75/23.93  | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.75/23.93  | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.75/23.93  | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10441), (10564), (10598),
% 156.75/23.93  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/23.93  | | | | | | | | | | | | |            #671.
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | |   (10599)   ~ (all_38_1 = e2) & op(e0, e0) = all_38_1 &
% 156.75/23.93  | | | | | | | | | | | |            $i(all_38_1)
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | ALPHA: (10599) implies:
% 156.75/23.93  | | | | | | | | | | | |   (10600)   ~ (all_38_1 = e2)
% 156.75/23.93  | | | | | | | | | | | |   (10601)  op(e0, e0) = all_38_1
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_38_1,
% 156.75/23.93  | | | | | | | | | | | |              e0, e0, simplifying with (10564), (10601) gives:
% 156.75/23.93  | | | | | | | | | | | |   (10602)  all_38_1 = e2
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | REDUCE: (10600), (10602) imply:
% 156.75/23.93  | | | | | | | | | | | |   (10603)  $false
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | CLOSE: (10603) is inconsistent.
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | | 
% 156.75/23.93  | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | 
% 156.75/23.93  | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | 
% 156.75/23.93  | | | | | | | |   (10604)  all_20_2 = e3
% 156.75/23.93  | | | | | | | | 
% 156.75/23.93  | | | | | | | | COMBINE_EQS: (325), (10604) imply:
% 156.75/23.93  | | | | | | | |   (10605)  all_10_2 = e3
% 156.75/23.93  | | | | | | | | 
% 156.75/23.93  | | | | | | | | REDUCE: (368), (10605) imply:
% 156.75/23.93  | | | | | | | |   (10606)   ~ (all_52_14 = e3)
% 156.75/23.93  | | | | | | | | 
% 156.75/23.93  | | | | | | | | REDUCE: (45), (10605) imply:
% 156.75/23.93  | | | | | | | |   (10607)  op(e1, e1) = e3
% 156.75/23.93  | | | | | | | | 
% 156.75/23.93  | | | | | | | | BETA: splitting (212) gives:
% 156.75/23.93  | | | | | | | | 
% 156.75/23.93  | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | 
% 156.75/23.93  | | | | | | | | |   (10608)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3
% 156.75/23.93  | | | | | | | | |              & op(e2, e0) = e3)
% 156.75/23.93  | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | BETA: splitting (10608) gives:
% 156.75/23.93  | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | |   (10609)  all_56_9 = e3 & op(e3, e0) = e3
% 156.75/23.93  | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | ALPHA: (10609) implies:
% 156.75/23.93  | | | | | | | | | |   (10610)  op(e3, e0) = e3
% 156.75/23.93  | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 156.75/23.93  | | | | | | | | | |              e3, e0, e3, simplifying with (168), (10610) gives:
% 156.75/23.93  | | | | | | | | | |   (10611)  all_52_12 = e3
% 156.75/23.93  | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | REDUCE: (348), (10611) imply:
% 156.75/23.93  | | | | | | | | | |   (10612)   ~ (all_6_2 = e3)
% 156.75/23.93  | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | SIMP: (10612) implies:
% 156.75/23.93  | | | | | | | | | |   (10613)   ~ (all_6_2 = e3)
% 156.75/23.93  | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | BETA: splitting (204) gives:
% 156.75/23.93  | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | |   (10614)  all_54_0 = e3
% 156.75/23.93  | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | REF_CLOSE: (279), (10613), (10614) are inconsistent by
% 156.75/23.93  | | | | | | | | | | |            sub-proof #390.
% 156.75/23.93  | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | |   (10615)   ~ (all_54_0 = e3)
% 156.75/23.93  | | | | | | | | | | |   (10616)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.75/23.93  | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | BETA: splitting (238) gives:
% 156.75/23.93  | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | |   (10617)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.75/23.93  | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 156.75/23.93  | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.75/23.93  | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.75/23.93  | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.75/23.93  | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 156.75/23.93  | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 156.75/23.93  | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 156.75/23.93  | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.75/23.93  | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 156.75/23.93  | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.75/23.93  | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.75/23.93  | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.75/23.93  | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 156.75/23.93  | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 156.75/23.93  | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | BETA: splitting (10617) gives:
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | |   (10618)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.75/23.93  | | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 156.75/23.93  | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.75/23.93  | | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.75/23.93  | | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.75/23.93  | | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 156.75/23.93  | | | | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 156.75/23.93  | | | | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | ALPHA: (10618) implies:
% 156.75/23.93  | | | | | | | | | | | | |   (10619)  op(e3, e3) = e3
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | REF_CLOSE: (39), (279), (9930), (9933), (10613), (10616),
% 156.75/23.93  | | | | | | | | | | | | |            (10619), (function-axioms) are inconsistent by
% 156.75/23.93  | | | | | | | | | | | | |            sub-proof #32.
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | |   (10620)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.75/23.93  | | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 156.75/23.93  | | | | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.75/23.93  | | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.75/23.93  | | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.75/23.93  | | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 156.75/23.93  | | | | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 156.75/23.93  | | | | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | ALPHA: (10620) implies:
% 156.75/23.93  | | | | | | | | | | | | |   (10621)  op(e2, e2) = e2
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10621), (function-axioms) are
% 156.75/23.93  | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | End of split
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | |   (10622)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 156.75/23.93  | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 156.75/23.93  | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.75/23.93  | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.75/23.93  | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.75/23.93  | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 156.75/23.93  | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 156.75/23.93  | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 156.75/23.93  | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.75/23.93  | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 156.75/23.93  | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.75/23.93  | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.75/23.93  | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.75/23.93  | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.75/23.93  | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.75/23.93  | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | BETA: splitting (10622) gives:
% 156.75/23.93  | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | |   (10623)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 156.75/23.93  | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 156.75/23.93  | | | | | | | | | | | | |                op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.75/23.93  | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.75/23.93  | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.75/23.93  | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 156.75/23.93  | | | | | | | | | | | | |                = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 156.75/23.93  | | | | | | | | | | | | |                all_57_8 & $i(all_57_8)))
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | ALPHA: (10623) implies:
% 156.75/23.93  | | | | | | | | | | | | |   (10624)  op(e1, e1) = e1
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | REF_CLOSE: (8), (10607), (10624), (function-axioms) are
% 156.75/23.93  | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | Case 2:
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | |   (10625)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.75/23.93  | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 156.75/23.93  | | | | | | | | | | | | |                op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.75/23.93  | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.75/23.93  | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.75/23.93  | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.75/23.93  | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.75/23.93  | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13)))
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | ALPHA: (10625) implies:
% 156.75/23.93  | | | | | | | | | | | | |   (10626)  (all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9
% 156.75/23.93  | | | | | | | | | | | | |                = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | BETA: splitting (10626) gives:
% 156.75/23.93  | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | Case 1:
% 156.75/23.93  | | | | | | | | | | | | | | 
% 156.75/23.93  | | | | | | | | | | | | | |   (10627)  all_57_10 = e0 & op(e3, e3) = e0
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | ALPHA: (10627) implies:
% 156.75/23.94  | | | | | | | | | | | | | |   (10628)  op(e3, e3) = e0
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e0,
% 156.75/23.94  | | | | | | | | | | | | | |              e3, e3, simplifying with (39), (10628) gives:
% 156.75/23.94  | | | | | | | | | | | | | |   (10629)  all_6_2 = e0
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | REDUCE: (9930), (10629) imply:
% 156.75/23.94  | | | | | | | | | | | | | |   (10630)  $false
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | CLOSE: (10630) is inconsistent.
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | |   (10631)   ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 156.75/23.94  | | | | | | | | | | | | | |            $i(all_57_9)
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | REF_CLOSE: (168), (10610), (10631), (function-axioms) are
% 156.75/23.94  | | | | | | | | | | | | | |            inconsistent by sub-proof #47.
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | End of split
% 156.75/23.94  | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | End of split
% 156.75/23.94  | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | End of split
% 156.75/23.94  | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | End of split
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | |   (10632)  all_56_10 = e3 & op(e2, e0) = e3
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | REF_CLOSE: (164), (9928), (10632), (function-axioms) are
% 156.75/23.94  | | | | | | | | | |            inconsistent by sub-proof #31.
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | End of split
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | |   (10633)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 156.75/23.94  | | | | | | | | |              e3 & op(e0, e0) = e3)
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | BETA: splitting (10633) gives:
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | |   (10634)  all_56_11 = e3 & op(e1, e0) = e3
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | ALPHA: (10634) implies:
% 156.75/23.94  | | | | | | | | | |   (10635)  op(e1, e0) = e3
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | REF_CLOSE: (160), (10606), (10635), (function-axioms) are
% 156.75/23.94  | | | | | | | | | |            inconsistent by sub-proof #677.
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | |   (10636)  all_56_15 = e3 & op(e0, e0) = e3
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | ALPHA: (10636) implies:
% 156.75/23.94  | | | | | | | | | |   (10637)  op(e0, e0) = e3
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | REF_CLOSE: (51), (9936), (10637), (function-axioms) are
% 156.75/23.94  | | | | | | | | | |            inconsistent by sub-proof #245.
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | End of split
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | End of split
% 156.75/23.94  | | | | | | | | 
% 156.75/23.94  | | | | | | | End of split
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | Case 2:
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | |   (10638)  all_18_2 = e3
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | | COMBINE_EQS: (301), (10638) imply:
% 156.75/23.94  | | | | | | |   (10639)  all_14_2 = e3
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | | SIMP: (10639) implies:
% 156.75/23.94  | | | | | | |   (10640)  all_14_2 = e3
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | | COMBINE_EQS: (299), (10640) imply:
% 156.75/23.94  | | | | | | |   (10641)  all_48_2 = e3
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | | REDUCE: (369), (10640) imply:
% 156.75/23.94  | | | | | | |   (10642)   ~ (all_52_11 = e3)
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | | REDUCE: (370), (10640) imply:
% 156.75/23.94  | | | | | | |   (10643)   ~ (all_52_12 = e3)
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | | REDUCE: (372), (10640) imply:
% 156.75/23.94  | | | | | | |   (10644)   ~ (all_52_14 = e3)
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | | REDUCE: (51), (10640) imply:
% 156.75/23.94  | | | | | | |   (10645)  op(e0, e0) = e3
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | | BETA: splitting (212) gives:
% 156.75/23.94  | | | | | | | 
% 156.75/23.94  | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | 
% 156.75/23.94  | | | | | | | |   (10646)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 &
% 156.75/23.94  | | | | | | | |              op(e2, e0) = e3)
% 156.75/23.94  | | | | | | | | 
% 156.75/23.94  | | | | | | | | BETA: splitting (10646) gives:
% 156.75/23.94  | | | | | | | | 
% 156.75/23.94  | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | |   (10647)  all_56_9 = e3 & op(e3, e0) = e3
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | ALPHA: (10647) implies:
% 156.75/23.94  | | | | | | | | |   (10648)  op(e3, e0) = e3
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | REF_CLOSE: (168), (10643), (10648), (function-axioms) are
% 156.75/23.94  | | | | | | | | |            inconsistent by sub-proof #976.
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | |   (10649)  all_56_10 = e3 & op(e2, e0) = e3
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | ALPHA: (10649) implies:
% 156.75/23.94  | | | | | | | | |   (10650)  all_56_10 = e3
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (210), (211),
% 156.75/23.94  | | | | | | | | |            (10645), (10650), (function-axioms) are
% 156.75/23.94  | | | | | | | | |            inconsistent by sub-proof #466.
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | End of split
% 156.75/23.94  | | | | | | | | 
% 156.75/23.94  | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | 
% 156.75/23.94  | | | | | | | |   (10651)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3
% 156.75/23.94  | | | | | | | |              & op(e0, e0) = e3)
% 156.75/23.94  | | | | | | | | 
% 156.75/23.94  | | | | | | | | BETA: splitting (10651) gives:
% 156.75/23.94  | | | | | | | | 
% 156.75/23.94  | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | |   (10652)  all_56_11 = e3 & op(e1, e0) = e3
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | ALPHA: (10652) implies:
% 156.75/23.94  | | | | | | | | |   (10653)  op(e1, e0) = e3
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | REF_CLOSE: (160), (10644), (10653), (function-axioms) are
% 156.75/23.94  | | | | | | | | |            inconsistent by sub-proof #677.
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | |   (10654)  all_56_15 = e3 & op(e0, e0) = e3
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | ALPHA: (10654) implies:
% 156.75/23.94  | | | | | | | | |   (10655)  all_56_15 = e3
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | BETA: splitting (61) gives:
% 156.75/23.94  | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | |   (10656)   ~ (all_20_2 = e3)
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | REDUCE: (325), (10656) imply:
% 156.75/23.94  | | | | | | | | | |   (10657)   ~ (all_10_2 = e3)
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | BETA: splitting (216) gives:
% 156.75/23.94  | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | |   (10658)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 156.75/23.94  | | | | | | | | | | |              & op(e1, e2) = e3)
% 156.75/23.94  | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | BETA: splitting (10658) gives:
% 156.75/23.94  | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | |   (10659)  all_56_6 = e3 & op(e1, e3) = e3
% 156.75/23.94  | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | ALPHA: (10659) implies:
% 156.75/23.94  | | | | | | | | | | | |   (10660)  op(e1, e3) = e3
% 156.75/23.94  | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | BETA: splitting (220) gives:
% 156.75/23.94  | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | |   (10661)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 156.75/23.94  | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 156.75/23.94  | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | BETA: splitting (10661) gives:
% 156.75/23.94  | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | |   (10662)  all_56_4 = e3 & op(e3, e1) = e3
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | ALPHA: (10662) implies:
% 156.75/23.94  | | | | | | | | | | | | | |   (10663)  all_56_4 = e3
% 156.75/23.94  | | | | | | | | | | | | | |   (10664)  op(e3, e1) = e3
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 156.75/23.94  | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (10660) gives:
% 156.75/23.94  | | | | | | | | | | | | | |   (10665)  all_52_2 = e3
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 156.75/23.94  | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (10664) gives:
% 156.75/23.94  | | | | | | | | | | | | | |   (10666)  all_52_8 = e3
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | REDUCE: (120), (10666) imply:
% 156.75/23.94  | | | | | | | | | | | | | |   (10667)   ~ (all_52_12 = e3)
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | REDUCE: (363), (10666) imply:
% 156.75/23.94  | | | | | | | | | | | | | |   (10668)   ~ (all_10_2 = e3)
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | REDUCE: (346), (10666) imply:
% 156.75/23.94  | | | | | | | | | | | | | |   (10669)   ~ (all_6_2 = e3)
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | SIMP: (10669) implies:
% 156.75/23.94  | | | | | | | | | | | | | |   (10670)   ~ (all_6_2 = e3)
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 156.75/23.94  | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | |   (10671)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.75/23.94  | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 156.75/23.94  | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.75/23.94  | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.75/23.94  | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.75/23.94  | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 156.75/23.94  | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 156.75/23.94  | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 156.75/23.94  | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.75/23.94  | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 156.75/23.94  | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.75/23.94  | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.75/23.94  | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.75/23.94  | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 156.75/23.94  | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 156.75/23.94  | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 156.75/23.94  | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | BETA: splitting (10671) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | |   (10672)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.75/23.94  | | | | | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 156.75/23.94  | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.75/23.94  | | | | | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.75/23.94  | | | | | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.75/23.94  | | | | | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 156.75/23.94  | | | | | | | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 156.75/23.94  | | | | | | | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | ALPHA: (10672) implies:
% 156.75/23.94  | | | | | | | | | | | | | | | |   (10673)  op(e3, e3) = e3
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | REF_CLOSE: (39), (204), (279), (9930), (9933), (10670),
% 156.75/23.94  | | | | | | | | | | | | | | | |            (10673), (function-axioms) are inconsistent by
% 156.75/23.94  | | | | | | | | | | | | | | | |            sub-proof #30.
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | |   (10674)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.75/23.94  | | | | | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 156.75/23.94  | | | | | | | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.75/23.94  | | | | | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.75/23.94  | | | | | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.75/23.94  | | | | | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 156.75/23.94  | | | | | | | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 156.75/23.94  | | | | | | | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | ALPHA: (10674) implies:
% 156.75/23.94  | | | | | | | | | | | | | | | |   (10675)  op(e2, e2) = e2
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10675), (function-axioms) are
% 156.75/23.94  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | End of split
% 156.75/23.94  | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | |   (10676)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 156.75/23.94  | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 156.75/23.94  | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.75/23.94  | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.75/23.94  | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.75/23.94  | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 156.75/23.94  | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 156.75/23.94  | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 156.75/23.94  | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.75/23.94  | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 156.75/23.94  | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.75/23.94  | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.75/23.94  | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.75/23.94  | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.75/23.94  | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.75/23.94  | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 156.75/23.94  | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | BETA: splitting (10676) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | |   (10677)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 156.75/23.94  | | | | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 156.75/23.94  | | | | | | | | | | | | | | | |                op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.75/23.94  | | | | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.75/23.94  | | | | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.75/23.94  | | | | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 156.75/23.94  | | | | | | | | | | | | | | | |                = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 156.75/23.94  | | | | | | | | | | | | | | | |                all_57_8 & $i(all_57_8)))
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | ALPHA: (10677) implies:
% 156.75/23.94  | | | | | | | | | | | | | | | |   (10678)  op(e1, e1) = e1
% 156.75/23.94  | | | | | | | | | | | | | | | |   (10679)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8
% 156.75/23.94  | | | | | | | | | | | | | | | |                = e0) & op(e0, e1) = all_57_8 & $i(all_57_8))
% 156.75/23.94  | | | | | | | | | | | | | | | |   (10680)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5
% 156.75/23.94  | | | | | | | | | | | | | | | |                = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))
% 156.75/23.94  | | | | | | | | | | | | | | | |   (10681)  (all_57_10 = e1 & op(e3, e3) = e1) | ( ~ (all_57_4
% 156.75/23.94  | | | | | | | | | | | | | | | |                = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | BETA: splitting (10680) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | |   (10682)  all_57_12 = e1 & op(e2, e2) = e1
% 156.75/23.94  | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | ALPHA: (10682) implies:
% 156.75/23.94  | | | | | | | | | | | | | | | | |   (10683)  op(e2, e2) = e1
% 156.75/23.94  | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (10683), (function-axioms) are
% 156.75/23.94  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 156.75/23.94  | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | |   (10684)   ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.75/23.94  | | | | | | | | | | | | | | | | |            $i(all_57_5)
% 156.75/23.94  | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | ALPHA: (10684) implies:
% 156.75/23.94  | | | | | | | | | | | | | | | | |   (10685)   ~ (all_57_5 = e2)
% 156.75/23.94  | | | | | | | | | | | | | | | | |   (10686)  op(e2, e1) = all_57_5
% 156.75/23.94  | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | |   (10687)  all_54_0 = e3
% 156.75/23.94  | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (10687) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | |   (10688)  all_6_2 = e3
% 156.75/23.94  | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | REDUCE: (10670), (10688) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | |   (10689)  $false
% 156.75/23.94  | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | CLOSE: (10689) is inconsistent.
% 156.75/23.94  | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | |   (10690)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.75/23.94  | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | BETA: splitting (10690) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | |   (10691)  all_54_0 = e2
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (10691) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | |   (10692)  all_6_2 = e2
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | REDUCE: (9933), (10692) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | |   (10693)  $false
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | CLOSE: (10693) is inconsistent.
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | |   (10694)  all_54_0 = e1 | all_54_0 = e0
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (10681) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | |   (10695)  all_57_10 = e1 & op(e3, e3) = e1
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (10695) implies:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | |   (10696)  all_57_10 = e1
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10694) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | |   (10697)  all_54_0 = e1
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (10697) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | |   (10698)  all_6_2 = e1
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (10698) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | |   (10699)   ~ (all_52_4 = e1)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (10698) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | |   (10700)   ~ (all_52_12 = e1)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (10698) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | |   (10701)  op(e3, e3) = e1
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | |   (10702)   ~ (all_48_2 = e3)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10641), (10702) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | |   (10703)  $false
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10703) is inconsistent.
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | |   (10704)  ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 &
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | |              $i(all_48_0)) | ( ~ (all_48_1 = e1) & op(e3, e3)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | |              = all_48_1 & $i(all_48_1))
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10704) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10705)   ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 &
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_48_0)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10705) implies:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10706)   ~ (all_48_0 = e2)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10707)  op(e3, e0) = all_48_0
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e1,
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (45), (10678) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10708)  all_10_2 = e1
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |              all_57_5, e1, e2, simplifying with (165), (10686)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10709)  all_57_5 = all_52_9
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |              all_48_0, e0, e3, simplifying with (168), (10707)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10710)  all_52_12 = all_48_0
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10710) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10711)  all_54_3 = all_48_0
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10685), (10709) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10712)   ~ (all_52_9 = e2)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (10708) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10713)   ~ (all_52_6 = e1)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (10708) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10714)   ~ (all_52_9 = e1)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (10710) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10715)   ~ (all_52_14 = all_48_0)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10715) implies:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10716)   ~ (all_52_14 = all_48_0)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10643), (10710) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10717)   ~ (all_48_0 = e3)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10700), (10710) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10718)   ~ (all_48_0 = e1)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (10708) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10719)   ~ (all_52_14 = e1)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10657), (10708) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10720)   ~ (e3 = e1)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9931), (10708) imply:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | |   (10721)   ~ (e2 = e1)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | |   (10722)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10722) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (10723)  all_56_0 = e2 & op(e3, e3) = e2
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10723) implies:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (10724)  op(e3, e3) = e2
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10701), (10724), (function-axioms) are
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (10725)  all_56_1 = e2 & op(e3, e2) = e2
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10725) implies:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (10726)  all_56_1 = e2
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (10727)  op(e3, e2) = e2
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10728)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10728) gives:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10729)  all_56_4 = e2 & op(e3, e1) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10729) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10730)  all_56_4 = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10663), (10730) imply:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10731)  e3 = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (10731) imply:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10732)  $false
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10732) is inconsistent.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10733)  all_56_5 = e2 & op(e2, e1) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10733) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10734)  op(e2, e1) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10712), (10734), (function-axioms) are
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10735)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10735) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10736)  all_56_8 = e2 & op(e1, e1) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10736) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10737)  op(e1, e1) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (133), (168), (170), (201),
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (238), (270), (272), (352), (10643),
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10645), (10699), (10700), (10701), (10704),
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10737), (function-axioms) are inconsistent by
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #415.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10738)  all_56_14 = e2 & op(e0, e1) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10738) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10739)  all_56_14 = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10740)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (229), (233),
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (9929), (10701), (10740), (function-axioms)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #29.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10741)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10741) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10742)  all_56_5 = e1 & op(e2, e1) = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10714), (10742), (function-axioms) are
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10743)  all_56_10 = e1 & op(e2, e0) = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10743) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10744)  all_56_10 = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10745)  op(e2, e0) = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10746)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10746) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10747)  all_56_1 = e1 & op(e3, e2) = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10747) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10748)  all_56_1 = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10726), (10748) are inconsistent by
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #680.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10749)  all_56_3 = e1 & op(e2, e2) = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10749) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10750)  op(e2, e2) = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (221), (223),
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (10712), (10744), (10750),
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #842.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10751)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10751) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10752)  all_56_7 = e1 & op(e1, e2) = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10752) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10753)  op(e1, e2) = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10713), (10753), (function-axioms) are
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #984.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10754)  all_56_13 = e1 & op(e0, e2) = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10754) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10755)  op(e0, e2) = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10756)  all_56_15 = e0 & op(e0, e0) = e0
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10756) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10757)  op(e0, e0) = e0
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10645), (10757), (function-axioms) are
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10758)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10758) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10759)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10760)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10760) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10761)  all_56_0 = e2 & op(e3, e3) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10761) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10762)  op(e3, e3) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10701), (10762), (function-axioms) are
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10763)  all_56_2 = e2 & op(e2, e3) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10763) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10764)  all_56_2 = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10765)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10765) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10766)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10766) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10767)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10767) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10768)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10768) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10769)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10769) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10770)  op(e3, e3) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10701), (10770), (function-axioms) are
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10771)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10771) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10772)  op(e3, e2) = e3
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10727), (10772), (function-axioms) are
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #433.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10773)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10773) gives:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10774)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10774) implies:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10775)  op(e1, e1) = e2
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (133), (168), (170), (201),
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (238), (270), (272), (352), (10643),
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10645), (10699), (10700), (10701), (10704),
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10775), (function-axioms) are inconsistent by
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #415.
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10776)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10776) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10777)   ~ (all_57_10 = e1)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10696), (10777) imply:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10778)  $false
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10778) is inconsistent.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10779)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_12))
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10779) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10780)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10780) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10781)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10781) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10782)  op(e0, e0) = e2
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (207), (209),
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10739), (10755), (10782), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #74.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10783)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10783) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10784)  op(e3, e0) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10643), (10784), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10785)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10785) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10786)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10786) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10787)  op(e2, e2) = e2
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10787), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10788)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10678), (10680), (10788), (function-axioms)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #270.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10789)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10789) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10790)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10790) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10791)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10791) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10792)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10792) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10793)  op(e3, e2) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10727), (10793), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #433.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10794)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e2) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10794) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10795)  op(e3, e3) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10701), (10795), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10796)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10796) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10797)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10797) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10798)  op(e2, e0) = e2
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10745), (10798), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10799)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10799) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10800)  op(e1, e3) = e1
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10660), (10800), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #28.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10801)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10801) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10802)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10802) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10803)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10803) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10804)  op(e1, e1) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10678), (10804), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10805)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10805) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10806)  op(e2, e2) = e1
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (221), (224), (10744),
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10764), (10806), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #843.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10807)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10807) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10808)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10808) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10809)  op(e0, e0) = e1
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10645), (10809), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10810)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10810) gives:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10811)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10811) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10812)  op(e1, e1) = e3
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10678), (10812), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10813)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e1
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10813) implies:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10814)  op(e1, e3) = e1
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10660), (10814), (function-axioms) are
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #28.
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10815)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10815) gives:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10816)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10816) gives:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10817)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14))
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10817) gives:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10818)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10818) gives:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10819)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10819) implies:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10820)  op(e1, e2) = e1
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10713), (10820), (function-axioms) are
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #984.
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10821)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10821) implies:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10822)  op(e2, e2) = e1
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (221), (224), (10744),
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10764), (10822), (function-axioms) are
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #843.
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10823)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (133), (168), (170), (201),
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (238), (270), (272), (352), (10643),
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10645), (10699), (10700), (10701), (10704),
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10823), (function-axioms) are inconsistent by
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #414.
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10824)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10824) gives:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10825)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (133), (162), (168), (170),
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (201), (203), (238), (270), (272), (352), (10643),
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10645), (10699), (10700), (10701), (10704),
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10713), (10825), (function-axioms) are
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #413.
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10826)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10826) gives:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10827)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10827) implies:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10828)   ~ (all_57_10 = e1)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10696), (10828) imply:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10829)  $false
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10829) is inconsistent.
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10830)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10701), (10719), (10830),
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #839.
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10831)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10831) gives:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10832)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10832) gives:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10833)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10833) gives:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10834)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10834) implies:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10835)  op(e0, e0) = e2
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (207), (209),
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10739), (10755), (10835), (function-axioms) are
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #74.
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10836)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10836) implies:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10837)  op(e2, e2) = e2
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10837), (function-axioms) are
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10838)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10838) gives:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10839)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10839) implies:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10840)  op(e2, e2) = e1
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (221), (224), (10744),
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10764), (10840), (function-axioms) are
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #843.
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10841)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10841) implies:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10842)  op(e3, e0) = e3
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10643), (10842), (function-axioms) are
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10843)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10843) gives:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10844)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10844) gives:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10845)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10845) implies:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10846)  op(e0, e0) = e2
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (206), (207), (209),
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10739), (10755), (10846), (function-axioms) are
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #74.
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10847)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10847) implies:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10848)  op(e3, e3) = e3
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10701), (10848), (function-axioms) are
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10849)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10849) gives:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10850)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10850) implies:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10851)  op(e2, e2) = e2
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10851), (function-axioms) are
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10852)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10852) gives:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10853)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10853) implies:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10854)  op(e1, e0) = e1
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10719), (10854), (function-axioms) are
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10855)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.75/23.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0))
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10855) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10856)  op(e0, e0) = all_57_15
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10857)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10857) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10858)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10858) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10859)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10859) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10860)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e3) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10860) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10861)  op(e3, e3) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (168), (236), (238), (9929),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10643), (10645), (10727), (10861),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #24.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10862)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (103), (133), (168),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (201), (203), (238), (270), (272), (352),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10641), (10643), (10645), (10699), (10700),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10701), (10745), (10862), (function-axioms) are
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #409.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10863)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10863) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10864)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10864) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10865)  all_57_15 = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10856), (10865) imply:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10866)  op(e0, e0) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10645), (10866), (function-axioms) are
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10867)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10867) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10868)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e2) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10868) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10869)  op(e3, e3) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (168), (236), (238), (9929),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10643), (10645), (10727), (10869),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #24.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10870)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e2) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10870) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10871)  op(e2, e0) = e2
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10745), (10871), (function-axioms) are
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10872)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10872) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10873)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10873) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10874)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e2) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10874) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10875)  op(e1, e1) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (103), (133), (168),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (201), (203), (238), (270), (272), (352),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10641), (10643), (10645), (10699), (10700),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10701), (10875), (function-axioms) are
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #410.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10876)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10876) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10877)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10877) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10878)  op(e0, e2) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10755), (10878), (function-axioms) are
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #832.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10879)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e1) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10879) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10880)  op(e3, e3) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (168), (236), (238), (9929),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10643), (10645), (10727), (10880),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #24.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10881)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10881) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10882)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (103), (133), (168),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (201), (203), (238), (270), (272), (352),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10641), (10643), (10645), (10699), (10700),
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10701), (10745), (10882), (function-axioms) are
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #408.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10883)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e1 = e0) & op(e0, e1) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10645), (10679), (10883), (function-axioms)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #205.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10884)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10884) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10885)  all_56_6 = e2 & op(e1, e3) = e2
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10885) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10886)  op(e1, e3) = e2
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10660), (10886), (function-axioms) are
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #617.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10887)  all_56_12 = e2 & op(e0, e3) = e2
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10887) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10888)  all_56_12 = e2
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10759) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10889)  all_56_12 = e0 & op(e0, e3) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10888), (10889) are inconsistent by
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #767.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10890)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10890) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10891)  all_56_13 = e0 & op(e0, e2) = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10891) implies:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10892)  all_56_13 = e0
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10893)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10893) gives:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10894)  all_56_12 = e1 & op(e0, e3) = e1
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10888), (10894) are inconsistent by
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #769.
% 156.75/23.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10754) implies:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10895)  all_56_13 = e1
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10892), (10895) are inconsistent by
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #131.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10896)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10896) gives:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10897)  all_56_14 = e1 & op(e0, e1) = e1
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10739), (10897) are inconsistent by
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #727.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10898)  all_56_15 = e1 & op(e0, e0) = e1
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10898) implies:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10899)  all_56_15 = e1
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10655), (10899) imply:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10900)  e3 = e1
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (10900) imply:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10901)  $false
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10901) is inconsistent.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10902)  all_56_14 = e0 & op(e0, e1) = e0
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10739), (10902) are inconsistent by
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #725.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | |   (10903)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10903) gives:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (10904)  all_56_4 = e2 & op(e3, e1) = e2
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10904) implies:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (10905)  all_56_4 = e2
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10663), (10905) imply:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (10906)  e3 = e2
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10906) implies:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (10907)  e3 = e2
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (10907) imply:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (10908)  $false
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10908) is inconsistent.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (10909)  all_56_9 = e2 & op(e3, e0) = e2
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10909) implies:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (10910)  all_56_9 = e2
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10911)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (229), (233),
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (9929), (10701), (10911), (function-axioms)
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #29.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10912)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10912) gives:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10913)  all_56_5 = e1 & op(e2, e1) = e1
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10714), (10913), (function-axioms) are
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10914)  all_56_10 = e1 & op(e2, e0) = e1
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10914) implies:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10915)  all_56_10 = e1
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10916)  all_54_3 = e3
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10711), (10916) imply:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10917)  all_48_0 = e3
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10717), (10917) imply:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10918)  $false
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10918) is inconsistent.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10919)   ~ (all_54_3 = e3)
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10920)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (206), (10645), (10706), (10711), (10716),
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10717), (10718), (10910), (10915), (10920),
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #404.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | |   (10921)   ~ (all_48_1 = e1) & op(e3, e3) = all_48_1 &
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_48_1)
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10701), (10921), (function-axioms) are
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #396.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | |   (10922)  all_54_0 = e0
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (10922) imply:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | |   (10923)  all_6_2 = e0
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | REDUCE: (9930), (10923) imply:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | |   (10924)  $false
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | CLOSE: (10924) is inconsistent.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | |   (10925)   ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10664), (10925), (function-axioms) are
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #39.
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | |   (10926)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.75/24.00  | | | | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 156.75/24.00  | | | | | | | | | | | | | | | |                op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.75/24.00  | | | | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.75/24.00  | | | | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.75/24.00  | | | | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.75/24.00  | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.75/24.00  | | | | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13)))
% 156.75/24.00  | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | ALPHA: (10926) implies:
% 156.75/24.00  | | | | | | | | | | | | | | | |   (10927)  op(e0, e0) = e0
% 156.75/24.00  | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10645), (10927), (function-axioms) are
% 156.75/24.00  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 156.75/24.00  | | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | |   (10928)  all_56_5 = e3 & op(e2, e1) = e3
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | ALPHA: (10928) implies:
% 156.75/24.00  | | | | | | | | | | | | | |   (10929)  op(e2, e1) = e3
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | REF_CLOSE: (165), (9927), (10929), (function-axioms) are
% 156.75/24.00  | | | | | | | | | | | | | |            inconsistent by sub-proof #763.
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | |   (10930)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 156.75/24.00  | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 156.75/24.00  | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | BETA: splitting (10930) gives:
% 156.75/24.00  | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | |   (10931)  all_56_8 = e3 & op(e1, e1) = e3
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | ALPHA: (10931) implies:
% 156.75/24.00  | | | | | | | | | | | | | |   (10932)  op(e1, e1) = e3
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 156.75/24.00  | | | | | | | | | | | | | |              e1, e1, simplifying with (45), (10932) gives:
% 156.75/24.00  | | | | | | | | | | | | | |   (10933)  all_10_2 = e3
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | REDUCE: (10657), (10933) imply:
% 156.75/24.00  | | | | | | | | | | | | | |   (10934)  $false
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | CLOSE: (10934) is inconsistent.
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | |   (10935)  all_56_14 = e3 & op(e0, e1) = e3
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | ALPHA: (10935) implies:
% 156.75/24.00  | | | | | | | | | | | | | |   (10936)  op(e0, e1) = e3
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | | REF_CLOSE: (157), (10642), (10936), (function-axioms) are
% 156.75/24.00  | | | | | | | | | | | | | |            inconsistent by sub-proof #720.
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | |   (10937)  all_56_7 = e3 & op(e1, e2) = e3
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | REF_CLOSE: (162), (9925), (10937), (function-axioms) are
% 156.75/24.00  | | | | | | | | | | | |            inconsistent by sub-proof #388.
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | |   (10938)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 156.75/24.00  | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 156.75/24.00  | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | BETA: splitting (10938) gives:
% 156.75/24.00  | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | |   (10939)  all_56_8 = e3 & op(e1, e1) = e3
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | ALPHA: (10939) implies:
% 156.75/24.00  | | | | | | | | | | | |   (10940)  op(e1, e1) = e3
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 156.75/24.00  | | | | | | | | | | | |              e1, e1, simplifying with (45), (10940) gives:
% 156.75/24.00  | | | | | | | | | | | |   (10941)  all_10_2 = e3
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | REDUCE: (10657), (10941) imply:
% 156.75/24.00  | | | | | | | | | | | |   (10942)  $false
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | CLOSE: (10942) is inconsistent.
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | |   (10943)  all_56_11 = e3 & op(e1, e0) = e3
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | ALPHA: (10943) implies:
% 156.75/24.00  | | | | | | | | | | | |   (10944)  op(e1, e0) = e3
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | REF_CLOSE: (160), (10644), (10944), (function-axioms) are
% 156.75/24.00  | | | | | | | | | | | |            inconsistent by sub-proof #677.
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | End of split
% 156.75/24.00  | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | Case 2:
% 156.75/24.00  | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | |   (10945)  all_20_2 = e3
% 156.75/24.00  | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | COMBINE_EQS: (325), (10945) imply:
% 156.75/24.00  | | | | | | | | | |   (10946)  all_10_2 = e3
% 156.75/24.00  | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | SIMP: (10946) implies:
% 156.75/24.00  | | | | | | | | | |   (10947)  all_10_2 = e3
% 156.75/24.00  | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | REDUCE: (363), (10947) imply:
% 156.75/24.00  | | | | | | | | | |   (10948)   ~ (all_52_8 = e3)
% 156.75/24.00  | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | REDUCE: (45), (10947) imply:
% 156.75/24.00  | | | | | | | | | |   (10949)  op(e1, e1) = e3
% 156.75/24.00  | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | BETA: splitting (238) gives:
% 156.75/24.00  | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | |   (10950)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.75/24.00  | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 156.75/24.00  | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.75/24.00  | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.75/24.00  | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.75/24.00  | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 156.75/24.00  | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 156.75/24.00  | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 156.75/24.00  | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.75/24.00  | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 156.75/24.00  | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.75/24.00  | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.75/24.00  | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.75/24.00  | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 156.75/24.00  | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 156.75/24.00  | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 156.75/24.00  | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | BETA: splitting (10950) gives:
% 156.75/24.00  | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | |   (10951)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 156.75/24.00  | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 156.75/24.00  | | | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 156.75/24.00  | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 156.75/24.00  | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 156.75/24.00  | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 156.75/24.00  | | | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 156.75/24.00  | | | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | ALPHA: (10951) implies:
% 156.75/24.00  | | | | | | | | | | | |   (10952)  op(e3, e3) = e3
% 156.75/24.00  | | | | | | | | | | | |   (10953)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 156.75/24.00  | | | | | | | | | | | |                = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | BETA: splitting (239) gives:
% 156.75/24.00  | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | |   (10954)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/24.00  | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.75/24.00  | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.00  | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/24.00  | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/24.00  | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.75/24.00  | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/24.00  | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.75/24.00  | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.75/24.00  | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.75/24.00  | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.00  | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.75/24.00  | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.00  | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.00  | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.75/24.00  | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.75/24.00  | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.75/24.00  | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.75/24.00  | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.75/24.00  | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.75/24.00  | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.75/24.00  | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.75/24.00  | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.75/24.00  | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.75/24.00  | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.75/24.00  | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.00  | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.00  | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.75/24.00  | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.75/24.00  | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.00  | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 156.75/24.00  | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.00  | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.00  | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.00  | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/24.00  | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/24.00  | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.75/24.00  | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.75/24.00  | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.00  | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.75/24.00  | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.00  | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.75/24.00  | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.00  | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.00  | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.00  | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.75/24.00  | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.00  | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.75/24.00  | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.75/24.00  | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.75/24.00  | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.75/24.00  | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.00  | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/24.00  | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.00  | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.00  | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.00  | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.00  | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.00  | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/24.00  | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.00  | | | | | | | | | | | | |              e1)
% 156.75/24.00  | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | BETA: splitting (10954) gives:
% 156.75/24.00  | | | | | | | | | | | | | 
% 156.75/24.00  | | | | | | | | | | | | | Case 1:
% 156.75/24.00  | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | |   (10955)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/24.01  | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/24.01  | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/24.01  | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.75/24.01  | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/24.01  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.75/24.01  | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.75/24.01  | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.75/24.01  | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.01  | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.75/24.01  | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.75/24.01  | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.75/24.01  | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.75/24.01  | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.75/24.01  | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.75/24.01  | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.75/24.01  | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.75/24.01  | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.75/24.01  | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.75/24.01  | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.75/24.01  | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.01  | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.75/24.01  | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.75/24.01  | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.75/24.01  | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | BETA: splitting (10955) gives:
% 156.75/24.01  | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | |   (10956)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/24.01  | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/24.01  | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/24.01  | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.75/24.01  | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/24.01  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.75/24.01  | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.75/24.01  | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.75/24.01  | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.01  | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.75/24.01  | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | BETA: splitting (10956) gives:
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | |   (10957)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/24.01  | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/24.01  | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.75/24.01  | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | BETA: splitting (10957) gives:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10958)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/24.01  | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 156.75/24.01  | | | | | | | | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.75/24.01  | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | ALPHA: (10958) implies:
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10959)  op(e3, e3) = e2
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (168), (170), (236), (238), (9924),
% 156.75/24.01  | | | | | | | | | | | | | | | | |            (9929), (10643), (10645), (10959),
% 156.75/24.01  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.01  | | | | | | | | | | | | | | | | |            #38.
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10960)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 & 
% 156.75/24.01  | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | ALPHA: (10960) implies:
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10961)  op(e3, e2) = e3
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (9924), (10961), (function-axioms) are
% 156.75/24.01  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | End of split
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | Case 2:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | |   (10962)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 156.75/24.01  | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.75/24.01  | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 156.75/24.01  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/24.01  | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.75/24.01  | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (10948), (10949), (10962),
% 156.75/24.01  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.01  | | | | | | | | | | | | | | | |            #23.
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | End of split
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | Case 2:
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | |   (10963)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/24.01  | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.75/24.01  | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.75/24.01  | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/24.01  | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/24.01  | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.01  | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/24.01  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 156.75/24.01  | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 156.75/24.01  | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 156.75/24.01  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 156.75/24.01  | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 156.75/24.01  | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 156.75/24.01  | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.75/24.01  | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 156.75/24.01  | | | | | | | | | | | | | | |              & $i(all_57_12))
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | BETA: splitting (10963) gives:
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | |   (10964)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/24.01  | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 156.75/24.01  | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 156.75/24.01  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/24.01  | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.01  | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (10643), (10645), (10964),
% 156.75/24.01  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.01  | | | | | | | | | | | | | | | |            #445.
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | Case 2:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | |   (10965)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.75/24.01  | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.75/24.01  | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.75/24.01  | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.01  | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.75/24.01  | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.75/24.01  | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | BETA: splitting (10965) gives:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10966)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.75/24.01  | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | ALPHA: (10966) implies:
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10967)  op(e2, e2) = e2
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (10967), (function-axioms) are
% 156.75/24.01  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10968)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.75/24.01  | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.01  | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.75/24.01  | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.75/24.01  | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | BETA: splitting (10968) gives:
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | |   (10969)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 156.75/24.01  | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.01  | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/24.01  | | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | | ALPHA: (10969) implies:
% 156.75/24.01  | | | | | | | | | | | | | | | | | |   (10970)  op(e3, e2) = e3
% 156.75/24.01  | | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (9924), (10970), (function-axioms) are
% 156.75/24.01  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #998.
% 156.75/24.01  | | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.01  | | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | |   (10971)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 156.75/24.01  | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 156.75/24.01  | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 156.75/24.01  | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.75/24.01  | | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | | ALPHA: (10971) implies:
% 156.75/24.01  | | | | | | | | | | | | | | | | | |   (10972)  op(e3, e3) = e2
% 156.75/24.01  | | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (168), (170), (236), (238), (9924),
% 156.75/24.01  | | | | | | | | | | | | | | | | | |            (9929), (10643), (10645), (10972),
% 156.75/24.01  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.01  | | | | | | | | | | | | | | | | | |            #38.
% 156.75/24.01  | | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | End of split
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | End of split
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | End of split
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | End of split
% 156.75/24.01  | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | Case 2:
% 156.75/24.01  | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | |   (10973)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.01  | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.01  | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/24.01  | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.75/24.01  | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.75/24.01  | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.01  | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.01  | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.01  | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.01  | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.75/24.01  | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.01  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.75/24.01  | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.75/24.01  | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.75/24.01  | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.75/24.01  | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.01  | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/24.01  | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.01  | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.01  | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.01  | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.01  | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.01  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/24.01  | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.01  | | | | | | | | | | | | | |              e1)
% 156.75/24.01  | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | BETA: splitting (10973) gives:
% 156.75/24.01  | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | |   (10974)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.01  | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.01  | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/24.01  | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.75/24.01  | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.01  | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.75/24.01  | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.01  | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.01  | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | BETA: splitting (10974) gives:
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | |   (10975)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.01  | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.01  | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/24.01  | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | | | |                e2) = e3)
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | REF_CLOSE: (170), (9924), (10975), (function-axioms) are
% 156.75/24.01  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #792.
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | Case 2:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | |   (10976)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 156.75/24.01  | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 156.75/24.01  | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 156.75/24.01  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 156.75/24.01  | | | | | | | | | | | | | | | |                e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | BETA: splitting (10976) gives:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10977)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 156.75/24.01  | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 156.75/24.01  | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.75/24.01  | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | ALPHA: (10977) implies:
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10978)  op(e3, e3) = e2
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (168), (170), (236), (238), (9924),
% 156.75/24.01  | | | | | | | | | | | | | | | | |            (9929), (10643), (10645), (10978),
% 156.75/24.01  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.01  | | | | | | | | | | | | | | | | |            #38.
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10979)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.01  | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/24.01  | | | | | | | | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.01  | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | ALPHA: (10979) implies:
% 156.75/24.01  | | | | | | | | | | | | | | | | |   (10980)  op(e3, e3) = e1
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10952), (10980), (function-axioms) are
% 156.75/24.01  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | End of split
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | End of split
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | Case 2:
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | |   (10981)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.75/24.01  | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.01  | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.75/24.01  | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.75/24.01  | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.75/24.01  | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.75/24.01  | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.01  | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/24.01  | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.01  | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.01  | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.01  | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.01  | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.01  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/24.01  | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.01  | | | | | | | | | | | | | | |              e1)
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | BETA: splitting (10981) gives:
% 156.75/24.01  | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | |   (10982)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.75/24.01  | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.01  | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.01  | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.75/24.01  | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.75/24.01  | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.75/24.01  | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | BETA: splitting (10982) gives:
% 156.75/24.01  | | | | | | | | | | | | | | | | 
% 156.75/24.01  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.01  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10983)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.75/24.02  | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.02  | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | ALPHA: (10983) implies:
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10984)  op(e3, e1) = e3
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10948), (10984), (function-axioms) are
% 156.75/24.02  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10985)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 156.75/24.02  | | | | | | | | | | | | | | | | |            = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.02  | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | ALPHA: (10985) implies:
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10986)  op(e2, e2) = e1
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (206), (210),
% 156.75/24.02  | | | | | | | | | | | | | | | | |            (211), (224), (229), (231), (233), (9927),
% 156.75/24.02  | | | | | | | | | | | | | | | | |            (10645), (10952), (10986), (function-axioms) are
% 156.75/24.02  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #460.
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | End of split
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | Case 2:
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | |   (10987)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/24.02  | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.02  | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.02  | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.02  | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.02  | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.02  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/24.02  | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | | | |              e1)
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | BETA: splitting (10987) gives:
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10988)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 156.75/24.02  | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.75/24.02  | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | ALPHA: (10988) implies:
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10989)  op(e0, e0) = e1
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (157), (158),
% 156.75/24.02  | | | | | | | | | | | | | | | | |            (209), (229), (231), (233), (238), (9926), (9929),
% 156.75/24.02  | | | | | | | | | | | | | | | | |            (10642), (10949), (10989), (function-axioms) are
% 156.75/24.02  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #21.
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10990)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 156.75/24.02  | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.75/24.02  | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 156.75/24.02  | | | | | | | | | | | | | | | | |              = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 156.75/24.02  | | | | | | | | | | | | | | | | |                e1) = e1)
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10643), (10949), (10990),
% 156.75/24.02  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.02  | | | | | | | | | | | | | | | | |            #578.
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | End of split
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | End of split
% 156.75/24.02  | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | End of split
% 156.75/24.02  | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | End of split
% 156.75/24.02  | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | Case 2:
% 156.75/24.02  | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | |   (10991)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/24.02  | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.02  | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/24.02  | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/24.02  | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.02  | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.75/24.02  | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/24.02  | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.75/24.02  | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.02  | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.75/24.02  | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.02  | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.02  | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.75/24.02  | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.75/24.02  | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.75/24.02  | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.75/24.02  | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.75/24.02  | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.75/24.02  | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.75/24.02  | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.75/24.02  | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.75/24.02  | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.75/24.02  | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.75/24.02  | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.75/24.02  | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/24.02  | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 156.75/24.02  | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/24.02  | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 156.75/24.02  | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.75/24.02  | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.75/24.02  | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 156.75/24.02  | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 156.75/24.02  | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.75/24.02  | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.75/24.02  | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 156.75/24.02  | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 156.75/24.02  | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 156.75/24.02  | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.75/24.02  | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 156.75/24.02  | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 156.75/24.02  | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 156.75/24.02  | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.75/24.02  | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.75/24.02  | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 156.75/24.02  | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 156.75/24.02  | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 156.75/24.02  | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 156.75/24.02  | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 156.75/24.02  | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 156.75/24.02  | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/24.02  | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 156.75/24.02  | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 156.75/24.02  | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/24.02  | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.75/24.02  | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.75/24.02  | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/24.02  | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 156.75/24.02  | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 156.75/24.02  | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/24.02  | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 156.75/24.02  | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 156.75/24.02  | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/24.02  | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 156.75/24.02  | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 156.75/24.02  | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/24.02  | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 156.75/24.02  | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 156.75/24.02  | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 156.75/24.02  | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.75/24.02  | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/24.02  | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.75/24.02  | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 156.75/24.02  | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/24.02  | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.75/24.02  | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 156.75/24.02  | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/24.02  | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.75/24.02  | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 156.75/24.02  | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 156.75/24.02  | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.75/24.02  | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.75/24.02  | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 156.75/24.02  | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 156.75/24.02  | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | BETA: splitting (10991) gives:
% 156.75/24.02  | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | Case 1:
% 156.75/24.02  | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | |   (10992)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/24.02  | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.02  | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/24.02  | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/24.02  | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.02  | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.75/24.02  | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/24.02  | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.75/24.02  | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.02  | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.75/24.02  | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.02  | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.02  | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.75/24.02  | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.75/24.02  | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.75/24.02  | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.75/24.02  | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.75/24.02  | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.75/24.02  | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.75/24.02  | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.75/24.02  | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.75/24.02  | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.75/24.02  | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.75/24.02  | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.75/24.02  | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/24.02  | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/24.02  | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | BETA: splitting (10992) gives:
% 156.75/24.02  | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | Case 1:
% 156.75/24.02  | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | |   (10993)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/24.02  | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.02  | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/24.02  | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/24.02  | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.02  | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.75/24.02  | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/24.02  | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.75/24.02  | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.02  | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.75/24.02  | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.02  | | | | | | | | | | | | | | |              = e1 & $i(all_57_14))
% 156.75/24.02  | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | BETA: splitting (10993) gives:
% 156.75/24.02  | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | Case 1:
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | |   (10994)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/24.02  | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.02  | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/24.02  | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/24.02  | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.02  | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | BETA: splitting (10994) gives:
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10995)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/24.02  | | | | | | | | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.02  | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | ALPHA: (10995) implies:
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10996)  op(e3, e3) = e1
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10952), (10996), (function-axioms) are
% 156.75/24.02  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10997)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 156.75/24.02  | | | | | | | | | | | | | | | | |            = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.02  | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | ALPHA: (10997) implies:
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (10998)  op(e2, e2) = e1
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (206), (210),
% 156.75/24.02  | | | | | | | | | | | | | | | | |            (211), (224), (229), (231), (233), (9927),
% 156.75/24.02  | | | | | | | | | | | | | | | | |            (10645), (10952), (10998), (function-axioms) are
% 156.75/24.02  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #460.
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | End of split
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | Case 2:
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | |   (10999)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.75/24.02  | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/24.02  | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 156.75/24.02  | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 156.75/24.02  | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.02  | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.75/24.02  | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | BETA: splitting (10999) gives:
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (11000)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.75/24.02  | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/24.02  | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | ALPHA: (11000) implies:
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (11001)  op(e1, e1) = e2
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10949), (11001), (function-axioms) are
% 156.75/24.02  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (11002)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.02  | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 156.75/24.02  | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.75/24.02  | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | ALPHA: (11002) implies:
% 156.75/24.02  | | | | | | | | | | | | | | | | |   (11003)  op(e0, e0) = e1
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (157), (158),
% 156.75/24.02  | | | | | | | | | | | | | | | | |            (209), (229), (231), (233), (238), (9926), (9929),
% 156.75/24.02  | | | | | | | | | | | | | | | | |            (10642), (10949), (11003), (function-axioms) are
% 156.75/24.02  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #21.
% 156.75/24.02  | | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | End of split
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | End of split
% 156.75/24.02  | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | Case 2:
% 156.75/24.02  | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | |   (11004)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.75/24.02  | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/24.02  | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.75/24.02  | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.75/24.02  | | | | | | | | | | | | | | |                e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 156.75/24.02  | | | | | | | | | | | | | | |              all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 156.75/24.02  | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 156.75/24.02  | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 156.75/24.02  | | | | | | | | | | | | | | |            (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.75/24.02  | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.75/24.02  | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.75/24.02  | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/24.02  | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.75/24.02  | | | | | | | | | | | | | | |              & $i(all_57_14))
% 156.75/24.02  | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | BETA: splitting (11004) gives:
% 156.75/24.02  | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | Case 1:
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | |   (11005)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.75/24.02  | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/24.02  | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.02  | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.75/24.02  | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.75/24.02  | | | | | | | | | | | | | | | |                e1) = e1)
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10949), (11005), (function-axioms) are
% 156.75/24.02  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #644.
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.02  | | | | | | | | | | | | | | | Case 2:
% 156.75/24.02  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | |   (11006)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.03  | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.03  | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 156.75/24.03  | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 156.75/24.03  | | | | | | | | | | | | | | | |                e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 156.75/24.03  | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 156.75/24.03  | | | | | | | | | | | | | | | |                e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 156.75/24.03  | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (10948), (10952), (11006),
% 156.75/24.03  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.03  | | | | | | | | | | | | | | | |            #787.
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | End of split
% 156.75/24.03  | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | End of split
% 156.75/24.03  | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | Case 2:
% 156.75/24.03  | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | |   (11007)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/24.03  | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/24.03  | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.75/24.03  | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.75/24.03  | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.75/24.03  | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.75/24.03  | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.75/24.03  | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.75/24.03  | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.75/24.03  | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.75/24.03  | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 156.75/24.03  | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 156.75/24.03  | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.75/24.03  | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.75/24.03  | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 156.75/24.03  | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 156.75/24.03  | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 156.75/24.03  | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 156.75/24.03  | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.75/24.03  | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.75/24.03  | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.75/24.03  | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/24.03  | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/24.03  | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/24.03  | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/24.03  | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/24.03  | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/24.03  | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.75/24.03  | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.03  | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/24.03  | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.03  | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.75/24.03  | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.03  | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.75/24.03  | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/24.03  | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/24.03  | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/24.03  | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.75/24.03  | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.75/24.03  | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/24.03  | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/24.03  | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/24.03  | | | | | | | | | | | | | |                  e0)))
% 156.75/24.03  | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | BETA: splitting (11007) gives:
% 156.75/24.03  | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | Case 1:
% 156.75/24.03  | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | |   (11008)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/24.03  | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/24.03  | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.75/24.03  | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.75/24.03  | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 156.75/24.03  | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 156.75/24.03  | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 156.75/24.03  | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 156.75/24.03  | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.75/24.03  | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.75/24.03  | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 156.75/24.03  | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | BETA: splitting (11008) gives:
% 156.75/24.03  | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | Case 1:
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | |   (11009)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/24.03  | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/24.03  | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 156.75/24.03  | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 156.75/24.03  | | | | | | | | | | | | | | | |                e1) = e2)
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | BETA: splitting (11009) gives:
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11010)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 156.75/24.03  | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/24.03  | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | ALPHA: (11010) implies:
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11011)  op(e0, e0) = e2
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10645), (11011), (function-axioms) are
% 156.75/24.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11012)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.75/24.03  | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | ALPHA: (11012) implies:
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11013)  op(e2, e2) = e2
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11013), (function-axioms) are
% 156.75/24.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | End of split
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | Case 2:
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | |   (11014)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 156.75/24.03  | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 156.75/24.03  | | | | | | | | | | | | | | | |                e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 156.75/24.03  | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.03  | | | | | | | | | | | | | | | |              & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.75/24.03  | | | | | | | | | | | | | | | |              $i(all_57_10))
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | BETA: splitting (11014) gives:
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11015)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 156.75/24.03  | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.75/24.03  | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/24.03  | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | ALPHA: (11015) implies:
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11016)  op(e2, e2) = e1
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (206), (210),
% 156.75/24.03  | | | | | | | | | | | | | | | | |            (211), (224), (229), (231), (233), (9927),
% 156.75/24.03  | | | | | | | | | | | | | | | | |            (10645), (10952), (11016), (function-axioms) are
% 156.75/24.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #460.
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11017)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 156.75/24.03  | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 156.75/24.03  | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | ALPHA: (11017) implies:
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11018)  op(e3, e0) = e3
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10643), (11018), (function-axioms) are
% 156.75/24.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | End of split
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | End of split
% 156.75/24.03  | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | Case 2:
% 156.75/24.03  | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | |   (11019)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.75/24.03  | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/24.03  | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.75/24.03  | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.75/24.03  | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 156.75/24.03  | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 156.75/24.03  | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 156.75/24.03  | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 156.75/24.03  | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.75/24.03  | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.75/24.03  | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/24.03  | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/24.03  | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 156.75/24.03  | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.75/24.03  | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 156.75/24.03  | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 156.75/24.03  | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 156.75/24.03  | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.75/24.03  | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 156.75/24.03  | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 156.75/24.03  | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.75/24.03  | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 156.75/24.03  | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.75/24.03  | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.75/24.03  | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.75/24.03  | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.75/24.03  | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.75/24.03  | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/24.03  | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 156.75/24.03  | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.75/24.03  | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 156.75/24.03  | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | BETA: splitting (11019) gives:
% 156.75/24.03  | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | Case 1:
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | |   (11020)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 156.75/24.03  | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/24.03  | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 156.75/24.03  | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 156.75/24.03  | | | | | | | | | | | | | | | |                e0) = e3)
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (10643), (10645), (11020),
% 156.75/24.03  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.03  | | | | | | | | | | | | | | | |            #451.
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | Case 2:
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | |   (11021)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.75/24.03  | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 156.75/24.03  | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 156.75/24.03  | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 156.75/24.03  | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/24.03  | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/24.03  | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/24.03  | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.75/24.03  | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.03  | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.03  | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.03  | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/24.03  | | | | | | | | | | | | | | | |                  e0)))
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | BETA: splitting (11021) gives:
% 156.75/24.03  | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11022)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 156.75/24.03  | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | ALPHA: (11022) implies:
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11023)  op(e2, e2) = e2
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11023), (function-axioms) are
% 156.75/24.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | |   (11024)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.75/24.03  | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 156.75/24.03  | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/24.03  | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/24.03  | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/24.03  | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/24.03  | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 156.75/24.03  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/24.03  | | | | | | | | | | | | | | | | |                  e0)))
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | BETA: splitting (11024) gives:
% 156.75/24.03  | | | | | | | | | | | | | | | | | 
% 156.75/24.03  | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.03  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | |   (11025)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 156.75/24.04  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | ALPHA: (11025) implies:
% 156.75/24.04  | | | | | | | | | | | | | | | | | |   (11026)  op(e1, e1) = e1
% 156.75/24.04  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10949), (11026), (function-axioms) are
% 156.75/24.04  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | |   (11027)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e0))
% 156.75/24.04  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | ALPHA: (11027) implies:
% 156.75/24.04  | | | | | | | | | | | | | | | | | |   (11028)  op(e0, e0) = all_57_15
% 156.75/24.04  | | | | | | | | | | | | | | | | | |   (11029)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 156.75/24.04  | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 156.75/24.04  | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (10645),
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              (11028) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | |   (11030)  all_57_15 = e3
% 156.75/24.04  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e3,
% 156.75/24.04  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (39), (10952) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | |   (11031)  all_6_2 = e3
% 156.75/24.04  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | BETA: splitting (11029) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |   (11032)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (11032) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |   (11033)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11033) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11034)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e3) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11034) implies:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11035)  all_57_6 = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11036)   ~ (all_57_15 = e3)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10953), (11035), (11036) are inconsistent by
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |            sub-proof #684.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11037)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11037) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11038)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e3) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11038) implies:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11039)  all_57_6 = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11040)   ~ (all_57_15 = e3)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10953), (11039), (11040) are inconsistent by
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #684.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11041)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e3) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11041) implies:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11042)  op(e1, e1) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10949), (11042), (function-axioms) are
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |   (11043)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11043) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11044)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11030), (11044) are inconsistent by sub-proof
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |            #450.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11045)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |                = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11045) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11046)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e2) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11046) implies:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11047)  op(e3, e3) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10952), (11047), (function-axioms) are
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11048)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e2) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11048) implies:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11049)  op(e2, e2) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (11049), (function-axioms) are
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |   (11050)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |                = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (11050) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |   (11051)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11051) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11052)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e2) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11052) implies:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11053)  op(e1, e1) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10949), (11053), (function-axioms) are
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11054)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10952), (11030), (11054), (function-axioms)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #448.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |   (11055)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | |              = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11055) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11056)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11056) gives:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11057)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e1) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11057) implies:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11058)  op(e2, e2) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (11058), (function-axioms) are
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11059)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e1) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11059) implies:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |   (11060)  op(e1, e1) = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10949), (11060), (function-axioms) are
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |   (11061)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |              &  ~ (e1 = e0) & op(e0, e1) = e0)
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (11030), (11061) are inconsistent by
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | |            sub-proof #142.
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | | End of split
% 156.75/24.04  | | | | | | | | | | | | 
% 156.75/24.04  | | | | | | | | | | | Case 2:
% 156.75/24.04  | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | |   (11062)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 156.75/24.05  | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 156.75/24.05  | | | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 156.75/24.05  | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 156.75/24.05  | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 156.75/24.05  | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 156.75/24.05  | | | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 156.75/24.05  | | | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 156.75/24.05  | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | ALPHA: (11062) implies:
% 156.75/24.05  | | | | | | | | | | | |   (11063)  op(e2, e2) = e2
% 156.75/24.05  | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11063), (function-axioms) are
% 156.75/24.05  | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 156.75/24.05  | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | End of split
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | Case 2:
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | |   (11064)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 156.75/24.05  | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 156.75/24.05  | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 156.75/24.05  | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 156.75/24.05  | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 156.75/24.05  | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 156.75/24.05  | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 156.75/24.05  | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 156.75/24.05  | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 156.75/24.05  | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 156.75/24.05  | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 156.75/24.05  | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 156.75/24.05  | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 156.75/24.05  | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 156.75/24.05  | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 156.75/24.05  | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | REF_CLOSE: (7), (8), (10645), (10949), (11064),
% 156.75/24.05  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.05  | | | | | | | | | | |            #389.
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | End of split
% 156.75/24.05  | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | End of split
% 156.75/24.05  | | | | | | | | | 
% 156.75/24.05  | | | | | | | | End of split
% 156.75/24.05  | | | | | | | | 
% 156.75/24.05  | | | | | | | End of split
% 156.75/24.05  | | | | | | | 
% 156.75/24.05  | | | | | | End of split
% 156.75/24.05  | | | | | | 
% 156.75/24.05  | | | | | Case 2:
% 156.75/24.05  | | | | | | 
% 156.75/24.05  | | | | | |   (11065)  all_14_2 = e1
% 156.75/24.05  | | | | | | 
% 156.75/24.05  | | | | | | REDUCE: (351), (11065) imply:
% 156.75/24.05  | | | | | |   (11066)   ~ (all_52_3 = e1)
% 156.75/24.05  | | | | | | 
% 156.75/24.05  | | | | | | REDUCE: (362), (11065) imply:
% 156.75/24.05  | | | | | |   (11067)   ~ (all_52_7 = e1)
% 156.75/24.05  | | | | | | 
% 156.75/24.05  | | | | | | REDUCE: (370), (11065) imply:
% 156.75/24.05  | | | | | |   (11068)   ~ (all_52_12 = e1)
% 156.75/24.05  | | | | | | 
% 156.75/24.05  | | | | | | REDUCE: (371), (11065) imply:
% 156.75/24.05  | | | | | |   (11069)   ~ (all_52_13 = e1)
% 156.75/24.05  | | | | | | 
% 156.75/24.05  | | | | | | REDUCE: (372), (11065) imply:
% 156.75/24.05  | | | | | |   (11070)   ~ (all_52_14 = e1)
% 156.75/24.05  | | | | | | 
% 156.75/24.05  | | | | | | REDUCE: (51), (11065) imply:
% 156.75/24.05  | | | | | |   (11071)  op(e0, e0) = e1
% 156.75/24.05  | | | | | | 
% 156.75/24.05  | | | | | | BETA: splitting (61) gives:
% 156.75/24.05  | | | | | | 
% 156.75/24.05  | | | | | | Case 1:
% 156.75/24.05  | | | | | | | 
% 156.75/24.05  | | | | | | |   (11072)   ~ (all_20_2 = e3)
% 156.75/24.05  | | | | | | | 
% 156.75/24.05  | | | | | | | REDUCE: (325), (11072) imply:
% 156.75/24.05  | | | | | | |   (11073)   ~ (all_10_2 = e3)
% 156.75/24.05  | | | | | | | 
% 156.75/24.05  | | | | | | | BETA: splitting (64) gives:
% 156.75/24.05  | | | | | | | 
% 156.75/24.05  | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | 
% 156.75/24.05  | | | | | | | |   (11074)   ~ (all_22_2 = e0)
% 156.75/24.05  | | | | | | | | 
% 156.75/24.05  | | | | | | | | REDUCE: (251), (11074) imply:
% 156.75/24.05  | | | | | | | |   (11075)   ~ (all_10_2 = e0)
% 156.75/24.05  | | | | | | | | 
% 156.75/24.05  | | | | | | | | BETA: splitting (194) gives:
% 156.75/24.05  | | | | | | | | 
% 156.75/24.05  | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | 
% 156.75/24.05  | | | | | | | | |   (11076)  all_54_10 = e3
% 156.75/24.05  | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | REF_CLOSE: (336), (11073), (11076) are inconsistent by
% 156.75/24.05  | | | | | | | | |            sub-proof #361.
% 156.75/24.05  | | | | | | | | | 
% 156.75/24.05  | | | | | | | | Case 2:
% 156.75/24.05  | | | | | | | | | 
% 156.75/24.05  | | | | | | | | |   (11077)   ~ (all_54_10 = e3)
% 156.75/24.05  | | | | | | | | |   (11078)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.75/24.05  | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | BETA: splitting (11078) gives:
% 156.75/24.05  | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | |   (11079)  all_54_10 = e2
% 156.75/24.05  | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | REF_CLOSE: (336), (9931), (11079) are inconsistent by
% 156.75/24.05  | | | | | | | | | |            sub-proof #360.
% 156.75/24.05  | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | Case 2:
% 156.75/24.05  | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | |   (11080)   ~ (all_54_10 = e2)
% 156.75/24.05  | | | | | | | | | |   (11081)  all_54_10 = e1 | all_54_10 = e0
% 156.75/24.05  | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | BETA: splitting (11081) gives:
% 156.75/24.05  | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | |   (11082)  all_54_10 = e1
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | COMBINE_EQS: (336), (11082) imply:
% 156.75/24.05  | | | | | | | | | | |   (11083)  all_10_2 = e1
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | SIMP: (11083) implies:
% 156.75/24.05  | | | | | | | | | | |   (11084)  all_10_2 = e1
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | REDUCE: (350), (11084) imply:
% 156.75/24.05  | | | | | | | | | | |   (11085)   ~ (all_52_2 = e1)
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | REDUCE: (361), (11084) imply:
% 156.75/24.05  | | | | | | | | | | |   (11086)   ~ (all_52_6 = e1)
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | REDUCE: (363), (11084) imply:
% 156.75/24.05  | | | | | | | | | | |   (11087)   ~ (all_52_8 = e1)
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | REDUCE: (364), (11084) imply:
% 156.75/24.05  | | | | | | | | | | |   (11088)   ~ (all_52_9 = e1)
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | REDUCE: (11073), (11084) imply:
% 156.75/24.05  | | | | | | | | | | |   (11089)   ~ (e3 = e1)
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | REDUCE: (9931), (11084) imply:
% 156.75/24.05  | | | | | | | | | | |   (11090)   ~ (e2 = e1)
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | REDUCE: (45), (11084) imply:
% 156.75/24.05  | | | | | | | | | | |   (11091)  op(e1, e1) = e1
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | BETA: splitting (226) gives:
% 156.75/24.05  | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | |   (11092)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 156.75/24.05  | | | | | | | | | | | |              & op(e2, e2) = e1)
% 156.75/24.05  | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | BETA: splitting (11092) gives:
% 156.75/24.05  | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | |   (11093)  all_56_1 = e1 & op(e3, e2) = e1
% 156.75/24.05  | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | ALPHA: (11093) implies:
% 156.75/24.05  | | | | | | | | | | | | |   (11094)  all_56_1 = e1
% 156.75/24.05  | | | | | | | | | | | | |   (11095)  op(e3, e2) = e1
% 156.75/24.05  | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | BETA: splitting (222) gives:
% 156.75/24.05  | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | |   (11096)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 156.75/24.05  | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 156.75/24.05  | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | BETA: splitting (11096) gives:
% 156.75/24.05  | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | |   (11097)  all_56_2 = e1 & op(e2, e3) = e1
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | ALPHA: (11097) implies:
% 156.75/24.05  | | | | | | | | | | | | | | |   (11098)  all_56_2 = e1
% 156.75/24.05  | | | | | | | | | | | | | | |   (11099)  op(e2, e3) = e1
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 156.75/24.05  | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (11099) gives:
% 156.75/24.05  | | | | | | | | | | | | | | |   (11100)  all_52_1 = e1
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1,
% 156.75/24.05  | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (11095) gives:
% 156.75/24.05  | | | | | | | | | | | | | | |   (11101)  all_52_4 = e1
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | REDUCE: (149), (11100) imply:
% 156.75/24.05  | | | | | | | | | | | | | | |   (11102)   ~ (all_52_2 = e1)
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | REDUCE: (148), (11100) imply:
% 156.75/24.05  | | | | | | | | | | | | | | |   (11103)   ~ (all_52_3 = e1)
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | REDUCE: (136), (11101) imply:
% 156.75/24.05  | | | | | | | | | | | | | | |   (11104)   ~ (all_52_6 = e1)
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | REDUCE: (135), (11101) imply:
% 156.75/24.05  | | | | | | | | | | | | | | |   (11105)   ~ (all_52_7 = e1)
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | REDUCE: (344), (11101) imply:
% 156.75/24.05  | | | | | | | | | | | | | | |   (11106)   ~ (all_6_2 = e1)
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | SIMP: (11106) implies:
% 156.75/24.05  | | | | | | | | | | | | | | |   (11107)   ~ (all_6_2 = e1)
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 156.75/24.05  | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | |   (11108)   ~ (all_40_2 = e3)
% 156.75/24.05  | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | REDUCE: (9922), (11108) imply:
% 156.75/24.05  | | | | | | | | | | | | | | | |   (11109)  $false
% 156.75/24.05  | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | CLOSE: (11109) is inconsistent.
% 156.75/24.05  | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | Case 2:
% 156.75/24.05  | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | |   (11110)  ( ~ (all_40_0 = e1) & op(e3, e2) = all_40_0 &
% 156.75/24.05  | | | | | | | | | | | | | | | |              $i(all_40_0)) | ( ~ (all_40_1 = e0) & op(e3, e3)
% 156.75/24.05  | | | | | | | | | | | | | | | |              = all_40_1 & $i(all_40_1))
% 156.75/24.05  | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | BETA: splitting (11110) gives:
% 156.75/24.05  | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | |   (11111)   ~ (all_40_0 = e1) & op(e3, e2) = all_40_0 &
% 156.75/24.05  | | | | | | | | | | | | | | | | |            $i(all_40_0)
% 156.75/24.05  | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | ALPHA: (11111) implies:
% 156.75/24.05  | | | | | | | | | | | | | | | | |   (11112)   ~ (all_40_0 = e1)
% 156.75/24.05  | | | | | | | | | | | | | | | | |   (11113)  op(e3, e2) = all_40_0
% 156.75/24.05  | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_40_0,
% 156.75/24.05  | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (11095), (11113) gives:
% 156.75/24.05  | | | | | | | | | | | | | | | | |   (11114)  all_40_0 = e1
% 156.75/24.05  | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | REDUCE: (11112), (11114) imply:
% 156.75/24.05  | | | | | | | | | | | | | | | | |   (11115)  $false
% 156.75/24.05  | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | CLOSE: (11115) is inconsistent.
% 156.75/24.05  | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.05  | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | |   (11116)   ~ (all_40_1 = e0) & op(e3, e3) = all_40_1 &
% 156.75/24.05  | | | | | | | | | | | | | | | | |            $i(all_40_1)
% 156.75/24.05  | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | ALPHA: (11116) implies:
% 156.75/24.05  | | | | | | | | | | | | | | | | |   (11117)   ~ (all_40_1 = e0)
% 156.75/24.05  | | | | | | | | | | | | | | | | |   (11118)  op(e3, e3) = all_40_1
% 156.75/24.05  | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 156.75/24.05  | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | |   (11119)  all_54_0 = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (11119) imply:
% 156.75/24.05  | | | | | | | | | | | | | | | | | |   (11120)  all_6_2 = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | REDUCE: (340), (11120) imply:
% 156.75/24.05  | | | | | | | | | | | | | | | | | |   (11121)   ~ (all_52_2 = e3)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | REDUCE: (346), (11120) imply:
% 156.75/24.05  | | | | | | | | | | | | | | | | | |   (11122)   ~ (all_52_8 = e3)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | REDUCE: (348), (11120) imply:
% 156.75/24.05  | | | | | | | | | | | | | | | | | |   (11123)   ~ (all_52_12 = e3)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | REDUCE: (39), (11120) imply:
% 156.75/24.05  | | | | | | | | | | | | | | | | | |   (11124)  op(e3, e3) = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | |   (11125)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (9927), (11122), (11125),
% 156.75/24.05  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.05  | | | | | | | | | | | | | | | | | | |            #48.
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | |   (11126)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (11126) gives:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | |   (11127)  all_56_8 = e3 & op(e1, e1) = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (11127) implies:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | |   (11128)  op(e1, e1) = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11091), (11128), (function-axioms) are
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | |   (11129)  all_56_14 = e3 & op(e0, e1) = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (11129) implies:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | |   (11130)  all_56_14 = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |   (11131)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11131) gives:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |   (11132)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (11091), (11099), (11124), (11132),
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | |            #346.
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.05  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |   (11133)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11133) gives:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |   (11134)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11134) gives:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |   (11135)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11071), (11095), (11135), (function-axioms)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #344.
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |   (11136)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |                e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11136) gives:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (11137)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11137) implies:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (11138)  op(e3, e3) = e2
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11124), (11138), (function-axioms) are
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (11139)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11139) implies:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (11140)  op(e3, e3) = e1
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (11098), (11099), (11121), (11140),
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            #75.
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |   (11141)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11141) gives:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |   (11142)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (223), (224),
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |            (11091), (11098), (11099), (11142),
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |            #93.
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |   (11143)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (11085), (11091), (11143),
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |            #354.
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |   (11144)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11144) gives:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |   (11145)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11145) gives:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |   (11146)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14))
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11146) gives:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |   (11147)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11147) gives:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (11148)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11148) implies:
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (11149)  op(e3, e3) = e1
% 156.75/24.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (11098), (11099), (11121), (11149),
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            #75.
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (11150)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11150) implies:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (11151)  op(e2, e2) = e1
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (223), (224),
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (11098), (11099), (11151), (function-axioms) are
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #259.
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |   (11152)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & op(e0, e0) = e1 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (11086), (11091), (11152),
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |            #351.
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |   (11153)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11153) gives:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |   (11154)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (11086), (11091), (11154),
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |            #983.
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |   (11155)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11155) gives:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (11156)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11156) implies:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (11157)  op(e0, e0) = e3
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11071), (11157), (function-axioms) are
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (11158)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11158) gives:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11159)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11159) implies:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11160)  op(e3, e1) = e3
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11122), (11160), (function-axioms) are
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.75/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11161)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11161) implies:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11162)  op(e3, e3) = e1
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (229), (233),
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (11098), (11099), (11121), (11162),
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            #75.
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |   (11163)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11163) gives:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |   (11164)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11164) gives:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |   (11165)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2)
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (158), (159), (207), (9929),
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |            (11066), (11067), (11130), (11165),
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |            #20.
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |   (11166)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11166) gives:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (11167)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11167) implies:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (11168)  op(e2, e2) = e1
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (223), (224),
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (11098), (11099), (11168), (function-axioms) are
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #259.
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (11169)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11169) implies:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (11170)  op(e0, e0) = e3
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11071), (11170), (function-axioms) are
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |   (11171)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11171) gives:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |   (11172)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (158), (159), (168), (207), (11066),
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |            (11067), (11123), (11130), (11172),
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | |            #19.
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |   (11173)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11173) gives:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (11174)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11174) implies:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (11175)  op(e2, e2) = e2
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11175), (function-axioms) are
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (11176)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11176) gives:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11177)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11177) implies:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11178)  op(e1, e0) = e1
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (11070), (11178), (function-axioms) are
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11179)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0))
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11179) implies:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11180)  op(e0, e0) = all_57_15
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11181)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (11071),
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              (11180) gives:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11182)  all_57_15 = e1
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_40_1,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (11118), (11124) gives:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11183)  all_40_1 = e3
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11181) gives:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11184)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11184) gives:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11185)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11185) gives:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11186)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e3) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11186) implies:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11187)  op(e3, e3) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11117), (11118), (11187), (function-axioms) are
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #18.
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11188)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11188) gives:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11189)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e3) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11189) implies:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11190)  op(e2, e2) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (11190), (function-axioms) are
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11191)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e3) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11191) implies:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11192)  op(e1, e1) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11091), (11192), (function-axioms) are
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11193)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11193) gives:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11194)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11182), (11194) are inconsistent by
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #372.
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11195)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11195) gives:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11196)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e2) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11196) implies:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11197)  op(e3, e3) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11117), (11118), (11197), (function-axioms) are
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #18.
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11198)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e2) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11198) implies:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11199)  op(e2, e2) = e0
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (11199), (function-axioms) are
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11200)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11200) gives:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11201)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11201) gives:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11202)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e2) = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11202) implies:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11203)  op(e1, e1) = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11091), (11203), (function-axioms) are
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11204)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11204) gives:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11205)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11182), (11205) are inconsistent by
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #371.
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11206)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e1) = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11206) implies:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11207)  op(e3, e3) = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11117), (11118), (11207), (function-axioms) are
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #18.
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11208)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11208) gives:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11209)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11209) gives:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11210)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e1) = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11210) implies:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11211)  op(e2, e2) = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (11211), (function-axioms) are
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11212)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e1) = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11212) implies:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11213)  op(e1, e1) = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11091), (11213), (function-axioms) are
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11214)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e1 = e0) & op(e0, e1) = e0)
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (11070), (11182), (11214),
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #349.
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | |   (11215)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 157.12/24.09  | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (9930), (9933), (11107), (11215) are
% 157.12/24.09  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 157.12/24.09  | | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | |   (11216)  all_56_3 = e1 & op(e2, e2) = e1
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | ALPHA: (11216) implies:
% 157.12/24.09  | | | | | | | | | | | | | | |   (11217)  op(e2, e2) = e1
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (225), (227), (228),
% 157.12/24.09  | | | | | | | | | | | | | | |            (11094), (11217), (function-axioms) are
% 157.12/24.09  | | | | | | | | | | | | | | |            inconsistent by sub-proof #332.
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | |   (11218)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 157.12/24.09  | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | BETA: splitting (11218) gives:
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | |   (11219)  all_56_5 = e1 & op(e2, e1) = e1
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | REF_CLOSE: (165), (11088), (11219), (function-axioms) are
% 157.12/24.09  | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | |   (11220)  all_56_10 = e1 & op(e2, e0) = e1
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | | REF_CLOSE: (164), (11069), (11220), (function-axioms) are
% 157.12/24.09  | | | | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 157.12/24.09  | | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | |   (11221)  all_56_3 = e1 & op(e2, e2) = e1
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | ALPHA: (11221) implies:
% 157.12/24.09  | | | | | | | | | | | | |   (11222)  op(e2, e2) = e1
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (160), (162),
% 157.12/24.09  | | | | | | | | | | | | |            (163), (168), (169), (214), (225), (227), (228),
% 157.12/24.09  | | | | | | | | | | | | |            (232), (238), (239), (11068), (11070), (11071),
% 157.12/24.09  | | | | | | | | | | | | |            (11085), (11086), (11087), (11091), (11222),
% 157.12/24.09  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.09  | | | | | | | | | | | | |            #330.
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | |   (11223)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 157.12/24.09  | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | REF_CLOSE: (158), (162), (11067), (11086), (11223),
% 157.12/24.09  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.09  | | | | | | | | | | | |            #338.
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | |   (11224)  all_54_10 = e0
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | REF_CLOSE: (336), (11075), (11224) are inconsistent by
% 157.12/24.09  | | | | | | | | | | |            sub-proof #329.
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | 
% 157.12/24.09  | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | |   (11225)  all_22_2 = e0
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | | COMBINE_EQS: (251), (11225) imply:
% 157.12/24.09  | | | | | | | |   (11226)  all_10_2 = e0
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | | SIMP: (11226) implies:
% 157.12/24.09  | | | | | | | |   (11227)  all_10_2 = e0
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | | REDUCE: (350), (11227) imply:
% 157.12/24.09  | | | | | | | |   (11228)   ~ (all_52_2 = e0)
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | | REDUCE: (361), (11227) imply:
% 157.12/24.09  | | | | | | | |   (11229)   ~ (all_52_6 = e0)
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | | REDUCE: (366), (11227) imply:
% 157.12/24.09  | | | | | | | |   (11230)   ~ (all_52_11 = e0)
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | | REDUCE: (11073), (11227) imply:
% 157.12/24.09  | | | | | | | |   (11231)   ~ (e3 = e0)
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | | REDUCE: (9931), (11227) imply:
% 157.12/24.09  | | | | | | | |   (11232)   ~ (e2 = e0)
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | | REDUCE: (45), (11227) imply:
% 157.12/24.09  | | | | | | | |   (11233)  op(e1, e1) = e0
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | | BETA: splitting (238) gives:
% 157.12/24.09  | | | | | | | | 
% 157.12/24.09  | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | 
% 157.12/24.09  | | | | | | | | |   (11234)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.12/24.09  | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 157.12/24.09  | | | | | | | | |                  op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.12/24.09  | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.12/24.09  | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.12/24.09  | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.12/24.09  | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.12/24.09  | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.12/24.09  | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.12/24.09  | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 157.12/24.09  | | | | | | | | |                  op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.12/24.09  | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.12/24.09  | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.12/24.09  | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.12/24.09  | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.12/24.09  | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.12/24.09  | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | BETA: splitting (11234) gives:
% 157.12/24.09  | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | |   (11235)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.12/24.09  | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 157.12/24.09  | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.12/24.09  | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.12/24.09  | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.12/24.09  | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 157.12/24.09  | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 157.12/24.09  | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 157.12/24.09  | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | ALPHA: (11235) implies:
% 157.12/24.09  | | | | | | | | | |   (11236)  op(e3, e3) = e3
% 157.12/24.09  | | | | | | | | | |   (11237)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 157.12/24.09  | | | | | | | | | |                = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 157.12/24.09  | | | | | | | | | |   (11238)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2
% 157.12/24.09  | | | | | | | | | |                = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))
% 157.12/24.09  | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | BETA: splitting (11238) gives:
% 157.12/24.09  | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | |   (11239)  all_57_14 = e3 & op(e1, e1) = e3
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | ALPHA: (11239) implies:
% 157.12/24.09  | | | | | | | | | | |   (11240)  op(e1, e1) = e3
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | REF_CLOSE: (7), (11233), (11240), (function-axioms) are
% 157.12/24.09  | | | | | | | | | | |            inconsistent by sub-proof #912.
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | |   (11241)   ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.12/24.09  | | | | | | | | | | |            $i(all_57_2)
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | ALPHA: (11241) implies:
% 157.12/24.09  | | | | | | | | | | |   (11242)   ~ (all_57_2 = e1)
% 157.12/24.09  | | | | | | | | | | |   (11243)  op(e1, e3) = all_57_2
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | BETA: splitting (11237) gives:
% 157.12/24.09  | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | |   (11244)  all_57_15 = e3 & op(e0, e0) = e3
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | ALPHA: (11244) implies:
% 157.12/24.09  | | | | | | | | | | | |   (11245)  op(e0, e0) = e3
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | REF_CLOSE: (8), (11071), (11245), (function-axioms) are
% 157.12/24.09  | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | |   (11246)   ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 &
% 157.12/24.09  | | | | | | | | | | | |            $i(all_57_6)
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | ALPHA: (11246) implies:
% 157.12/24.09  | | | | | | | | | | | |   (11247)   ~ (all_57_6 = e0)
% 157.12/24.09  | | | | | | | | | | | |   (11248)  op(e0, e3) = all_57_6
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 157.12/24.09  | | | | | | | | | | | |              all_57_6, e3, e0, simplifying with (159), (11248)
% 157.12/24.09  | | | | | | | | | | | |              gives:
% 157.12/24.09  | | | | | | | | | | | |   (11249)  all_57_6 = all_52_3
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 157.12/24.09  | | | | | | | | | | | |              all_57_2, e3, e1, simplifying with (163), (11243)
% 157.12/24.09  | | | | | | | | | | | |              gives:
% 157.12/24.09  | | | | | | | | | | | |   (11250)  all_57_2 = all_52_2
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e3,
% 157.12/24.09  | | | | | | | | | | | |              e3, e3, simplifying with (39), (11236) gives:
% 157.12/24.09  | | | | | | | | | | | |   (11251)  all_6_2 = e3
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | REDUCE: (11242), (11250) imply:
% 157.12/24.09  | | | | | | | | | | | |   (11252)   ~ (all_52_2 = e1)
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | REDUCE: (11247), (11249) imply:
% 157.12/24.09  | | | | | | | | | | | |   (11253)   ~ (all_52_3 = e0)
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | REDUCE: (346), (11251) imply:
% 157.12/24.09  | | | | | | | | | | | |   (11254)   ~ (all_52_8 = e3)
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | REDUCE: (348), (11251) imply:
% 157.12/24.09  | | | | | | | | | | | |   (11255)   ~ (all_52_12 = e3)
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | BETA: splitting (209) gives:
% 157.12/24.09  | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | |   (11256)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 157.12/24.09  | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | BETA: splitting (11256) gives:
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | |   (11257)  all_56_12 = e3 & op(e0, e3) = e3
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | ALPHA: (11257) implies:
% 157.12/24.09  | | | | | | | | | | | | | |   (11258)  all_56_12 = e3
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (128),
% 157.12/24.09  | | | | | | | | | | | | | |            (158), (162), (191), (195), (229), (231), (233),
% 157.12/24.09  | | | | | | | | | | | | | |            (238), (248), (258), (354), (356), (11067),
% 157.12/24.09  | | | | | | | | | | | | | |            (11071), (11229), (11233), (11258),
% 157.12/24.09  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.09  | | | | | | | | | | | | | |            #56.
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | |   (11259)  all_56_13 = e3 & op(e0, e2) = e3
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | REF_CLOSE: (158), (9926), (11259), (function-axioms) are
% 157.12/24.09  | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | End of split
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | Case 2:
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | |   (11260)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 157.12/24.09  | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | BETA: splitting (11260) gives:
% 157.12/24.09  | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | Case 1:
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | |   (11261)  all_56_14 = e3 & op(e0, e1) = e3
% 157.12/24.09  | | | | | | | | | | | | | | 
% 157.12/24.09  | | | | | | | | | | | | | | ALPHA: (11261) implies:
% 157.12/24.10  | | | | | | | | | | | | | |   (11262)  all_56_14 = e3
% 157.12/24.10  | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 157.12/24.10  | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | Case 1:
% 157.12/24.10  | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | |   (11263)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 157.12/24.10  | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 157.12/24.10  | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | BETA: splitting (11263) gives:
% 157.12/24.10  | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | Case 1:
% 157.12/24.10  | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | |   (11264)  all_56_0 = e0 & op(e3, e3) = e0
% 157.12/24.10  | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | ALPHA: (11264) implies:
% 157.12/24.10  | | | | | | | | | | | | | | | |   (11265)  op(e3, e3) = e0
% 157.12/24.10  | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11236), (11265), (function-axioms) are
% 157.12/24.10  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 157.12/24.10  | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | Case 2:
% 157.12/24.10  | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | |   (11266)  all_56_2 = e0 & op(e2, e3) = e0
% 157.12/24.10  | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | ALPHA: (11266) implies:
% 157.12/24.10  | | | | | | | | | | | | | | | |   (11267)  all_56_2 = e0
% 157.12/24.10  | | | | | | | | | | | | | | | |   (11268)  op(e2, e3) = e0
% 157.12/24.10  | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 157.12/24.10  | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.10  | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | |   (11269)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.12/24.10  | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.12/24.10  | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.12/24.10  | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.12/24.10  | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.12/24.10  | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.12/24.10  | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.10  | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.12/24.10  | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.10  | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.12/24.10  | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.10  | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.12/24.10  | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.12/24.10  | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.12/24.10  | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.12/24.10  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.12/24.10  | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.10  | | | | | | | | | | | | | | | | |              e1)
% 157.12/24.10  | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | BETA: splitting (11269) gives:
% 157.12/24.10  | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | |   (11270)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.12/24.10  | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | BETA: splitting (11270) gives:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |   (11271)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11268), (11271), (function-axioms) are
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #242.
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |   (11272)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              & $i(all_57_12))
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | BETA: splitting (11272) gives:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |   (11273)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11268), (11273), (function-axioms) are
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #241.
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |   (11274)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11274) gives:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |   (11275)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11275) implies:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |   (11276)  op(e2, e3) = e2
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11268), (11276), (function-axioms) are
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #709.
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |   (11277)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (11233), (11236), (11277),
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            #321.
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.10  | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | |   (11278)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | |              e1)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | BETA: splitting (11278) gives:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |   (11279)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | BETA: splitting (11279) gives:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |   (11280)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |                e2) = e3)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (9924), (11071), (11280),
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |            #378.
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |   (11281)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |                e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11281) gives:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |   (11282)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11282) implies:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |   (11283)  op(e3, e3) = e2
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11236), (11283), (function-axioms) are
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |   (11284)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11284) implies:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |   (11285)  op(e3, e3) = e1
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (51), (160), (163), (214), (238),
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            (11070), (11071), (11233), (11252), (11285),
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | |            #628.
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.10  | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.10  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |   (11286)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              e1)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (11286) gives:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |   (11287)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9929), (11233), (11287),
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |            #41.
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |   (11288)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              e1)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (157), (11230), (11233), (11288),
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |            #377.
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.11  | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | End of split
% 157.12/24.11  | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.11  | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | |   (11289)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.12/24.11  | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.12/24.11  | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.12/24.11  | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.12/24.11  | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.12/24.11  | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.12/24.11  | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.12/24.11  | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.12/24.11  | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.12/24.11  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.12/24.11  | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.12/24.11  | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 157.12/24.11  | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 157.12/24.11  | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.12/24.11  | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 157.12/24.11  | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 157.12/24.11  | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.12/24.11  | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 157.12/24.11  | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 157.12/24.11  | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.12/24.11  | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 157.12/24.11  | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 157.12/24.11  | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 157.12/24.11  | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 157.12/24.11  | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 157.12/24.11  | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 157.12/24.11  | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 157.12/24.11  | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 157.12/24.11  | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.12/24.11  | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 157.12/24.11  | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 157.12/24.11  | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | BETA: splitting (11289) gives:
% 157.12/24.11  | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | |   (11290)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.12/24.11  | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.12/24.11  | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.12/24.11  | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.12/24.11  | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.12/24.11  | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.12/24.11  | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.12/24.11  | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.12/24.11  | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | BETA: splitting (11290) gives:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |   (11291)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14))
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (11291) gives:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |   (11292)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11292) gives:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |   (11293)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11293) implies:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |   (11294)  op(e3, e3) = e1
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (51), (160), (163), (214), (238),
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            (11070), (11071), (11233), (11252), (11294),
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            #628.
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |   (11295)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11295) implies:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |   (11296)  op(e2, e2) = e1
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (11296), (function-axioms) are
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |   (11297)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (11230), (11233), (11297),
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |            #376.
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |   (11298)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |                e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |            (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.12/24.11  | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (11298) gives:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |   (11299)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (11233), (11299), (function-axioms) are
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |   (11300)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |                e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |                e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11300) gives:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |   (11301)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11301) implies:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |   (11302)  op(e0, e0) = e3
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11071), (11302), (function-axioms) are
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |   (11303)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11303) gives:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | |   (11304)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11304) implies:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | |   (11305)  op(e3, e1) = e3
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11254), (11305), (function-axioms) are
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | |   (11306)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11306) implies:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | |   (11307)  op(e3, e3) = e1
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (51), (160), (163), (214), (238),
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | |            (11070), (11071), (11233), (11252), (11307),
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | |            #628.
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.12  | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | |   (11308)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.12/24.12  | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | |                  e0)))
% 157.12/24.12  | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | BETA: splitting (11308) gives:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |   (11309)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (11309) gives:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |   (11310)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                e1) = e2)
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (158), (159), (207), (9929),
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |            (11066), (11067), (11262), (11310),
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |            #20.
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |   (11311)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11311) gives:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |   (11312)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11312) implies:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |   (11313)  op(e2, e2) = e1
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (11313), (function-axioms) are
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |   (11314)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11314) implies:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |   (11315)  op(e0, e0) = e3
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11071), (11315), (function-axioms) are
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |   (11316)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (11316) gives:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |   (11317)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (158), (159), (168), (207), (11066),
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |            (11067), (11255), (11262), (11317),
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |            #19.
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |   (11318)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11318) gives:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |   (11319)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11319) implies:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |   (11320)  op(e2, e2) = e2
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11320), (function-axioms) are
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |   (11321)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.12/24.12  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11321) gives:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |   (11322)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11322) implies:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |   (11323)  op(e1, e1) = e1
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11233), (11323), (function-axioms) are
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |   (11324)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e0))
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11324) implies:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |   (11325)  op(e0, e0) = all_57_15
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |   (11326)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11326) gives:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |   (11327)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11327) gives:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |   (11328)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11253), (11328), (function-axioms) are
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #99.
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |   (11329)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11329) gives:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (11330)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11330) implies:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (11331)  op(e0, e3) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11253), (11331), (function-axioms) are
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (11332)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11332) gives:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11333)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e2) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11333) implies:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11334)  op(e3, e3) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11236), (11334), (function-axioms) are
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11335)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e2) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11335) implies:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11336)  op(e2, e2) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (164), (222),
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (229), (231), (233), (11066),
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (11069), (11236), (11267), (11336),
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            #328.
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |   (11337)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11337) gives:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |   (11338)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11338) gives:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (11339)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e2) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11339) implies:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (11340)  op(e1, e0) = e1
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (11070), (11340), (function-axioms) are
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (11341)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (51), (11071), (11236), (11325),
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |            (11341), (function-axioms) are inconsistent by
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #306.
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |   (11342)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11342) gives:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (11343)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11343) gives:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11344)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e1) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11344) implies:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11345)  op(e2, e2) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (164), (222),
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (229), (231), (233), (11066),
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (11069), (11236), (11267), (11345),
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            #328.
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11346)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e1) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11346) implies:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11347)  op(e0, e1) = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (11230), (11347), (function-axioms) are
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (11348)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e1 = e0) & op(e0, e1) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (11230), (11348), (function-axioms) are
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | |   (11349)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 157.12/24.13  | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 157.12/24.13  | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (11228), (11253), (11349),
% 157.12/24.13  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.13  | | | | | | | | | | | | | | |            #698.
% 157.12/24.13  | | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | |   (11350)  all_56_15 = e3 & op(e0, e0) = e3
% 157.12/24.13  | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | ALPHA: (11350) implies:
% 157.12/24.13  | | | | | | | | | | | | | |   (11351)  op(e0, e0) = e3
% 157.12/24.13  | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | | REF_CLOSE: (8), (11071), (11351), (function-axioms) are
% 157.12/24.13  | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 157.12/24.13  | | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | |   (11352)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.12/24.13  | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 157.12/24.13  | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.12/24.13  | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.12/24.13  | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.12/24.13  | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 157.12/24.13  | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 157.12/24.13  | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 157.12/24.13  | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | ALPHA: (11352) implies:
% 157.12/24.13  | | | | | | | | | |   (11353)  op(e2, e2) = e2
% 157.12/24.13  | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | | REF_CLOSE: (9), (9929), (11353), (function-axioms) are
% 157.12/24.13  | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.12/24.13  | | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | | 
% 157.12/24.13  | | | | | | | | Case 2:
% 157.12/24.13  | | | | | | | | | 
% 157.12/24.13  | | | | | | | | |   (11354)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.12/24.13  | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 157.12/24.13  | | | | | | | | |                  op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.12/24.13  | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.12/24.13  | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.12/24.13  | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.12/24.13  | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.12/24.13  | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.12/24.13  | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.12/24.13  | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 157.12/24.13  | | | | | | | | |                  op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.12/24.13  | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.12/24.13  | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.12/24.13  | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.12/24.13  | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.12/24.13  | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.12/24.13  | | | | | | | | | 
% 157.12/24.13  | | | | | | | | | REF_CLOSE: (4), (51), (11071), (11233), (11354),
% 157.12/24.13  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.13  | | | | | | | | |            #629.
% 157.12/24.13  | | | | | | | | | 
% 157.12/24.13  | | | | | | | | End of split
% 157.12/24.13  | | | | | | | | 
% 157.12/24.14  | | | | | | | End of split
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | Case 2:
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | |   (11355)  all_20_2 = e3
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | COMBINE_EQS: (325), (11355) imply:
% 157.12/24.14  | | | | | | |   (11356)  all_10_2 = e3
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | REDUCE: (366), (11356) imply:
% 157.12/24.14  | | | | | | |   (11357)   ~ (all_52_11 = e3)
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | REDUCE: (45), (11356) imply:
% 157.12/24.14  | | | | | | |   (11358)  op(e1, e1) = e3
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (157), (158),
% 157.12/24.14  | | | | | | |            (209), (229), (231), (233), (238), (9926), (9929),
% 157.12/24.14  | | | | | | |            (11071), (11357), (11358), (function-axioms) are
% 157.12/24.14  | | | | | | |            inconsistent by sub-proof #21.
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | End of split
% 157.12/24.14  | | | | | | 
% 157.12/24.14  | | | | | End of split
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | Case 2:
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | |   (11359)  all_12_2 = e2
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | | COMBINE_EQS: (324), (11359) imply:
% 157.12/24.14  | | | | |   (11360)  all_6_2 = e2
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | | REDUCE: (338), (11360) imply:
% 157.12/24.14  | | | | |   (11361)   ~ (all_52_1 = e2)
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | | REDUCE: (346), (11360) imply:
% 157.12/24.14  | | | | |   (11362)   ~ (all_52_8 = e2)
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | | REDUCE: (39), (11360) imply:
% 157.12/24.14  | | | | |   (11363)  op(e3, e3) = e2
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (51), (52), (58),
% 157.12/24.14  | | | | |            (61), (64), (73), (123), (157), (158), (159), (160), (162),
% 157.12/24.14  | | | | |            (163), (164), (165), (167), (168), (169), (170), (189),
% 157.12/24.14  | | | | |            (194), (202), (214), (221), (222), (223), (225), (227),
% 157.12/24.14  | | | | |            (228), (230), (232), (234), (236), (238), (239), (246),
% 157.12/24.14  | | | | |            (251), (271), (301), (325), (330), (336), (350), (351),
% 157.12/24.14  | | | | |            (358), (361), (362), (363), (364), (368), (369), (370),
% 157.12/24.14  | | | | |            (371), (9924), (9929), (9931), (11361), (11362), (11363),
% 157.12/24.14  | | | | |            (function-axioms) are inconsistent by sub-proof #34.
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | End of split
% 157.12/24.14  | | | | 
% 157.12/24.14  | | | Case 2:
% 157.12/24.14  | | | | 
% 157.12/24.14  | | | |   (11364)  all_10_2 = e2
% 157.12/24.14  | | | | 
% 157.12/24.14  | | | | COMBINE_EQS: (332), (11364) imply:
% 157.12/24.14  | | | |   (11365)  all_34_2 = e2
% 157.12/24.14  | | | | 
% 157.12/24.14  | | | | REDUCE: (350), (11364) imply:
% 157.12/24.14  | | | |   (11366)   ~ (all_52_2 = e2)
% 157.12/24.14  | | | | 
% 157.12/24.14  | | | | REDUCE: (363), (11364) imply:
% 157.12/24.14  | | | |   (11367)   ~ (all_52_8 = e2)
% 157.12/24.14  | | | | 
% 157.12/24.14  | | | | REDUCE: (364), (11364) imply:
% 157.12/24.14  | | | |   (11368)   ~ (all_52_9 = e2)
% 157.12/24.14  | | | | 
% 157.12/24.14  | | | | REDUCE: (366), (11364) imply:
% 157.12/24.14  | | | |   (11369)   ~ (all_52_11 = e2)
% 157.12/24.14  | | | | 
% 157.12/24.14  | | | | REDUCE: (368), (11364) imply:
% 157.12/24.14  | | | |   (11370)   ~ (all_52_14 = e2)
% 157.12/24.14  | | | | 
% 157.12/24.14  | | | | BETA: splitting (82) gives:
% 157.12/24.14  | | | | 
% 157.12/24.14  | | | | Case 1:
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | |   (11371)   ~ (all_34_2 = e2)
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | | REDUCE: (11365), (11371) imply:
% 157.12/24.14  | | | | |   (11372)  $false
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | | CLOSE: (11372) is inconsistent.
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | Case 2:
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | |   (11373)  ( ~ (all_34_0 = e0) & op(e2, e1) = all_34_0 & $i(all_34_0))
% 157.12/24.14  | | | | |            | ( ~ (all_34_1 = e3) & op(e2, e2) = all_34_1 &
% 157.12/24.14  | | | | |              $i(all_34_1))
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | | BETA: splitting (219) gives:
% 157.12/24.14  | | | | | 
% 157.12/24.14  | | | | | Case 1:
% 157.12/24.14  | | | | | | 
% 157.12/24.14  | | | | | |   (11374)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 &
% 157.12/24.14  | | | | | |              op(e2, e1) = e2)
% 157.12/24.14  | | | | | | 
% 157.12/24.14  | | | | | | BETA: splitting (11374) gives:
% 157.12/24.14  | | | | | | 
% 157.12/24.14  | | | | | | Case 1:
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | |   (11375)  all_56_4 = e2 & op(e3, e1) = e2
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | ALPHA: (11375) implies:
% 157.12/24.14  | | | | | | |   (11376)  op(e3, e1) = e2
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | REF_CLOSE: (169), (11367), (11376), (function-axioms) are
% 157.12/24.14  | | | | | | |            inconsistent by sub-proof #670.
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | Case 2:
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | |   (11377)  all_56_5 = e2 & op(e2, e1) = e2
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | ALPHA: (11377) implies:
% 157.12/24.14  | | | | | | |   (11378)  op(e2, e1) = e2
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | REF_CLOSE: (165), (11368), (11378), (function-axioms) are
% 157.12/24.14  | | | | | | |            inconsistent by sub-proof #1002.
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | End of split
% 157.12/24.14  | | | | | | 
% 157.12/24.14  | | | | | Case 2:
% 157.12/24.14  | | | | | | 
% 157.12/24.14  | | | | | |   (11379)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 &
% 157.12/24.14  | | | | | |              op(e0, e1) = e2)
% 157.12/24.14  | | | | | | 
% 157.12/24.14  | | | | | | BETA: splitting (11379) gives:
% 157.12/24.14  | | | | | | 
% 157.12/24.14  | | | | | | Case 1:
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | |   (11380)  all_56_8 = e2 & op(e1, e1) = e2
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | ALPHA: (11380) implies:
% 157.12/24.14  | | | | | | |   (11381)  all_56_8 = e2
% 157.12/24.14  | | | | | | |   (11382)  op(e1, e1) = e2
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | BETA: splitting (11373) gives:
% 157.12/24.14  | | | | | | | 
% 157.12/24.14  | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | |   (11383)   ~ (all_34_0 = e0) & op(e2, e1) = all_34_0 &
% 157.12/24.14  | | | | | | | |            $i(all_34_0)
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | ALPHA: (11383) implies:
% 157.12/24.14  | | | | | | | |   (11384)   ~ (all_34_0 = e0)
% 157.12/24.14  | | | | | | | |   (11385)  op(e2, e1) = all_34_0
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 157.12/24.14  | | | | | | | |              all_34_0, e1, e2, simplifying with (165), (11385)
% 157.12/24.14  | | | | | | | |              gives:
% 157.12/24.14  | | | | | | | |   (11386)  all_52_9 = all_34_0
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | COMBINE_EQS: (261), (11386) imply:
% 157.12/24.14  | | | | | | | |   (11387)  all_54_6 = all_34_0
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | REDUCE: (123), (11386) imply:
% 157.12/24.14  | | | | | | | |   (11388)   ~ (all_52_8 = all_34_0)
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | REDUCE: (118), (11386) imply:
% 157.12/24.14  | | | | | | | |   (11389)   ~ (all_52_11 = all_34_0)
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | SIMP: (11389) implies:
% 157.12/24.14  | | | | | | | |   (11390)   ~ (all_52_11 = all_34_0)
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | REDUCE: (117), (11386) imply:
% 157.12/24.14  | | | | | | | |   (11391)   ~ (all_52_13 = all_34_0)
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | SIMP: (11391) implies:
% 157.12/24.14  | | | | | | | |   (11392)   ~ (all_52_13 = all_34_0)
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | REDUCE: (9927), (11386) imply:
% 157.12/24.14  | | | | | | | |   (11393)   ~ (all_34_0 = e3)
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | REDUCE: (11368), (11386) imply:
% 157.12/24.14  | | | | | | | |   (11394)   ~ (all_34_0 = e2)
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | BETA: splitting (198) gives:
% 157.12/24.14  | | | | | | | | 
% 157.12/24.14  | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | 
% 157.12/24.14  | | | | | | | | |   (11395)  all_54_6 = e3
% 157.12/24.14  | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | COMBINE_EQS: (11387), (11395) imply:
% 157.12/24.14  | | | | | | | | |   (11396)  all_34_0 = e3
% 157.12/24.14  | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | REDUCE: (11393), (11396) imply:
% 157.12/24.14  | | | | | | | | |   (11397)  $false
% 157.12/24.14  | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | CLOSE: (11397) is inconsistent.
% 157.12/24.14  | | | | | | | | | 
% 157.12/24.14  | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | 
% 157.12/24.14  | | | | | | | | |   (11398)   ~ (all_54_6 = e3)
% 157.12/24.14  | | | | | | | | |   (11399)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.12/24.14  | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | BETA: splitting (11399) gives:
% 157.12/24.14  | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | |   (11400)  all_54_6 = e2
% 157.12/24.14  | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | COMBINE_EQS: (11387), (11400) imply:
% 157.12/24.14  | | | | | | | | | |   (11401)  all_34_0 = e2
% 157.12/24.14  | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | REDUCE: (11394), (11401) imply:
% 157.12/24.14  | | | | | | | | | |   (11402)  $false
% 157.12/24.14  | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | CLOSE: (11402) is inconsistent.
% 157.12/24.14  | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | |   (11403)   ~ (all_54_6 = e2)
% 157.12/24.14  | | | | | | | | | |   (11404)  all_54_6 = e1 | all_54_6 = e0
% 157.12/24.14  | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | BETA: splitting (11404) gives:
% 157.12/24.14  | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | |   (11405)  all_54_6 = e1
% 157.12/24.14  | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | COMBINE_EQS: (11387), (11405) imply:
% 157.12/24.14  | | | | | | | | | | |   (11406)  all_34_0 = e1
% 157.12/24.14  | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | REDUCE: (11388), (11406) imply:
% 157.12/24.14  | | | | | | | | | | |   (11407)   ~ (all_52_8 = e1)
% 157.12/24.14  | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | REDUCE: (11390), (11406) imply:
% 157.12/24.14  | | | | | | | | | | |   (11408)   ~ (all_52_11 = e1)
% 157.12/24.14  | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | REDUCE: (11392), (11406) imply:
% 157.12/24.14  | | | | | | | | | | |   (11409)   ~ (all_52_13 = e1)
% 157.12/24.14  | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | REDUCE: (11393), (11406) imply:
% 157.12/24.14  | | | | | | | | | | |   (11410)   ~ (e3 = e1)
% 157.12/24.14  | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | REDUCE: (11394), (11406) imply:
% 157.12/24.14  | | | | | | | | | | |   (11411)   ~ (e2 = e1)
% 157.12/24.14  | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | BETA: splitting (218) gives:
% 157.12/24.14  | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | |   (11412)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 157.12/24.14  | | | | | | | | | | | |              & op(e2, e1) = e1)
% 157.12/24.14  | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | BETA: splitting (11412) gives:
% 157.12/24.14  | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | |   (11413)  all_56_4 = e1 & op(e3, e1) = e1
% 157.12/24.14  | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | REF_CLOSE: (169), (11407), (11413), (function-axioms) are
% 157.12/24.14  | | | | | | | | | | | | |            inconsistent by sub-proof #331.
% 157.12/24.14  | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | |   (11414)  all_56_5 = e1 & op(e2, e1) = e1
% 157.12/24.14  | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | ALPHA: (11414) implies:
% 157.12/24.14  | | | | | | | | | | | | |   (11415)  all_56_5 = e1
% 157.12/24.14  | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | BETA: splitting (49) gives:
% 157.12/24.14  | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | |   (11416)   ~ (all_12_2 = e2)
% 157.12/24.14  | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | REDUCE: (324), (11416) imply:
% 157.12/24.14  | | | | | | | | | | | | | |   (11417)   ~ (all_6_2 = e2)
% 157.12/24.14  | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 157.12/24.14  | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | |   (11418)   ~ (all_14_2 = e1)
% 157.12/24.14  | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | |   (11419)   ~ (all_18_2 = e3)
% 157.12/24.14  | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | REDUCE: (301), (11419) imply:
% 157.12/24.14  | | | | | | | | | | | | | | | |   (11420)   ~ (all_14_2 = e3)
% 157.12/24.14  | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | |   (11421)   ~ (all_26_2 = e1)
% 157.12/24.14  | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | REDUCE: (307), (11421) imply:
% 157.12/24.14  | | | | | | | | | | | | | | | | |   (11422)   ~ (all_6_2 = e1)
% 157.12/24.14  | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | |   (11423)  all_54_0 = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (11423) imply:
% 157.12/24.14  | | | | | | | | | | | | | | | | | |   (11424)  all_6_2 = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | REDUCE: (346), (11424) imply:
% 157.12/24.14  | | | | | | | | | | | | | | | | | |   (11425)   ~ (all_52_8 = e3)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | REDUCE: (348), (11424) imply:
% 157.12/24.14  | | | | | | | | | | | | | | | | | |   (11426)   ~ (all_52_12 = e3)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | REDUCE: (39), (11424) imply:
% 157.12/24.14  | | | | | | | | | | | | | | | | | |   (11427)  op(e3, e3) = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | |   (11428)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 157.12/24.14  | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (11428) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | |   (11429)  all_56_9 = e3 & op(e3, e0) = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | ALPHA: (11429) implies:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | |   (11430)  all_56_9 = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | |            (11427), (11430), (function-axioms) are
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #632.
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | |   (11431)  all_56_10 = e3 & op(e2, e0) = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9928), (11431), (function-axioms) are
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #31.
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | |   (11432)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 157.12/24.14  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (11432) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | |   (11433)  all_56_11 = e3 & op(e1, e0) = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | ALPHA: (11433) implies:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | |   (11434)  all_56_11 = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | |   (11435)  op(e1, e0) = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | |   (11436)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11436) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | |   (11437)  all_56_12 = e3 & op(e0, e3) = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11437) implies:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | |   (11438)  all_56_12 = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | |            (11427), (11438), (function-axioms) are
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #729.
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | |   (11439)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (9930), (11417), (11422), (11439) are
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | |   (11440)  all_56_13 = e3 & op(e0, e2) = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9926), (11440), (function-axioms) are
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | |   (11441)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11441) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | |   (11442)  all_56_14 = e3 & op(e0, e1) = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11442) implies:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | |   (11443)  all_56_14 = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | |   (11444)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11444) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11445)  all_56_4 = e0 & op(e3, e1) = e0
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11445) implies:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11446)  all_56_4 = e0
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11447)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11447) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11448)  all_56_9 = e1 & op(e3, e0) = e1
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11448) implies:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11449)  all_56_9 = e1
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11450)  op(e3, e0) = e1
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11451)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11451) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11452)  all_56_0 = e2 & op(e3, e3) = e2
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11452) implies:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11453)  op(e3, e3) = e2
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11427), (11453), (function-axioms) are
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11454)  all_56_1 = e2 & op(e3, e2) = e2
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11454) implies:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11455)  all_56_1 = e2
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11456)  op(e3, e2) = e2
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11457)  all_54_2 = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (11457) imply:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11458)  all_52_8 = e3
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11425), (11458) imply:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11459)  $false
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11459) is inconsistent.
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11460)   ~ (all_54_2 = e3)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11461)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11461) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11462)  all_54_2 = e2
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (11462) imply:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11463)  all_52_8 = e2
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11367), (11463) imply:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11464)  $false
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11464) is inconsistent.
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11465)   ~ (all_54_2 = e2)
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11466)  all_54_2 = e1 | all_54_2 = e0
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11466) gives:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11467)  all_54_2 = e1
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (11467) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11468)  all_52_8 = e1
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11407), (11468) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11469)  $false
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11469) is inconsistent.
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11470)  all_54_2 = e0
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (11470) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11471)  all_52_8 = e0
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (11471) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11472)   ~ (all_52_4 = e0)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (11471) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11473)   ~ (all_52_11 = e0)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11473) implies:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11474)   ~ (all_52_11 = e0)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (11471) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11475)   ~ (all_52_12 = e0)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11475) implies:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11476)   ~ (all_52_12 = e0)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11425), (11471) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11477)   ~ (e3 = e0)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (160), (11435) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11478)  all_52_14 = e3
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (168), (11450) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11479)  all_52_12 = e1
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (11456) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11480)  all_52_4 = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (11478) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11481)   ~ (all_52_2 = e3)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (11479) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11482)   ~ (all_14_2 = e1)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (11478) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11483)   ~ (all_14_2 = e3)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11484)   ~ (all_28_2 = e2)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (11484) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11485)   ~ (all_14_2 = e2)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11486)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11486) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11487)  all_56_9 = e2 & op(e3, e0) = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11487) implies:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11488)  all_56_9 = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (232), (11427), (11446), (11455),
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11488), (function-axioms) are inconsistent by
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #300.
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11489)  all_56_10 = e2 & op(e2, e0) = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11489) implies:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11490)  all_56_10 = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11491)  op(e2, e0) = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11492)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11492) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11493)  all_56_2 = e0 & op(e2, e3) = e0
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11493) implies:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11494)  op(e2, e3) = e0
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11495)  all_54_15 = e3
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (11495) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11496)  all_14_2 = e3
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11420), (11496) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11497)  $false
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11497) is inconsistent.
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11498)   ~ (all_54_15 = e3)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11499)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11499) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11500)  all_54_15 = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (11500) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11501)  all_14_2 = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11485), (11501) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11502)  $false
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11502) is inconsistent.
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11503)   ~ (all_54_15 = e2)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11504)  all_54_15 = e1 | all_54_15 = e0
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11505)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11505) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11506)  all_56_0 = e2 & op(e3, e3) = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11506) implies:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11507)  all_56_0 = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11508)  op(e3, e3) = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (236), (11449),
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11455), (11456), (11507), (11508),
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #152.
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11509)  all_56_2 = e2 & op(e2, e3) = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11509) implies:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11510)  op(e2, e3) = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11494), (11510), (function-axioms) are
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #709.
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11511)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11511) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11512)  all_56_6 = e2 & op(e1, e3) = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11366), (11512), (function-axioms) are
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11513)  all_56_12 = e2 & op(e0, e3) = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11513) implies:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11514)  all_56_12 = e2
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11504) gives:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11515)  all_54_15 = e1
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (11515) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11516)  all_14_2 = e1
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11418), (11516) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11517)  $false
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11517) is inconsistent.
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11518)  all_54_15 = e0
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (11518) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11519)  all_14_2 = e0
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (11519) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11520)   ~ (all_52_7 = e0)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11485), (11519) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11521)   ~ (e2 = e0)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11418), (11519) imply:
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11522)   ~ (e1 = e0)
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.12/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (11519) imply:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11523)  op(e0, e0) = e0
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11524)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11524) gives:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11525)  all_56_1 = e0 & op(e3, e2) = e0
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11525) implies:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11526)  all_56_1 = e0
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (169), (232), (234),
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11367), (11427), (11446), (11526),
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #514.
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11527)  all_56_3 = e0 & op(e2, e2) = e0
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11527) implies:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11528)  op(e2, e2) = e0
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (229),
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (11415), (11427), (11514), (11528),
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #530.
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11529)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11529) gives:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11530)  all_56_7 = e0 & op(e1, e2) = e0
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11530) implies:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11531)  all_56_7 = e0
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11532)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11532) gives:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11533)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11533) gives:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11534)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11494), (11534), (function-axioms) are
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #242.
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11535)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_12))
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11535) gives:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11536)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11494), (11536), (function-axioms) are
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #241.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11537)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11537) gives:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11538)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11538) implies:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11539)  op(e2, e3) = e2
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11494), (11539), (function-axioms) are
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #709.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11540)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (11368), (11382), (11540),
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #140.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11541)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11541) gives:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11542)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11542) gives:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11543)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11543) gives:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11544)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11544) implies:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11545)  op(e0, e0) = e3
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11523), (11545), (function-axioms) are
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11546)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e2) = e3
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11546) implies:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11547)  op(e3, e2) = e3
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11456), (11547), (function-axioms) are
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #433.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11548)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11548) gives:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11549)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11549) implies:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11550)  op(e3, e3) = e2
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11427), (11550), (function-axioms) are
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11551)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11551) implies:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11552)  op(e3, e3) = e1
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (236), (11449),
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11455), (11456), (11552), (function-axioms) are
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #148.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11553)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11553) gives:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11554)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11554) gives:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11555)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11555) implies:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11556)  op(e1, e1) = e3
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11382), (11556), (function-axioms) are
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11557)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11557) implies:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11558)  op(e2, e2) = e1
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (11558), (function-axioms) are
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11559)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11559) gives:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11560)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11560) implies:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11561)  op(e0, e0) = e1
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (11418), (11504), (11561),
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #790.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11562)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11382), (11562), (function-axioms) are
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #139.
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11563)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11563) gives:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11564)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11564) gives:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11565)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14))
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11565) gives:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11566)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11566) gives:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11567)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11567) implies:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11568)  op(e3, e3) = e1
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (236), (11449),
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11455), (11456), (11568), (function-axioms) are
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #148.
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11569)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11569) implies:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11570)  op(e2, e2) = e1
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9929), (11570), (function-axioms) are
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11571)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11571) gives:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11572)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11572) implies:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11573)  op(e2, e1) = e2
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (11368), (11573), (function-axioms) are
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11574)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11574) implies:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11575)  op(e0, e0) = e1
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (11418), (11504), (11575),
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #790.
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11576)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11576) gives:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11577)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11577) gives:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11578)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11578) implies:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11579)  all_57_11 = e2
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11580)   ~ (all_57_12 = e0)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11581)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11581) gives:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11582)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.54/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11582) implies:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11583)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11584)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11584) gives:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11585)  all_56_6 = e1 & op(e1, e3) = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11585) implies:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11586)  op(e1, e3) = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11583) gives:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11587)  all_57_14 = e3 & op(e1, e1) = e3
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11587) implies:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11588)  op(e1, e1) = e3
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11382), (11588), (function-axioms) are
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11589)   ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2)
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11586), (11589), (function-axioms) are
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #607.
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11590)  all_56_7 = e1 & op(e1, e2) = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11590) implies:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11591)  all_56_7 = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11531), (11591) imply:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11592)  e1 = e0
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11449), (11592) imply:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11593)  all_56_9 = e0
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (232), (11427), (11446), (11455),
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11593), (function-axioms) are inconsistent by
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #525.
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11594)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11594) gives:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11595)  all_56_8 = e1 & op(e1, e1) = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11595) implies:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11596)  op(e1, e1) = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11382), (11596), (function-axioms) are
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11597)  all_56_11 = e1 & op(e1, e0) = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11597) implies:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11598)  all_56_11 = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11434), (11598) imply:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11599)  e3 = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11599) implies:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11600)  e3 = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (217), (220), (11382),
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11415), (11443), (11600), (function-axioms) are
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #17.
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11601)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11601) implies:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11602)  op(e2, e2) = e2
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (11491), (11602),
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11603)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11603) gives:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11604)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_8 & $i(all_57_8)))
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11604) implies:
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11605)  op(e1, e1) = e1
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11382), (11605), (function-axioms) are
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 157.59/24.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11606)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13)))
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11606) implies:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11607)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11))
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11607) gives:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11608)  all_57_12 = e0 & op(e2, e2) = e0
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11608) implies:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11609)  all_57_12 = e0
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11580), (11609) imply:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11610)  $false
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11610) is inconsistent.
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11611)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11611) implies:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11612)   ~ (all_57_11 = e2)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11579), (11612) imply:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11613)  $false
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11613) is inconsistent.
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11614)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e1
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11614) implies:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11615)  op(e1, e1) = e1
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11382), (11615), (function-axioms) are
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11616)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11616) gives:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11617)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11617) implies:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11618)  op(e0, e0) = e3
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11523), (11618), (function-axioms) are
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11619)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (169), (230), (236),
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11425), (11449), (11455), (11456), (11619),
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #16.
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11620)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11620) gives:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11621)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11621) gives:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11622)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11622) gives:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11623)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11623) implies:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11624)  op(e0, e0) = e2
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (11418), (11485), (11504), (11624),
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #799.
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11625)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11625) implies:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11626)  op(e2, e2) = e2
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (11491), (11626),
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11627)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9929), (11523), (11627),
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #50.
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11628)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11628) gives:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11629)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11629) gives:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11630)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11630) implies:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11631)  op(e0, e0) = e2
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (246), (11418), (11485), (11504), (11631),
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #799.
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11632)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11632) implies:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11633)  op(e3, e0) = e3
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11450), (11633), (function-axioms) are
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #796.
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11634)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.59/24.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11634) gives:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11635)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11635) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11636)  op(e2, e2) = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (164), (360), (11491), (11636),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #972.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11637)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11637) gives:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11638)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11638) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11639)  op(e1, e1) = e1
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11382), (11639), (function-axioms) are
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11640)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0))
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11640) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11641)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (246), (351), (362), (369),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11382), (11418), (11420), (11427), (11485),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11499), (11641), (function-axioms) are
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #742.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11642)  all_56_13 = e0 & op(e0, e2) = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11642) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11643)  op(e0, e2) = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11520), (11643), (function-axioms) are
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11644)  all_56_3 = e0 & op(e2, e2) = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11644) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11645)  op(e2, e2) = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (11645), (function-axioms) are
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11646)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11646) gives:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11647)  all_56_5 = e0 & op(e2, e1) = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11647) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11648)  op(e2, e1) = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (165), (271), (11407), (11466), (11648),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #37.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11649)  all_56_10 = e0 & op(e2, e0) = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11649) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11650)  all_56_10 = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11490), (11650) imply:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11651)  e2 = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11651) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11652)  e2 = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11455), (11652) imply:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11653)  all_56_1 = e0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (169), (232), (234),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11367), (11427), (11446), (11653),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #514.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11654)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11654) gives:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11655)  all_56_11 = e2 & op(e1, e0) = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (213), (214),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (11381), (11481), (11655),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #115.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11656)  all_56_15 = e2 & op(e0, e0) = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11656) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11657)  op(e0, e0) = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (189), (246), (11418), (11420), (11485),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11657), (function-axioms) are inconsistent by
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #797.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11658)  all_28_2 = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (11658) imply:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11659)  all_14_2 = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (11659) imply:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11660)   ~ (all_52_3 = e2)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (11659) imply:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11661)   ~ (all_52_13 = e2)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11420), (11659) imply:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11662)   ~ (e3 = e2)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (11659) imply:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11663)  op(e0, e0) = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11664)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11664) gives:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11665)  all_56_0 = e2 & op(e3, e3) = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11665) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11666)  all_56_0 = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11667)  op(e3, e3) = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (236), (11449),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11455), (11456), (11666), (11667),
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #152.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11668)  all_56_2 = e2 & op(e2, e3) = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11668) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11669)  op(e2, e3) = e2
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11670)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11670) gives:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11671)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11671) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11672)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11673)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11672) gives:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11674)  all_57_15 = e3 & op(e0, e0) = e3
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11674) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11675)  op(e0, e0) = e3
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11663), (11675), (function-axioms) are
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11676)   ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 &
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11676) implies:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11677)   ~ (all_57_6 = e0)
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11678)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11678) gives:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11679)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11679) gives:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11680)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11680) gives:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11681)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11681) gives:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11682)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11682) implies:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11683)  op(e3, e3) = e2
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11427), (11683), (function-axioms) are
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11684)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11684) implies:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11685)  op(e3, e2) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11456), (11685), (function-axioms) are
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #433.
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11686)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11686) gives:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11687)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11687) implies:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11688)   ~ (all_57_12 = e3)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11669), (11673), (11688), (function-axioms) are
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #15.
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11689)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11689) implies:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11690)  op(e3, e1) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11425), (11690), (function-axioms) are
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11691)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_12))
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11691) gives:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11692)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11692) gives:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11693)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11693) implies:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11694)   ~ (all_57_12 = e3)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11669), (11673), (11694), (function-axioms) are
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #15.
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11695)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11695) implies:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11696)  op(e3, e0) = e3
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11450), (11696), (function-axioms) are
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #796.
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11697)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11697) gives:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11698)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11698) implies:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11699)  op(e2, e2) = e2
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11699), (function-axioms) are
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11700)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (11368), (11382), (11700),
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #140.
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11701)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.59/24.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11701) gives:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11702)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11702) gives:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11703)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11456), (11663), (11703), (function-axioms)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #33.
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11704)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11704) gives:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11705)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11705) implies:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11706)  op(e2, e0) = e2
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (11661), (11706), (function-axioms) are
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11707)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11707) implies:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11708)  op(e3, e3) = e1
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (236), (11449),
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11455), (11456), (11708), (function-axioms) are
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #148.
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11709)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11709) gives:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11710)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11710) gives:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11711)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11711) implies:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11712)  op(e1, e1) = e3
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11382), (11712), (function-axioms) are
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11713)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11713) implies:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11714)  op(e2, e2) = e1
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11669), (11673), (11714), (function-axioms)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #782.
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11715)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11382), (11663), (11715),
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #107.
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11716)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11716) gives:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11717)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11717) gives:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11718)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14))
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11718) gives:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11719)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11719) gives:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11720)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11720) implies:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11721)  op(e3, e3) = e1
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (236), (11449),
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11455), (11456), (11721), (function-axioms) are
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #148.
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11722)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.59/24.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11722) implies:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11723)  op(e2, e2) = e1
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11669), (11673), (11723), (function-axioms)
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #782.
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11724)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (165), (11368), (11663), (11724),
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #106.
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11725)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11725) gives:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11726)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (11382), (11661), (11726),
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #198.
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11727)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11727) gives:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11728)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11728) implies:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11729)  op(e0, e0) = e3
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11663), (11729), (function-axioms) are
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11730)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14))
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (169), (230), (236),
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11425), (11449), (11455), (11456), (11730),
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #16.
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.59/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11731)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11731) gives:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11732)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11732) gives:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11733)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2)
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11733) gives:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11734)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & $i(all_57_12)
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11734) implies:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11735)  op(e2, e1) = e2
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (11368), (11735), (function-axioms) are
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11736)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11736) implies:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11737)  op(e2, e2) = e2
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11737), (function-axioms) are
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11738)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11738) gives:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11739)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11739) implies:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11740)  op(e2, e2) = e1
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11669), (11673), (11740), (function-axioms)
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #782.
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11741)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11741) implies:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11742)  op(e0, e0) = e3
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11663), (11742), (function-axioms) are
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #878.
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11743)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11743) gives:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11744)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (11450), (11661), (11744),
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #715.
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11745)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11745) gives:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11746)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11746) implies:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11747)  op(e2, e2) = e2
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11747), (function-axioms) are
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11748)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11748) gives:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11749)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11749) implies:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11750)  op(e1, e1) = e1
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11382), (11750), (function-axioms) are
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11751)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0))
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11751) implies:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11752)  op(e0, e0) = all_57_15
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11753)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11753) gives:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11754)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (11382), (11427), (11661),
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11672), (11677), (11754), (function-axioms) are
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #122.
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11755)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11755) gives:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11756)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11756) gives:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11757)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e2) = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11757) implies:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11758)  op(e1, e1) = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11382), (11758), (function-axioms) are
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11759)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11759) gives:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11760)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11760) implies:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11761)  all_57_15 = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11752), (11761) imply:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11762)  op(e0, e0) = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11663), (11762), (function-axioms) are
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11763)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e1) = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11763) implies:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11764)  op(e3, e3) = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11427), (11764), (function-axioms) are
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11765)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11765) gives:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11766)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (11382), (11661), (11766),
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #164.
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11767)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e1 = e0) & op(e0, e1) = e0)
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (11474), (11767), (function-axioms) are
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #965.
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11768)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11768) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11769)  op(e2, e2) = e2
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11769), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11770)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (11382), (11663), (11770),
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #780.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11771)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11771) gives:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11772)  all_56_6 = e2 & op(e1, e3) = e2
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11366), (11772), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #761.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11773)  all_56_12 = e2 & op(e0, e3) = e2
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11660), (11773), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11774)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (11367), (11449), (11774),
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #177.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11775)  all_56_10 = e1 & op(e2, e0) = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (11409), (11775), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (11776)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11776) gives:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11777)  all_56_11 = e1 & op(e1, e0) = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11777) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11778)  all_56_11 = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11434), (11778) imply:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11779)  e3 = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (217), (220), (11382),
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (11415), (11443), (11779), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #17.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11780)  all_56_15 = e1 & op(e0, e0) = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11780) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11781)  op(e0, e0) = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (11418), (11781), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #805.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |   (11782)  all_56_5 = e0 & op(e2, e1) = e0
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11782) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |   (11783)  op(e2, e1) = e0
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (165), (202), (271), (11367), (11407),
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |            (11425), (11783), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #36.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | |   (11784)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11784) gives:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |   (11785)  all_56_8 = e0 & op(e1, e1) = e0
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11785) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |   (11786)  op(e1, e1) = e0
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11382), (11786), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #914.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |   (11787)  all_56_14 = e0 & op(e0, e1) = e0
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11787) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |   (11788)  all_56_14 = e0
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11443), (11788) imply:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |   (11789)  e3 = e0
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (11789) imply:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | |   (11790)  $false
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11790) is inconsistent.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | |   (11791)  all_56_15 = e3 & op(e0, e0) = e3
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11791) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | |   (11792)  op(e0, e0) = e3
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (11420), (11792), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #245.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | |   (11793)  all_56_15 = e3 & op(e0, e0) = e3
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | ALPHA: (11793) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | |   (11794)  op(e0, e0) = e3
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (11420), (11794), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #245.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | |   (11795)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 157.67/24.24  | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (9930), (11417), (11422), (11795) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | |   (11796)  all_26_2 = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (11796) imply:
% 157.67/24.24  | | | | | | | | | | | | | | | | |   (11797)  all_6_2 = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | SIMP: (11797) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | |   (11798)  all_6_2 = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | REDUCE: (39), (11798) imply:
% 157.67/24.24  | | | | | | | | | | | | | | | | |   (11799)  op(e3, e3) = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.67/24.24  | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | |   (11800)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.67/24.24  | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.67/24.24  | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9929), (11799), (11800),
% 157.67/24.24  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.67/24.24  | | | | | | | | | | | | | | | | | |            #49.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | |   (11801)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.67/24.24  | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.67/24.24  | | | | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.67/24.24  | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | BETA: splitting (11801) gives:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |   (11802)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                all_57_8 & $i(all_57_8)))
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | ALPHA: (11802) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |   (11803)  op(e1, e1) = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11382), (11803), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |   (11804)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13)))
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | ALPHA: (11804) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |   (11805)  op(e0, e0) = e0
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |   (11806)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 157.67/24.24  | | | | | | | | | | | | | | | | | | |              $i(all_57_13))
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | |   (11807)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11807) gives:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | |   (11808)  all_56_9 = e1 & op(e3, e0) = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11808) implies:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | |   (11809)  all_56_9 = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (230), (234),
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | |            (236), (11367), (11799), (11809),
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | |            #147.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | |   (11810)  all_56_10 = e1 & op(e2, e0) = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (11409), (11810), (function-axioms) are
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | End of split
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | |   (11811)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11811) gives:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | |   (11812)  all_56_11 = e1 & op(e1, e0) = e1
% 157.67/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11812) implies:
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | |   (11813)  op(e1, e0) = e1
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (11382), (11806), (11813),
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | |            #146.
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | |   (11814)  all_56_15 = e1 & op(e0, e0) = e1
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11814) implies:
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | |   (11815)  op(e0, e0) = e1
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (11805), (11815), (function-axioms) are
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.24  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.24  | | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | End of split
% 157.69/24.24  | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | End of split
% 157.69/24.24  | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | Case 2:
% 157.69/24.24  | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | |   (11816)  all_18_2 = e3
% 157.69/24.24  | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (11816) imply:
% 157.69/24.24  | | | | | | | | | | | | | | | |   (11817)  all_14_2 = e3
% 157.69/24.24  | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | REDUCE: (369), (11817) imply:
% 157.69/24.24  | | | | | | | | | | | | | | | |   (11818)   ~ (all_52_11 = e3)
% 157.69/24.24  | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | REDUCE: (51), (11817) imply:
% 157.69/24.24  | | | | | | | | | | | | | | | |   (11819)  op(e0, e0) = e3
% 157.69/24.24  | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 157.69/24.24  | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.24  | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | |   (11820)  all_54_14 = e3
% 157.69/24.24  | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (11818), (11820) are inconsistent by
% 157.69/24.24  | | | | | | | | | | | | | | | | |            sub-proof #587.
% 157.69/24.24  | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.24  | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | |   (11821)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.69/24.24  | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.69/24.24  | | | | | | | | | | | | | | | | | 
% 157.69/24.24  | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.24  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | |   (11822)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.69/24.25  | | | | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.69/24.25  | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.69/24.25  | | | | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | BETA: splitting (11822) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11823)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | ALPHA: (11823) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11824)  op(e3, e3) = e3
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (11821) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | |   (11825)  all_54_14 = e2
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (11369), (11825) are inconsistent by
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | |            sub-proof #95.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | |   (11826)  all_54_14 = e1 | all_54_14 = e0
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11826) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |   (11827)  all_54_14 = e1
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (11408), (11827) are inconsistent by
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |            sub-proof #586.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |   (11828)  all_54_14 = e0
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (11828) imply:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |   (11829)  all_52_11 = e0
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | SIMP: (11829) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |   (11830)  all_52_11 = e0
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (11830) imply:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |   (11831)   ~ (all_52_8 = e0)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |   (11832)  all_54_2 = e3
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (11832) imply:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |   (11833)  all_52_8 = e3
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (11833) imply:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |   (11834)   ~ (all_6_2 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | SIMP: (11834) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |   (11835)   ~ (all_6_2 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (204), (279), (9930), (11417), (11824),
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |            (11835), (function-axioms) are inconsistent by
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #30.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |   (11836)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (11367), (11407), (11831), (11836) are
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #14.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11837)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | ALPHA: (11837) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11838)  op(e2, e2) = e2
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11838), (function-axioms) are
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | |   (11839)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.25  | | | | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.69/24.25  | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.25  | | | | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.25  | | | | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (11382), (11819), (11839),
% 157.69/24.25  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.25  | | | | | | | | | | | | | | | | | |            #416.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | |   (11840)  all_14_2 = e1
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | REDUCE: (351), (11840) imply:
% 157.69/24.25  | | | | | | | | | | | | | | |   (11841)   ~ (all_52_3 = e1)
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | REDUCE: (51), (11840) imply:
% 157.69/24.25  | | | | | | | | | | | | | | |   (11842)  op(e0, e0) = e1
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | |   (11843)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.69/24.25  | | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.69/24.25  | | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.69/24.25  | | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.25  | | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.69/24.25  | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.69/24.25  | | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.69/24.25  | | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.69/24.25  | | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.69/24.25  | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | BETA: splitting (11843) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | |   (11844)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.69/24.25  | | | | | | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 157.69/24.25  | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.69/24.25  | | | | | | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.25  | | | | | | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 157.69/24.25  | | | | | | | | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 157.69/24.25  | | | | | | | | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 157.69/24.25  | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | ALPHA: (11844) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | |   (11845)  op(e3, e3) = e3
% 157.69/24.25  | | | | | | | | | | | | | | | | |   (11846)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6
% 157.69/24.25  | | | | | | | | | | | | | | | | |                = e0) & op(e0, e3) = all_57_6 & $i(all_57_6))
% 157.69/24.25  | | | | | | | | | | | | | | | | |   (11847)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2
% 157.69/24.25  | | | | | | | | | | | | | | | | |                = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))
% 157.69/24.25  | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | BETA: splitting (11847) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | |   (11848)  all_57_14 = e3 & op(e1, e1) = e3
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | ALPHA: (11848) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | |   (11849)  op(e1, e1) = e3
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11382), (11849), (function-axioms) are
% 157.69/24.25  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | |   (11850)   ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.25  | | | | | | | | | | | | | | | | | |            $i(all_57_2)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | ALPHA: (11850) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | |   (11851)   ~ (all_57_2 = e1)
% 157.69/24.25  | | | | | | | | | | | | | | | | | |   (11852)  op(e1, e3) = all_57_2
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | BETA: splitting (11846) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11853)  all_57_15 = e3 & op(e0, e0) = e3
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | ALPHA: (11853) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11854)  op(e0, e0) = e3
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11842), (11854), (function-axioms) are
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11855)   ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 &
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |            $i(all_57_6)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | ALPHA: (11855) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11856)  op(e0, e3) = all_57_6
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |              all_57_6, e3, e0, simplifying with (159), (11856)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |              gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11857)  all_57_6 = all_52_3
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |              all_57_2, e3, e1, simplifying with (163), (11852)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |              gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11858)  all_57_2 = all_52_2
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e3,
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (39), (11845) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11859)  all_6_2 = e3
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | REDUCE: (11851), (11858) imply:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11860)   ~ (all_52_2 = e1)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | REDUCE: (346), (11859) imply:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | |   (11861)   ~ (all_52_8 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | |   (11862)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11862) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |   (11863)  all_56_0 = e1 & op(e3, e3) = e1
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11863) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |   (11864)  op(e3, e3) = e1
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11845), (11864), (function-axioms) are
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #995.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |   (11865)  all_56_2 = e1 & op(e2, e3) = e1
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11865) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |   (11866)  all_56_2 = e1
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | |   (11867)  op(e2, e3) = e1
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |   (11868)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (9929), (11867), (11868),
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |            #13.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |   (11869)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11869) gives:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | |   (11870)  all_56_5 = e2 & op(e2, e1) = e2
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11870) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | |   (11871)  op(e2, e1) = e2
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (11368), (11871), (function-axioms) are
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | |   (11872)  all_56_10 = e2 & op(e2, e0) = e2
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11872) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | |   (11873)  all_56_10 = e2
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (123), (165), (202), (221), (271),
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | |            (9929), (11367), (11407), (11861), (11866),
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | |            (11873), (function-axioms) are inconsistent by
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #35.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | |   (11874)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (11841), (11860), (11874),
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | |            #202.
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | |   (11875)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.69/24.25  | | | | | | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 157.69/24.25  | | | | | | | | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.69/24.25  | | | | | | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.69/24.25  | | | | | | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 157.69/24.25  | | | | | | | | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 157.69/24.25  | | | | | | | | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 157.69/24.25  | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | ALPHA: (11875) implies:
% 157.69/24.25  | | | | | | | | | | | | | | | | |   (11876)  op(e2, e2) = e2
% 157.69/24.25  | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11876), (function-axioms) are
% 157.69/24.25  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.69/24.25  | | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | |   (11877)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.25  | | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.25  | | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.25  | | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.69/24.25  | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.25  | | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.25  | | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.25  | | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.25  | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.25  | | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.69/24.25  | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (11382), (11842), (11877),
% 157.69/24.25  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.25  | | | | | | | | | | | | | | | |            #748.
% 157.69/24.25  | | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | End of split
% 157.69/24.25  | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | |   (11878)  all_12_2 = e2
% 157.69/24.25  | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | COMBINE_EQS: (324), (11878) imply:
% 157.69/24.25  | | | | | | | | | | | | | |   (11879)  all_6_2 = e2
% 157.69/24.25  | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | SIMP: (11879) implies:
% 157.69/24.25  | | | | | | | | | | | | | |   (11880)  all_6_2 = e2
% 157.69/24.25  | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | REDUCE: (348), (11880) imply:
% 157.69/24.25  | | | | | | | | | | | | | |   (11881)   ~ (all_52_12 = e2)
% 157.69/24.25  | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | REDUCE: (39), (11880) imply:
% 157.69/24.25  | | | | | | | | | | | | | |   (11882)  op(e3, e3) = e2
% 157.69/24.25  | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.69/24.25  | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | Case 1:
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | |   (11883)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.69/24.25  | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.69/24.25  | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.69/24.25  | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.25  | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.69/24.25  | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.69/24.25  | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.69/24.25  | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.69/24.25  | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.69/24.25  | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.69/24.25  | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (11882), (11883), (function-axioms)
% 157.69/24.25  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #42.
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | Case 2:
% 157.69/24.25  | | | | | | | | | | | | | | | 
% 157.69/24.25  | | | | | | | | | | | | | | |   (11884)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.25  | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.69/24.25  | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.25  | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.26  | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.26  | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.69/24.26  | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.69/24.26  | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.69/24.26  | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.26  | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.69/24.26  | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.26  | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.26  | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.26  | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.26  | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.26  | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.69/24.26  | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (51), (160), (164), (168), (197),
% 157.69/24.26  | | | | | | | | | | | | | | |            (211), (260), (371), (9928), (9929), (11370),
% 157.69/24.26  | | | | | | | | | | | | | | |            (11382), (11881), (11884), (function-axioms) are
% 157.69/24.26  | | | | | | | | | | | | | | |            inconsistent by sub-proof #12.
% 157.69/24.26  | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | End of split
% 157.69/24.26  | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | End of split
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | End of split
% 157.69/24.26  | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | |   (11885)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 157.69/24.26  | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 157.69/24.26  | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | BETA: splitting (11885) gives:
% 157.69/24.26  | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | |   (11886)  all_56_8 = e1 & op(e1, e1) = e1
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | ALPHA: (11886) implies:
% 157.69/24.26  | | | | | | | | | | | | |   (11887)  op(e1, e1) = e1
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | REF_CLOSE: (6), (11382), (11887), (function-axioms) are
% 157.69/24.26  | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | |   (11888)  all_56_14 = e1 & op(e0, e1) = e1
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | REF_CLOSE: (157), (11408), (11888), (function-axioms) are
% 157.69/24.26  | | | | | | | | | | | | |            inconsistent by sub-proof #803.
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | End of split
% 157.69/24.26  | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | End of split
% 157.69/24.26  | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | |   (11889)  all_54_6 = e0
% 157.69/24.26  | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | COMBINE_EQS: (11387), (11889) imply:
% 157.69/24.26  | | | | | | | | | | |   (11890)  all_34_0 = e0
% 157.69/24.26  | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | REDUCE: (11384), (11890) imply:
% 157.69/24.26  | | | | | | | | | | |   (11891)  $false
% 157.69/24.26  | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | CLOSE: (11891) is inconsistent.
% 157.69/24.26  | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | End of split
% 157.69/24.26  | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | End of split
% 157.69/24.26  | | | | | | | | | 
% 157.69/24.26  | | | | | | | | End of split
% 157.69/24.26  | | | | | | | | 
% 157.69/24.26  | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | 
% 157.69/24.26  | | | | | | | |   (11892)   ~ (all_34_1 = e3) & op(e2, e2) = all_34_1 &
% 157.69/24.26  | | | | | | | |            $i(all_34_1)
% 157.69/24.26  | | | | | | | | 
% 157.69/24.26  | | | | | | | | ALPHA: (11892) implies:
% 157.69/24.26  | | | | | | | |   (11893)   ~ (all_34_1 = e3)
% 157.69/24.26  | | | | | | | |   (11894)  op(e2, e2) = all_34_1
% 157.69/24.26  | | | | | | | | 
% 157.69/24.26  | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_34_1,
% 157.69/24.26  | | | | | | | |              e2, e2, simplifying with (9929), (11894) gives:
% 157.69/24.26  | | | | | | | |   (11895)  all_34_1 = e3
% 157.69/24.26  | | | | | | | | 
% 157.69/24.26  | | | | | | | | REDUCE: (11893), (11895) imply:
% 157.69/24.26  | | | | | | | |   (11896)  $false
% 157.69/24.26  | | | | | | | | 
% 157.69/24.26  | | | | | | | | CLOSE: (11896) is inconsistent.
% 157.69/24.26  | | | | | | | | 
% 157.69/24.26  | | | | | | | End of split
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | Case 2:
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | |   (11897)  all_56_14 = e2 & op(e0, e1) = e2
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | | REF_CLOSE: (157), (11369), (11897), (function-axioms) are
% 157.69/24.26  | | | | | | |            inconsistent by sub-proof #263.
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | End of split
% 157.69/24.26  | | | | | | 
% 157.69/24.26  | | | | | End of split
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | End of split
% 157.69/24.26  | | | | 
% 157.69/24.26  | | | End of split
% 157.69/24.26  | | | 
% 157.69/24.26  | | Case 2:
% 157.69/24.26  | | | 
% 157.69/24.26  | | |   (11898)  all_6_2 = e0
% 157.69/24.26  | | |   (11899)  ( ~ (all_6_0 = e1) & op(e0, e3) = all_6_0 & $i(all_6_0)) | ( ~
% 157.69/24.26  | | |              (all_6_1 = e2) & op(e0, e0) = all_6_1 & $i(all_6_1))
% 157.69/24.26  | | | 
% 157.69/24.26  | | | REDUCE: (338), (11898) imply:
% 157.69/24.26  | | |   (11900)   ~ (all_52_1 = e0)
% 157.69/24.26  | | | 
% 157.69/24.26  | | | REDUCE: (342), (11898) imply:
% 157.69/24.26  | | |   (11901)   ~ (all_52_3 = e0)
% 157.69/24.26  | | | 
% 157.69/24.26  | | | REDUCE: (344), (11898) imply:
% 157.69/24.26  | | |   (11902)   ~ (all_52_4 = e0)
% 157.69/24.26  | | | 
% 157.69/24.26  | | | REDUCE: (346), (11898) imply:
% 157.69/24.26  | | |   (11903)   ~ (all_52_8 = e0)
% 157.69/24.26  | | | 
% 157.69/24.26  | | | REDUCE: (348), (11898) imply:
% 157.69/24.26  | | |   (11904)   ~ (all_52_12 = e0)
% 157.69/24.26  | | | 
% 157.69/24.26  | | | REDUCE: (39), (11898) imply:
% 157.69/24.26  | | |   (11905)  op(e3, e3) = e0
% 157.69/24.26  | | | 
% 157.69/24.26  | | | BETA: splitting (91) gives:
% 157.69/24.26  | | | 
% 157.69/24.26  | | | Case 1:
% 157.69/24.26  | | | | 
% 157.69/24.26  | | | |   (11906)   ~ (all_40_2 = e3)
% 157.69/24.26  | | | | 
% 157.69/24.26  | | | | REDUCE: (9922), (11906) imply:
% 157.69/24.26  | | | |   (11907)  $false
% 157.69/24.26  | | | | 
% 157.69/24.26  | | | | CLOSE: (11907) is inconsistent.
% 157.69/24.26  | | | | 
% 157.69/24.26  | | | Case 2:
% 157.69/24.26  | | | | 
% 157.69/24.26  | | | |   (11908)  ( ~ (all_40_0 = e1) & op(e3, e2) = all_40_0 & $i(all_40_0)) |
% 157.69/24.26  | | | |            ( ~ (all_40_1 = e0) & op(e3, e3) = all_40_1 & $i(all_40_1))
% 157.69/24.26  | | | | 
% 157.69/24.26  | | | | BETA: splitting (11908) gives:
% 157.69/24.26  | | | | 
% 157.69/24.26  | | | | Case 1:
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | |   (11909)   ~ (all_40_0 = e1) & op(e3, e2) = all_40_0 & $i(all_40_0)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | ALPHA: (11909) implies:
% 157.69/24.26  | | | | |   (11910)   ~ (all_40_0 = e1)
% 157.69/24.26  | | | | |   (11911)  op(e3, e2) = all_40_0
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, all_40_0,
% 157.69/24.26  | | | | |              e2, e3, simplifying with (170), (11911) gives:
% 157.69/24.26  | | | | |   (11912)  all_52_4 = all_40_0
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | COMBINE_EQS: (272), (11912) imply:
% 157.69/24.26  | | | | |   (11913)  all_54_1 = all_40_0
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | REDUCE: (136), (11912) imply:
% 157.69/24.26  | | | | |   (11914)   ~ (all_52_6 = all_40_0)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | SIMP: (11914) implies:
% 157.69/24.26  | | | | |   (11915)   ~ (all_52_6 = all_40_0)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | REDUCE: (135), (11912) imply:
% 157.69/24.26  | | | | |   (11916)   ~ (all_52_7 = all_40_0)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | SIMP: (11916) implies:
% 157.69/24.26  | | | | |   (11917)   ~ (all_52_7 = all_40_0)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | REDUCE: (134), (11912) imply:
% 157.69/24.26  | | | | |   (11918)   ~ (all_52_8 = all_40_0)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | SIMP: (11918) implies:
% 157.69/24.26  | | | | |   (11919)   ~ (all_52_8 = all_40_0)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | REDUCE: (133), (11912) imply:
% 157.69/24.26  | | | | |   (11920)   ~ (all_52_12 = all_40_0)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | SIMP: (11920) implies:
% 157.69/24.26  | | | | |   (11921)   ~ (all_52_12 = all_40_0)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | REDUCE: (9924), (11912) imply:
% 157.69/24.26  | | | | |   (11922)   ~ (all_40_0 = e3)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | REDUCE: (11902), (11912) imply:
% 157.69/24.26  | | | | |   (11923)   ~ (all_40_0 = e0)
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | BETA: splitting (203) gives:
% 157.69/24.26  | | | | | 
% 157.69/24.26  | | | | | Case 1:
% 157.69/24.26  | | | | | | 
% 157.69/24.26  | | | | | |   (11924)  all_54_1 = e3
% 157.69/24.26  | | | | | | 
% 157.69/24.26  | | | | | | COMBINE_EQS: (11913), (11924) imply:
% 157.69/24.26  | | | | | |   (11925)  all_40_0 = e3
% 157.69/24.26  | | | | | | 
% 157.69/24.26  | | | | | | REDUCE: (11922), (11925) imply:
% 157.69/24.26  | | | | | |   (11926)  $false
% 157.69/24.26  | | | | | | 
% 157.69/24.26  | | | | | | CLOSE: (11926) is inconsistent.
% 157.69/24.26  | | | | | | 
% 157.69/24.26  | | | | | Case 2:
% 157.69/24.26  | | | | | | 
% 157.69/24.26  | | | | | |   (11927)   ~ (all_54_1 = e3)
% 157.69/24.26  | | | | | |   (11928)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.69/24.26  | | | | | | 
% 157.69/24.26  | | | | | | BETA: splitting (11928) gives:
% 157.69/24.26  | | | | | | 
% 157.69/24.26  | | | | | | Case 1:
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | |   (11929)  all_54_1 = e2
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | | COMBINE_EQS: (11913), (11929) imply:
% 157.69/24.26  | | | | | | |   (11930)  all_40_0 = e2
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | | REDUCE: (11915), (11930) imply:
% 157.69/24.26  | | | | | | |   (11931)   ~ (all_52_6 = e2)
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | | REDUCE: (11917), (11930) imply:
% 157.69/24.26  | | | | | | |   (11932)   ~ (all_52_7 = e2)
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | | REDUCE: (11919), (11930) imply:
% 157.69/24.26  | | | | | | |   (11933)   ~ (all_52_8 = e2)
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | | REDUCE: (11921), (11930) imply:
% 157.69/24.26  | | | | | | |   (11934)   ~ (all_52_12 = e2)
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | | REDUCE: (11922), (11930) imply:
% 157.69/24.26  | | | | | | |   (11935)   ~ (e3 = e2)
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | | BETA: splitting (234) gives:
% 157.69/24.26  | | | | | | | 
% 157.69/24.26  | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | 
% 157.69/24.26  | | | | | | | |   (11936)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 &
% 157.69/24.26  | | | | | | | |              op(e3, e2) = e2)
% 157.69/24.26  | | | | | | | | 
% 157.69/24.26  | | | | | | | | BETA: splitting (11936) gives:
% 157.69/24.26  | | | | | | | | 
% 157.69/24.26  | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | 
% 157.69/24.26  | | | | | | | | |   (11937)  all_56_0 = e2 & op(e3, e3) = e2
% 157.69/24.26  | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | ALPHA: (11937) implies:
% 157.69/24.26  | | | | | | | | |   (11938)  op(e3, e3) = e2
% 157.69/24.26  | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | REF_CLOSE: (5), (11905), (11938), (function-axioms) are
% 157.69/24.26  | | | | | | | | |            inconsistent by sub-proof #281.
% 157.69/24.26  | | | | | | | | | 
% 157.69/24.26  | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | 
% 157.69/24.26  | | | | | | | | |   (11939)  all_56_1 = e2 & op(e3, e2) = e2
% 157.69/24.26  | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | ALPHA: (11939) implies:
% 157.69/24.26  | | | | | | | | |   (11940)  all_56_1 = e2
% 157.69/24.26  | | | | | | | | |   (11941)  op(e3, e2) = e2
% 157.69/24.26  | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | BETA: splitting (46) gives:
% 157.69/24.26  | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | |   (11942)   ~ (all_10_2 = e2)
% 157.69/24.26  | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | BETA: splitting (52) gives:
% 157.69/24.26  | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | |   (11943)   ~ (all_14_2 = e1)
% 157.69/24.26  | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | BETA: splitting (58) gives:
% 157.69/24.26  | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | |   (11944)   ~ (all_18_2 = e3)
% 157.69/24.26  | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | REDUCE: (301), (11944) imply:
% 157.69/24.26  | | | | | | | | | | | |   (11945)   ~ (all_14_2 = e3)
% 157.69/24.26  | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | BETA: splitting (61) gives:
% 157.69/24.26  | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | |   (11946)   ~ (all_20_2 = e3)
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | REDUCE: (325), (11946) imply:
% 157.69/24.26  | | | | | | | | | | | | |   (11947)   ~ (all_10_2 = e3)
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 157.69/24.26  | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | |   (11948)   ~ (all_22_2 = e0)
% 157.69/24.26  | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | REDUCE: (251), (11948) imply:
% 157.69/24.26  | | | | | | | | | | | | | |   (11949)   ~ (all_10_2 = e0)
% 157.69/24.26  | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 157.69/24.26  | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | |   (11950)  all_54_10 = e3
% 157.69/24.26  | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | REF_CLOSE: (336), (11947), (11950) are inconsistent by
% 157.69/24.26  | | | | | | | | | | | | | | |            sub-proof #361.
% 157.69/24.26  | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | |   (11951)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.69/24.26  | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | BETA: splitting (11951) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | |   (11952)  all_54_10 = e2
% 157.69/24.26  | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | REF_CLOSE: (336), (11942), (11952) are inconsistent by
% 157.69/24.26  | | | | | | | | | | | | | | | |            sub-proof #360.
% 157.69/24.26  | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | |   (11953)   ~ (all_54_10 = e2)
% 157.69/24.26  | | | | | | | | | | | | | | | |   (11954)  all_54_10 = e1 | all_54_10 = e0
% 157.69/24.26  | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | BETA: splitting (11954) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | |   (11955)  all_54_10 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (11955) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | |   (11956)  all_10_2 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | SIMP: (11956) implies:
% 157.69/24.26  | | | | | | | | | | | | | | | | |   (11957)  all_10_2 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | REDUCE: (350), (11957) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | |   (11958)   ~ (all_52_2 = e1)
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | REDUCE: (361), (11957) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | |   (11959)   ~ (all_52_6 = e1)
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | REDUCE: (363), (11957) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | |   (11960)   ~ (all_52_8 = e1)
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | REDUCE: (364), (11957) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | |   (11961)   ~ (all_52_9 = e1)
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | REDUCE: (11942), (11957) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | |   (11962)   ~ (e2 = e1)
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | REDUCE: (45), (11957) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | |   (11963)  op(e1, e1) = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | |   (11964)  all_54_9 = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11964) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | |   (11965)  all_52_6 = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | REDUCE: (9925), (11965) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | |   (11966)  $false
% 157.69/24.26  | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | CLOSE: (11966) is inconsistent.
% 157.69/24.26  | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | |   (11967)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.69/24.26  | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | BETA: splitting (11967) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | |   (11968)  all_54_9 = e2
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11968) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | |   (11969)  all_52_6 = e2
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | REDUCE: (11931), (11969) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | |   (11970)  $false
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | CLOSE: (11970) is inconsistent.
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | |   (11971)   ~ (all_54_9 = e2)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | |   (11972)  all_54_9 = e1 | all_54_9 = e0
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (11972) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | |   (11973)  all_54_9 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11973) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | |   (11974)  all_52_6 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (11959), (11974) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | |   (11975)  $false
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | CLOSE: (11975) is inconsistent.
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | |   (11976)  all_54_9 = e0
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11976) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | |   (11977)  all_52_6 = e0
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (11977) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | |   (11978)   ~ (all_52_7 = e0)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | SIMP: (11978) implies:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | |   (11979)   ~ (all_52_7 = e0)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (11931), (11977) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | |   (11980)   ~ (e2 = e0)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (11959), (11977) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | |   (11981)   ~ (e1 = e0)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | |   (11982)  all_54_2 = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (11982) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | |   (11983)  all_52_8 = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (11983) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | |   (11984)   ~ (all_52_9 = e3)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (11983) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | |   (11985)   ~ (all_52_11 = e3)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | SIMP: (11985) implies:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | |   (11986)   ~ (all_52_11 = e3)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (11983) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | |   (11987)   ~ (all_52_12 = e3)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | SIMP: (11987) implies:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | |   (11988)   ~ (all_52_12 = e3)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | |   (11989)  all_54_13 = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (9926), (11989) are inconsistent by
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #385.
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | |   (11990)   ~ (all_54_13 = e3)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | |   (11991)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | |   (11992)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11905), (11940), (11992),
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | |            #11.
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | |   (11993)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11993) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | |   (11994)  all_56_4 = e1 & op(e3, e1) = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11960), (11994), (function-axioms) are
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #331.
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | |   (11995)  all_56_9 = e1 & op(e3, e0) = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11995) implies:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | |   (11996)  all_56_9 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | |   (11997)  op(e3, e0) = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (11998)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11998) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11999)  all_56_9 = e3 & op(e3, e0) = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11999) implies:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12000)  op(e3, e0) = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11997), (12000), (function-axioms) are
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #796.
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12001)  all_56_10 = e3 & op(e2, e0) = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12001) implies:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12002)  all_56_10 = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12003)  op(e2, e0) = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11991) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12004)  all_54_13 = e2
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (11932), (12004) are inconsistent by
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #505.
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12005)   ~ (all_54_13 = e2)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12006)  all_54_13 = e1 | all_54_13 = e0
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12006) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12007)  all_54_13 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (12007) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12008)  all_52_7 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12008) implies:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12009)  all_52_7 = e1
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (12009) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12010)   ~ (all_52_3 = e1)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9926), (12009) imply:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12011)   ~ (e3 = e1)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12012)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12012) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12013)  all_56_4 = e3 & op(e3, e1) = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12013) implies:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12014)  all_56_4 = e3
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12015)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (9929), (11900), (12015),
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #10.
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12016)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12016) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12017)  all_56_5 = e0 & op(e2, e1) = e0
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12017) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12018)  all_56_5 = e0
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12019)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12019) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12020)  all_56_0 = e1 & op(e3, e3) = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12020) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12021)  op(e3, e3) = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (11940), (11996), (12014),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12021), (function-axioms) are inconsistent by
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #149.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12022)  all_56_2 = e1 & op(e2, e3) = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12022) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12023)  op(e2, e3) = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12024)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12024) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12025)  all_56_4 = e2 & op(e3, e1) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12025) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12026)  op(e3, e1) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11933), (12026), (function-axioms) are
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12027)  all_56_5 = e2 & op(e2, e1) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12027) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12028)  all_56_5 = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12018), (12028) imply:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12029)  e2 = e0
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (12029) imply:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12030)  $false
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12030) is inconsistent.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12031)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12031) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12032)  all_56_8 = e2 & op(e1, e1) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12032) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12033)  op(e1, e1) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11963), (12033), (function-axioms) are
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12034)  all_56_14 = e2 & op(e0, e1) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12034) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12035)  all_56_14 = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12036)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (9929), (12023), (12036),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #13.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12037)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12037) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12038)  all_56_5 = e2 & op(e2, e1) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12038) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12039)  all_56_5 = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12040)  op(e2, e1) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (217), (220), (11963),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12035), (12039), (12040), (function-axioms) are
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #9.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12041)  all_56_10 = e2 & op(e2, e0) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12041) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12042)  op(e2, e0) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12003), (12042), (function-axioms) are
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #580.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12043)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (11958), (12010), (12043),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #202.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12044)  all_56_10 = e0 & op(e2, e0) = e0
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12002), (12044) are inconsistent by
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #551.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12045)  all_56_5 = e3 & op(e2, e1) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12045) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12046)  op(e2, e1) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9927), (12046), (function-axioms) are
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #763.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12047)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (11963), (11986), (12047),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #402.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12048)  all_54_13 = e0
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (11979), (12048) are inconsistent by
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #503.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (12049)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12049) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12050)  all_56_11 = e3 & op(e1, e0) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12050) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12051)  all_56_11 = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12052)  op(e1, e0) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12053)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12053) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12054)  all_56_6 = e2 & op(e1, e3) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12054) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12055)  all_56_6 = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12056)  op(e1, e3) = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12057)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12057) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12058)  all_56_4 = e3 & op(e3, e1) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12058) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12059)  all_56_4 = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12060)  op(e3, e1) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11991) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12061)  all_54_13 = e2
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (11932), (12061) are inconsistent by
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #505.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12062)   ~ (all_54_13 = e2)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12063)  all_54_13 = e1 | all_54_13 = e0
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12064)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12064) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12065)  all_56_0 = e3 & op(e3, e3) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12065) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12066)  op(e3, e3) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11905), (12066), (function-axioms) are
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #971.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12067)  all_56_2 = e3 & op(e2, e3) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12067) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12068)  all_56_2 = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12069)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12069) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12070)  all_56_12 = e3 & op(e0, e3) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12070) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12071)  all_56_12 = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12072)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12072) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12073)  all_56_2 = e1 & op(e2, e3) = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12073) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12074)  all_56_2 = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12068), (12074) are inconsistent by
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #484.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12075)  all_56_3 = e1 & op(e2, e2) = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12075) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12076)  op(e2, e2) = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (112), (144),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (160), (162), (163), (168),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (189), (221), (223), (224), (225), (227),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (231), (232), (239), (246), (362), (369),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (370), (11899), (11901), (11904), (11905),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11945), (11958), (11959), (11960), (11963),
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12076), (function-axioms) are inconsistent by
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #85.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12077)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12077) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12078)  all_56_5 = e1 & op(e2, e1) = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (11961), (12078), (function-axioms) are
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #423.
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12079)  all_56_10 = e1 & op(e2, e0) = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12079) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12080)  op(e2, e0) = e1
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12081)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12081) gives:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12082)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12082) implies:
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12083)  op(e3, e3) = e3
% 157.69/24.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (229), (231), (12055),
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12068), (12083), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #770.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12084)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12084) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12085)  op(e2, e2) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (12085), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12086)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12086) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12087)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_8 & $i(all_57_8)))
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11905), (12060), (12087), (function-axioms)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #25.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12088)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13)))
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12088) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12089)  op(e0, e0) = e0
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12090)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12090) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12091)  all_56_2 = e2 & op(e2, e3) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12068), (12091) are inconsistent by
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #778.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12092)  all_56_3 = e2 & op(e2, e2) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12092) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12093)  op(e2, e2) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (12093), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12094)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12094) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12095)  all_56_5 = e2 & op(e2, e1) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12095) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12096)  all_56_5 = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12097)  op(e2, e1) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12098)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12098) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12099)  all_56_12 = e2 & op(e0, e3) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12099) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12100)  all_56_12 = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12071), (12100) are inconsistent by
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #616.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12101)  all_56_13 = e2 & op(e0, e2) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11932), (12101), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #594.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12102)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12102) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12103)  all_56_14 = e2 & op(e0, e1) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12103) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12104)  all_56_14 = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (217), (220), (11963),
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12096), (12097), (12104), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #9.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12105)  all_56_15 = e2 & op(e0, e0) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12105) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12106)  op(e0, e0) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12089), (12106), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12107)  all_56_10 = e2 & op(e2, e0) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12107) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12108)  op(e2, e0) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12080), (12108), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12109)  all_56_13 = e3 & op(e0, e2) = e3
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9926), (12109), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12110)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12110) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12111)  all_56_14 = e3 & op(e0, e1) = e3
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12111) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12112)  op(e0, e1) = e3
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (11986), (12112), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #720.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12113)  all_56_15 = e3 & op(e0, e0) = e3
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12113) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12114)  op(e0, e0) = e3
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (168), (236), (238), (9929),
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11905), (11941), (11988), (12114),
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #24.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12115)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12115) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12116)  all_56_6 = e3 & op(e1, e3) = e3
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12116) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12117)  op(e1, e3) = e3
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12056), (12117), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #617.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12118)  all_56_12 = e3 & op(e0, e3) = e3
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12118) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12119)  all_56_12 = e3
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12063) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12120)  all_54_13 = e1
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (12120) imply:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12121)  all_52_7 = e1
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12121) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12122)  all_52_7 = e1
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (12122) imply:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12123)   ~ (all_52_3 = e1)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9926), (12122) imply:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12124)   ~ (e3 = e1)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12125)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9929), (12119), (12125), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #22.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12126)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12126) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12127)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_8 & $i(all_57_8)))
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11905), (12060), (12127), (function-axioms)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #25.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12128)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13)))
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12128) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12129)  op(e0, e0) = e0
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12130)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_13))
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12131)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11))
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12131) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12132)  all_57_12 = e0 & op(e2, e2) = e0
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12132) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12133)  op(e2, e2) = e0
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (12133), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12134)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12134) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12135)   ~ (all_57_11 = e2)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12136)  op(e2, e0) = all_57_11
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12130) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12137)  all_57_14 = e0 & op(e1, e1) = e0
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12137) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12138)  op(e1, e1) = e0
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11963), (12138), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12139)   ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12139) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12140)  op(e1, e0) = all_57_13
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12141)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12141) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12142)  all_56_0 = e1 & op(e3, e3) = e1
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12142) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12143)  op(e3, e3) = e1
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (11940), (11996), (12059),
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12143), (function-axioms) are inconsistent by
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #149.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12144)  all_56_2 = e1 & op(e2, e3) = e1
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12144) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12145)  op(e2, e3) = e1
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12146)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12146) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12147)  all_56_0 = e2 & op(e3, e3) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12147) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12148)  all_56_0 = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (11940), (11996), (12059),
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12148) are inconsistent by sub-proof #153.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12149)  all_56_2 = e2 & op(e2, e3) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12149) implies:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12150)  op(e2, e3) = e2
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12145), (12150), (function-axioms) are
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #428.
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12151)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12151) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e0,
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (51), (12129) gives:
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12152)  all_14_2 = e0
% 157.69/24.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13, e0, e1, simplifying with (160), (12140)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12153)  all_57_13 = all_52_14
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13, e0, e1, simplifying with (12052),
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (12140) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12154)  all_57_13 = e3
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11, e0, e2, simplifying with (164), (12136)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12155)  all_57_11 = all_52_13
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (12145) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12156)  all_52_1 = e1
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12153), (12154) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12157)  all_52_14 = e3
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12157) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12158)  all_52_14 = e3
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12135), (12155) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12159)   ~ (all_52_13 = e2)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (12156) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12160)   ~ (all_52_13 = e1)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12160) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12161)   ~ (all_52_13 = e1)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (12152) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12162)   ~ (all_52_13 = e0)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (260), (9928), (12159), (12161), (12162)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #234.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12163)  all_56_12 = e2 & op(e0, e3) = e2
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12163) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12164)  all_56_12 = e2
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12119), (12164) are inconsistent by
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #616.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12165)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (11958), (12123), (12165),
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #202.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12166)  all_54_13 = e0
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (11979), (12166) are inconsistent by
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #503.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12167)  all_56_5 = e3 & op(e2, e1) = e3
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12167) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12168)  op(e2, e1) = e3
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9927), (12168), (function-axioms) are
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #763.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12169)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (11963), (11986), (12169),
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #402.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12170)  all_56_7 = e2 & op(e1, e2) = e2
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11931), (12170), (function-axioms) are
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12171)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12171) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12172)  all_56_8 = e2 & op(e1, e1) = e2
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12172) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12173)  op(e1, e1) = e2
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11963), (12173), (function-axioms) are
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12174)  all_56_11 = e2 & op(e1, e0) = e2
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12051), (12174) are inconsistent by
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #249.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12175)  all_56_15 = e3 & op(e0, e0) = e3
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12175) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12176)  op(e0, e0) = e3
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (168), (236), (238), (9929),
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | |            (11905), (11941), (11988), (12176),
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | |            #24.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |   (12177)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (11903), (11933), (11960), (12177) are
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #14.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | |   (12178)  all_54_10 = e0
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (11949), (12178) are inconsistent by
% 157.69/24.29  | | | | | | | | | | | | | | | | |            sub-proof #329.
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | |   (12179)  all_22_2 = e0
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | COMBINE_EQS: (251), (12179) imply:
% 157.69/24.29  | | | | | | | | | | | | | |   (12180)  all_10_2 = e0
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | SIMP: (12180) implies:
% 157.69/24.29  | | | | | | | | | | | | | |   (12181)  all_10_2 = e0
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | REDUCE: (364), (12181) imply:
% 157.69/24.29  | | | | | | | | | | | | | |   (12182)   ~ (all_52_9 = e0)
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | REDUCE: (11947), (12181) imply:
% 157.69/24.29  | | | | | | | | | | | | | |   (12183)   ~ (e3 = e0)
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | REDUCE: (45), (12181) imply:
% 157.69/24.29  | | | | | | | | | | | | | |   (12184)  op(e1, e1) = e0
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | |   (12185)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.69/24.29  | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.69/24.29  | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.69/24.29  | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.69/24.29  | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.29  | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.69/24.29  | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.69/24.29  | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.69/24.29  | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.69/24.29  | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.69/24.29  | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.69/24.29  | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.69/24.29  | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.69/24.29  | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.69/24.29  | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.69/24.29  | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (9929), (11905), (12185),
% 157.69/24.29  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.29  | | | | | | | | | | | | | | |            #26.
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | |   (12186)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.29  | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.69/24.29  | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.29  | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.29  | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.29  | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.69/24.29  | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.69/24.29  | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.69/24.29  | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.29  | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.69/24.29  | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.29  | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.29  | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.29  | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.29  | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.29  | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | BETA: splitting (12186) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | |   (12187)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.29  | | | | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 157.69/24.29  | | | | | | | | | | | | | | | |                op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.29  | | | | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.29  | | | | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.29  | | | | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 157.69/24.29  | | | | | | | | | | | | | | | |                = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 157.69/24.29  | | | | | | | | | | | | | | | |                all_57_8 & $i(all_57_8)))
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | ALPHA: (12187) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | |   (12188)  op(e1, e1) = e1
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12184), (12188), (function-axioms) are
% 157.69/24.29  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | |   (12189)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.29  | | | | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 157.69/24.29  | | | | | | | | | | | | | | | |                op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.29  | | | | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.29  | | | | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.29  | | | | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.29  | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.29  | | | | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13)))
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | ALPHA: (12189) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | |   (12190)  op(e0, e0) = e0
% 157.69/24.29  | | | | | | | | | | | | | | | |   (12191)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.29  | | | | | | | | | | | | | | | |              (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.29  | | | | | | | | | | | | | | | |              $i(all_57_11))
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | BETA: splitting (12191) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | |   (12192)  all_57_12 = e0 & op(e2, e2) = e0
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | ALPHA: (12192) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | |   (12193)  op(e2, e2) = e0
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (12193), (function-axioms) are
% 157.69/24.29  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | |   (12194)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.29  | | | | | | | | | | | | | | | | |            $i(all_57_11)
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | ALPHA: (12194) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | |   (12195)  op(e2, e0) = all_57_11
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12196)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 157.69/24.29  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (9929), (11900), (12196),
% 157.69/24.29  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.29  | | | | | | | | | | | | | | | | | |            #10.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12197)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 157.69/24.29  | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (164), (165), (371), (12182), (12190),
% 157.69/24.29  | | | | | | | | | | | | | | | | | |            (12195), (12197), (function-axioms) are
% 157.69/24.29  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #78.
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | End of split
% 157.69/24.29  | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | |   (12198)  all_20_2 = e3
% 157.69/24.29  | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | COMBINE_EQS: (325), (12198) imply:
% 157.69/24.29  | | | | | | | | | | | | |   (12199)  all_10_2 = e3
% 157.69/24.29  | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | SIMP: (12199) implies:
% 157.69/24.29  | | | | | | | | | | | | |   (12200)  all_10_2 = e3
% 157.69/24.29  | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | COMBINE_EQS: (331), (12200) imply:
% 157.69/24.29  | | | | | | | | | | | | |   (12201)  all_30_2 = e3
% 157.69/24.29  | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | REDUCE: (363), (12200) imply:
% 157.69/24.29  | | | | | | | | | | | | |   (12202)   ~ (all_52_8 = e3)
% 157.69/24.29  | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | REDUCE: (366), (12200) imply:
% 157.69/24.29  | | | | | | | | | | | | |   (12203)   ~ (all_52_11 = e3)
% 157.69/24.29  | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | REDUCE: (45), (12200) imply:
% 157.69/24.29  | | | | | | | | | | | | |   (12204)  op(e1, e1) = e3
% 157.69/24.29  | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | BETA: splitting (202) gives:
% 157.69/24.29  | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | |   (12205)  all_54_2 = e3
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | COMBINE_EQS: (271), (12205) imply:
% 157.69/24.29  | | | | | | | | | | | | | |   (12206)  all_52_8 = e3
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | REDUCE: (12202), (12206) imply:
% 157.69/24.29  | | | | | | | | | | | | | |   (12207)  $false
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | CLOSE: (12207) is inconsistent.
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | |   (12208)   ~ (all_54_2 = e3)
% 157.69/24.29  | | | | | | | | | | | | | |   (12209)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 157.69/24.29  | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | |   (12210)   ~ (all_30_2 = e3)
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | REDUCE: (12201), (12210) imply:
% 157.69/24.29  | | | | | | | | | | | | | | |   (12211)  $false
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | CLOSE: (12211) is inconsistent.
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | |   (12212)  ( ~ (all_30_0 = e2) & op(e3, e1) = all_30_0 &
% 157.69/24.29  | | | | | | | | | | | | | | |              $i(all_30_0)) | ( ~ (all_30_1 = e0) & op(e3, e3)
% 157.69/24.29  | | | | | | | | | | | | | | |              = all_30_1 & $i(all_30_1))
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | BETA: splitting (12212) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | |   (12213)   ~ (all_30_0 = e2) & op(e3, e1) = all_30_0 &
% 157.69/24.29  | | | | | | | | | | | | | | | |            $i(all_30_0)
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | ALPHA: (12213) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | |   (12214)   ~ (all_30_0 = e2)
% 157.69/24.29  | | | | | | | | | | | | | | | |   (12215)  op(e3, e1) = all_30_0
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | BETA: splitting (12209) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | |   (12216)  all_54_2 = e2
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (12216) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | |   (12217)  all_52_8 = e2
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | REDUCE: (11933), (12217) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | |   (12218)  $false
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | CLOSE: (12218) is inconsistent.
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | |   (12219)   ~ (all_54_2 = e2)
% 157.69/24.29  | | | | | | | | | | | | | | | | |   (12220)  all_54_2 = e1 | all_54_2 = e0
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | BETA: splitting (12220) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12221)  all_54_2 = e1
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (12221) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12222)  all_52_8 = e1
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | REDUCE: (121), (12222) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12223)   ~ (all_52_11 = e1)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | SIMP: (12223) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12224)   ~ (all_52_11 = e1)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | REDUCE: (120), (12222) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12225)   ~ (all_52_12 = e1)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | SIMP: (12225) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12226)   ~ (all_52_12 = e1)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | REDUCE: (12202), (12222) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12227)   ~ (e3 = e1)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | REDUCE: (11933), (12222) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12228)   ~ (e2 = e1)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | REDUCE: (169), (12222) imply:
% 157.69/24.29  | | | | | | | | | | | | | | | | | |   (12229)  op(e3, e1) = e1
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | |   (12230)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 157.69/24.29  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | BETA: splitting (12230) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | |   (12231)  all_56_12 = e3 & op(e0, e3) = e3
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | ALPHA: (12231) implies:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | |   (12232)  all_56_12 = e3
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |   (12233)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.69/24.29  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (233),
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |            (9929), (12232), (12233), (function-axioms) are
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #22.
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |   (12234)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12234) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |   (12235)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                all_57_8 & $i(all_57_8)))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12235) implies:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |   (12236)  op(e1, e1) = e1
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12204), (12236), (function-axioms) are
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |   (12237)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13)))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12237) implies:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |   (12238)  all_57_15 = e0
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |   (12239)  op(e0, e0) = e0
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |   (12240)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_13))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |   (12241)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |              (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |   (12242)  (all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12241) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | |   (12243)  all_57_12 = e0 & op(e2, e2) = e0
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12243) implies:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | |   (12244)  op(e2, e2) = e0
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9929), (12244), (function-axioms) are
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #945.
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | |   (12245)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12245) implies:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | |   (12246)   ~ (all_57_11 = e2)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | |   (12247)  op(e2, e0) = all_57_11
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | |   (12248)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12248) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (12249)  all_56_12 = e1 & op(e0, e3) = e1
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12232), (12249) are inconsistent by
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #736.
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (12250)  all_56_13 = e1 & op(e0, e2) = e1
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12250) implies:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (12251)  op(e0, e2) = e1
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12242) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12252)  all_57_10 = e0 & op(e3, e3) = e0
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12252) implies:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12253)  all_57_10 = e0
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12240) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12254)  all_57_14 = e0 & op(e1, e1) = e0
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12254) implies:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12255)  op(e1, e1) = e0
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12204), (12255), (function-axioms) are
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12256)   ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12256) implies:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12257)   ~ (all_57_13 = e1)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12258)  op(e1, e0) = all_57_13
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12259)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12259) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12260)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12260) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12261)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (169), (11905), (11941), (12202),
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12204), (12261), (function-axioms) are
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #8.
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12262)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_12))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12262) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12263)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12263) gives:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12264)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12264) implies:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12265)  op(e0, e0) = e2
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12239), (12265), (function-axioms) are
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12266)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12266) implies:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12267)   ~ (all_57_10 = e0)
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12253), (12267) imply:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12268)  $false
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12268) is inconsistent.
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12269)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (9929), (11905), (11941), (12269),
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #7.
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12270)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12270) gives:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12271)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (135), (158),
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (170), (191), (203), (229), (231), (233),
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (248), (272), (352), (356), (9926),
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11902), (11905), (12204), (12232), (12246),
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12247), (12271), (function-axioms) are
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #6.
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12272)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12272) gives:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12273)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (9929), (12202), (12273),
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #5.
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12274)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12274) gives:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12275)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12275) implies:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12276)  op(e0, e0) = e1
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (12239), (12276), (function-axioms) are
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12277)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12277) gives:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12278)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12278) implies:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12279)   ~ (all_57_10 = e0)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12253), (12279) imply:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12280)  $false
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12280) is inconsistent.
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12281)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e1
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12281) implies:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12282)  op(e1, e1) = e1
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12204), (12282), (function-axioms) are
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12283)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12283) gives:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12284)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (135),
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (170), (191), (203), (229), (231), (233),
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (248), (272), (352), (356), (9926), (9929),
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11902), (11905), (12204), (12232), (12239),
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12284), (function-axioms) are inconsistent by
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #4.
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12285)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12285) gives:
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12286)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (36), (135), (158), (170),
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (203), (238), (248), (272), (352), (356),
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9926), (9929), (11902), (11905), (12204),
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12239), (12286), (function-axioms) are
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #3.
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12287)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12287) gives:
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12288)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (229), (231), (233),
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12232), (12239), (12288), (function-axioms) are
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2.
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12289)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12289) gives:
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12290)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12290) implies:
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12291)  op(e2, e2) = e2
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (12291), (function-axioms) are
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.69/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12292)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12292) gives:
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12293)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12293) implies:
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12294)  op(e1, e1) = e1
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12204), (12294), (function-axioms) are
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12295)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0))
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12295) implies:
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12296)  op(e0, e0) = all_57_15
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12297)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e0,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (51), (12239) gives:
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12298)  all_14_2 = e0
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e1,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (12251) gives:
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12299)  all_52_7 = e1
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13, e0, e1, simplifying with (160), (12258)
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12300)  all_57_13 = all_52_14
% 157.78/24.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_30_0,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (12215), (12229) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12301)  all_30_0 = e1
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (12298) imply:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12302)   ~ (all_52_11 = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11945), (12298) imply:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12303)   ~ (e3 = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11943), (12298) imply:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12304)   ~ (e1 = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12305)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12305) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12306)  all_56_9 = e1 & op(e3, e0) = e1
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (12226), (12306), (function-axioms) are
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #851.
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12307)  all_56_10 = e1 & op(e2, e0) = e1
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12307) implies:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12308)  op(e2, e0) = e1
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12297) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12309)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12309) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12310)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12310) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12311)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e3) = e0
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12311) implies:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12312)  op(e0, e3) = e0
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11901), (12312), (function-axioms) are
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12313)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (12204), (12308), (12313),
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #220.
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12314)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12314) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12315)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12315) implies:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12316)  op(e0, e3) = e0
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11901), (12316), (function-axioms) are
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12317)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12317) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12318)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e2) = e0
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12318) implies:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12319)  op(e0, e2) = e0
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12251), (12319), (function-axioms) are
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #832.
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12320)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e2) = e0
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12320) implies:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12321)  op(e2, e0) = e2
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12308), (12321), (function-axioms) are
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #813.
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12322)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12322) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12323)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (157), (12204), (12251), (12302),
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12323), (function-axioms) are inconsistent by
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #72.
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12324)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (157), (12204), (12302), (12308),
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12324), (function-axioms) are inconsistent by
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #217.
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12325)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (160), (12239), (12257), (12258),
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12325), (function-axioms) are inconsistent by
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #213.
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12326)   ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_9)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12326) implies:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12327)   ~ (all_57_9 = e3)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12328)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12328) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12329)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12329) gives:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12330)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (169), (11905), (11941), (12202),
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12204), (12330), (function-axioms) are
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #8.
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12331)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_12))
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12331) gives:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12332)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12332) gives:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12333)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12333) implies:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12334)  op(e0, e0) = e2
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12239), (12334), (function-axioms) are
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12335)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12335) implies:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12336)  all_57_9 = e3
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12327), (12336) imply:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12337)  $false
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12337) is inconsistent.
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12338)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (9929), (11905), (11941), (12338),
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #7.
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12339)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12339) gives:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12340)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14))
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (135), (158),
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (170), (191), (203), (229), (231), (233),
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (248), (272), (352), (356), (9926),
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11902), (11905), (12204), (12232), (12246),
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12247), (12340), (function-axioms) are
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #6.
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12341)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12341) gives:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12342)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (9929), (12202), (12342),
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #5.
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12343)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12343) gives:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12344)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12344) implies:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12345)  op(e0, e0) = e1
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (12239), (12345), (function-axioms) are
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12346)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12346) gives:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12347)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12347) implies:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12348)  all_57_9 = e3
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12327), (12348) imply:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12349)  $false
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12349) is inconsistent.
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12350)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e1
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12350) implies:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12351)  op(e1, e1) = e1
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12204), (12351), (function-axioms) are
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12352)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.78/24.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e2) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e2) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e2) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12352) gives:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12353)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (135),
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (170), (191), (203), (229), (231), (233),
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (248), (272), (352), (356), (9926), (9929),
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11902), (11905), (12204), (12232), (12239),
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12353), (function-axioms) are inconsistent by
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #4.
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12354)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12354) gives:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12355)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & $i(all_57_10))
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (36), (135), (158), (170),
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (203), (238), (248), (272), (352), (356),
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9926), (9929), (11902), (11905), (12204),
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12239), (12355), (function-axioms) are
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #3.
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12356)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e3) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e3) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e3) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e1) = e0)))
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12356) gives:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12357)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3)
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (229), (231), (233),
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12232), (12239), (12357), (function-axioms) are
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2.
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12358)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12358) gives:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12359)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12359) implies:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12360)  op(e2, e2) = e2
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (12360), (function-axioms) are
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12361)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0)))
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12361) gives:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12362)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12362) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12363)  op(e1, e1) = e1
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12204), (12363), (function-axioms) are
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1003.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12364)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0))
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12364) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12365)  op(e0, e0) = all_57_15
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12366)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12366) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12367)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12367) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12368)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12368) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12369)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e3) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12369) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12370)  op(e0, e3) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11901), (12370), (function-axioms) are
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12371)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12371) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12372)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e3) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12372) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12373)  op(e2, e0) = e2
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (12246), (12247), (12373),
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #627.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12374)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e3) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12374) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12375)  op(e1, e1) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12204), (12375), (function-axioms) are
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12376)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12376) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12377)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12377) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12378)  op(e0, e3) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11901), (12378), (function-axioms) are
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12379)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12379) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12380)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e2) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12380) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12381)  op(e0, e2) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12251), (12381), (function-axioms) are
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #832.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12382)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e2) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12382) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12383)  op(e2, e0) = e2
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (12246), (12247), (12383),
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #627.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12384)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12384) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12385)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e1) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12385) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12386)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e2) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12386) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12387)  op(e1, e1) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12204), (12387), (function-axioms) are
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12388)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12388) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12389)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12389) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12390)  op(e0, e2) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12251), (12390), (function-axioms) are
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #832.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12391)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & op(e0, e1) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12391) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12392)  all_57_9 = e3
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12327), (12392) imply:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12393)  $false
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12393) is inconsistent.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12394)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12394) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12395)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12395) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12396)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e0, e1) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12396) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12397)  op(e2, e0) = e2
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (12246), (12247), (12397),
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #627.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12398)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1 & op(e0, e1) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12398) implies:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12399)  op(e1, e1) = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12204), (12399), (function-axioms) are
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12400)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (e1 = e0) & op(e0, e1) = e0)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12400) gives:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12401)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 & 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12401) implies:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12402)  op(e0, e1) = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (157), (369), (12239), (12402),
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12403)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12403) implies:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12404)  op(e0, e1) = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (157), (369), (12239), (12404),
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | |   (12405)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (157), (12224), (12239), (12405),
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | |            #215.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12406)  all_56_13 = e3 & op(e0, e2) = e3
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9926), (12406), (function-axioms) are
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |   (12407)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (12407) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12408)  all_56_14 = e3 & op(e0, e1) = e3
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (12408) implies:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12409)  op(e0, e1) = e3
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (12203), (12409), (function-axioms) are
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #720.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12410)  all_56_15 = e3 & op(e0, e0) = e3
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (12410) implies:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12411)  op(e0, e0) = e3
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (36), (135), (158), (170),
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            (191), (203), (238), (248), (272), (352), (356),
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            (9926), (11902), (11905), (12204), (12411),
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            #70.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12412)  all_54_2 = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (12412) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12413)  all_52_8 = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | REDUCE: (11903), (12413) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12414)  $false
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | CLOSE: (12414) is inconsistent.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | |   (12415)   ~ (all_30_1 = e0) & op(e3, e3) = all_30_1 &
% 157.78/24.37  | | | | | | | | | | | | | | | |            $i(all_30_1)
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | ALPHA: (12415) implies:
% 157.78/24.37  | | | | | | | | | | | | | | | |   (12416)   ~ (all_30_1 = e0)
% 157.78/24.37  | | | | | | | | | | | | | | | |   (12417)  op(e3, e3) = all_30_1
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_30_1,
% 157.78/24.37  | | | | | | | | | | | | | | | |              e3, e3, simplifying with (11905), (12417) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | |   (12418)  all_30_1 = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | REDUCE: (12416), (12418) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | |   (12419)  $false
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | CLOSE: (12419) is inconsistent.
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | |   (12420)  all_18_2 = e3
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | COMBINE_EQS: (301), (12420) imply:
% 157.78/24.37  | | | | | | | | | | | |   (12421)  all_14_2 = e3
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | SIMP: (12421) implies:
% 157.78/24.37  | | | | | | | | | | | |   (12422)  all_14_2 = e3
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | REDUCE: (370), (12422) imply:
% 157.78/24.37  | | | | | | | | | | | |   (12423)   ~ (all_52_12 = e3)
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | REDUCE: (51), (12422) imply:
% 157.78/24.37  | | | | | | | | | | | |   (12424)  op(e0, e0) = e3
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (168), (236), (238), (9929),
% 157.78/24.37  | | | | | | | | | | | |            (11905), (11941), (12423), (12424),
% 157.78/24.37  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.37  | | | | | | | | | | | |            #24.
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | |   (12425)  all_14_2 = e1
% 157.78/24.37  | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | REDUCE: (362), (12425) imply:
% 157.78/24.37  | | | | | | | | | | |   (12426)   ~ (all_52_7 = e1)
% 157.78/24.37  | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | REDUCE: (370), (12425) imply:
% 157.78/24.37  | | | | | | | | | | |   (12427)   ~ (all_52_12 = e1)
% 157.78/24.37  | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | REDUCE: (51), (12425) imply:
% 157.78/24.37  | | | | | | | | | | |   (12428)  op(e0, e0) = e1
% 157.78/24.37  | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | BETA: splitting (232) gives:
% 157.78/24.37  | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | |   (12429)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 157.78/24.37  | | | | | | | | | | | |              & op(e3, e2) = e1)
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | REF_CLOSE: (4), (6), (11905), (11940), (12429),
% 157.78/24.37  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.37  | | | | | | | | | | | |            #11.
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | |   (12430)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 157.78/24.37  | | | | | | | | | | | |              & op(e3, e0) = e1)
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | BETA: splitting (12430) gives:
% 157.78/24.37  | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | |   (12431)  all_56_4 = e1 & op(e3, e1) = e1
% 157.78/24.37  | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | ALPHA: (12431) implies:
% 157.78/24.37  | | | | | | | | | | | | |   (12432)  all_56_4 = e1
% 157.78/24.37  | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | BETA: splitting (236) gives:
% 157.78/24.37  | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | |   (12433)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 157.78/24.37  | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 157.78/24.37  | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (11905), (11941), (12433),
% 157.78/24.37  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.78/24.37  | | | | | | | | | | | | | |            #27.
% 157.78/24.37  | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | |   (12434)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 157.78/24.37  | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 157.78/24.37  | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | BETA: splitting (12434) gives:
% 157.78/24.37  | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | |   (12435)  all_56_4 = e3 & op(e3, e1) = e3
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | ALPHA: (12435) implies:
% 157.78/24.37  | | | | | | | | | | | | | | |   (12436)  all_56_4 = e3
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | COMBINE_EQS: (12432), (12436) imply:
% 157.78/24.37  | | | | | | | | | | | | | | |   (12437)  e3 = e1
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | SIMP: (12437) implies:
% 157.78/24.37  | | | | | | | | | | | | | | |   (12438)  e3 = e1
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | REDUCE: (8), (12438) imply:
% 157.78/24.37  | | | | | | | | | | | | | | |   (12439)  $false
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | CLOSE: (12439) is inconsistent.
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | |   (12440)  all_56_9 = e3 & op(e3, e0) = e3
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | ALPHA: (12440) implies:
% 157.78/24.37  | | | | | | | | | | | | | | |   (12441)  all_56_9 = e3
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | |   (12442)  all_54_13 = e3
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | REF_CLOSE: (248), (9926), (12442) are inconsistent by
% 157.78/24.37  | | | | | | | | | | | | | | | |            sub-proof #385.
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | |   (12443)   ~ (all_54_13 = e3)
% 157.78/24.37  | | | | | | | | | | | | | | | |   (12444)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | BETA: splitting (12444) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | |   (12445)  all_54_13 = e2
% 157.78/24.37  | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (11932), (12445) are inconsistent by
% 157.78/24.37  | | | | | | | | | | | | | | | | |            sub-proof #505.
% 157.78/24.37  | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | |   (12446)   ~ (all_54_13 = e2)
% 157.78/24.37  | | | | | | | | | | | | | | | | |   (12447)  all_54_13 = e1 | all_54_13 = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | BETA: splitting (12447) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12448)  all_54_13 = e1
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (12426), (12448) are inconsistent by
% 157.78/24.37  | | | | | | | | | | | | | | | | | |            sub-proof #504.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12449)  all_54_13 = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (12449) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12450)  all_52_7 = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | SIMP: (12450) implies:
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12451)  all_52_7 = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | REDUCE: (128), (12451) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12452)   ~ (all_52_6 = e0)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | REDUCE: (9926), (12451) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12453)   ~ (e3 = e0)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | REDUCE: (11932), (12451) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12454)   ~ (e2 = e0)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | REDUCE: (12426), (12451) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | |   (12455)   ~ (e1 = e0)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |   (12456)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (12456) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12457)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                all_57_6 & $i(all_57_6)))
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (12457) implies:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12458)  op(e3, e3) = e3
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (230), (232), (11940),
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            (12441), (12458), (function-axioms) are
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #633.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12459)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                all_57_7 & $i(all_57_7)))
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (12459) implies:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12460)  op(e2, e2) = e2
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9929), (12460), (function-axioms) are
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | End of split
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |   (12461)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.78/24.37  | | | | | | | | | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (12461) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12462)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |                all_57_8 & $i(all_57_8)))
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (12462) implies:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | |   (12463)  op(e1, e1) = e1
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | |   (12464)  all_54_9 = e3
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (9925), (12464) are inconsistent by
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | |            sub-proof #656.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | |   (12465)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12465) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | |   (12466)  all_54_9 = e2
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (12466) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | |   (12467)  all_52_6 = e2
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11931), (12467) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | |   (12468)  $false
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12468) is inconsistent.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | |   (12469)  all_54_9 = e1 | all_54_9 = e0
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12469) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | |   (12470)  all_54_9 = e1
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (12470) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | |   (12471)  all_52_6 = e1
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (12471) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | |   (12472)   ~ (all_10_2 = e1)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12472) implies:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | |   (12473)   ~ (all_10_2 = e1)
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e1,
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (45), (12463) gives:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | |   (12474)  all_10_2 = e1
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12473), (12474) imply:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | |   (12475)  $false
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12475) is inconsistent.
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.78/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | |   (12476)  all_54_9 = e0
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (12476) imply:
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | |   (12477)  all_52_6 = e0
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12452), (12477) imply:
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | |   (12478)  $false
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12478) is inconsistent.
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | |   (12479)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | |                op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13)))
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (12479) implies:
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | |   (12480)  op(e0, e0) = e0
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (51), (12428), (12480), (function-axioms) are
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | Case 2:
% 157.85/24.37  | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | |   (12481)  all_56_9 = e1 & op(e3, e0) = e1
% 157.85/24.37  | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | | REF_CLOSE: (168), (12427), (12481), (function-axioms) are
% 157.85/24.37  | | | | | | | | | | | | |            inconsistent by sub-proof #851.
% 157.85/24.37  | | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | | End of split
% 157.85/24.37  | | | | | | | | | | 
% 157.85/24.37  | | | | | | | | | Case 2:
% 157.85/24.37  | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | |   (12482)  all_10_2 = e2
% 157.85/24.38  | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | | REDUCE: (368), (12482) imply:
% 157.85/24.38  | | | | | | | | | |   (12483)   ~ (all_52_14 = e2)
% 157.85/24.38  | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | | REDUCE: (45), (12482) imply:
% 157.85/24.38  | | | | | | | | | |   (12484)  op(e1, e1) = e2
% 157.85/24.38  | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | | BETA: splitting (238) gives:
% 157.85/24.38  | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | | Case 1:
% 157.85/24.38  | | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | | |   (12485)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.85/24.38  | | | | | | | | | | |                  e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.85/24.38  | | | | | | | | | | |                  & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.85/24.38  | | | | | | | | | | |              ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.85/24.38  | | | | | | | | | | |                  (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.85/24.38  | | | | | | | | | | |                  $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.85/24.38  | | | | | | | | | | |                    e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.85/24.38  | | | | | | | | | | |                    e3) = all_57_6 & $i(all_57_6)))) |
% 157.85/24.38  | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.85/24.38  | | | | | | | | | | |                  e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.85/24.38  | | | | | | | | | | |                  & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.85/24.38  | | | | | | | | | | |              ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.85/24.38  | | | | | | | | | | |                  (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.85/24.38  | | | | | | | | | | |                  $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.85/24.38  | | | | | | | | | | |                    e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.85/24.38  | | | | | | | | | | |                    e2) = all_57_7 & $i(all_57_7))))
% 157.85/24.38  | | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | | | REF_CLOSE: (7), (9), (9929), (11905), (12485),
% 157.85/24.38  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 157.85/24.38  | | | | | | | | | | |            #26.
% 157.85/24.38  | | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | | Case 2:
% 157.85/24.38  | | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | | |   (12486)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.85/24.38  | | | | | | | | | | |                  e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.85/24.38  | | | | | | | | | | |                  & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.85/24.38  | | | | | | | | | | |              ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.85/24.38  | | | | | | | | | | |                  (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.85/24.38  | | | | | | | | | | |                  $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.85/24.38  | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.85/24.38  | | | | | | | | | | |                    e1) = all_57_8 & $i(all_57_8)))) |
% 157.85/24.38  | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.85/24.38  | | | | | | | | | | |                  e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.85/24.38  | | | | | | | | | | |                  & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.85/24.38  | | | | | | | | | | |              ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.85/24.38  | | | | | | | | | | |                  (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.85/24.38  | | | | | | | | | | |                  $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.85/24.38  | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.85/24.38  | | | | | | | | | | |                    e0) = all_57_13 & $i(all_57_13))))
% 157.85/24.38  | | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (51), (160), (164), (168), (197),
% 157.85/24.38  | | | | | | | | | | |            (211), (260), (371), (9928), (9929), (11934),
% 157.85/24.38  | | | | | | | | | | |            (12483), (12484), (12486), (function-axioms) are
% 157.85/24.38  | | | | | | | | | | |            inconsistent by sub-proof #12.
% 157.85/24.38  | | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | | End of split
% 157.85/24.38  | | | | | | | | | | 
% 157.85/24.38  | | | | | | | | | End of split
% 157.85/24.38  | | | | | | | | | 
% 157.85/24.38  | | | | | | | | End of split
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | Case 2:
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | |   (12487)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 &
% 157.85/24.38  | | | | | | | |              op(e3, e0) = e2)
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | | REF_CLOSE: (168), (169), (11933), (11934), (12487),
% 157.85/24.38  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #511.
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | End of split
% 157.85/24.38  | | | | | | | 
% 157.85/24.38  | | | | | | Case 2:
% 157.85/24.38  | | | | | | | 
% 157.85/24.38  | | | | | | |   (12488)  all_54_1 = e1 | all_54_1 = e0
% 157.85/24.38  | | | | | | | 
% 157.85/24.38  | | | | | | | BETA: splitting (12488) gives:
% 157.85/24.38  | | | | | | | 
% 157.85/24.38  | | | | | | | Case 1:
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | |   (12489)  all_54_1 = e1
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | | COMBINE_EQS: (11913), (12489) imply:
% 157.85/24.38  | | | | | | | |   (12490)  all_40_0 = e1
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | | REDUCE: (11910), (12490) imply:
% 157.85/24.38  | | | | | | | |   (12491)  $false
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | | CLOSE: (12491) is inconsistent.
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | Case 2:
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | |   (12492)  all_54_1 = e0
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | | COMBINE_EQS: (11913), (12492) imply:
% 157.85/24.38  | | | | | | | |   (12493)  all_40_0 = e0
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | | REDUCE: (11923), (12493) imply:
% 157.85/24.38  | | | | | | | |   (12494)  $false
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | | CLOSE: (12494) is inconsistent.
% 157.85/24.38  | | | | | | | | 
% 157.85/24.38  | | | | | | | End of split
% 157.85/24.38  | | | | | | | 
% 157.85/24.38  | | | | | | End of split
% 157.85/24.38  | | | | | | 
% 157.85/24.38  | | | | | End of split
% 157.85/24.38  | | | | | 
% 157.85/24.38  | | | | Case 2:
% 157.85/24.38  | | | | | 
% 157.85/24.38  | | | | |   (12495)   ~ (all_40_1 = e0) & op(e3, e3) = all_40_1 & $i(all_40_1)
% 157.85/24.38  | | | | | 
% 157.85/24.38  | | | | | ALPHA: (12495) implies:
% 157.85/24.38  | | | | |   (12496)   ~ (all_40_1 = e0)
% 157.85/24.38  | | | | |   (12497)  op(e3, e3) = all_40_1
% 157.85/24.38  | | | | | 
% 157.85/24.38  | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_40_1, e3,
% 157.85/24.38  | | | | |              e3, simplifying with (11905), (12497) gives:
% 157.85/24.38  | | | | |   (12498)  all_40_1 = e0
% 157.85/24.38  | | | | | 
% 157.85/24.38  | | | | | REDUCE: (12496), (12498) imply:
% 157.85/24.38  | | | | |   (12499)  $false
% 157.85/24.38  | | | | | 
% 157.85/24.38  | | | | | CLOSE: (12499) is inconsistent.
% 157.85/24.38  | | | | | 
% 157.85/24.38  | | | | End of split
% 157.85/24.38  | | | | 
% 157.85/24.38  | | | End of split
% 157.85/24.38  | | | 
% 157.85/24.38  | | End of split
% 157.85/24.38  | | 
% 157.85/24.38  | End of split
% 157.85/24.38  | 
% 157.85/24.38  End of proof
% 157.85/24.38  
% 157.85/24.38  Sub-proof #1 shows that the following formulas are inconsistent:
% 157.85/24.38  ----------------------------------------------------------------
% 157.85/24.38    (1)  op(e0, e1) = all_52_11
% 157.85/24.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.38    (3)   ~ (all_52_11 = all_14_2)
% 157.85/24.38    (4)  op(e0, e0) = e0
% 157.85/24.38    (5)  op(e0, e0) = all_14_2
% 157.85/24.38    (6)  op(e0, e1) = e0
% 157.85/24.38  
% 157.85/24.38  Begin of proof
% 157.85/24.38  | 
% 157.85/24.38  | GROUND_INST: instantiating (2) with all_14_2, e0, e0, e0, simplifying with
% 157.85/24.38  |              (4), (5) gives:
% 157.85/24.38  |   (7)  all_14_2 = e0
% 157.85/24.38  | 
% 157.85/24.38  | GROUND_INST: instantiating (2) with all_52_11, e0, e1, e0, simplifying with
% 157.85/24.38  |              (1), (6) gives:
% 157.85/24.38  |   (8)  all_52_11 = e0
% 157.85/24.38  | 
% 157.85/24.38  | REDUCE: (3), (7), (8) imply:
% 157.85/24.38  |   (9)  $false
% 157.85/24.38  | 
% 157.85/24.38  | CLOSE: (9) is inconsistent.
% 157.85/24.38  | 
% 157.85/24.38  End of proof
% 157.85/24.38  
% 157.85/24.38  Sub-proof #2 shows that the following formulas are inconsistent:
% 157.85/24.38  ----------------------------------------------------------------
% 157.85/24.38    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 157.85/24.38         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 157.85/24.38    (2)   ~ (e3 = e2)
% 157.85/24.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.38    (4)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 157.85/24.38           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 157.85/24.38           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 157.85/24.38           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 157.85/24.38    (5)  op(e0, e0) = e0
% 157.85/24.38    (6)  all_56_12 = e3
% 157.85/24.38    (7)   ~ (e1 = e0)
% 157.85/24.38    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 157.85/24.38         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 157.85/24.38    (9)   ~ (e2 = e1)
% 157.85/24.38    (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 157.85/24.38          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 157.85/24.38    (11)   ~ (e3 = e1)
% 157.85/24.38    (12)   ~ (e2 = e0)
% 157.85/24.38  
% 157.85/24.38  Begin of proof
% 157.85/24.38  | 
% 157.85/24.38  | BETA: splitting (4) gives:
% 157.85/24.38  | 
% 157.85/24.38  | Case 1:
% 157.85/24.38  | | 
% 157.85/24.38  | |   (13)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 157.85/24.38  | |           e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 &
% 157.85/24.38  | |         op(e0, e0) = e2 & $i(all_57_12)
% 157.85/24.38  | | 
% 157.85/24.38  | | ALPHA: (13) implies:
% 157.85/24.38  | |   (14)  op(e0, e0) = e2
% 157.85/24.38  | | 
% 157.85/24.38  | | REF_CLOSE: (3), (5), (12), (14) are inconsistent by sub-proof #979.
% 157.85/24.38  | | 
% 157.85/24.38  | Case 2:
% 157.85/24.38  | | 
% 157.85/24.38  | |   (15)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 157.85/24.38  | |         op(e3, e0) = e3
% 157.85/24.38  | | 
% 157.85/24.38  | | ALPHA: (15) implies:
% 157.85/24.38  | |   (16)   ~ (e3 = e0)
% 157.85/24.38  | |   (17)  op(e3, e3) = e3
% 157.85/24.38  | | 
% 157.85/24.38  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (16), (17)
% 157.85/24.38  | |            are inconsistent by sub-proof #729.
% 157.85/24.38  | | 
% 157.85/24.38  | End of split
% 157.85/24.38  | 
% 157.85/24.38  End of proof
% 157.85/24.38  
% 157.85/24.38  Sub-proof #3 shows that the following formulas are inconsistent:
% 157.85/24.38  ----------------------------------------------------------------
% 157.85/24.38    (1)  all_54_13 = all_52_7
% 157.85/24.38    (2)  op(e1, e1) = e3
% 157.85/24.38    (3)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 157.85/24.38             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.85/24.38           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 157.85/24.38               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 157.85/24.38             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 157.85/24.38         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 157.85/24.38             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.85/24.38           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 157.85/24.38               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 157.85/24.38             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 157.85/24.38         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 157.85/24.38             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.85/24.38           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 157.85/24.38               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 157.85/24.38             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 157.85/24.38         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 157.85/24.38             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.85/24.38           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 157.85/24.38               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 157.85/24.38             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 157.85/24.38    (4)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.85/24.38    (5)   ~ (e3 = e2)
% 157.85/24.38    (6)   ~ (all_52_7 = e3)
% 157.85/24.38    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.38    (8)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 157.85/24.38           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 157.85/24.38           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 157.85/24.38           & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 157.85/24.38           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 157.85/24.38           e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.85/24.38         (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 157.85/24.38           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 157.85/24.38           = e3 & $i(all_57_10))
% 157.85/24.38    (9)  op(e0, e2) = all_52_7
% 157.85/24.38    (10)  all_54_1 = all_52_4
% 157.85/24.38    (11)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.85/24.38    (12)  op(e0, e0) = e0
% 157.85/24.38    (13)  op(e2, e2) = all_4_2
% 157.85/24.38    (14)   ~ (all_52_4 = all_4_2)
% 157.85/24.38    (15)  op(e3, e3) = e0
% 157.85/24.38    (16)   ~ (all_52_4 = all_52_7)
% 157.85/24.38    (17)  op(e3, e2) = all_52_4
% 157.85/24.38    (18)   ~ (all_52_7 = all_4_2)
% 157.85/24.38    (19)  op(e2, e2) = e3
% 157.85/24.38    (20)   ~ (all_52_4 = e0)
% 157.85/24.38    (21)   ~ (e3 = e1)
% 157.85/24.38    (22)   ~ (e2 = e0)
% 157.85/24.38    (23)   ~ (e3 = e0)
% 157.85/24.38  
% 157.85/24.38  Begin of proof
% 157.85/24.38  | 
% 157.85/24.38  | BETA: splitting (8) gives:
% 157.85/24.38  | 
% 157.85/24.38  | Case 1:
% 157.85/24.38  | | 
% 157.85/24.38  | |   (24)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 157.85/24.38  | |             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0
% 157.85/24.38  | |           & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 =
% 157.85/24.38  | |           e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 157.85/24.38  | | 
% 157.85/24.38  | | REF_CLOSE: (5), (7), (12), (19), (22), (24) are inconsistent by sub-proof
% 157.85/24.38  | |            #51.
% 157.85/24.38  | | 
% 157.85/24.38  | Case 2:
% 157.85/24.38  | | 
% 157.85/24.39  | |   (25)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 157.85/24.39  | |             e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 157.85/24.39  | |           & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 157.85/24.39  | |           e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 157.85/24.39  | |           & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.85/24.39  | |           $i(all_57_10))
% 157.85/24.39  | | 
% 157.85/24.39  | | BETA: splitting (25) gives:
% 157.85/24.39  | | 
% 157.85/24.39  | | Case 1:
% 157.85/24.39  | | | 
% 157.85/24.39  | | |   (26)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 157.85/24.39  | | |           e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 157.85/24.39  | | |         & op(e1, e0) = e1 & $i(all_57_14)
% 157.85/24.39  | | | 
% 157.85/24.39  | | | ALPHA: (26) implies:
% 157.85/24.39  | | |   (27)  op(e2, e2) = e1
% 157.85/24.39  | | | 
% 157.85/24.39  | | | REF_CLOSE: (7), (19), (21), (27) are inconsistent by sub-proof #847.
% 157.85/24.39  | | | 
% 157.85/24.39  | | Case 2:
% 157.85/24.39  | | | 
% 157.85/24.39  | | |   (28)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 157.85/24.39  | | |           e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0
% 157.85/24.39  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 157.85/24.39  | | | 
% 157.85/24.39  | | | ALPHA: (28) implies:
% 157.85/24.39  | | |   (29)  op(e0, e0) = e3
% 157.85/24.39  | | | 
% 157.85/24.39  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 157.85/24.39  | | |            (15), (16), (17), (18), (20), (21), (22), (23), (29) are
% 157.85/24.39  | | |            inconsistent by sub-proof #70.
% 157.85/24.39  | | | 
% 157.85/24.39  | | End of split
% 157.85/24.39  | | 
% 157.85/24.39  | End of split
% 157.85/24.39  | 
% 157.85/24.39  End of proof
% 157.85/24.39  
% 157.85/24.39  Sub-proof #4 shows that the following formulas are inconsistent:
% 157.85/24.39  ----------------------------------------------------------------
% 157.85/24.39    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 157.85/24.39         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 157.85/24.39    (2)  all_54_13 = all_52_7
% 157.85/24.39    (3)  op(e1, e1) = e3
% 157.85/24.39    (4)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 157.85/24.39             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.85/24.39           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 157.85/24.39               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 157.85/24.39             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 157.85/24.39         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 157.85/24.39             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.85/24.39           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 157.85/24.39               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 157.85/24.39             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 157.85/24.39         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 157.85/24.39             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.85/24.39           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 157.85/24.39               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 157.85/24.39             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 157.85/24.39         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 157.85/24.39             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.85/24.39           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 157.85/24.39               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 157.85/24.39             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 157.85/24.39    (5)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.85/24.39    (6)   ~ (e3 = e2)
% 157.85/24.39    (7)   ~ (all_52_7 = e3)
% 157.85/24.39    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.39    (9)  op(e0, e2) = all_52_7
% 157.85/24.39    (10)  all_54_1 = all_52_4
% 157.85/24.39    (11)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.85/24.39    (12)  op(e0, e0) = e0
% 157.85/24.39    (13)  op(e2, e2) = all_4_2
% 157.85/24.39    (14)   ~ (all_52_4 = all_4_2)
% 157.85/24.39    (15)  all_56_12 = e3
% 157.85/24.39    (16)  op(e3, e3) = e0
% 157.85/24.39    (17)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 157.85/24.39            op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.85/24.39            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 157.85/24.39            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 157.85/24.39            e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.85/24.39          (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 157.85/24.39            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 157.85/24.39              e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 &
% 157.85/24.39            all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 157.85/24.39            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 157.85/24.39          (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 157.85/24.39            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1,
% 157.85/24.39              e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2
% 157.85/24.39              = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) | (all_57_4 = e3 &
% 157.85/24.39            all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.85/24.39            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.85/24.39            $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.85/24.39            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 157.85/24.39            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 157.85/24.39            e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 157.85/24.39    (18)   ~ (all_52_4 = all_52_7)
% 157.85/24.39    (19)  op(e0, e0) = all_14_2
% 157.85/24.39    (20)  op(e3, e2) = all_52_4
% 157.85/24.39    (21)   ~ (all_52_7 = all_4_2)
% 157.85/24.39    (22)   ~ (e1 = e0)
% 157.85/24.39    (23)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 157.85/24.39          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 157.85/24.39    (24)  op(e2, e2) = e3
% 157.85/24.39    (25)   ~ (e2 = e1)
% 157.85/24.39    (26)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 157.85/24.39          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 157.85/24.39    (27)   ~ (all_52_4 = e0)
% 157.85/24.39    (28)   ~ (e3 = e1)
% 157.85/24.39    (29)   ~ (e2 = e0)
% 157.85/24.39    (30)   ~ (e3 = e0)
% 157.85/24.39  
% 157.85/24.39  Begin of proof
% 157.85/24.39  | 
% 157.85/24.39  | BETA: splitting (17) gives:
% 157.85/24.39  | 
% 157.85/24.39  | Case 1:
% 157.85/24.39  | | 
% 157.85/24.39  | |   (31)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 157.85/24.39  | |             e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 &
% 157.85/24.39  | |           op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.85/24.39  | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 157.85/24.39  | |           = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 157.85/24.39  | |           & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2
% 157.85/24.39  | |           &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 157.85/24.39  | |           op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 =
% 157.85/24.39  | |           e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1,
% 157.85/24.39  | |             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.85/24.39  | |           = e1 & $i(all_57_14))
% 157.85/24.39  | | 
% 157.85/24.39  | | BETA: splitting (31) gives:
% 157.85/24.39  | | 
% 157.85/24.39  | | Case 1:
% 157.85/24.39  | | | 
% 157.85/24.39  | | |   (32)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 157.85/24.39  | | |             e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 &
% 157.85/24.39  | | |           op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.85/24.39  | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2,
% 157.85/24.39  | | |             e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.85/24.39  | | |           all_57_14 & $i(all_57_14))
% 157.85/24.39  | | | 
% 157.85/24.39  | | | BETA: splitting (32) gives:
% 157.85/24.39  | | | 
% 157.85/24.39  | | | Case 1:
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | |   (33)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 157.85/24.39  | | | |           e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 &
% 157.85/24.39  | | | |         op(e1, e1) = all_57_14 & $i(all_57_14)
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | | ALPHA: (33) implies:
% 157.85/24.39  | | | |   (34)  op(e3, e3) = e1
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | | REF_CLOSE: (8), (16), (22), (34) are inconsistent by sub-proof #834.
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | Case 2:
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | |   (35)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.85/24.39  | | | |           e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 &
% 157.85/24.39  | | | |         op(e1, e1) = all_57_14 & $i(all_57_14)
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | | ALPHA: (35) implies:
% 157.85/24.39  | | | |   (36)  op(e2, e2) = e1
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | | REF_CLOSE: (8), (24), (28), (36) are inconsistent by sub-proof #847.
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | End of split
% 157.85/24.39  | | | 
% 157.85/24.39  | | Case 2:
% 157.85/24.39  | | | 
% 157.85/24.39  | | |   (37)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 157.85/24.39  | | |             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) =
% 157.85/24.39  | | |           e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 157.85/24.39  | | |           all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1,
% 157.85/24.39  | | |             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 157.85/24.39  | | |             e0) = e1 & $i(all_57_14))
% 157.85/24.39  | | | 
% 157.85/24.39  | | | REF_CLOSE: (3), (6), (8), (12), (19), (22), (37) are inconsistent by
% 157.85/24.39  | | |            sub-proof #645.
% 157.85/24.39  | | | 
% 157.85/24.39  | | End of split
% 157.85/24.39  | | 
% 157.85/24.39  | Case 2:
% 157.85/24.39  | | 
% 157.85/24.39  | |   (38)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 157.85/24.39  | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1
% 157.85/24.39  | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 =
% 157.85/24.39  | |           e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) | (all_57_4
% 157.85/24.39  | |           = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 157.85/24.39  | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.85/24.39  | |           op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3
% 157.85/24.39  | |           &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 157.85/24.39  | |           e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 157.85/24.39  | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 157.85/24.39  | |           op(e1, e0) = e1 & $i(all_57_14))
% 157.85/24.39  | | 
% 157.85/24.39  | | BETA: splitting (38) gives:
% 157.85/24.39  | | 
% 157.85/24.39  | | Case 1:
% 157.85/24.39  | | | 
% 157.85/24.39  | | |   (39)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 157.85/24.39  | | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) =
% 157.85/24.39  | | |           e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 157.85/24.39  | | |           all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.85/24.39  | | |           e1)
% 157.85/24.39  | | | 
% 157.85/24.39  | | | REF_CLOSE: (3), (6), (8), (28), (39) are inconsistent by sub-proof #644.
% 157.85/24.39  | | | 
% 157.85/24.39  | | Case 2:
% 157.85/24.39  | | | 
% 157.85/24.39  | | |   (40)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 157.85/24.39  | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) =
% 157.85/24.39  | | |           e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 157.85/24.39  | | |           all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) =
% 157.85/24.39  | | |           e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.85/24.39  | | |           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 157.85/24.39  | | |             e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 157.85/24.39  | | | 
% 157.85/24.39  | | | BETA: splitting (40) gives:
% 157.85/24.39  | | | 
% 157.85/24.39  | | | Case 1:
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | |   (41)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 157.85/24.39  | | | |           e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) =
% 157.85/24.39  | | | |         e0 & op(e0, e0) = e3 & $i(all_57_10)
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | | ALPHA: (41) implies:
% 157.85/24.39  | | | |   (42)  op(e0, e0) = e3
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 157.85/24.39  | | | |            (14), (16), (18), (20), (21), (27), (28), (29), (30), (42)
% 157.85/24.39  | | | |            are inconsistent by sub-proof #70.
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | Case 2:
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | |   (43)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3
% 157.85/24.39  | | | |           & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 157.85/24.39  | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 &
% 157.85/24.39  | | | |           op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.85/24.39  | | | |           $i(all_57_14))
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | | BETA: splitting (43) gives:
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | | Case 1:
% 157.85/24.39  | | | | | 
% 157.85/24.39  | | | | |   (44)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) =
% 157.85/24.39  | | | | |         e3 & op(e3, e1) = e3
% 157.85/24.39  | | | | | 
% 157.85/24.39  | | | | | ALPHA: (44) implies:
% 157.85/24.39  | | | | |   (45)  op(e3, e3) = e3
% 157.85/24.39  | | | | | 
% 157.85/24.39  | | | | | REF_CLOSE: (1), (6), (8), (15), (22), (23), (25), (26), (28), (29),
% 157.85/24.39  | | | | |            (30), (45) are inconsistent by sub-proof #729.
% 157.85/24.39  | | | | | 
% 157.85/24.39  | | | | Case 2:
% 157.85/24.39  | | | | | 
% 157.85/24.39  | | | | |   (46)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.85/24.39  | | | | |         (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 157.85/24.39  | | | | |           e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)
% 157.85/24.39  | | | | | 
% 157.85/24.39  | | | | | ALPHA: (46) implies:
% 157.85/24.39  | | | | |   (47)  op(e3, e3) = e1
% 157.85/24.39  | | | | | 
% 157.85/24.39  | | | | | REF_CLOSE: (8), (16), (22), (47) are inconsistent by sub-proof #834.
% 157.85/24.39  | | | | | 
% 157.85/24.39  | | | | End of split
% 157.85/24.39  | | | | 
% 157.85/24.39  | | | End of split
% 157.85/24.39  | | | 
% 157.85/24.39  | | End of split
% 157.85/24.39  | | 
% 157.85/24.39  | End of split
% 157.85/24.39  | 
% 157.85/24.39  End of proof
% 157.85/24.39  
% 157.85/24.39  Sub-proof #5 shows that the following formulas are inconsistent:
% 157.85/24.39  ----------------------------------------------------------------
% 157.85/24.39    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 157.85/24.39           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 157.85/24.39           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 157.85/24.39           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 157.85/24.39           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 157.85/24.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.39    (3)  op(e3, e1) = all_52_8
% 157.85/24.39    (4)  op(e2, e2) = e3
% 157.85/24.39    (5)   ~ (e3 = e1)
% 157.85/24.39    (6)   ~ (all_52_8 = e3)
% 157.85/24.39  
% 157.85/24.39  Begin of proof
% 157.85/24.39  | 
% 157.85/24.39  | BETA: splitting (1) gives:
% 157.85/24.39  | 
% 157.85/24.39  | Case 1:
% 157.85/24.39  | | 
% 157.85/24.39  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 157.85/24.39  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 157.85/24.39  | |          e1) = e3 & $i(all_57_10)
% 157.85/24.39  | | 
% 157.85/24.39  | | ALPHA: (7) implies:
% 157.85/24.40  | |   (8)  op(e3, e1) = e3
% 157.85/24.40  | | 
% 157.85/24.40  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #982.
% 157.85/24.40  | | 
% 157.85/24.40  | Case 2:
% 157.85/24.40  | | 
% 157.85/24.40  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 157.85/24.40  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 157.85/24.40  | |        all_57_14 & $i(all_57_14)
% 157.85/24.40  | | 
% 157.85/24.40  | | ALPHA: (9) implies:
% 157.85/24.40  | |   (10)  op(e2, e2) = e1
% 157.85/24.40  | | 
% 157.85/24.40  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #847.
% 157.85/24.40  | | 
% 157.85/24.40  | End of split
% 157.85/24.40  | 
% 157.85/24.40  End of proof
% 157.85/24.40  
% 157.85/24.40  Sub-proof #6 shows that the following formulas are inconsistent:
% 157.85/24.40  ----------------------------------------------------------------
% 157.85/24.40    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 157.85/24.40         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 157.85/24.40    (2)  all_54_13 = all_52_7
% 157.85/24.40    (3)  op(e1, e1) = e3
% 157.85/24.40    (4)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 157.85/24.40             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.85/24.40           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 157.85/24.40               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 157.85/24.40             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 157.85/24.40         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 157.85/24.40             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.85/24.40           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 157.85/24.40               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 157.85/24.40             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 157.85/24.40         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 157.85/24.40             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.85/24.40           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 157.85/24.40               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 157.85/24.40             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 157.85/24.40         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 157.85/24.40             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.85/24.40           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 157.85/24.40               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 157.85/24.40             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 157.85/24.40    (5)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.85/24.40    (6)   ~ (e3 = e2)
% 157.85/24.40    (7)   ~ (all_52_7 = e3)
% 157.85/24.40    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.40    (9)   ~ (all_57_11 = e2)
% 157.85/24.40    (10)  op(e0, e2) = all_52_7
% 157.85/24.40    (11)  all_54_1 = all_52_4
% 157.85/24.40    (12)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.85/24.40    (13)  op(e2, e2) = all_4_2
% 157.85/24.40    (14)   ~ (all_52_4 = all_4_2)
% 157.85/24.40    (15)  all_56_12 = e3
% 157.85/24.40    (16)  op(e3, e3) = e0
% 157.85/24.40    (17)   ~ (all_52_4 = all_52_7)
% 157.85/24.40    (18)  op(e3, e2) = all_52_4
% 157.85/24.40    (19)   ~ (all_52_7 = all_4_2)
% 157.85/24.40    (20)   ~ (e1 = e0)
% 157.85/24.40    (21)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 157.85/24.40          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 157.85/24.40    (22)  op(e2, e0) = all_52_13
% 157.85/24.40    (23)   ~ (e2 = e1)
% 157.85/24.40    (24)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 157.85/24.40            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 157.85/24.40              e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3
% 157.85/24.40              = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) | (all_57_1 = e3 &
% 157.85/24.40            all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) =
% 157.85/24.40            e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.85/24.40            $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 157.85/24.40            (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1
% 157.85/24.40            & op(e1, e1) = all_57_14 & $i(all_57_14))
% 157.85/24.40    (25)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 157.85/24.40          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 157.85/24.40    (26)   ~ (all_52_4 = e0)
% 157.85/24.40    (27)   ~ (e3 = e1)
% 157.85/24.40    (28)   ~ (e2 = e0)
% 157.85/24.40    (29)  op(e2, e0) = all_57_11
% 157.85/24.40    (30)   ~ (e3 = e0)
% 157.85/24.40  
% 157.85/24.40  Begin of proof
% 157.85/24.40  | 
% 157.85/24.40  | BETA: splitting (24) gives:
% 157.85/24.40  | 
% 157.85/24.40  | Case 1:
% 157.85/24.40  | | 
% 157.85/24.40  | |   (31)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 157.85/24.40  | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0
% 157.85/24.40  | |           & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 =
% 157.85/24.40  | |           e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 157.85/24.40  | | 
% 157.85/24.40  | | BETA: splitting (31) gives:
% 157.85/24.40  | | 
% 157.85/24.40  | | Case 1:
% 157.85/24.40  | | | 
% 157.85/24.40  | | |   (32)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 157.85/24.40  | | |           e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0
% 157.85/24.40  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 157.85/24.40  | | | 
% 157.85/24.40  | | | ALPHA: (32) implies:
% 157.85/24.40  | | |   (33)  op(e0, e0) = e3
% 157.85/24.40  | | | 
% 157.85/24.40  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 157.85/24.40  | | |            (14), (16), (17), (18), (19), (26), (27), (28), (30), (33) are
% 157.85/24.40  | | |            inconsistent by sub-proof #70.
% 157.85/24.40  | | | 
% 157.85/24.40  | | Case 2:
% 157.85/24.40  | | | 
% 157.85/24.40  | | |   (34)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 157.85/24.40  | | |         op(e3, e2) = e3
% 157.85/24.40  | | | 
% 157.85/24.40  | | | ALPHA: (34) implies:
% 157.85/24.40  | | |   (35)  op(e3, e3) = e3
% 157.85/24.40  | | | 
% 157.85/24.40  | | | REF_CLOSE: (1), (6), (8), (15), (20), (21), (23), (25), (27), (28), (30),
% 157.85/24.40  | | |            (35) are inconsistent by sub-proof #729.
% 157.85/24.40  | | | 
% 157.85/24.40  | | End of split
% 157.85/24.40  | | 
% 157.85/24.40  | Case 2:
% 157.85/24.40  | | 
% 157.85/24.40  | |   (36)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 =
% 157.85/24.40  | |             e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12
% 157.85/24.40  | |           & op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 =
% 157.85/24.40  | |           e3 & all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 157.85/24.40  | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.85/24.40  | |           $i(all_57_14))
% 157.85/24.40  | | 
% 157.85/24.40  | | BETA: splitting (36) gives:
% 157.85/24.40  | | 
% 157.85/24.40  | | Case 1:
% 157.85/24.40  | | | 
% 157.85/24.40  | | |   (37)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 =
% 157.85/24.40  | | |           e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12
% 157.85/24.40  | | |         & op(e2, e0) = e2 & $i(all_57_12)
% 157.85/24.40  | | | 
% 157.85/24.40  | | | ALPHA: (37) implies:
% 157.85/24.40  | | |   (38)  op(e2, e0) = e2
% 157.85/24.40  | | | 
% 157.85/24.40  | | | REF_CLOSE: (8), (9), (22), (29), (38) are inconsistent by sub-proof #627.
% 157.85/24.40  | | | 
% 157.85/24.40  | | Case 2:
% 157.85/24.40  | | | 
% 157.85/24.40  | | |   (39)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 157.85/24.40  | | |           e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 157.85/24.40  | | |         op(e1, e1) = all_57_14 & $i(all_57_14)
% 157.85/24.40  | | | 
% 157.85/24.40  | | | ALPHA: (39) implies:
% 157.85/24.40  | | |   (40)  op(e3, e3) = e1
% 157.85/24.40  | | | 
% 157.85/24.40  | | | REF_CLOSE: (8), (16), (20), (40) are inconsistent by sub-proof #834.
% 157.85/24.40  | | | 
% 157.85/24.40  | | End of split
% 157.85/24.40  | | 
% 157.85/24.40  | End of split
% 157.85/24.40  | 
% 157.85/24.40  End of proof
% 157.85/24.40  
% 157.85/24.40  Sub-proof #7 shows that the following formulas are inconsistent:
% 157.85/24.40  ----------------------------------------------------------------
% 157.85/24.40    (1)   ~ (e3 = e2)
% 157.85/24.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.40    (3)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2,
% 157.85/24.40             e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.85/24.40           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 157.85/24.40             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 157.85/24.40           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 157.85/24.40           & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 157.85/24.40           $i(all_57_12))
% 157.85/24.40    (4)  op(e3, e3) = e0
% 157.85/24.40    (5)  op(e3, e2) = e2
% 157.85/24.40    (6)  op(e2, e2) = e3
% 157.85/24.40    (7)   ~ (e2 = e0)
% 157.85/24.40  
% 157.85/24.40  Begin of proof
% 157.85/24.40  | 
% 157.85/24.40  | BETA: splitting (3) gives:
% 157.85/24.40  | 
% 157.85/24.40  | Case 1:
% 157.85/24.40  | | 
% 157.85/24.40  | |   (8)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 157.85/24.40  | |        op(e2, e2) = e2
% 157.85/24.40  | | 
% 157.85/24.40  | | ALPHA: (8) implies:
% 157.85/24.40  | |   (9)  op(e2, e2) = e2
% 157.85/24.40  | | 
% 157.85/24.40  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #54.
% 157.85/24.40  | | 
% 157.85/24.40  | Case 2:
% 157.85/24.40  | | 
% 157.85/24.40  | |   (10)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.85/24.40  | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1
% 157.85/24.40  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 =
% 157.85/24.40  | |           e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 157.85/24.40  | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 157.85/24.40  | |           $i(all_57_12))
% 157.85/24.40  | | 
% 157.85/24.40  | | BETA: splitting (10) gives:
% 157.85/24.40  | | 
% 157.85/24.40  | | Case 1:
% 157.85/24.40  | | | 
% 157.85/24.40  | | |   (11)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.85/24.40  | | |           e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1
% 157.85/24.40  | | |         & op(e1, e1) = e3 & $i(all_57_10)
% 157.85/24.40  | | | 
% 157.85/24.40  | | | ALPHA: (11) implies:
% 157.85/24.40  | | |   (12)  op(e3, e2) = e3
% 157.85/24.40  | | | 
% 157.85/24.40  | | | REF_CLOSE: (1), (2), (5), (12) are inconsistent by sub-proof #433.
% 157.85/24.40  | | | 
% 157.85/24.40  | | Case 2:
% 157.85/24.40  | | | 
% 157.85/24.40  | | |   (13)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 =
% 157.85/24.40  | | |           e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12
% 157.85/24.40  | | |         & op(e2, e1) = e2 & $i(all_57_12)
% 157.85/24.40  | | | 
% 157.85/24.40  | | | ALPHA: (13) implies:
% 157.85/24.40  | | |   (14)  op(e3, e3) = e2
% 157.85/24.40  | | | 
% 157.85/24.40  | | | REF_CLOSE: (2), (4), (7), (14) are inconsistent by sub-proof #281.
% 157.85/24.40  | | | 
% 157.85/24.40  | | End of split
% 157.85/24.40  | | 
% 157.85/24.40  | End of split
% 157.85/24.40  | 
% 157.85/24.40  End of proof
% 157.85/24.40  
% 157.85/24.40  Sub-proof #8 shows that the following formulas are inconsistent:
% 157.85/24.40  ----------------------------------------------------------------
% 157.85/24.40    (1)  op(e1, e1) = e3
% 157.85/24.40    (2)   ~ (e3 = e2)
% 157.85/24.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.40    (4)  op(e3, e1) = all_52_8
% 157.85/24.40    (5)  op(e3, e3) = e0
% 157.85/24.40    (6)  op(e3, e2) = e2
% 157.85/24.40    (7)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 157.85/24.40           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.85/24.40           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 157.85/24.40           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 157.85/24.40           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 157.85/24.40           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 157.85/24.40           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.85/24.40           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 157.85/24.40           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 157.85/24.40             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 157.85/24.40    (8)   ~ (e2 = e0)
% 157.85/24.40    (9)   ~ (all_52_8 = e3)
% 157.85/24.40  
% 157.85/24.40  Begin of proof
% 157.85/24.40  | 
% 157.85/24.40  | BETA: splitting (7) gives:
% 157.85/24.40  | 
% 157.85/24.40  | Case 1:
% 157.85/24.40  | | 
% 157.85/24.40  | |   (10)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 =
% 157.85/24.40  | |             e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 157.85/24.40  | |           op(e2, e2) = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.85/24.40  | |           all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 157.85/24.40  | |           = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3
% 157.85/24.40  | |           & $i(all_57_10))
% 157.85/24.40  | | 
% 157.85/24.40  | | BETA: splitting (10) gives:
% 157.85/24.40  | | 
% 157.85/24.40  | | Case 1:
% 157.85/24.40  | | | 
% 157.85/24.40  | | |   (11)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 =
% 157.85/24.40  | | |           e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 157.85/24.40  | | |         op(e2, e2) = all_57_12 & $i(all_57_12)
% 157.85/24.40  | | | 
% 157.85/24.40  | | | ALPHA: (11) implies:
% 157.85/24.40  | | |   (12)  op(e3, e3) = e2
% 157.85/24.40  | | | 
% 157.85/24.40  | | | REF_CLOSE: (3), (5), (8), (12) are inconsistent by sub-proof #281.
% 157.85/24.40  | | | 
% 157.85/24.40  | | Case 2:
% 157.85/24.40  | | | 
% 157.85/24.40  | | |   (13)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.85/24.40  | | |           e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2
% 157.85/24.40  | | |         & op(e2, e2) = e3 & $i(all_57_10)
% 157.85/24.40  | | | 
% 157.85/24.40  | | | ALPHA: (13) implies:
% 157.85/24.40  | | |   (14)  op(e3, e2) = e3
% 157.85/24.40  | | | 
% 157.85/24.40  | | | REF_CLOSE: (2), (3), (6), (14) are inconsistent by sub-proof #433.
% 157.85/24.40  | | | 
% 157.85/24.40  | | End of split
% 157.85/24.40  | | 
% 157.85/24.40  | Case 2:
% 157.85/24.40  | | 
% 157.85/24.40  | |   (15)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 157.85/24.40  | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 157.85/24.40  | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 =
% 157.85/24.41  | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 157.85/24.41  | |           & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.85/24.41  | |           $i(all_57_10))
% 157.85/24.41  | | 
% 157.85/24.41  | | REF_CLOSE: (1), (2), (3), (4), (9), (15) are inconsistent by sub-proof #23.
% 157.85/24.41  | | 
% 157.85/24.41  | End of split
% 157.85/24.41  | 
% 157.85/24.41  End of proof
% 157.85/24.41  
% 157.85/24.41  Sub-proof #9 shows that the following formulas are inconsistent:
% 157.85/24.41  ----------------------------------------------------------------
% 157.85/24.41    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 157.85/24.41         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 157.85/24.41    (2)  all_56_5 = e2
% 157.85/24.41    (3)   ~ (e3 = e2)
% 157.85/24.41    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.41    (5)  op(e1, e1) = e1
% 157.85/24.41    (6)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 157.85/24.41         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 157.85/24.41    (7)   ~ (e1 = e0)
% 157.85/24.41    (8)  op(e2, e1) = e2
% 157.85/24.41    (9)  all_56_14 = e2
% 157.85/24.41    (10)   ~ (e3 = e1)
% 157.85/24.41    (11)   ~ (e2 = e0)
% 157.85/24.41    (12)   ~ (e3 = e0)
% 157.85/24.41  
% 157.85/24.41  Begin of proof
% 157.85/24.41  | 
% 157.85/24.41  | BETA: splitting (1) gives:
% 157.85/24.41  | 
% 157.85/24.41  | Case 1:
% 157.85/24.41  | | 
% 157.85/24.41  | |   (13)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 157.85/24.41  | |           e0)
% 157.85/24.41  | | 
% 157.85/24.41  | | BETA: splitting (13) gives:
% 157.85/24.41  | | 
% 157.85/24.41  | | Case 1:
% 157.85/24.41  | | | 
% 157.85/24.41  | | |   (14)  all_56_4 = e0 & op(e3, e1) = e0
% 157.85/24.41  | | | 
% 157.85/24.41  | | | ALPHA: (14) implies:
% 157.85/24.41  | | |   (15)  all_56_4 = e0
% 157.85/24.41  | | | 
% 157.85/24.41  | | | BETA: splitting (6) gives:
% 157.85/24.41  | | | 
% 157.85/24.41  | | | Case 1:
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | |   (16)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1)
% 157.85/24.41  | | | |           = e3)
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | BETA: splitting (16) gives:
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | Case 1:
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | |   (17)  all_56_4 = e3 & op(e3, e1) = e3
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | | ALPHA: (17) implies:
% 157.85/24.41  | | | | |   (18)  all_56_4 = e3
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | | REF_CLOSE: (12), (15), (18) are inconsistent by sub-proof #150.
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | Case 2:
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | |   (19)  all_56_5 = e3 & op(e2, e1) = e3
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | | ALPHA: (19) implies:
% 157.85/24.41  | | | | |   (20)  op(e2, e1) = e3
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | | REF_CLOSE: (3), (4), (8), (20) are inconsistent by sub-proof #456.
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | End of split
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | Case 2:
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | |   (21)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1)
% 157.85/24.41  | | | |           = e3)
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | REF_CLOSE: (3), (4), (5), (9), (10), (21) are inconsistent by sub-proof
% 157.85/24.41  | | | |            #247.
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | End of split
% 157.85/24.41  | | | 
% 157.85/24.41  | | Case 2:
% 157.85/24.41  | | | 
% 157.85/24.41  | | |   (22)  all_56_5 = e0 & op(e2, e1) = e0
% 157.85/24.41  | | | 
% 157.85/24.41  | | | REF_CLOSE: (2), (11), (22) are inconsistent by sub-proof #257.
% 157.85/24.41  | | | 
% 157.85/24.41  | | End of split
% 157.85/24.41  | | 
% 157.85/24.41  | Case 2:
% 157.85/24.41  | | 
% 157.85/24.41  | |   (23)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 157.85/24.41  | |           e0)
% 157.85/24.41  | | 
% 157.85/24.41  | | BETA: splitting (23) gives:
% 157.85/24.41  | | 
% 157.85/24.41  | | Case 1:
% 157.85/24.41  | | | 
% 157.85/24.41  | | |   (24)  all_56_8 = e0 & op(e1, e1) = e0
% 157.85/24.41  | | | 
% 157.85/24.41  | | | ALPHA: (24) implies:
% 157.85/24.41  | | |   (25)  op(e1, e1) = e0
% 157.85/24.41  | | | 
% 157.85/24.41  | | | REF_CLOSE: (4), (5), (7), (25) are inconsistent by sub-proof #903.
% 157.85/24.41  | | | 
% 157.85/24.41  | | Case 2:
% 157.85/24.41  | | | 
% 157.85/24.41  | | |   (26)  all_56_14 = e0 & op(e0, e1) = e0
% 157.85/24.41  | | | 
% 157.85/24.41  | | | REF_CLOSE: (9), (11), (26) are inconsistent by sub-proof #725.
% 157.85/24.41  | | | 
% 157.85/24.41  | | End of split
% 157.85/24.41  | | 
% 157.85/24.41  | End of split
% 157.85/24.41  | 
% 157.85/24.41  End of proof
% 157.85/24.41  
% 157.85/24.41  Sub-proof #10 shows that the following formulas are inconsistent:
% 157.85/24.41  ----------------------------------------------------------------
% 157.85/24.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.41    (2)   ~ (all_52_1 = e0)
% 157.85/24.41    (3)  op(e2, e3) = all_52_1
% 157.85/24.41    (4)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 157.85/24.41    (5)  op(e2, e2) = e3
% 157.85/24.41    (6)   ~ (e3 = e0)
% 157.85/24.41  
% 157.85/24.41  Begin of proof
% 157.85/24.41  | 
% 157.85/24.41  | BETA: splitting (4) gives:
% 157.85/24.41  | 
% 157.85/24.41  | Case 1:
% 157.85/24.41  | | 
% 157.85/24.41  | |   (7)  all_56_2 = e0 & op(e2, e3) = e0
% 157.85/24.41  | | 
% 157.85/24.41  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #80.
% 157.85/24.41  | | 
% 157.85/24.41  | Case 2:
% 157.85/24.41  | | 
% 157.85/24.41  | |   (8)  all_56_3 = e0 & op(e2, e2) = e0
% 157.85/24.41  | | 
% 157.85/24.41  | | ALPHA: (8) implies:
% 157.85/24.41  | |   (9)  op(e2, e2) = e0
% 157.85/24.41  | | 
% 157.85/24.41  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #945.
% 157.85/24.41  | | 
% 157.85/24.41  | End of split
% 157.85/24.41  | 
% 157.85/24.41  End of proof
% 157.85/24.41  
% 157.85/24.41  Sub-proof #11 shows that the following formulas are inconsistent:
% 157.85/24.41  ----------------------------------------------------------------
% 157.85/24.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.41    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1)
% 157.85/24.41    (3)  op(e3, e3) = e0
% 157.85/24.41    (4)  all_56_1 = e2
% 157.85/24.41    (5)   ~ (e1 = e0)
% 157.85/24.41    (6)   ~ (e2 = e1)
% 157.85/24.41  
% 157.85/24.41  Begin of proof
% 157.85/24.41  | 
% 157.85/24.41  | BETA: splitting (2) gives:
% 157.85/24.41  | 
% 157.85/24.41  | Case 1:
% 157.85/24.41  | | 
% 157.85/24.41  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 157.85/24.41  | | 
% 157.85/24.41  | | ALPHA: (7) implies:
% 157.85/24.41  | |   (8)  op(e3, e3) = e1
% 157.85/24.41  | | 
% 157.85/24.41  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #834.
% 157.85/24.41  | | 
% 157.85/24.41  | Case 2:
% 157.85/24.41  | | 
% 157.85/24.41  | |   (9)  all_56_1 = e1 & op(e3, e2) = e1
% 157.85/24.41  | | 
% 157.85/24.41  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #911.
% 157.85/24.41  | | 
% 157.85/24.41  | End of split
% 157.85/24.41  | 
% 157.85/24.41  End of proof
% 157.85/24.41  
% 157.85/24.41  Sub-proof #12 shows that the following formulas are inconsistent:
% 157.85/24.41  ----------------------------------------------------------------
% 157.85/24.41    (1)   ~ (all_52_12 = e2)
% 157.85/24.41    (2)   ~ (all_52_13 = all_14_2)
% 157.85/24.41    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.41    (4)  op(e1, e1) = e2
% 157.85/24.41    (5)   ~ (all_52_13 = e3)
% 157.85/24.41    (6)  op(e1, e0) = all_52_14
% 157.85/24.41    (7)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 157.85/24.41         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 157.85/24.41    (8)   ~ (all_52_14 = e2)
% 157.85/24.41    (9)  op(e0, e0) = all_14_2
% 157.85/24.41    (10)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.85/24.41    (11)  op(e2, e0) = all_52_13
% 157.85/24.41    (12)  op(e2, e2) = e3
% 157.85/24.41    (13)   ~ (e2 = e1)
% 157.85/24.41    (14)  op(e3, e0) = all_52_12
% 157.85/24.41    (15)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 157.85/24.41              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.85/24.41            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 157.85/24.41                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 157.85/24.41              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 157.85/24.41          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 157.85/24.41              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.85/24.41            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 157.85/24.41                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.85/24.41                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 157.85/24.41                $i(all_57_13))))
% 157.85/24.41    (16)  all_54_7 = all_52_13
% 157.85/24.41    (17)   ~ (e2 = e0)
% 157.85/24.41    (18)   ~ (e3 = e0)
% 157.85/24.41  
% 157.85/24.41  Begin of proof
% 157.85/24.41  | 
% 157.85/24.41  | BETA: splitting (15) gives:
% 157.85/24.41  | 
% 157.85/24.41  | Case 1:
% 157.85/24.41  | | 
% 157.85/24.41  | |   (19)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 157.85/24.41  | |             e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 157.85/24.41  | |             $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.85/24.41  | |             (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 157.85/24.41  | |         ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.85/24.41  | |               e1) = all_57_8 & $i(all_57_8)))
% 157.85/24.41  | | 
% 157.85/24.41  | | ALPHA: (19) implies:
% 157.85/24.41  | |   (20)  op(e1, e1) = e1
% 157.85/24.41  | | 
% 157.85/24.41  | | REF_CLOSE: (3), (4), (13), (20) are inconsistent by sub-proof #986.
% 157.85/24.41  | | 
% 157.85/24.41  | Case 2:
% 157.85/24.41  | | 
% 157.85/24.41  | |   (21)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 157.85/24.41  | |             e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 157.85/24.41  | |             $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.85/24.41  | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 157.85/24.41  | |         ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.85/24.41  | |               e0) = all_57_13 & $i(all_57_13)))
% 157.85/24.41  | | 
% 157.85/24.41  | | ALPHA: (21) implies:
% 157.85/24.41  | |   (22)  op(e0, e0) = e0
% 157.85/24.41  | |   (23)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.85/24.41  | |             e0) = all_57_13 & $i(all_57_13))
% 157.85/24.41  | |   (24)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 157.85/24.41  | |             e0) = all_57_11 & $i(all_57_11))
% 157.85/24.41  | | 
% 157.85/24.41  | | BETA: splitting (24) gives:
% 157.85/24.41  | | 
% 157.85/24.41  | | Case 1:
% 157.85/24.41  | | | 
% 157.85/24.41  | | |   (25)  all_57_12 = e0 & op(e2, e2) = e0
% 157.85/24.41  | | | 
% 157.85/24.41  | | | ALPHA: (25) implies:
% 157.85/24.41  | | |   (26)  op(e2, e2) = e0
% 157.85/24.41  | | | 
% 157.85/24.41  | | | REF_CLOSE: (3), (12), (18), (26) are inconsistent by sub-proof #945.
% 157.85/24.41  | | | 
% 157.85/24.41  | | Case 2:
% 157.85/24.41  | | | 
% 157.85/24.41  | | |   (27)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11)
% 157.85/24.41  | | | 
% 157.85/24.41  | | | ALPHA: (27) implies:
% 157.85/24.41  | | |   (28)   ~ (all_57_11 = e2)
% 157.85/24.41  | | |   (29)  op(e2, e0) = all_57_11
% 157.85/24.41  | | | 
% 157.85/24.41  | | | BETA: splitting (23) gives:
% 157.85/24.41  | | | 
% 157.85/24.41  | | | Case 1:
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | |   (30)  all_57_14 = e0 & op(e1, e1) = e0
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | ALPHA: (30) implies:
% 157.85/24.41  | | | |   (31)  op(e1, e1) = e0
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | REF_CLOSE: (3), (4), (17), (31) are inconsistent by sub-proof #914.
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | Case 2:
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | |   (32)   ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13)
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | ALPHA: (32) implies:
% 157.85/24.41  | | | |   (33)  op(e1, e0) = all_57_13
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | GROUND_INST: instantiating (3) with all_14_2, e0, e0, e0, simplifying
% 157.85/24.41  | | | |              with (9), (22) gives:
% 157.85/24.41  | | | |   (34)  all_14_2 = e0
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | GROUND_INST: instantiating (3) with all_52_14, all_57_13, e0, e1,
% 157.85/24.41  | | | |              simplifying with (6), (33) gives:
% 157.85/24.41  | | | |   (35)  all_57_13 = all_52_14
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | GROUND_INST: instantiating (3) with all_52_13, all_57_11, e0, e2,
% 157.85/24.41  | | | |              simplifying with (11), (29) gives:
% 157.85/24.41  | | | |   (36)  all_57_11 = all_52_13
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | REDUCE: (28), (36) imply:
% 157.85/24.41  | | | |   (37)   ~ (all_52_13 = e2)
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | REDUCE: (2), (34) imply:
% 157.85/24.41  | | | |   (38)   ~ (all_52_13 = e0)
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | BETA: splitting (10) gives:
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | | Case 1:
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | |   (39)  all_54_7 = e3
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | | REF_CLOSE: (5), (16), (39) are inconsistent by sub-proof #383.
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | Case 2:
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | |   (40)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | | BETA: splitting (40) gives:
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | | Case 1:
% 157.85/24.41  | | | | | | 
% 157.85/24.41  | | | | | |   (41)  all_54_7 = e2
% 157.85/24.41  | | | | | | 
% 157.85/24.41  | | | | | | REF_CLOSE: (16), (37), (41) are inconsistent by sub-proof #382.
% 157.85/24.41  | | | | | | 
% 157.85/24.41  | | | | | Case 2:
% 157.85/24.41  | | | | | | 
% 157.85/24.41  | | | | | |   (42)   ~ (all_54_7 = e2)
% 157.85/24.41  | | | | | |   (43)  all_54_7 = e1 | all_54_7 = e0
% 157.85/24.41  | | | | | | 
% 157.85/24.41  | | | | | | BETA: splitting (43) gives:
% 157.85/24.41  | | | | | | 
% 157.85/24.41  | | | | | | Case 1:
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | |   (44)  all_54_7 = e1
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | | COMBINE_EQS: (16), (44) imply:
% 157.85/24.41  | | | | | | |   (45)  all_52_13 = e1
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | | SIMP: (45) implies:
% 157.85/24.41  | | | | | | |   (46)  all_52_13 = e1
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | | REDUCE: (37), (46) imply:
% 157.85/24.41  | | | | | | |   (47)   ~ (e2 = e1)
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | | REDUCE: (11), (46) imply:
% 157.85/24.41  | | | | | | |   (48)  op(e2, e0) = e1
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | | BETA: splitting (7) gives:
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | | Case 1:
% 157.85/24.41  | | | | | | | | 
% 157.85/24.41  | | | | | | | |   (49)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 &
% 157.85/24.41  | | | | | | | |           op(e2, e0) = e2)
% 157.85/24.41  | | | | | | | | 
% 157.85/24.41  | | | | | | | | REF_CLOSE: (1), (3), (13), (14), (48), (49) are inconsistent by
% 157.85/24.41  | | | | | | | |            sub-proof #225.
% 157.85/24.41  | | | | | | | | 
% 157.85/24.41  | | | | | | | Case 2:
% 157.85/24.41  | | | | | | | | 
% 157.85/24.41  | | | | | | | |   (50)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 &
% 157.85/24.41  | | | | | | | |           op(e0, e0) = e2)
% 157.85/24.41  | | | | | | | | 
% 157.85/24.41  | | | | | | | | BETA: splitting (50) gives:
% 157.85/24.41  | | | | | | | | 
% 157.85/24.41  | | | | | | | | Case 1:
% 157.85/24.41  | | | | | | | | | 
% 157.85/24.41  | | | | | | | | |   (51)  all_56_11 = e2 & op(e1, e0) = e2
% 157.85/24.41  | | | | | | | | | 
% 157.85/24.41  | | | | | | | | | REF_CLOSE: (3), (6), (8), (51) are inconsistent by sub-proof
% 157.85/24.41  | | | | | | | | |            #879.
% 157.85/24.41  | | | | | | | | | 
% 157.85/24.41  | | | | | | | | Case 2:
% 157.85/24.41  | | | | | | | | | 
% 157.85/24.41  | | | | | | | | |   (52)  all_56_15 = e2 & op(e0, e0) = e2
% 157.85/24.41  | | | | | | | | | 
% 157.85/24.41  | | | | | | | | | ALPHA: (52) implies:
% 157.85/24.41  | | | | | | | | |   (53)  op(e0, e0) = e2
% 157.85/24.41  | | | | | | | | | 
% 157.85/24.41  | | | | | | | | | REF_CLOSE: (3), (17), (22), (53) are inconsistent by sub-proof
% 157.85/24.41  | | | | | | | | |            #979.
% 157.85/24.41  | | | | | | | | | 
% 157.85/24.41  | | | | | | | | End of split
% 157.85/24.41  | | | | | | | | 
% 157.85/24.41  | | | | | | | End of split
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | Case 2:
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | |   (54)  all_54_7 = e0
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | | REF_CLOSE: (16), (38), (54) are inconsistent by sub-proof #368.
% 157.85/24.41  | | | | | | | 
% 157.85/24.41  | | | | | | End of split
% 157.85/24.41  | | | | | | 
% 157.85/24.41  | | | | | End of split
% 157.85/24.41  | | | | | 
% 157.85/24.41  | | | | End of split
% 157.85/24.41  | | | | 
% 157.85/24.41  | | | End of split
% 157.85/24.41  | | | 
% 157.85/24.41  | | End of split
% 157.85/24.41  | | 
% 157.85/24.41  | End of split
% 157.85/24.41  | 
% 157.85/24.41  End of proof
% 157.85/24.41  
% 157.85/24.41  Sub-proof #13 shows that the following formulas are inconsistent:
% 157.85/24.41  ----------------------------------------------------------------
% 157.85/24.41    (1)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 157.85/24.41    (2)   ~ (e3 = e2)
% 157.85/24.41    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.41    (4)  op(e2, e3) = e1
% 157.85/24.41    (5)  op(e2, e2) = e3
% 157.85/24.41    (6)   ~ (e2 = e1)
% 157.85/24.41  
% 157.85/24.41  Begin of proof
% 157.85/24.41  | 
% 157.85/24.41  | BETA: splitting (1) gives:
% 157.85/24.41  | 
% 157.85/24.41  | Case 1:
% 157.85/24.41  | | 
% 157.85/24.42  | |   (7)  all_56_2 = e2 & op(e2, e3) = e2
% 157.85/24.42  | | 
% 157.85/24.42  | | ALPHA: (7) implies:
% 157.85/24.42  | |   (8)  op(e2, e3) = e2
% 157.85/24.42  | | 
% 157.85/24.42  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #428.
% 157.85/24.42  | | 
% 157.85/24.42  | Case 2:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (9)  all_56_3 = e2 & op(e2, e2) = e2
% 157.85/24.42  | | 
% 157.85/24.42  | | ALPHA: (9) implies:
% 157.85/24.42  | |   (10)  op(e2, e2) = e2
% 157.85/24.42  | | 
% 157.85/24.42  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #54.
% 157.85/24.42  | | 
% 157.85/24.42  | End of split
% 157.85/24.42  | 
% 157.85/24.42  End of proof
% 157.85/24.42  
% 157.85/24.42  Sub-proof #14 shows that the following formulas are inconsistent:
% 157.85/24.42  ----------------------------------------------------------------
% 157.85/24.42    (1)  all_54_2 = all_52_8
% 157.85/24.42    (2)   ~ (all_52_8 = e0)
% 157.85/24.42    (3)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.85/24.42    (4)   ~ (all_52_8 = e1)
% 157.85/24.42    (5)   ~ (all_52_8 = e2)
% 157.85/24.42  
% 157.85/24.42  Begin of proof
% 157.85/24.42  | 
% 157.85/24.42  | BETA: splitting (3) gives:
% 157.85/24.42  | 
% 157.85/24.42  | Case 1:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (6)  all_54_2 = e2
% 157.85/24.42  | | 
% 157.85/24.42  | | COMBINE_EQS: (1), (6) imply:
% 157.85/24.42  | |   (7)  all_52_8 = e2
% 157.85/24.42  | | 
% 157.85/24.42  | | REDUCE: (5), (7) imply:
% 157.85/24.42  | |   (8)  $false
% 157.85/24.42  | | 
% 157.85/24.42  | | CLOSE: (8) is inconsistent.
% 157.85/24.42  | | 
% 157.85/24.42  | Case 2:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (9)  all_54_2 = e1 | all_54_2 = e0
% 157.85/24.42  | | 
% 157.85/24.42  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #364.
% 157.85/24.42  | | 
% 157.85/24.42  | End of split
% 157.85/24.42  | 
% 157.85/24.42  End of proof
% 157.85/24.42  
% 157.85/24.42  Sub-proof #15 shows that the following formulas are inconsistent:
% 157.85/24.42  ----------------------------------------------------------------
% 157.85/24.42    (1)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 157.85/24.42           all_57_0 & $i(all_57_0))
% 157.85/24.42    (2)   ~ (all_57_12 = e3)
% 157.85/24.42    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.42    (4)  op(e2, e3) = e2
% 157.85/24.42  
% 157.85/24.42  Begin of proof
% 157.85/24.42  | 
% 157.85/24.42  | BETA: splitting (1) gives:
% 157.85/24.42  | 
% 157.85/24.42  | Case 1:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (5)  all_57_12 = e3 & op(e2, e2) = e3
% 157.85/24.42  | | 
% 157.85/24.42  | | ALPHA: (5) implies:
% 157.85/24.42  | |   (6)  all_57_12 = e3
% 157.85/24.42  | | 
% 157.85/24.42  | | REDUCE: (2), (6) imply:
% 157.85/24.42  | |   (7)  $false
% 157.85/24.42  | | 
% 157.85/24.42  | | CLOSE: (7) is inconsistent.
% 157.85/24.42  | | 
% 157.85/24.42  | Case 2:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (8)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0)
% 157.85/24.42  | | 
% 157.85/24.42  | | ALPHA: (8) implies:
% 157.85/24.42  | |   (9)   ~ (all_57_0 = e2)
% 157.85/24.42  | |   (10)  op(e2, e3) = all_57_0
% 157.85/24.42  | | 
% 157.85/24.42  | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #783.
% 157.85/24.42  | | 
% 157.85/24.42  | End of split
% 157.85/24.42  | 
% 157.85/24.42  End of proof
% 157.85/24.42  
% 157.85/24.42  Sub-proof #16 shows that the following formulas are inconsistent:
% 157.85/24.42  ----------------------------------------------------------------
% 157.85/24.42    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 157.85/24.42         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 157.85/24.42    (2)   ~ (e3 = e2)
% 157.85/24.42    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.42    (4)  op(e3, e1) = all_52_8
% 157.85/24.42    (5)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 157.85/24.42             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.85/24.42           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 157.85/24.42           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 157.85/24.42    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 157.85/24.42         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 157.85/24.42    (7)  all_56_1 = e2
% 157.85/24.42    (8)  all_56_9 = e1
% 157.85/24.42    (9)  op(e3, e2) = e2
% 157.85/24.42    (10)   ~ (e1 = e0)
% 157.85/24.42    (11)   ~ (e3 = e1)
% 157.85/24.42    (12)   ~ (e2 = e0)
% 157.85/24.42    (13)   ~ (all_52_8 = e3)
% 157.85/24.42    (14)   ~ (e3 = e0)
% 157.85/24.42  
% 157.85/24.42  Begin of proof
% 157.85/24.42  | 
% 157.85/24.42  | BETA: splitting (5) gives:
% 157.85/24.42  | 
% 157.85/24.42  | Case 1:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (15)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 157.85/24.42  | |         op(e3, e1) = e3
% 157.85/24.42  | | 
% 157.85/24.42  | | ALPHA: (15) implies:
% 157.85/24.42  | |   (16)  op(e3, e1) = e3
% 157.85/24.42  | | 
% 157.85/24.42  | | REF_CLOSE: (3), (4), (13), (16) are inconsistent by sub-proof #982.
% 157.85/24.42  | | 
% 157.85/24.42  | Case 2:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (17)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 157.85/24.42  | |           e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 157.85/24.42  | |         op(e1, e0) = e1 & $i(all_57_14)
% 157.85/24.42  | | 
% 157.85/24.42  | | ALPHA: (17) implies:
% 157.85/24.42  | |   (18)  op(e3, e3) = e1
% 157.85/24.42  | | 
% 157.85/24.42  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (14), (18)
% 157.85/24.42  | |            are inconsistent by sub-proof #148.
% 157.85/24.42  | | 
% 157.85/24.42  | End of split
% 157.85/24.42  | 
% 157.85/24.42  End of proof
% 157.85/24.42  
% 157.85/24.42  Sub-proof #17 shows that the following formulas are inconsistent:
% 157.85/24.42  ----------------------------------------------------------------
% 157.85/24.42    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 157.85/24.42         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 157.85/24.42    (2)   ~ (e3 = e2)
% 157.85/24.42    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.42    (4)  op(e1, e1) = e2
% 157.85/24.42    (5)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 157.85/24.42         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 157.85/24.42    (6)  all_56_14 = e3
% 157.85/24.42    (7)  all_56_5 = e1
% 157.85/24.42    (8)   ~ (e1 = e0)
% 157.85/24.42    (9)   ~ (e3 = e1)
% 157.85/24.42    (10)  e3 = e1
% 157.85/24.42    (11)   ~ (e2 = e0)
% 157.85/24.42    (12)   ~ (e3 = e0)
% 157.85/24.42  
% 157.85/24.42  Begin of proof
% 157.85/24.42  | 
% 157.85/24.42  | COMBINE_EQS: (6), (10) imply:
% 157.85/24.42  |   (13)  all_56_14 = e1
% 157.85/24.42  | 
% 157.85/24.42  | BETA: splitting (1) gives:
% 157.85/24.42  | 
% 157.85/24.42  | Case 1:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (14)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 157.85/24.42  | |           e0)
% 157.85/24.42  | | 
% 157.85/24.42  | | BETA: splitting (14) gives:
% 157.85/24.42  | | 
% 157.85/24.42  | | Case 1:
% 157.85/24.42  | | | 
% 157.85/24.42  | | |   (15)  all_56_4 = e0 & op(e3, e1) = e0
% 157.85/24.42  | | | 
% 157.85/24.42  | | | ALPHA: (15) implies:
% 157.85/24.42  | | |   (16)  all_56_4 = e0
% 157.85/24.42  | | | 
% 157.85/24.42  | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (12), (13), (16) are inconsistent
% 157.85/24.42  | | |            by sub-proof #125.
% 157.85/24.42  | | | 
% 157.85/24.42  | | Case 2:
% 157.85/24.42  | | | 
% 157.85/24.42  | | |   (17)  all_56_5 = e0 & op(e2, e1) = e0
% 157.85/24.42  | | | 
% 157.85/24.42  | | | ALPHA: (17) implies:
% 157.85/24.42  | | |   (18)  all_56_5 = e0
% 157.85/24.42  | | | 
% 157.85/24.42  | | | COMBINE_EQS: (7), (18) imply:
% 157.85/24.42  | | |   (19)  e1 = e0
% 157.85/24.42  | | | 
% 157.85/24.42  | | | REDUCE: (8), (19) imply:
% 157.85/24.42  | | |   (20)  $false
% 157.85/24.42  | | | 
% 157.85/24.42  | | | CLOSE: (20) is inconsistent.
% 157.85/24.42  | | | 
% 157.85/24.42  | | End of split
% 157.85/24.42  | | 
% 157.85/24.42  | Case 2:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (21)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 157.85/24.42  | |           e0)
% 157.85/24.42  | | 
% 157.85/24.42  | | BETA: splitting (21) gives:
% 157.85/24.42  | | 
% 157.85/24.42  | | Case 1:
% 157.85/24.42  | | | 
% 157.85/24.42  | | |   (22)  all_56_8 = e0 & op(e1, e1) = e0
% 157.85/24.42  | | | 
% 157.85/24.42  | | | ALPHA: (22) implies:
% 157.85/24.42  | | |   (23)  op(e1, e1) = e0
% 157.85/24.42  | | | 
% 157.85/24.42  | | | REF_CLOSE: (3), (4), (11), (23) are inconsistent by sub-proof #914.
% 157.85/24.42  | | | 
% 157.85/24.42  | | Case 2:
% 157.85/24.42  | | | 
% 157.85/24.42  | | |   (24)  all_56_14 = e0 & op(e0, e1) = e0
% 157.85/24.42  | | | 
% 157.85/24.42  | | | ALPHA: (24) implies:
% 157.85/24.42  | | |   (25)  all_56_14 = e0
% 157.85/24.42  | | | 
% 157.85/24.42  | | | REF_CLOSE: (8), (13), (25) are inconsistent by sub-proof #542.
% 157.85/24.42  | | | 
% 157.85/24.42  | | End of split
% 157.85/24.42  | | 
% 157.85/24.42  | End of split
% 157.85/24.42  | 
% 157.85/24.42  End of proof
% 157.85/24.42  
% 157.85/24.42  Sub-proof #18 shows that the following formulas are inconsistent:
% 157.85/24.42  ----------------------------------------------------------------
% 157.85/24.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.42    (2)  op(e3, e3) = all_40_1
% 157.85/24.42    (3)  op(e3, e3) = e0
% 157.85/24.42    (4)   ~ (all_40_1 = e0)
% 157.85/24.42  
% 157.85/24.42  Begin of proof
% 157.85/24.42  | 
% 157.85/24.42  | GROUND_INST: instantiating (1) with e0, all_40_1, e3, e3, simplifying with
% 157.85/24.42  |              (2), (3) gives:
% 157.85/24.42  |   (5)  all_40_1 = e0
% 157.85/24.42  | 
% 157.85/24.42  | REDUCE: (4), (5) imply:
% 157.85/24.42  |   (6)  $false
% 157.85/24.42  | 
% 157.85/24.42  | CLOSE: (6) is inconsistent.
% 157.85/24.42  | 
% 157.85/24.42  End of proof
% 157.85/24.42  
% 157.85/24.42  Sub-proof #19 shows that the following formulas are inconsistent:
% 157.85/24.42  ----------------------------------------------------------------
% 157.85/24.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.42    (2)  op(e0, e3) = all_52_3
% 157.85/24.42    (3)   ~ (all_52_12 = e3)
% 157.85/24.42    (4)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 157.85/24.42           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 157.85/24.42           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 157.85/24.42           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 157.85/24.42    (5)  all_56_14 = e3
% 157.85/24.42    (6)  op(e0, e2) = all_52_7
% 157.85/24.42    (7)   ~ (all_52_3 = e1)
% 157.85/24.42    (8)   ~ (e2 = e1)
% 157.85/24.42    (9)  op(e3, e0) = all_52_12
% 157.85/24.42    (10)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 157.85/24.42          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 157.85/24.42            e1)
% 157.85/24.42    (11)   ~ (all_52_7 = e1)
% 157.85/24.42    (12)   ~ (e3 = e1)
% 157.85/24.42  
% 157.85/24.42  Begin of proof
% 157.85/24.42  | 
% 157.85/24.42  | BETA: splitting (4) gives:
% 157.85/24.42  | 
% 157.85/24.42  | Case 1:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (13)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 157.85/24.42  | |           e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 &
% 157.85/24.42  | |         op(e0, e0) = e2 & $i(all_57_12)
% 157.85/24.42  | | 
% 157.85/24.42  | | ALPHA: (13) implies:
% 157.85/24.42  | |   (14)  op(e0, e0) = e2
% 157.85/24.42  | | 
% 157.85/24.42  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (14) are
% 157.85/24.42  | |            inconsistent by sub-proof #666.
% 157.85/24.42  | | 
% 157.85/24.42  | Case 2:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (15)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 157.85/24.42  | |         op(e3, e0) = e3
% 157.85/24.42  | | 
% 157.85/24.42  | | ALPHA: (15) implies:
% 157.85/24.42  | |   (16)  op(e3, e0) = e3
% 157.85/24.42  | | 
% 157.85/24.42  | | REF_CLOSE: (1), (3), (9), (16) are inconsistent by sub-proof #976.
% 157.85/24.42  | | 
% 157.85/24.42  | End of split
% 157.85/24.42  | 
% 157.85/24.42  End of proof
% 157.85/24.42  
% 157.85/24.42  Sub-proof #20 shows that the following formulas are inconsistent:
% 157.85/24.42  ----------------------------------------------------------------
% 157.85/24.42    (1)   ~ (e3 = e2)
% 157.85/24.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.42    (3)  op(e0, e3) = all_52_3
% 157.85/24.42    (4)  all_56_14 = e3
% 157.85/24.42    (5)  op(e0, e2) = all_52_7
% 157.85/24.42    (6)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 157.85/24.42           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 157.85/24.42           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 157.85/24.42           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 157.85/24.42    (7)   ~ (all_52_3 = e1)
% 157.85/24.42    (8)  op(e2, e2) = e3
% 157.85/24.42    (9)   ~ (e2 = e1)
% 157.85/24.42    (10)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 157.85/24.42          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 157.85/24.42            e1)
% 157.85/24.42    (11)   ~ (all_52_7 = e1)
% 157.85/24.42    (12)   ~ (e3 = e1)
% 157.85/24.42  
% 157.85/24.42  Begin of proof
% 157.85/24.42  | 
% 157.85/24.42  | BETA: splitting (6) gives:
% 157.85/24.42  | 
% 157.85/24.42  | Case 1:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (13)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 157.85/24.42  | |         & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 &
% 157.85/24.42  | |         op(e0, e0) = e2 & $i(all_57_12)
% 157.85/24.42  | | 
% 157.85/24.42  | | ALPHA: (13) implies:
% 157.85/24.42  | |   (14)  op(e0, e0) = e2
% 157.85/24.42  | | 
% 157.85/24.42  | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (12), (14) are
% 157.85/24.42  | |            inconsistent by sub-proof #666.
% 157.85/24.42  | | 
% 157.85/24.42  | Case 2:
% 157.85/24.42  | | 
% 157.85/24.42  | |   (15)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 157.85/24.42  | |         op(e2, e1) = e2
% 157.85/24.42  | | 
% 157.85/24.42  | | ALPHA: (15) implies:
% 157.85/24.42  | |   (16)  op(e2, e2) = e2
% 157.85/24.42  | | 
% 157.85/24.42  | | REF_CLOSE: (1), (2), (8), (16) are inconsistent by sub-proof #54.
% 157.85/24.42  | | 
% 157.85/24.42  | End of split
% 157.85/24.42  | 
% 157.85/24.42  End of proof
% 157.85/24.42  
% 157.85/24.42  Sub-proof #21 shows that the following formulas are inconsistent:
% 157.85/24.42  ----------------------------------------------------------------
% 157.85/24.42    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 157.85/24.42         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 157.85/24.42    (2)  op(e0, e0) = e1
% 157.85/24.42    (3)  op(e1, e1) = e3
% 157.85/24.43    (4)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 157.85/24.43             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.85/24.43           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 157.85/24.43               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 157.85/24.43             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 157.85/24.43         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 157.85/24.43             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.85/24.43           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 157.85/24.43               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 157.85/24.43             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 157.85/24.43         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 157.85/24.43             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.85/24.43           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 157.85/24.43               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 157.85/24.43             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 157.85/24.43         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 157.85/24.43             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.85/24.43           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 157.85/24.43               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 157.85/24.43             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 157.85/24.43    (5)  op(e0, e1) = all_52_11
% 157.85/24.43    (6)   ~ (e3 = e2)
% 157.85/24.43    (7)   ~ (all_52_7 = e3)
% 157.85/24.43    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.43    (9)  op(e0, e2) = all_52_7
% 157.85/24.43    (10)  op(e0, e0) = all_14_2
% 157.85/24.43    (11)   ~ (e1 = e0)
% 157.85/24.43    (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 157.85/24.43          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 157.85/24.43    (13)  op(e2, e2) = e3
% 157.85/24.43    (14)   ~ (e2 = e1)
% 157.85/24.43    (15)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 157.85/24.43          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 157.85/24.43            e3)
% 157.85/24.43    (16)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 157.85/24.43          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 157.85/24.43    (17)   ~ (e3 = e1)
% 157.85/24.43    (18)   ~ (e2 = e0)
% 157.85/24.43    (19)   ~ (all_52_11 = e3)
% 157.85/24.43    (20)   ~ (e3 = e0)
% 157.85/24.43  
% 157.85/24.43  Begin of proof
% 157.85/24.43  | 
% 157.85/24.43  | BETA: splitting (15) gives:
% 157.85/24.43  | 
% 157.85/24.43  | Case 1:
% 157.85/24.43  | | 
% 157.85/24.43  | |   (21)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 157.85/24.43  | |           e3)
% 157.85/24.43  | | 
% 157.85/24.43  | | BETA: splitting (21) gives:
% 157.85/24.43  | | 
% 157.85/24.43  | | Case 1:
% 157.85/24.43  | | | 
% 157.85/24.43  | | |   (22)  all_56_12 = e3 & op(e0, e3) = e3
% 157.85/24.43  | | | 
% 157.85/24.43  | | | ALPHA: (22) implies:
% 157.85/24.43  | | |   (23)  all_56_12 = e3
% 157.85/24.43  | | | 
% 157.85/24.43  | | | BETA: splitting (4) gives:
% 157.85/24.43  | | | 
% 157.85/24.43  | | | Case 1:
% 157.85/24.43  | | | | 
% 157.85/24.43  | | | |   (24)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2,
% 157.85/24.43  | | | |                 e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0
% 157.85/24.43  | | | |               & $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | (
% 157.85/24.43  | | | |               ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)))
% 157.85/24.43  | | | |           & ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 157.85/24.43  | | | |               op(e0, e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2
% 157.85/24.43  | | | |           & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 157.85/24.43  | | | |               (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.85/24.43  | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 157.85/24.43  | | | |               op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2
% 157.85/24.43  | | | |               & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 157.85/24.43  | | | |               all_57_7 & $i(all_57_7))))
% 157.85/24.43  | | | | 
% 157.85/24.43  | | | | REF_CLOSE: (1), (6), (8), (11), (12), (13), (14), (16), (17), (18),
% 157.85/24.43  | | | |            (20), (23), (24) are inconsistent by sub-proof #22.
% 157.85/24.43  | | | | 
% 157.85/24.43  | | | Case 2:
% 157.85/24.43  | | | | 
% 157.85/24.43  | | | |   (25)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 157.85/24.43  | | | |                 e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4
% 157.85/24.43  | | | |               & $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | (
% 157.85/24.43  | | | |               ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)))
% 157.85/24.43  | | | |           & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 157.85/24.43  | | | |               op(e0, e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0
% 157.85/24.43  | | | |           & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 157.85/24.43  | | | |               (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.85/24.43  | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 157.85/24.43  | | | |               op(e2, e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 =
% 157.85/24.43  | | | |               e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0)
% 157.85/24.43  | | | |               = all_57_13 & $i(all_57_13))))
% 157.85/24.43  | | | | 
% 157.85/24.43  | | | | REF_CLOSE: (2), (3), (8), (10), (11), (17), (25) are inconsistent by
% 157.85/24.43  | | | |            sub-proof #297.
% 157.85/24.43  | | | | 
% 157.85/24.43  | | | End of split
% 157.85/24.43  | | | 
% 157.85/24.43  | | Case 2:
% 157.85/24.43  | | | 
% 157.85/24.43  | | |   (26)  all_56_13 = e3 & op(e0, e2) = e3
% 157.85/24.43  | | | 
% 157.85/24.43  | | | REF_CLOSE: (7), (8), (9), (26) are inconsistent by sub-proof #429.
% 157.85/24.43  | | | 
% 157.85/24.43  | | End of split
% 157.85/24.43  | | 
% 157.85/24.43  | Case 2:
% 157.85/24.43  | | 
% 157.85/24.43  | |   (27)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 157.85/24.43  | |           e3)
% 157.85/24.43  | | 
% 157.85/24.43  | | REF_CLOSE: (2), (5), (8), (17), (19), (27) are inconsistent by sub-proof
% 157.85/24.43  | |            #290.
% 157.85/24.43  | | 
% 157.85/24.43  | End of split
% 157.85/24.43  | 
% 157.85/24.43  End of proof
% 157.85/24.43  
% 157.85/24.43  Sub-proof #22 shows that the following formulas are inconsistent:
% 157.85/24.43  ----------------------------------------------------------------
% 157.85/24.43    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 157.85/24.43         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 157.85/24.43    (2)   ~ (e3 = e2)
% 157.85/24.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.43    (4)  all_56_12 = e3
% 157.85/24.43    (5)   ~ (e1 = e0)
% 157.85/24.43    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 157.85/24.43         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 157.85/24.43    (7)  op(e2, e2) = e3
% 157.85/24.43    (8)   ~ (e2 = e1)
% 157.85/24.43    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 157.85/24.43         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 157.85/24.43    (10)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 157.85/24.43              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.85/24.43            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 157.85/24.43                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 157.85/24.43              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 157.85/24.43          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 157.85/24.43              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.85/24.43            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 157.85/24.43                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 157.85/24.43              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 157.85/24.43    (11)   ~ (e3 = e1)
% 157.85/24.43    (12)   ~ (e2 = e0)
% 157.85/24.43    (13)   ~ (e3 = e0)
% 157.85/24.43  
% 157.85/24.43  Begin of proof
% 157.85/24.43  | 
% 157.85/24.43  | BETA: splitting (10) gives:
% 157.85/24.43  | 
% 157.85/24.43  | Case 1:
% 157.85/24.43  | | 
% 157.85/24.43  | |   (14)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 157.85/24.43  | |             e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 157.85/24.43  | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.85/24.43  | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 157.85/24.43  | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.85/24.43  | |               e3) = all_57_6 & $i(all_57_6)))
% 157.85/24.43  | | 
% 157.85/24.43  | | ALPHA: (14) implies:
% 157.85/24.43  | |   (15)  op(e3, e3) = e3
% 157.85/24.43  | | 
% 157.85/24.43  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (15)
% 157.85/24.43  | |            are inconsistent by sub-proof #729.
% 157.85/24.43  | | 
% 157.85/24.43  | Case 2:
% 157.85/24.43  | | 
% 157.85/24.43  | |   (16)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 157.85/24.43  | |             e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 157.85/24.43  | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.85/24.43  | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 157.85/24.43  | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.85/24.43  | |               e2) = all_57_7 & $i(all_57_7)))
% 157.85/24.43  | | 
% 157.85/24.43  | | ALPHA: (16) implies:
% 157.85/24.43  | |   (17)  op(e2, e2) = e2
% 157.85/24.43  | | 
% 157.85/24.43  | | REF_CLOSE: (2), (3), (7), (17) are inconsistent by sub-proof #54.
% 157.85/24.43  | | 
% 157.85/24.43  | End of split
% 157.85/24.43  | 
% 157.85/24.43  End of proof
% 157.85/24.43  
% 157.85/24.43  Sub-proof #23 shows that the following formulas are inconsistent:
% 157.85/24.43  ----------------------------------------------------------------
% 157.85/24.43    (1)  op(e1, e1) = e3
% 157.85/24.43    (2)   ~ (e3 = e2)
% 157.85/24.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.43    (4)  op(e3, e1) = all_52_8
% 157.85/24.43    (5)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 157.85/24.43           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 157.85/24.43           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3
% 157.85/24.43           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 157.85/24.43           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 157.85/24.43    (6)   ~ (all_52_8 = e3)
% 157.85/24.43  
% 157.85/24.43  Begin of proof
% 157.85/24.43  | 
% 157.85/24.43  | BETA: splitting (5) gives:
% 157.85/24.43  | 
% 157.85/24.43  | Case 1:
% 157.85/24.43  | | 
% 157.85/24.43  | |   (7)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 157.85/24.43  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 157.85/24.43  | |          e1) = e2 & $i(all_57_12)
% 157.85/24.43  | | 
% 157.85/24.43  | | ALPHA: (7) implies:
% 157.85/24.43  | |   (8)  op(e1, e1) = e2
% 157.85/24.43  | | 
% 157.85/24.43  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #646.
% 157.85/24.43  | | 
% 157.85/24.43  | Case 2:
% 157.85/24.43  | | 
% 157.85/24.43  | |   (9)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1)
% 157.85/24.43  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 157.85/24.43  | |          e2) = e3 & $i(all_57_10)
% 157.85/24.43  | | 
% 157.85/24.43  | | ALPHA: (9) implies:
% 157.85/24.43  | |   (10)  op(e3, e1) = e3
% 157.85/24.43  | | 
% 157.85/24.43  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #982.
% 157.85/24.43  | | 
% 157.85/24.43  | End of split
% 157.85/24.43  | 
% 157.85/24.43  End of proof
% 157.85/24.43  
% 157.85/24.43  Sub-proof #24 shows that the following formulas are inconsistent:
% 157.85/24.43  ----------------------------------------------------------------
% 157.85/24.43    (1)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 157.85/24.43             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.85/24.43           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 157.85/24.43               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 157.85/24.43             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 157.85/24.43         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 157.85/24.43             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.85/24.43           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 157.85/24.43               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 157.85/24.43             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 157.85/24.43         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 157.85/24.43             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.85/24.43           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 157.85/24.43               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 157.85/24.43             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 157.85/24.43         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 157.85/24.43             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.85/24.43           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 157.85/24.43               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 157.85/24.43             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 157.85/24.43    (2)   ~ (e3 = e2)
% 157.85/24.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.43    (4)   ~ (all_52_12 = e3)
% 157.85/24.43    (5)  op(e0, e0) = e3
% 157.85/24.43    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 157.85/24.43         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 157.85/24.43    (7)  op(e3, e3) = e0
% 157.85/24.43    (8)  op(e3, e2) = e2
% 157.85/24.43    (9)   ~ (e1 = e0)
% 157.85/24.43    (10)  op(e2, e2) = e3
% 157.85/24.43    (11)  op(e3, e0) = all_52_12
% 157.85/24.43    (12)   ~ (e3 = e0)
% 157.85/24.43  
% 157.85/24.43  Begin of proof
% 157.85/24.43  | 
% 157.85/24.43  | BETA: splitting (6) gives:
% 157.85/24.43  | 
% 157.85/24.43  | Case 1:
% 157.85/24.43  | | 
% 157.85/24.43  | |   (13)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 157.85/24.43  | |           e3)
% 157.85/24.43  | | 
% 157.85/24.43  | | REF_CLOSE: (2), (3), (7), (8), (12), (13) are inconsistent by sub-proof #27.
% 157.85/24.43  | | 
% 157.85/24.43  | Case 2:
% 157.85/24.43  | | 
% 157.85/24.43  | |   (14)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 157.85/24.43  | |           e3)
% 157.85/24.43  | | 
% 157.85/24.43  | | BETA: splitting (14) gives:
% 157.85/24.43  | | 
% 157.85/24.43  | | Case 1:
% 157.85/24.43  | | | 
% 157.85/24.43  | | |   (15)  all_56_4 = e3 & op(e3, e1) = e3
% 157.85/24.43  | | | 
% 157.85/24.43  | | | ALPHA: (15) implies:
% 157.85/24.43  | | |   (16)  op(e3, e1) = e3
% 157.85/24.43  | | | 
% 157.85/24.43  | | | BETA: splitting (1) gives:
% 157.85/24.43  | | | 
% 157.85/24.43  | | | Case 1:
% 157.85/24.43  | | | | 
% 157.85/24.44  | | | |   (17)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2,
% 157.85/24.44  | | | |                 e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0
% 157.85/24.44  | | | |               & $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | (
% 157.85/24.44  | | | |               ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)))
% 157.85/24.44  | | | |           & ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 157.85/24.44  | | | |               op(e0, e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2
% 157.85/24.44  | | | |           & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 157.85/24.44  | | | |               (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.85/24.44  | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 157.85/24.44  | | | |               op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2
% 157.85/24.44  | | | |               & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 157.85/24.44  | | | |               all_57_7 & $i(all_57_7))))
% 157.85/24.44  | | | | 
% 157.85/24.44  | | | | REF_CLOSE: (2), (3), (7), (10), (12), (17) are inconsistent by sub-proof
% 157.85/24.44  | | | |            #26.
% 157.85/24.44  | | | | 
% 157.85/24.44  | | | Case 2:
% 157.85/24.44  | | | | 
% 157.85/24.44  | | | |   (18)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 157.85/24.44  | | | |                 e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4
% 157.85/24.44  | | | |               & $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | (
% 157.85/24.44  | | | |               ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)))
% 157.85/24.44  | | | |           & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 157.85/24.44  | | | |               op(e0, e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0
% 157.85/24.44  | | | |           & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 157.85/24.44  | | | |               (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.85/24.44  | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 157.85/24.44  | | | |               op(e2, e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 =
% 157.85/24.44  | | | |               e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0)
% 157.85/24.44  | | | |               = all_57_13 & $i(all_57_13))))
% 157.85/24.44  | | | | 
% 157.85/24.44  | | | | BETA: splitting (18) gives:
% 157.85/24.44  | | | | 
% 157.85/24.44  | | | | Case 1:
% 157.85/24.44  | | | | | 
% 157.85/24.44  | | | | |   (19)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 157.85/24.44  | | | | |               e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4
% 157.85/24.44  | | | | |             & $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | (
% 157.85/24.44  | | | | |             ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)))
% 157.85/24.44  | | | | |         & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 157.85/24.44  | | | | |             op(e0, e1) = all_57_8 & $i(all_57_8)))
% 157.85/24.44  | | | | | 
% 157.85/24.44  | | | | | REF_CLOSE: (3), (7), (9), (16), (19) are inconsistent by sub-proof
% 157.85/24.44  | | | | |            #25.
% 157.85/24.44  | | | | | 
% 157.85/24.44  | | | | Case 2:
% 157.85/24.44  | | | | | 
% 157.85/24.44  | | | | |   (20)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3,
% 157.85/24.44  | | | | |               e3) = e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9
% 157.85/24.44  | | | | |             & $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | (
% 157.85/24.44  | | | | |             ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.85/24.44  | | | | |             $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0) | (
% 157.85/24.44  | | | | |             ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 157.85/24.44  | | | | |             $i(all_57_13)))
% 157.85/24.44  | | | | | 
% 157.85/24.44  | | | | | ALPHA: (20) implies:
% 157.85/24.44  | | | | |   (21)  op(e0, e0) = e0
% 157.85/24.44  | | | | | 
% 157.85/24.44  | | | | | REF_CLOSE: (3), (5), (12), (21) are inconsistent by sub-proof #999.
% 157.85/24.44  | | | | | 
% 157.85/24.44  | | | | End of split
% 157.85/24.44  | | | | 
% 157.85/24.44  | | | End of split
% 157.85/24.44  | | | 
% 157.85/24.44  | | Case 2:
% 157.85/24.44  | | | 
% 157.85/24.44  | | |   (22)  all_56_9 = e3 & op(e3, e0) = e3
% 157.85/24.44  | | | 
% 157.85/24.44  | | | ALPHA: (22) implies:
% 157.85/24.44  | | |   (23)  op(e3, e0) = e3
% 157.85/24.44  | | | 
% 157.85/24.44  | | | REF_CLOSE: (3), (4), (11), (23) are inconsistent by sub-proof #976.
% 157.85/24.44  | | | 
% 157.85/24.44  | | End of split
% 157.85/24.44  | | 
% 157.85/24.44  | End of split
% 157.85/24.44  | 
% 157.85/24.44  End of proof
% 157.85/24.44  
% 157.85/24.44  Sub-proof #25 shows that the following formulas are inconsistent:
% 157.85/24.44  ----------------------------------------------------------------
% 157.85/24.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.44    (2)  op(e3, e3) = e0
% 157.85/24.44    (3)   ~ (e1 = e0)
% 157.85/24.44    (4)  op(e3, e1) = e3
% 157.85/24.44    (5)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 157.85/24.44           ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.85/24.44         ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 157.85/24.44             all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~
% 157.85/24.44             (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))
% 157.85/24.44  
% 157.85/24.44  Begin of proof
% 157.85/24.44  | 
% 157.85/24.44  | ALPHA: (5) implies:
% 157.85/24.44  |   (6)  (all_57_10 = e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) =
% 157.85/24.44  |          all_57_4 & $i(all_57_4))
% 157.85/24.44  | 
% 157.85/24.44  | BETA: splitting (6) gives:
% 157.85/24.44  | 
% 157.85/24.44  | Case 1:
% 157.85/24.44  | | 
% 157.85/24.44  | |   (7)  all_57_10 = e1 & op(e3, e3) = e1
% 157.85/24.44  | | 
% 157.85/24.44  | | ALPHA: (7) implies:
% 157.85/24.44  | |   (8)  op(e3, e3) = e1
% 157.85/24.44  | | 
% 157.85/24.44  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #834.
% 157.85/24.44  | | 
% 157.85/24.44  | Case 2:
% 157.85/24.44  | | 
% 157.85/24.44  | |   (9)   ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4)
% 157.85/24.44  | | 
% 157.85/24.44  | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #39.
% 157.85/24.44  | | 
% 157.85/24.44  | End of split
% 157.85/24.44  | 
% 157.85/24.44  End of proof
% 157.85/24.44  
% 157.85/24.44  Sub-proof #26 shows that the following formulas are inconsistent:
% 157.85/24.44  ----------------------------------------------------------------
% 157.85/24.44    (1)   ~ (e3 = e2)
% 157.85/24.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.44    (3)  op(e3, e3) = e0
% 157.85/24.44    (4)  op(e2, e2) = e3
% 157.85/24.44    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 157.85/24.44             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.85/24.44           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 157.85/24.44               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 157.85/24.44             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 157.85/24.44         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 157.85/24.44             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.85/24.44           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 157.85/24.44               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 157.85/24.44             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 157.85/24.44    (6)   ~ (e3 = e0)
% 157.85/24.44  
% 157.85/24.44  Begin of proof
% 157.85/24.44  | 
% 157.85/24.44  | BETA: splitting (5) gives:
% 157.85/24.44  | 
% 157.85/24.44  | Case 1:
% 157.85/24.44  | | 
% 157.85/24.44  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 157.85/24.44  | |            e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 157.85/24.44  | |            $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.85/24.44  | |            (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 157.85/24.44  | |        ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.85/24.44  | |              e3) = all_57_6 & $i(all_57_6)))
% 157.85/24.44  | | 
% 157.85/24.44  | | ALPHA: (7) implies:
% 157.85/24.44  | |   (8)  op(e3, e3) = e3
% 157.85/24.44  | | 
% 157.85/24.44  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #971.
% 157.85/24.44  | | 
% 157.85/24.44  | Case 2:
% 157.85/24.44  | | 
% 157.85/24.44  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 157.85/24.44  | |            e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 157.85/24.44  | |            $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.85/24.44  | |            (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 157.85/24.44  | |        ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.85/24.44  | |              e2) = all_57_7 & $i(all_57_7)))
% 157.85/24.44  | | 
% 157.85/24.44  | | ALPHA: (9) implies:
% 157.85/24.44  | |   (10)  op(e2, e2) = e2
% 157.85/24.44  | | 
% 157.85/24.44  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #54.
% 157.85/24.44  | | 
% 157.85/24.44  | End of split
% 157.85/24.44  | 
% 157.85/24.44  End of proof
% 157.85/24.44  
% 157.85/24.44  Sub-proof #27 shows that the following formulas are inconsistent:
% 157.85/24.44  ----------------------------------------------------------------
% 157.85/24.44    (1)   ~ (e3 = e2)
% 157.85/24.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.44    (3)  op(e3, e3) = e0
% 157.85/24.44    (4)  op(e3, e2) = e2
% 157.85/24.44    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 157.85/24.44    (6)   ~ (e3 = e0)
% 157.85/24.44  
% 157.85/24.44  Begin of proof
% 157.85/24.44  | 
% 157.85/24.44  | BETA: splitting (5) gives:
% 157.85/24.44  | 
% 157.85/24.44  | Case 1:
% 157.85/24.44  | | 
% 157.85/24.44  | |   (7)  all_56_0 = e3 & op(e3, e3) = e3
% 157.85/24.44  | | 
% 157.85/24.44  | | ALPHA: (7) implies:
% 157.85/24.44  | |   (8)  op(e3, e3) = e3
% 157.85/24.44  | | 
% 157.85/24.44  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #971.
% 157.85/24.44  | | 
% 157.85/24.44  | Case 2:
% 157.85/24.44  | | 
% 157.85/24.44  | |   (9)  all_56_1 = e3 & op(e3, e2) = e3
% 157.85/24.44  | | 
% 157.85/24.44  | | ALPHA: (9) implies:
% 157.85/24.44  | |   (10)  op(e3, e2) = e3
% 157.85/24.44  | | 
% 157.85/24.44  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #433.
% 157.85/24.44  | | 
% 157.85/24.44  | End of split
% 157.85/24.44  | 
% 157.85/24.44  End of proof
% 157.85/24.44  
% 157.85/24.44  Sub-proof #28 shows that the following formulas are inconsistent:
% 157.85/24.44  ----------------------------------------------------------------
% 157.85/24.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.44    (2)  op(e1, e3) = e3
% 157.85/24.44    (3)  op(e1, e3) = e1
% 157.85/24.44    (4)   ~ (e3 = e1)
% 157.85/24.44  
% 157.85/24.44  Begin of proof
% 157.85/24.44  | 
% 157.85/24.44  | GROUND_INST: instantiating (1) with e3, e1, e3, e1, simplifying with (2), (3)
% 157.85/24.44  |              gives:
% 157.85/24.44  |   (5)  e3 = e1
% 157.85/24.44  | 
% 157.85/24.44  | REDUCE: (4), (5) imply:
% 157.85/24.44  |   (6)  $false
% 157.85/24.44  | 
% 157.85/24.44  | CLOSE: (6) is inconsistent.
% 157.85/24.44  | 
% 157.85/24.44  End of proof
% 157.85/24.44  
% 157.85/24.44  Sub-proof #29 shows that the following formulas are inconsistent:
% 157.85/24.44  ----------------------------------------------------------------
% 157.85/24.44    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 157.85/24.44         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 157.85/24.44    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 157.85/24.44         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 157.85/24.44    (3)   ~ (e3 = e2)
% 157.85/24.44    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.44    (5)  op(e0, e3) = all_52_3
% 157.85/24.44    (6)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 157.85/24.44    (7)  op(e3, e3) = e1
% 157.85/24.44    (8)   ~ (e1 = e0)
% 157.85/24.44    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 157.85/24.44         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 157.85/24.44    (10)  op(e2, e2) = e3
% 157.85/24.44    (11)   ~ (e2 = e1)
% 157.85/24.44    (12)   ~ (e3 = e1)
% 157.85/24.44    (13)   ~ (e2 = e0)
% 157.85/24.44    (14)   ~ (e3 = e0)
% 157.85/24.44  
% 157.85/24.44  Begin of proof
% 157.85/24.44  | 
% 157.85/24.44  | BETA: splitting (6) gives:
% 157.85/24.44  | 
% 157.85/24.44  | Case 1:
% 157.85/24.44  | | 
% 157.85/24.44  | |   (15)  all_56_2 = e1 & op(e2, e3) = e1
% 157.85/24.44  | | 
% 157.85/24.44  | | ALPHA: (15) implies:
% 157.85/24.44  | |   (16)  all_56_2 = e1
% 157.85/24.44  | |   (17)  op(e2, e3) = e1
% 157.85/24.44  | | 
% 157.85/24.44  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14),
% 157.85/24.44  | |            (16), (17) are inconsistent by sub-proof #424.
% 157.85/24.44  | | 
% 157.85/24.44  | Case 2:
% 157.85/24.44  | | 
% 157.85/24.44  | |   (18)  all_56_3 = e1 & op(e2, e2) = e1
% 157.85/24.44  | | 
% 157.85/24.44  | | ALPHA: (18) implies:
% 157.85/24.44  | |   (19)  op(e2, e2) = e1
% 157.85/24.44  | | 
% 157.85/24.44  | | REF_CLOSE: (4), (10), (12), (19) are inconsistent by sub-proof #847.
% 157.85/24.44  | | 
% 157.85/24.44  | End of split
% 157.85/24.44  | 
% 157.85/24.44  End of proof
% 157.85/24.44  
% 157.85/24.44  Sub-proof #30 shows that the following formulas are inconsistent:
% 157.85/24.44  ----------------------------------------------------------------
% 157.85/24.44    (1)   ~ (all_6_2 = e0)
% 157.85/24.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.44    (3)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 157.85/24.44    (4)  op(e3, e3) = e3
% 157.85/24.44    (5)   ~ (all_6_2 = e3)
% 157.85/24.44    (6)  all_54_0 = all_6_2
% 157.85/24.44    (7)  op(e3, e3) = all_6_2
% 157.85/24.44    (8)   ~ (all_6_2 = e2)
% 157.85/24.44  
% 157.85/24.44  Begin of proof
% 157.85/24.44  | 
% 157.85/24.44  | BETA: splitting (3) gives:
% 157.85/24.44  | 
% 157.85/24.44  | Case 1:
% 157.85/24.44  | | 
% 157.85/24.44  | |   (9)  all_54_0 = e3
% 157.85/24.44  | | 
% 157.85/24.44  | | COMBINE_EQS: (6), (9) imply:
% 157.85/24.44  | |   (10)  all_6_2 = e3
% 157.85/24.44  | | 
% 157.85/24.44  | | REDUCE: (5), (10) imply:
% 157.85/24.44  | |   (11)  $false
% 157.85/24.44  | | 
% 157.85/24.44  | | CLOSE: (11) is inconsistent.
% 157.85/24.44  | | 
% 157.85/24.44  | Case 2:
% 157.85/24.44  | | 
% 157.85/24.44  | |   (12)   ~ (all_54_0 = e3)
% 157.85/24.44  | |   (13)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 157.85/24.44  | | 
% 157.85/24.44  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (13) are inconsistent by
% 157.85/24.44  | |            sub-proof #32.
% 157.85/24.44  | | 
% 157.85/24.44  | End of split
% 157.85/24.44  | 
% 157.85/24.44  End of proof
% 157.85/24.44  
% 157.85/24.44  Sub-proof #31 shows that the following formulas are inconsistent:
% 157.85/24.44  ----------------------------------------------------------------
% 157.85/24.44    (1)  all_56_10 = e3 & op(e2, e0) = e3
% 157.85/24.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.44    (3)  op(e2, e0) = all_52_13
% 157.85/24.44    (4)   ~ (all_52_13 = e3)
% 157.85/24.44  
% 157.85/24.44  Begin of proof
% 157.85/24.44  | 
% 157.85/24.44  | ALPHA: (1) implies:
% 157.85/24.44  |   (5)  op(e2, e0) = e3
% 157.85/24.44  | 
% 157.85/24.44  | GROUND_INST: instantiating (2) with all_52_13, e3, e0, e2, simplifying with
% 157.85/24.44  |              (3), (5) gives:
% 157.85/24.44  |   (6)  all_52_13 = e3
% 157.85/24.44  | 
% 157.85/24.44  | REDUCE: (4), (6) imply:
% 157.85/24.44  |   (7)  $false
% 157.85/24.44  | 
% 157.85/24.44  | CLOSE: (7) is inconsistent.
% 157.85/24.44  | 
% 157.85/24.45  End of proof
% 157.85/24.45  
% 157.85/24.45  Sub-proof #32 shows that the following formulas are inconsistent:
% 157.85/24.45  ----------------------------------------------------------------
% 157.85/24.45    (1)   ~ (all_6_2 = e0)
% 157.85/24.45    (2)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 157.85/24.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.45    (4)  op(e3, e3) = e3
% 157.85/24.45    (5)   ~ (all_6_2 = e3)
% 157.85/24.45    (6)  all_54_0 = all_6_2
% 157.85/24.45    (7)  op(e3, e3) = all_6_2
% 157.85/24.45    (8)   ~ (all_6_2 = e2)
% 157.85/24.45  
% 157.85/24.45  Begin of proof
% 157.85/24.45  | 
% 157.85/24.45  | BETA: splitting (2) gives:
% 157.85/24.45  | 
% 157.85/24.45  | Case 1:
% 157.85/24.45  | | 
% 157.85/24.45  | |   (9)  all_54_0 = e2
% 157.85/24.45  | | 
% 157.85/24.45  | | COMBINE_EQS: (6), (9) imply:
% 157.85/24.45  | |   (10)  all_6_2 = e2
% 157.85/24.45  | | 
% 157.85/24.45  | | REDUCE: (8), (10) imply:
% 157.85/24.45  | |   (11)  $false
% 157.85/24.45  | | 
% 157.85/24.45  | | CLOSE: (11) is inconsistent.
% 157.85/24.45  | | 
% 157.85/24.45  | Case 2:
% 157.85/24.45  | | 
% 157.85/24.45  | |   (12)  all_54_0 = e1 | all_54_0 = e0
% 157.85/24.45  | | 
% 157.85/24.45  | | BETA: splitting (12) gives:
% 157.85/24.45  | | 
% 157.85/24.45  | | Case 1:
% 157.85/24.45  | | | 
% 157.85/24.45  | | |   (13)  all_54_0 = e1
% 157.85/24.45  | | | 
% 157.85/24.45  | | | COMBINE_EQS: (6), (13) imply:
% 157.85/24.45  | | |   (14)  all_6_2 = e1
% 157.85/24.45  | | | 
% 157.85/24.45  | | | REDUCE: (5), (14) imply:
% 157.85/24.45  | | |   (15)   ~ (e3 = e1)
% 157.85/24.45  | | | 
% 157.85/24.45  | | | SIMP: (15) implies:
% 157.85/24.45  | | |   (16)   ~ (e3 = e1)
% 157.85/24.45  | | | 
% 157.85/24.45  | | | REDUCE: (7), (14) imply:
% 157.85/24.45  | | |   (17)  op(e3, e3) = e1
% 157.85/24.45  | | | 
% 157.85/24.45  | | | REF_CLOSE: (3), (4), (16), (17) are inconsistent by sub-proof #995.
% 157.85/24.45  | | | 
% 157.85/24.45  | | Case 2:
% 157.85/24.45  | | | 
% 157.85/24.45  | | |   (18)  all_54_0 = e0
% 157.85/24.45  | | | 
% 157.85/24.45  | | | COMBINE_EQS: (6), (18) imply:
% 157.85/24.45  | | |   (19)  all_6_2 = e0
% 157.85/24.45  | | | 
% 157.85/24.45  | | | REDUCE: (1), (19) imply:
% 157.85/24.45  | | |   (20)  $false
% 157.85/24.45  | | | 
% 157.85/24.45  | | | CLOSE: (20) is inconsistent.
% 157.85/24.45  | | | 
% 157.85/24.45  | | End of split
% 157.85/24.45  | | 
% 157.85/24.45  | End of split
% 157.85/24.45  | 
% 157.85/24.45  End of proof
% 157.85/24.45  
% 157.85/24.45  Sub-proof #33 shows that the following formulas are inconsistent:
% 157.85/24.45  ----------------------------------------------------------------
% 157.85/24.45    (1)  op(e0, e0) = e2
% 157.85/24.45    (2)   ~ (e3 = e2)
% 157.85/24.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.85/24.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.85/24.45    (4)  op(e3, e2) = e2
% 157.85/24.45    (5)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 157.85/24.45           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 157.85/24.45           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 157.85/24.45           & op(e3, e3) = e3 & op(e3, e2) = e3)
% 157.85/24.45  
% 157.85/24.45  Begin of proof
% 157.85/24.45  | 
% 157.85/24.45  | BETA: splitting (5) gives:
% 157.85/24.45  | 
% 157.85/24.45  | Case 1:
% 157.85/24.45  | | 
% 157.85/24.45  | |   (6)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 157.85/24.45  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 157.85/24.45  | |          e0) = e3 & $i(all_57_10)
% 157.85/24.45  | | 
% 157.85/24.45  | | ALPHA: (6) implies:
% 157.85/24.45  | |   (7)  op(e0, e0) = e3
% 157.85/24.45  | | 
% 157.85/24.45  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #878.
% 157.85/24.45  | | 
% 157.85/24.45  | Case 2:
% 157.85/24.45  | | 
% 157.85/24.45  | |   (8)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 157.85/24.45  | |        op(e3, e2) = e3
% 157.85/24.45  | | 
% 157.85/24.45  | | ALPHA: (8) implies:
% 157.85/24.45  | |   (9)  op(e3, e2) = e3
% 157.85/24.45  | | 
% 157.85/24.45  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #433.
% 157.85/24.45  | | 
% 157.85/24.45  | End of split
% 157.85/24.45  | 
% 157.85/24.45  End of proof
% 157.85/24.45  
% 157.85/24.45  Sub-proof #34 shows that the following formulas are inconsistent:
% 157.85/24.45  ----------------------------------------------------------------
% 157.85/24.45    (1)   ~ (all_52_7 = all_14_2)
% 157.85/24.45    (2)   ~ (all_22_2 = e0) | ( ~ (all_22_0 = e2) & op(e0, e1) = all_22_0 &
% 157.85/24.45           $i(all_22_0)) | ( ~ (all_22_1 = e3) & op(e0, e0) = all_22_1 &
% 157.85/24.45           $i(all_22_1))
% 157.85/24.45    (3)  all_54_2 = all_52_8
% 157.85/24.45    (4)   ~ (all_52_3 = all_14_2)
% 157.85/24.45    (5)   ~ (all_52_1 = e2)
% 157.85/24.45    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 157.85/24.45         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 157.85/24.45    (7)   ~ (all_52_9 = all_10_2)
% 157.85/24.45    (8)   ~ (all_52_4 = e3)
% 157.85/24.45    (9)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 157.85/24.45         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 157.85/24.45    (10)   ~ (all_52_2 = all_10_2)
% 157.93/24.45    (11)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 157.93/24.45              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.93/24.45            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 157.93/24.45                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 157.93/24.45              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 157.93/24.45          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 157.93/24.45              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.93/24.45            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 157.93/24.45                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 157.93/24.45              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 157.93/24.45          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 157.93/24.45              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.93/24.45            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 157.93/24.45                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 157.93/24.45              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 157.93/24.45          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 157.93/24.45              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.93/24.45            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 157.93/24.45                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.93/24.45                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 157.93/24.45                $i(all_57_13))))
% 157.93/24.45    (12)   ~ (all_52_13 = all_14_2)
% 157.93/24.45    (13)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 157.93/24.45          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 157.93/24.45    (14)  op(e0, e1) = all_52_11
% 157.93/24.45    (15)   ~ (e3 = e2)
% 157.93/24.45    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 157.93/24.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 157.93/24.45    (17)  op(e0, e3) = all_52_3
% 157.93/24.45    (18)  op(e3, e1) = all_52_8
% 157.93/24.45    (19)  all_28_2 = all_14_2
% 157.93/24.45    (20)   ~ (all_52_9 = all_4_2)
% 157.93/24.45    (21)   ~ (all_14_2 = e1) | ( ~ (all_14_0 = e2) & op(e1, e0) = all_14_0 &
% 157.93/24.45            $i(all_14_0)) | ( ~ (all_14_1 = e3) & op(e1, e1) = all_14_1 &
% 157.93/24.45            $i(all_14_1))
% 157.93/24.45    (22)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.93/24.45    (23)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.93/24.45    (24)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 157.93/24.45          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 157.93/24.45    (25)   ~ (all_52_11 = all_14_2)
% 157.93/24.45    (26)   ~ (all_52_12 = all_14_2)
% 157.93/24.45    (27)   ~ (all_18_2 = e3) | ( ~ (all_18_0 = e1) & op(e3, e0) = all_18_0 &
% 157.93/24.45            $i(all_18_0)) | ( ~ (all_18_1 = e2) & op(e3, e3) = all_18_1 &
% 157.93/24.45            $i(all_18_1))
% 157.93/24.45    (28)  op(e1, e3) = all_52_2
% 157.93/24.45    (29)  all_54_15 = all_14_2
% 157.93/24.45    (30)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 157.93/24.45          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 157.93/24.45    (31)  op(e0, e2) = all_52_7
% 157.93/24.45    (32)   ~ (all_52_14 = all_10_2)
% 157.93/24.45    (33)   ~ (all_52_6 = all_10_2)
% 157.93/24.45    (34)  op(e1, e2) = all_52_6
% 157.93/24.45    (35)   ~ (all_28_2 = e2) | ( ~ (all_28_0 = e1) & op(e2, e0) = all_28_0 &
% 157.93/24.45            $i(all_28_0)) | ( ~ (all_28_1 = e3) & op(e2, e2) = all_28_1 &
% 157.93/24.45            $i(all_28_1))
% 157.93/24.45    (36)  op(e1, e0) = all_52_14
% 157.93/24.45    (37)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 157.93/24.45          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 157.93/24.45    (38)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 157.93/24.45          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 157.93/24.45    (39)  all_18_2 = all_14_2
% 157.93/24.45    (40)  op(e2, e2) = all_4_2
% 157.93/24.45    (41)  all_54_10 = all_10_2
% 157.93/24.45    (42)  op(e0, e0) = all_14_2
% 157.93/24.45    (43)  op(e2, e3) = all_52_1
% 157.93/24.45    (44)  op(e3, e2) = all_52_4
% 157.93/24.45    (45)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 157.93/24.45          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 157.93/24.45    (46)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 157.93/24.45          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 157.93/24.45    (47)   ~ (e1 = e0)
% 157.93/24.45    (48)  op(e2, e1) = all_52_9
% 157.93/24.45    (49)   ~ (all_52_8 = all_52_9)
% 157.93/24.45    (50)  all_22_2 = all_10_2
% 157.93/24.45    (51)  op(e2, e0) = all_52_13
% 157.93/24.45    (52)  op(e3, e3) = e2
% 157.93/24.45    (53)  all_20_2 = all_10_2
% 157.93/24.45    (54)  op(e2, e2) = e3
% 157.93/24.45    (55)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.93/24.45    (56)   ~ (e2 = e1)
% 157.93/24.45    (57)  op(e3, e0) = all_52_12
% 157.93/24.45    (58)   ~ (all_20_2 = e3) | ( ~ (all_20_0 = e0) & op(e3, e1) = all_20_0 &
% 157.93/24.45            $i(all_20_0)) | ( ~ (all_20_1 = e2) & op(e3, e3) = all_20_1 &
% 157.93/24.45            $i(all_20_1))
% 157.93/24.45    (59)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 157.93/24.45          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 157.93/24.45    (60)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 157.93/24.45          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 157.93/24.45    (61)   ~ (all_52_8 = e2)
% 157.93/24.45    (62)   ~ (all_52_8 = all_10_2)
% 157.93/24.46    (63)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 157.93/24.46            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.93/24.46            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 157.93/24.46            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 157.93/24.46              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.93/24.46          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 157.93/24.46            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 157.93/24.46              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 157.93/24.46            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 157.93/24.46              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.93/24.46          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.93/24.46            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 157.93/24.46              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 157.93/24.46            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 157.93/24.46              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.93/24.46          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 157.93/24.46            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 157.93/24.46            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 157.93/24.46              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 157.93/24.46            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 157.93/24.46            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 157.93/24.46            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 157.93/24.46            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 157.93/24.46              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 157.93/24.46            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 157.93/24.46          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 157.93/24.46            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 157.93/24.46              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 157.93/24.46            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 157.93/24.46            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.93/24.46          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 157.93/24.46            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 157.93/24.46              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 157.93/24.46            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 157.93/24.46            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.93/24.46          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 157.93/24.46            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 157.93/24.46              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 157.93/24.46            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 157.93/24.46              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 157.93/24.46          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 157.93/24.46            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.93/24.46            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 157.93/24.46            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.93/24.46            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 157.93/24.46            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.93/24.46            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 157.93/24.46            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 157.93/24.46              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 157.93/24.46            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 157.93/24.46            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.93/24.46            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 157.93/24.46            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 157.93/24.46              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 157.93/24.46            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 157.93/24.46          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 157.93/24.46            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 157.93/24.46              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 157.93/24.46              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.93/24.46            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 157.93/24.46            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.93/24.46            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 157.93/24.46            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 157.93/24.46              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 157.93/24.46            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 157.93/24.46          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 157.93/24.46            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 157.93/24.46              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 157.93/24.46            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 157.93/24.46              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 157.93/24.46          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 157.93/24.46            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 157.93/24.46              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 157.93/24.46              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 157.93/24.46            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 157.93/24.46          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 157.93/24.46            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.93/24.46            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 157.93/24.46                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 157.93/24.46                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 157.93/24.46                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.93/24.46                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.93/24.46                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.93/24.46                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 157.93/24.46                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.93/24.46                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 157.93/24.46                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.93/24.46                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 157.93/24.46                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.93/24.46                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 157.93/24.46                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 157.93/24.46                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.93/24.46                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 157.93/24.46                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.93/24.46                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 157.93/24.46                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.93/24.46                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 157.93/24.46                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.93/24.46                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.93/24.46                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.93/24.46                op(e0, e1) = e0)))
% 157.93/24.46    (64)   ~ (e3 = e1)
% 157.93/24.46    (65)   ~ (all_10_2 = e2)
% 157.93/24.46    (66)  op(e1, e1) = all_10_2
% 157.93/24.46    (67)   ~ (e2 = e0)
% 157.93/24.46    (68)   ~ (e3 = e0)
% 157.93/24.46  
% 157.93/24.46  Begin of proof
% 157.93/24.46  | 
% 157.93/24.46  | BETA: splitting (21) gives:
% 157.93/24.46  | 
% 157.93/24.46  | Case 1:
% 157.93/24.46  | | 
% 157.93/24.46  | |   (69)   ~ (all_14_2 = e1)
% 157.93/24.46  | | 
% 157.93/24.46  | | BETA: splitting (27) gives:
% 157.93/24.46  | | 
% 157.93/24.46  | | Case 1:
% 157.93/24.46  | | | 
% 157.93/24.46  | | |   (70)   ~ (all_18_2 = e3)
% 157.93/24.46  | | | 
% 157.93/24.46  | | | REDUCE: (39), (70) imply:
% 157.93/24.46  | | |   (71)   ~ (all_14_2 = e3)
% 157.93/24.46  | | | 
% 157.93/24.46  | | | BETA: splitting (58) gives:
% 157.93/24.46  | | | 
% 157.93/24.46  | | | Case 1:
% 157.93/24.46  | | | | 
% 157.93/24.46  | | | |   (72)   ~ (all_20_2 = e3)
% 157.93/24.46  | | | | 
% 157.93/24.46  | | | | REDUCE: (53), (72) imply:
% 157.93/24.46  | | | |   (73)   ~ (all_10_2 = e3)
% 157.93/24.46  | | | | 
% 157.93/24.46  | | | | BETA: splitting (2) gives:
% 157.93/24.46  | | | | 
% 157.93/24.46  | | | | Case 1:
% 157.93/24.46  | | | | | 
% 157.93/24.46  | | | | |   (74)   ~ (all_22_2 = e0)
% 157.93/24.46  | | | | | 
% 157.93/24.46  | | | | | REDUCE: (50), (74) imply:
% 157.93/24.46  | | | | |   (75)   ~ (all_10_2 = e0)
% 157.93/24.46  | | | | | 
% 157.93/24.46  | | | | | BETA: splitting (55) gives:
% 157.93/24.46  | | | | | 
% 157.93/24.46  | | | | | Case 1:
% 157.93/24.46  | | | | | | 
% 157.93/24.46  | | | | | |   (76)  all_54_10 = e3
% 157.93/24.46  | | | | | | 
% 157.93/24.46  | | | | | | REF_CLOSE: (41), (73), (76) are inconsistent by sub-proof #361.
% 157.93/24.46  | | | | | | 
% 157.93/24.46  | | | | | Case 2:
% 157.93/24.46  | | | | | | 
% 157.93/24.46  | | | | | |   (77)   ~ (all_54_10 = e3)
% 157.93/24.46  | | | | | |   (78)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.93/24.46  | | | | | | 
% 157.93/24.46  | | | | | | BETA: splitting (78) gives:
% 157.93/24.46  | | | | | | 
% 157.93/24.46  | | | | | | Case 1:
% 157.93/24.46  | | | | | | | 
% 157.93/24.46  | | | | | | |   (79)  all_54_10 = e2
% 157.93/24.46  | | | | | | | 
% 157.93/24.46  | | | | | | | REF_CLOSE: (41), (65), (79) are inconsistent by sub-proof #360.
% 157.93/24.46  | | | | | | | 
% 157.93/24.46  | | | | | | Case 2:
% 157.93/24.46  | | | | | | | 
% 157.93/24.46  | | | | | | |   (80)   ~ (all_54_10 = e2)
% 157.93/24.46  | | | | | | |   (81)  all_54_10 = e1 | all_54_10 = e0
% 157.93/24.46  | | | | | | | 
% 157.93/24.46  | | | | | | | BETA: splitting (81) gives:
% 157.93/24.46  | | | | | | | 
% 157.93/24.46  | | | | | | | Case 1:
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | |   (82)  all_54_10 = e1
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | | COMBINE_EQS: (41), (82) imply:
% 157.93/24.46  | | | | | | | |   (83)  all_10_2 = e1
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | | SIMP: (83) implies:
% 157.93/24.46  | | | | | | | |   (84)  all_10_2 = e1
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | | REDUCE: (10), (84) imply:
% 157.93/24.46  | | | | | | | |   (85)   ~ (all_52_2 = e1)
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | | REDUCE: (33), (84) imply:
% 157.93/24.46  | | | | | | | |   (86)   ~ (all_52_6 = e1)
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | | REDUCE: (32), (84) imply:
% 157.93/24.46  | | | | | | | |   (87)   ~ (all_52_14 = e1)
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | | REDUCE: (73), (84) imply:
% 157.93/24.46  | | | | | | | |   (88)   ~ (e3 = e1)
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | | REDUCE: (65), (84) imply:
% 157.93/24.46  | | | | | | | |   (89)   ~ (e2 = e1)
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | | REDUCE: (66), (84) imply:
% 157.93/24.46  | | | | | | | |   (90)  op(e1, e1) = e1
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | | BETA: splitting (35) gives:
% 157.93/24.46  | | | | | | | | 
% 157.93/24.46  | | | | | | | | Case 1:
% 157.93/24.46  | | | | | | | | | 
% 157.93/24.46  | | | | | | | | |   (91)   ~ (all_28_2 = e2)
% 157.93/24.46  | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | REDUCE: (19), (91) imply:
% 157.93/24.46  | | | | | | | | |   (92)   ~ (all_14_2 = e2)
% 157.93/24.46  | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | BETA: splitting (22) gives:
% 157.93/24.46  | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | Case 1:
% 157.93/24.46  | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | |   (93)  all_54_15 = e3
% 157.93/24.46  | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | REF_CLOSE: (29), (71), (93) are inconsistent by sub-proof
% 157.93/24.46  | | | | | | | | | |            #1010.
% 157.93/24.46  | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | Case 2:
% 157.93/24.46  | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | |   (94)   ~ (all_54_15 = e3)
% 157.93/24.46  | | | | | | | | | |   (95)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.93/24.46  | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | BETA: splitting (95) gives:
% 157.93/24.46  | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | Case 1:
% 157.93/24.46  | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | |   (96)  all_54_15 = e2
% 157.93/24.46  | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | REF_CLOSE: (29), (92), (96) are inconsistent by sub-proof
% 157.93/24.46  | | | | | | | | | | |            #1009.
% 157.93/24.46  | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | Case 2:
% 157.93/24.46  | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | |   (97)   ~ (all_54_15 = e2)
% 157.93/24.46  | | | | | | | | | | |   (98)  all_54_15 = e1 | all_54_15 = e0
% 157.93/24.46  | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | BETA: splitting (63) gives:
% 157.93/24.46  | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | Case 1:
% 157.93/24.46  | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | |   (99)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.93/24.46  | | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.93/24.46  | | | | | | | | | | | |             e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | |           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.93/24.46  | | | | | | | | | | | |           all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.93/24.46  | | | | | | | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.93/24.46  | | | | | | | | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.93/24.46  | | | | | | | | | | | |           $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.93/24.46  | | | | | | | | | | | |           & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.93/24.46  | | | | | | | | | | | |             e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.93/24.46  | | | | | | | | | | | |           = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.93/24.46  | | | | | | | | | | | |         (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.93/24.46  | | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.93/24.46  | | | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.93/24.46  | | | | | | | | | | | |           = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.93/24.46  | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.93/24.46  | | | | | | | | | | | |           op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.93/24.46  | | | | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.93/24.46  | | | | | | | | | | | |           & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.93/24.46  | | | | | | | | | | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.93/24.46  | | | | | | | | | | | |           = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.93/24.46  | | | | | | | | | | | |         (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.93/24.46  | | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.93/24.46  | | | | | | | | | | | |           e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.93/24.46  | | | | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.93/24.46  | | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.46  | | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.93/24.46  | | | | | | | | | | | |           = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.93/24.46  | | | | | | | | | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 157.93/24.46  | | | | | | | | | | | |         (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.93/24.46  | | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.93/24.46  | | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.93/24.46  | | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.93/24.46  | | | | | | | | | | | |           = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.93/24.46  | | | | | | | | | | | |             e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.93/24.46  | | | | | | | | | | | |           all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.93/24.46  | | | | | | | | | | | |             e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.93/24.46  | | | | | | | | | | | |         (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.93/24.46  | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.93/24.46  | | | | | | | | | | | |             e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.46  | | | | | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.93/24.46  | | | | | | | | | | | |           all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.93/24.46  | | | | | | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.93/24.46  | | | | | | | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.93/24.46  | | | | | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.93/24.46  | | | | | | | | | | | |           & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.93/24.46  | | | | | | | | | | | |             e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.93/24.46  | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.93/24.46  | | | | | | | | | | | |         (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.93/24.46  | | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.93/24.46  | | | | | | | | | | | |             e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.93/24.46  | | | | | | | | | | | |           = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.93/24.46  | | | | | | | | | | | |           all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.93/24.46  | | | | | | | | | | | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.93/24.46  | | | | | | | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.93/24.46  | | | | | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.93/24.46  | | | | | | | | | | | |           &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.46  | | | | | | | | | | | |           e1)
% 157.93/24.46  | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | BETA: splitting (99) gives:
% 157.93/24.46  | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | Case 1:
% 157.93/24.46  | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | |   (100)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.93/24.46  | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.93/24.46  | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.93/24.46  | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.93/24.46  | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.93/24.46  | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.93/24.46  | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.93/24.46  | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.93/24.46  | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.93/24.46  | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.93/24.46  | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.93/24.46  | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.93/24.46  | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 157.93/24.46  | | | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 157.93/24.46  | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.93/24.46  | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.93/24.46  | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 157.93/24.46  | | | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 157.93/24.46  | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 157.93/24.46  | | | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 157.93/24.46  | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.93/24.46  | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.93/24.46  | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.93/24.46  | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.93/24.46  | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.46  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.93/24.46  | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.93/24.46  | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.93/24.46  | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | BETA: splitting (100) gives:
% 157.93/24.46  | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | Case 1:
% 157.93/24.46  | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | |   (101)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.93/24.46  | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.93/24.46  | | | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.93/24.46  | | | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.93/24.46  | | | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.93/24.46  | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.93/24.46  | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.93/24.46  | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.93/24.46  | | | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.93/24.46  | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.93/24.46  | | | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.93/24.46  | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.93/24.46  | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 157.93/24.46  | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (43), (101) are inconsistent by
% 157.93/24.46  | | | | | | | | | | | | | |            sub-proof #1005.
% 157.93/24.46  | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | Case 2:
% 157.93/24.46  | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | |   (102)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.93/24.46  | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.93/24.46  | | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.93/24.46  | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.93/24.46  | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.93/24.46  | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.93/24.46  | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.93/24.46  | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 157.93/24.46  | | | | | | | | | | | | | |            &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | | | |            e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 157.93/24.46  | | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 157.93/24.46  | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 157.93/24.46  | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 157.93/24.46  | | | | | | | | | | | | | |            e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 157.93/24.46  | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 157.93/24.46  | | | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 157.93/24.46  | | | | | | | | | | | | | |            & $i(all_57_12))
% 157.93/24.46  | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 157.93/24.46  | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | | Case 1:
% 157.93/24.46  | | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | | |   (103)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.93/24.46  | | | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.93/24.46  | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.93/24.46  | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.93/24.46  | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.93/24.46  | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.93/24.46  | | | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.93/24.46  | | | | | | | | | | | | | | |            $i(all_57_10))
% 157.93/24.46  | | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (43), (103) are inconsistent by
% 157.93/24.46  | | | | | | | | | | | | | | |            sub-proof #1004.
% 157.93/24.46  | | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | | Case 2:
% 157.93/24.46  | | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | | |   (104)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.93/24.46  | | | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.93/24.46  | | | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.93/24.46  | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.93/24.46  | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.46  | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.93/24.46  | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.93/24.46  | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.93/24.46  | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.93/24.46  | | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 157.93/24.46  | | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | | | Case 1:
% 157.93/24.46  | | | | | | | | | | | | | | | | 
% 157.93/24.46  | | | | | | | | | | | | | | | |   (105)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.93/24.47  | | | | | | | | | | | | | | | |          op(e2, e3) = e2 & op(e2, e2) = e2
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 157.93/24.47  | | | | | | | | | | | | | | | |   (106)  op(e2, e3) = e2
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (43), (106) are inconsistent by
% 157.93/24.47  | | | | | | | | | | | | | | | |            sub-proof #1007.
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | Case 2:
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | |   (107)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 157.93/24.47  | | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.93/24.47  | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.47  | | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.93/24.47  | | | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.93/24.47  | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.93/24.47  | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | Case 1:
% 157.93/24.47  | | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | |   (108)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 157.93/24.47  | | | | | | | | | | | | | | | | |          ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.93/24.47  | | | | | | | | | | | | | | | | |          op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.47  | | | | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 157.93/24.47  | | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 157.93/24.47  | | | | | | | | | | | | | | | | |   (109)  op(e1, e1) = e3
% 157.93/24.47  | | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (64), (90), (109) are inconsistent by
% 157.93/24.47  | | | | | | | | | | | | | | | | |            sub-proof #1003.
% 157.93/24.47  | | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | Case 2:
% 157.93/24.47  | | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | |   (110)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 157.93/24.47  | | | | | | | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 157.93/24.47  | | | | | | | | | | | | | | | | |          = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 157.93/24.47  | | | | | | | | | | | | | | | | |          $i(all_57_12)
% 157.93/24.47  | | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 157.93/24.47  | | | | | | | | | | | | | | | | |   (111)  op(e3, e2) = e3
% 157.93/24.47  | | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (44), (111) are inconsistent by
% 157.93/24.47  | | | | | | | | | | | | | | | | |            sub-proof #998.
% 157.93/24.47  | | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | End of split
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | End of split
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | End of split
% 157.93/24.47  | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | End of split
% 157.93/24.47  | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | Case 2:
% 157.93/24.47  | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | |   (112)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.93/24.47  | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.93/24.47  | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.93/24.47  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.93/24.47  | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.93/24.47  | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.93/24.47  | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.93/24.47  | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.93/24.47  | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.93/24.47  | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.93/24.47  | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.93/24.47  | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.47  | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.93/24.47  | | | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.93/24.47  | | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 157.93/24.47  | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.93/24.47  | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 157.93/24.47  | | | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 157.93/24.47  | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 157.93/24.47  | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.93/24.47  | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.93/24.47  | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.93/24.47  | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.93/24.47  | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.93/24.47  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.93/24.47  | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.93/24.47  | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.93/24.47  | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.93/24.47  | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.47  | | | | | | | | | | | | |            e1)
% 157.93/24.47  | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | BETA: splitting (112) gives:
% 157.93/24.47  | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | Case 1:
% 157.93/24.47  | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | |   (113)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.93/24.47  | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.93/24.47  | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.93/24.47  | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.93/24.47  | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.93/24.47  | | | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.93/24.47  | | | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.93/24.47  | | | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.93/24.47  | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.93/24.47  | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.93/24.47  | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.93/24.47  | | | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.47  | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 157.93/24.47  | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 157.93/24.47  | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | Case 1:
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | |   (114)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.93/24.47  | | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.93/24.47  | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.93/24.47  | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.93/24.47  | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.93/24.47  | | | | | | | | | | | | | | |              e2) = e3)
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | Case 1:
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | |   (115)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.93/24.47  | | | | | | | | | | | | | | | |          ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.93/24.47  | | | | | | | | | | | | | | | |          op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.93/24.47  | | | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 157.93/24.47  | | | | | | | | | | | | | | | |   (116)  op(e0, e0) = e3
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (42), (71), (116) are inconsistent by
% 157.93/24.47  | | | | | | | | | | | | | | | |            sub-proof #245.
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | Case 2:
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | |   (117)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 157.93/24.47  | | | | | | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e2) = e3
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 157.93/24.47  | | | | | | | | | | | | | | | |   (118)  op(e3, e3) = e3
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (52), (118) are inconsistent by
% 157.93/24.47  | | | | | | | | | | | | | | | |            sub-proof #958.
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | End of split
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | Case 2:
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | |   (119)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 157.93/24.47  | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 157.93/24.47  | | | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 157.93/24.47  | | | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 157.93/24.47  | | | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 157.93/24.47  | | | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.93/24.47  | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.93/24.47  | | | | | | | | | | | | | | |            $i(all_57_14))
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | Case 1:
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | |   (120)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 157.93/24.47  | | | | | | | | | | | | | | | |          ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 157.93/24.47  | | | | | | | | | | | | | | | |          = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.93/24.47  | | | | | | | | | | | | | | | |          $i(all_57_12)
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 157.93/24.47  | | | | | | | | | | | | | | | |   (121)  op(e3, e2) = e3
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (44), (121) are inconsistent by
% 157.93/24.47  | | | | | | | | | | | | | | | |            sub-proof #998.
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | Case 2:
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | |   (122)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.93/24.47  | | | | | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 157.93/24.47  | | | | | | | | | | | | | | | |          = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.93/24.47  | | | | | | | | | | | | | | | |          $i(all_57_14)
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 157.93/24.47  | | | | | | | | | | | | | | | |   (123)  op(e3, e3) = e1
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (52), (56), (123) are inconsistent by
% 157.93/24.47  | | | | | | | | | | | | | | | |            sub-proof #828.
% 157.93/24.47  | | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | End of split
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | End of split
% 157.93/24.47  | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | Case 2:
% 157.93/24.47  | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | |   (124)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.93/24.47  | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.93/24.47  | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.47  | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.93/24.47  | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.93/24.47  | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.93/24.47  | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.93/24.47  | | | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.93/24.47  | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.93/24.47  | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.93/24.47  | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.93/24.47  | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.93/24.47  | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.93/24.47  | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.93/24.47  | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.93/24.47  | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.47  | | | | | | | | | | | | | |            e1)
% 157.93/24.47  | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 157.93/24.47  | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | Case 1:
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | |   (125)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.93/24.47  | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.93/24.47  | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.47  | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.93/24.47  | | | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.93/24.47  | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.93/24.47  | | | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | REF_CLOSE: (16), (54), (64), (90), (125) are inconsistent by
% 157.93/24.47  | | | | | | | | | | | | | | |            sub-proof #53.
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | Case 2:
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | |   (126)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.93/24.47  | | | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.93/24.47  | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.93/24.47  | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.93/24.47  | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.93/24.47  | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.93/24.47  | | | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.93/24.47  | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.93/24.47  | | | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.93/24.47  | | | | | | | | | | | | | | |            e1)
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | | REF_CLOSE: (16), (28), (29), (42), (64), (69), (85), (90),
% 157.93/24.47  | | | | | | | | | | | | | | |            (98), (126) are inconsistent by sub-proof #255.
% 157.93/24.47  | | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | | End of split
% 157.93/24.47  | | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | | End of split
% 157.93/24.47  | | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | | End of split
% 157.93/24.47  | | | | | | | | | | | | 
% 157.93/24.47  | | | | | | | | | | | Case 2:
% 157.93/24.47  | | | | | | | | | | | | 
% 157.95/24.47  | | | | | | | | | | | |   (127)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.95/24.47  | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.95/24.47  | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.47  | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.95/24.47  | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.95/24.47  | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.95/24.47  | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.47  | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.95/24.47  | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.95/24.47  | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.95/24.47  | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.95/24.47  | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.95/24.47  | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.95/24.47  | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.95/24.47  | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.95/24.47  | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.95/24.47  | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.95/24.47  | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.95/24.47  | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.95/24.47  | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.47  | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.95/24.47  | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.95/24.47  | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.95/24.47  | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.95/24.47  | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.95/24.47  | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.95/24.47  | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.95/24.47  | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.95/24.47  | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.95/24.47  | | | | | | | | | | | |            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 157.95/24.47  | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.95/24.47  | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 157.95/24.47  | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.95/24.47  | | | | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 157.95/24.47  | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 157.95/24.47  | | | | | | | | | | | |            e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 157.95/24.47  | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 157.95/24.47  | | | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.95/24.47  | | | | | | | | | | | |            & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 157.95/24.47  | | | | | | | | | | | |            e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 157.95/24.47  | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 157.95/24.47  | | | | | | | | | | | |            op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.95/24.47  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 157.95/24.47  | | | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 157.95/24.47  | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 157.95/24.47  | | | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 157.95/24.47  | | | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 157.95/24.47  | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 157.95/24.47  | | | | | | | | | | | |            = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 157.95/24.47  | | | | | | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 157.95/24.47  | | | | | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 157.95/24.47  | | | | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 157.95/24.47  | | | | | | | | | | | |            & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 =
% 157.95/24.47  | | | | | | | | | | | |                e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 157.95/24.47  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.95/24.47  | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 157.95/24.47  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 157.95/24.47  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.95/24.47  | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.95/24.47  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.95/24.47  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.95/24.47  | | | | | | | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 157.95/24.47  | | | | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 157.95/24.47  | | | | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 157.95/24.47  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 157.95/24.47  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) |
% 157.95/24.47  | | | | | | | | | | | |              (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 157.95/24.47  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 157.95/24.47  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e2) = e0) |
% 157.95/24.47  | | | | | | | | | | | |              (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 157.95/24.47  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 157.95/24.47  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) |
% 157.95/24.47  | | | | | | | | | | | |              (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 157.95/24.47  | | | | | | | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.95/24.47  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.95/24.47  | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.95/24.47  | | | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 157.95/24.47  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.95/24.47  | | | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 157.95/24.47  | | | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 157.95/24.47  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.95/24.47  | | | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.95/24.47  | | | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 157.95/24.47  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 157.95/24.47  | | | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 157.95/24.47  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 157.95/24.47  | | | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15
% 157.95/24.47  | | | | | | | | | | | |                = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 157.95/24.47  | | | | | | | | | | | | 
% 157.95/24.47  | | | | | | | | | | | | BETA: splitting (127) gives:
% 157.95/24.47  | | | | | | | | | | | | 
% 157.95/24.47  | | | | | | | | | | | | Case 1:
% 157.95/24.47  | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | |   (128)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.95/24.48  | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.95/24.48  | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.95/24.48  | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.95/24.48  | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.95/24.48  | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.48  | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.95/24.48  | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.95/24.48  | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.95/24.48  | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.95/24.48  | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.95/24.48  | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.95/24.48  | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.95/24.48  | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.95/24.48  | | | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 157.95/24.48  | | | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 157.95/24.48  | | | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.95/24.48  | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 157.95/24.48  | | | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 157.95/24.48  | | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.95/24.48  | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.95/24.48  | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 157.95/24.48  | | | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 157.95/24.48  | | | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 157.95/24.48  | | | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 157.95/24.48  | | | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.95/24.48  | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.95/24.48  | | | | | | | | | | | | |            $i(all_57_14))
% 157.95/24.48  | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | BETA: splitting (128) gives:
% 157.95/24.48  | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | Case 1:
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | |   (129)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.95/24.48  | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.95/24.48  | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.95/24.48  | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.95/24.48  | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.95/24.48  | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.48  | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.95/24.48  | | | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.95/24.48  | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.95/24.48  | | | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.95/24.48  | | | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.95/24.48  | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.95/24.48  | | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.95/24.48  | | | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | Case 1:
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | |   (130)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.95/24.48  | | | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.95/24.48  | | | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.95/24.48  | | | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.95/24.48  | | | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.95/24.48  | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.48  | | | | | | | | | | | | | | |            $i(all_57_14))
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | REF_CLOSE: (16), (52), (54), (56), (64), (130) are
% 157.95/24.48  | | | | | | | | | | | | | | |            inconsistent by sub-proof #44.
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | Case 2:
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | |   (131)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 157.95/24.48  | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.95/24.48  | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 157.95/24.48  | | | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 157.95/24.48  | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.48  | | | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.95/24.48  | | | | | | | | | | | | | | |            $i(all_57_14))
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | REF_CLOSE: (16), (29), (42), (56), (69), (90), (98), (131)
% 157.95/24.48  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #102.
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | End of split
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | Case 2:
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | |   (132)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 157.95/24.48  | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.95/24.48  | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.95/24.48  | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.95/24.48  | | | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 157.95/24.48  | | | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 157.95/24.48  | | | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 157.95/24.48  | | | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 157.95/24.48  | | | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.95/24.48  | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 157.95/24.48  | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.95/24.48  | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.95/24.48  | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.95/24.48  | | | | | | | | | | | | | |            & $i(all_57_14))
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | Case 1:
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | |   (133)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 157.95/24.48  | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.95/24.48  | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.95/24.48  | | | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.95/24.48  | | | | | | | | | | | | | | |              e1) = e1)
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | REF_CLOSE: (16), (34), (56), (86), (90), (133) are
% 157.95/24.48  | | | | | | | | | | | | | | |            inconsistent by sub-proof #983.
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | Case 2:
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | |   (134)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.95/24.48  | | | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.95/24.48  | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.95/24.48  | | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 157.95/24.48  | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 157.95/24.48  | | | | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 157.95/24.48  | | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 157.95/24.48  | | | | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | Case 1:
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | |   (135)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.95/24.48  | | | | | | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.95/24.48  | | | | | | | | | | | | | | | |          op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.95/24.48  | | | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 157.95/24.48  | | | | | | | | | | | | | | | |   (136)  op(e0, e0) = e3
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (42), (71), (136) are inconsistent by
% 157.95/24.48  | | | | | | | | | | | | | | | |            sub-proof #245.
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | Case 2:
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | |   (137)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.95/24.48  | | | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 157.95/24.48  | | | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.95/24.48  | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.95/24.48  | | | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.95/24.48  | | | | | | | | | | | | | | | |            & $i(all_57_14))
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (52), (56), (137) are inconsistent by
% 157.95/24.48  | | | | | | | | | | | | | | | |            sub-proof #284.
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | End of split
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | End of split
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | End of split
% 157.95/24.48  | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | Case 2:
% 157.95/24.48  | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | |   (138)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.95/24.48  | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.95/24.48  | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.95/24.48  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.95/24.48  | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.95/24.48  | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.95/24.48  | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.95/24.48  | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.95/24.48  | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.95/24.48  | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.95/24.48  | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.95/24.48  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 157.95/24.48  | | | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 157.95/24.48  | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.95/24.48  | | | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.95/24.48  | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 157.95/24.48  | | | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 157.95/24.48  | | | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 157.95/24.48  | | | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 157.95/24.48  | | | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.95/24.48  | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.95/24.48  | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.95/24.48  | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.95/24.48  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.95/24.48  | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.95/24.48  | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.95/24.48  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.95/24.48  | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.95/24.48  | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.95/24.48  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.95/24.48  | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.95/24.48  | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.95/24.48  | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.95/24.48  | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.95/24.48  | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.95/24.48  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.95/24.48  | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.95/24.48  | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.95/24.48  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.95/24.48  | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.95/24.48  | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.95/24.48  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.95/24.48  | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.95/24.48  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.95/24.48  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.95/24.48  | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.95/24.48  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.95/24.48  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.95/24.48  | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.95/24.48  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.95/24.48  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.95/24.48  | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.95/24.48  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.95/24.48  | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.95/24.48  | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.95/24.48  | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.95/24.48  | | | | | | | | | | | | |                e0)))
% 157.95/24.48  | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | BETA: splitting (138) gives:
% 157.95/24.48  | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | Case 1:
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | |   (139)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.95/24.48  | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.95/24.48  | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.95/24.48  | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.95/24.48  | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.95/24.48  | | | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 157.95/24.48  | | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 157.95/24.48  | | | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 157.95/24.48  | | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 157.95/24.48  | | | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.95/24.48  | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.95/24.48  | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.95/24.48  | | | | | | | | | | | | | |            e3 & $i(all_57_10))
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | Case 1:
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | |   (140)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.95/24.48  | | | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.95/24.48  | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.95/24.48  | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 157.95/24.48  | | | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 157.95/24.48  | | | | | | | | | | | | | | |              e1) = e2)
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | Case 1:
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | |   (141)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.95/24.48  | | | | | | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.95/24.48  | | | | | | | | | | | | | | | |          op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.95/24.48  | | | | | | | | | | | | | | | |          e2 & $i(all_57_12)
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 157.95/24.48  | | | | | | | | | | | | | | | |   (142)  op(e0, e0) = e2
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (29), (42), (69), (92), (98), (142) are
% 157.95/24.48  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #799.
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | Case 2:
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | |   (143)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 157.95/24.48  | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e1) = e2
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 157.95/24.48  | | | | | | | | | | | | | | | |   (144)  op(e2, e2) = e2
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (54), (144) are inconsistent by
% 157.95/24.48  | | | | | | | | | | | | | | | |            sub-proof #54.
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | End of split
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | Case 2:
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | |   (145)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 157.95/24.48  | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 157.95/24.48  | | | | | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 157.95/24.48  | | | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 157.95/24.48  | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 157.95/24.48  | | | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.95/24.48  | | | | | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 157.95/24.48  | | | | | | | | | | | | | | |            $i(all_57_10))
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | Case 1:
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | |   (146)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 157.95/24.48  | | | | | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 157.95/24.48  | | | | | | | | | | | | | | | |          = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.95/24.48  | | | | | | | | | | | | | | | |          $i(all_57_14)
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 157.95/24.48  | | | | | | | | | | | | | | | |   (147)  op(e2, e2) = e1
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (54), (64), (147) are inconsistent by
% 157.95/24.48  | | | | | | | | | | | | | | | |            sub-proof #847.
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | Case 2:
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | |   (148)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 157.95/24.48  | | | | | | | | | | | | | | | |          ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 157.95/24.48  | | | | | | | | | | | | | | | |          op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.95/24.48  | | | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 157.95/24.48  | | | | | | | | | | | | | | | |   (149)  op(e0, e0) = e3
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (42), (71), (149) are inconsistent by
% 157.95/24.48  | | | | | | | | | | | | | | | |            sub-proof #245.
% 157.95/24.48  | | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | | End of split
% 157.95/24.48  | | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | | End of split
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | Case 2:
% 157.95/24.48  | | | | | | | | | | | | | | 
% 157.95/24.48  | | | | | | | | | | | | | |   (150)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.95/24.48  | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.95/24.48  | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.95/24.48  | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.95/24.48  | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.95/24.48  | | | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 157.95/24.48  | | | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 157.95/24.48  | | | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 157.95/24.48  | | | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 157.95/24.48  | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.95/24.48  | | | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 157.95/24.48  | | | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 157.95/24.48  | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 157.95/24.48  | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 157.95/24.48  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 157.95/24.48  | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 157.95/24.48  | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 157.95/24.48  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 157.95/24.48  | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 157.95/24.48  | | | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 157.95/24.48  | | | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.95/24.48  | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.95/24.48  | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.95/24.48  | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 157.95/24.48  | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.95/24.48  | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 157.95/24.48  | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 157.95/24.48  | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.95/24.48  | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 157.95/24.48  | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 157.95/24.48  | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 157.95/24.48  | | | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 157.95/24.48  | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.95/24.48  | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.95/24.48  | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 157.95/24.49  | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.95/24.49  | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.95/24.49  | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 157.95/24.49  | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.95/24.49  | | | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.95/24.49  | | | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.95/24.49  | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 157.95/24.49  | | | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.95/24.49  | | | | | | | | | | | | | |                op(e0, e1) = e0)))
% 157.95/24.49  | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 157.95/24.49  | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | Case 1:
% 157.95/24.49  | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | |   (151)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 157.95/24.49  | | | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.95/24.49  | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.95/24.49  | | | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 157.95/24.49  | | | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 157.95/24.49  | | | | | | | | | | | | | | |              e0) = e3)
% 157.95/24.49  | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 157.95/24.49  | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | Case 1:
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | |   (152)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 157.95/24.49  | | | | | | | | | | | | | | | |          ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.95/24.49  | | | | | | | | | | | | | | | |          op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 157.95/24.49  | | | | | | | | | | | | | | | |          e2 & $i(all_57_12)
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 157.95/24.49  | | | | | | | | | | | | | | | |   (153)  op(e0, e0) = e2
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (29), (42), (69), (92), (98), (153) are
% 157.95/24.49  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #799.
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | Case 2:
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | |   (154)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 157.95/24.49  | | | | | | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e0) = e3
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 157.95/24.49  | | | | | | | | | | | | | | | |   (155)  op(e3, e3) = e3
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (52), (155) are inconsistent by
% 157.95/24.49  | | | | | | | | | | | | | | | |            sub-proof #958.
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | End of split
% 157.95/24.49  | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | Case 2:
% 157.95/24.49  | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | |   (156)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.95/24.49  | | | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 157.95/24.49  | | | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 157.95/24.49  | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 157.95/24.49  | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.95/24.49  | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.95/24.49  | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.95/24.49  | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.95/24.49  | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.95/24.49  | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.95/24.49  | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.95/24.49  | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.95/24.49  | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.95/24.49  | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.95/24.49  | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.95/24.49  | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.95/24.49  | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.95/24.49  | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.95/24.49  | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.95/24.49  | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.95/24.49  | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.95/24.49  | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.95/24.49  | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.95/24.49  | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.95/24.49  | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.95/24.49  | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.95/24.49  | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.95/24.49  | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.95/24.49  | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.95/24.49  | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.95/24.49  | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.95/24.49  | | | | | | | | | | | | | | |                e0)))
% 157.95/24.49  | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 157.95/24.49  | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | Case 1:
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | |   (157)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 157.95/24.49  | | | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 157.95/24.49  | | | | | | | | | | | | | | | |   (158)  op(e2, e2) = e2
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (54), (158) are inconsistent by
% 157.95/24.49  | | | | | | | | | | | | | | | |            sub-proof #54.
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | Case 2:
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | |   (159)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.95/24.49  | | | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 157.95/24.49  | | | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 157.95/24.49  | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.95/24.49  | | | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.95/24.49  | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.95/24.49  | | | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.95/24.49  | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.95/24.49  | | | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 157.95/24.49  | | | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 157.95/24.49  | | | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.95/24.49  | | | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 157.95/24.49  | | | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.95/24.49  | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 157.95/24.49  | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 157.95/24.49  | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 157.95/24.49  | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 157.95/24.49  | | | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.95/24.49  | | | | | | | | | | | | | | | |                e0)))
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | Case 1:
% 157.95/24.49  | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | |   (160)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 157.95/24.49  | | | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 157.95/24.49  | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 157.95/24.49  | | | | | | | | | | | | | | | | |   (161)  op(e1, e0) = e1
% 157.95/24.49  | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (36), (87), (161) are inconsistent by
% 157.95/24.49  | | | | | | | | | | | | | | | | |            sub-proof #974.
% 157.95/24.49  | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | Case 2:
% 157.95/24.49  | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | |   (162)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.95/24.49  | | | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.95/24.49  | | | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.95/24.49  | | | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.95/24.49  | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 157.95/24.49  | | | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.95/24.49  | | | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 157.95/24.49  | | | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 157.95/24.49  | | | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.95/24.49  | | | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 157.95/24.49  | | | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 157.95/24.49  | | | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.95/24.49  | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 157.95/24.49  | | | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 157.95/24.49  | | | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 157.95/24.49  | | | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 157.95/24.49  | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 157.95/24.49  | | | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 157.95/24.49  | | | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 157.95/24.49  | | | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 157.95/24.49  | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e0))
% 157.95/24.49  | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 157.95/24.49  | | | | | | | | | | | | | | | | |   (163)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.95/24.49  | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 157.95/24.49  | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 157.95/24.49  | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 157.95/24.49  | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 157.95/24.49  | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 157.95/24.49  | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 157.95/24.49  | | | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 157.95/24.49  | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 157.95/24.49  | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 157.95/24.49  | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 157.95/24.49  | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 157.95/24.49  | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 157.95/24.49  | | | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 157.95/24.49  | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 157.95/24.49  | | | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 157.95/24.49  | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 157.95/24.49  | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 157.95/24.49  | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | Case 1:
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | |   (164)  all_54_15 = e1
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (69), (164) are inconsistent by sub-proof
% 157.95/24.49  | | | | | | | | | | | | | | | | | |            #1008.
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | Case 2:
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | |   (165)  all_54_15 = e0
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (165) imply:
% 157.95/24.49  | | | | | | | | | | | | | | | | | |   (166)  all_14_2 = e0
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | | SIMP: (166) implies:
% 157.95/24.49  | | | | | | | | | | | | | | | | | |   (167)  all_14_2 = e0
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | | REDUCE: (4), (167) imply:
% 157.95/24.49  | | | | | | | | | | | | | | | | | |   (168)   ~ (all_52_3 = e0)
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | | REDUCE: (1), (167) imply:
% 157.95/24.49  | | | | | | | | | | | | | | | | | |   (169)   ~ (all_52_7 = e0)
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | | REDUCE: (25), (167) imply:
% 157.95/24.49  | | | | | | | | | | | | | | | | | |   (170)   ~ (all_52_11 = e0)
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | | REDUCE: (92), (167) imply:
% 157.95/24.49  | | | | | | | | | | | | | | | | | |   (171)   ~ (e2 = e0)
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | | REDUCE: (69), (167) imply:
% 157.95/24.49  | | | | | | | | | | | | | | | | | |   (172)   ~ (e1 = e0)
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (17), (31), (47), (52), (67), (90),
% 157.95/24.49  | | | | | | | | | | | | | | | | | |            (163), (168), (169), (170) are inconsistent by
% 157.95/24.49  | | | | | | | | | | | | | | | | | |            sub-proof #277.
% 157.95/24.49  | | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | | End of split
% 157.95/24.49  | | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | | End of split
% 157.95/24.49  | | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | | End of split
% 157.95/24.49  | | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | | End of split
% 157.95/24.49  | | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | End of split
% 157.95/24.49  | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | End of split
% 157.95/24.49  | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | End of split
% 157.95/24.49  | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | End of split
% 157.95/24.49  | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | End of split
% 157.95/24.49  | | | | | | | | | 
% 157.95/24.49  | | | | | | | | Case 2:
% 157.95/24.49  | | | | | | | | | 
% 157.95/24.49  | | | | | | | | |   (173)  all_28_2 = e2
% 157.95/24.49  | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | COMBINE_EQS: (19), (173) imply:
% 157.95/24.49  | | | | | | | | |   (174)  all_14_2 = e2
% 157.95/24.49  | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | SIMP: (174) implies:
% 157.95/24.49  | | | | | | | | |   (175)  all_14_2 = e2
% 157.95/24.49  | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | REDUCE: (12), (175) imply:
% 157.95/24.49  | | | | | | | | |   (176)   ~ (all_52_13 = e2)
% 157.95/24.49  | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | REDUCE: (71), (175) imply:
% 157.95/24.49  | | | | | | | | |   (177)   ~ (e3 = e2)
% 157.95/24.49  | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | REDUCE: (42), (175) imply:
% 157.95/24.49  | | | | | | | | |   (178)  op(e0, e0) = e2
% 157.95/24.49  | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | BETA: splitting (60) gives:
% 157.95/24.49  | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | Case 1:
% 157.95/24.49  | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | |   (179)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 157.95/24.49  | | | | | | | | | |            & op(e2, e2) = e2)
% 157.95/24.49  | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | REF_CLOSE: (5), (15), (16), (43), (54), (179) are
% 157.95/24.49  | | | | | | | | | |            inconsistent by sub-proof #43.
% 157.95/24.49  | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | Case 2:
% 157.95/24.49  | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | |   (180)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2
% 157.95/24.49  | | | | | | | | | |            & op(e2, e0) = e2)
% 157.95/24.49  | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | BETA: splitting (180) gives:
% 157.95/24.49  | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | Case 1:
% 157.95/24.49  | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | |   (181)  all_56_5 = e2 & op(e2, e1) = e2
% 157.95/24.49  | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | ALPHA: (181) implies:
% 157.95/24.49  | | | | | | | | | | |   (182)  op(e2, e1) = e2
% 157.95/24.49  | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | BETA: splitting (11) gives:
% 157.95/24.49  | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | Case 1:
% 157.95/24.49  | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | |   (183)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 157.95/24.49  | | | | | | | | | | | |                e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2)
% 157.95/24.49  | | | | | | | | | | | |                & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 157.95/24.49  | | | | | | | | | | | |            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 157.95/24.49  | | | | | | | | | | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 157.95/24.49  | | | | | | | | | | | |                $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.95/24.49  | | | | | | | | | | | |                  e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 157.95/24.49  | | | | | | | | | | | |                  e3) = all_57_6 & $i(all_57_6)))) |
% 157.95/24.49  | | | | | | | | | | | |          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 157.95/24.49  | | | | | | | | | | | |                e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3)
% 157.95/24.49  | | | | | | | | | | | |                & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 157.95/24.49  | | | | | | | | | | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 157.95/24.49  | | | | | | | | | | | |                (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.95/24.49  | | | | | | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 157.95/24.49  | | | | | | | | | | | |                  e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 157.95/24.49  | | | | | | | | | | | |                  e2) = all_57_7 & $i(all_57_7))))
% 157.95/24.49  | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | REF_CLOSE: (15), (16), (20), (40), (48), (52), (182), (183)
% 157.95/24.49  | | | | | | | | | | | |            are inconsistent by sub-proof #236.
% 157.95/24.49  | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | Case 2:
% 157.95/24.49  | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | |   (184)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.95/24.49  | | | | | | | | | | | |                e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3)
% 157.95/24.49  | | | | | | | | | | | |                & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.95/24.49  | | | | | | | | | | | |            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.95/24.49  | | | | | | | | | | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.95/24.49  | | | | | | | | | | | |                $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.95/24.49  | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 157.95/24.49  | | | | | | | | | | | |                  e1) = all_57_8 & $i(all_57_8)))) |
% 157.95/24.49  | | | | | | | | | | | |          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.95/24.49  | | | | | | | | | | | |                e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3)
% 157.95/24.49  | | | | | | | | | | | |                & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.95/24.49  | | | | | | | | | | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.95/24.49  | | | | | | | | | | | |                (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.95/24.49  | | | | | | | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.95/24.49  | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.95/24.49  | | | | | | | | | | | |                  e0) = all_57_13 & $i(all_57_13))))
% 157.95/24.49  | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | BETA: splitting (184) gives:
% 157.95/24.49  | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | Case 1:
% 157.95/24.49  | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | |   (185)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 =
% 157.95/24.49  | | | | | | | | | | | | |              e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 157.95/24.49  | | | | | | | | | | | | |              op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 157.95/24.49  | | | | | | | | | | | | |          ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 157.95/24.49  | | | | | | | | | | | | |              (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.95/24.49  | | | | | | | | | | | | |              $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 157.95/24.49  | | | | | | | | | | | | |              = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 157.95/24.49  | | | | | | | | | | | | |              all_57_8 & $i(all_57_8)))
% 157.95/24.49  | | | | | | | | | | | | | 
% 157.95/24.49  | | | | | | | | | | | | | ALPHA: (185) implies:
% 157.95/24.50  | | | | | | | | | | | | |   (186)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5
% 157.95/24.50  | | | | | | | | | | | | |              = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))
% 157.95/24.50  | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | BETA: splitting (186) gives:
% 157.95/24.50  | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | Case 1:
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | |   (187)  all_57_12 = e1 & op(e2, e2) = e1
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | | ALPHA: (187) implies:
% 157.95/24.50  | | | | | | | | | | | | | |   (188)  op(e2, e2) = e1
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | | REF_CLOSE: (16), (54), (64), (188) are inconsistent by
% 157.95/24.50  | | | | | | | | | | | | | |            sub-proof #847.
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | Case 2:
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | |   (189)   ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 157.95/24.50  | | | | | | | | | | | | | |          $i(all_57_5)
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | | ALPHA: (189) implies:
% 157.95/24.50  | | | | | | | | | | | | | |   (190)   ~ (all_57_5 = e2)
% 157.95/24.50  | | | | | | | | | | | | | |   (191)  op(e2, e1) = all_57_5
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_52_9, all_57_5, e1,
% 157.95/24.50  | | | | | | | | | | | | | |              e2, simplifying with (48), (191) gives:
% 157.95/24.50  | | | | | | | | | | | | | |   (192)  all_57_5 = all_52_9
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with e2, all_57_5, e1, e2,
% 157.95/24.50  | | | | | | | | | | | | | |              simplifying with (182), (191) gives:
% 157.95/24.50  | | | | | | | | | | | | | |   (193)  all_57_5 = e2
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | | COMBINE_EQS: (192), (193) imply:
% 157.95/24.50  | | | | | | | | | | | | | |   (194)  all_52_9 = e2
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | | REDUCE: (190), (193) imply:
% 157.95/24.50  | | | | | | | | | | | | | |   (195)  $false
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 157.95/24.50  | | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | End of split
% 157.95/24.50  | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | Case 2:
% 157.95/24.50  | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | |   (196)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 =
% 157.95/24.50  | | | | | | | | | | | | |              e0 & op(e3, e3) = e0) | ( ~ (all_57_9 = e3) &
% 157.95/24.50  | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 157.95/24.50  | | | | | | | | | | | | |          ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 157.95/24.50  | | | | | | | | | | | | |              (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.95/24.50  | | | | | | | | | | | | |              $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 157.95/24.50  | | | | | | | | | | | | |                e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 157.95/24.50  | | | | | | | | | | | | |                e0) = all_57_13 & $i(all_57_13)))
% 157.95/24.50  | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | ALPHA: (196) implies:
% 157.95/24.50  | | | | | | | | | | | | |   (197)  op(e0, e0) = e0
% 157.95/24.50  | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | | REF_CLOSE: (16), (67), (178), (197) are inconsistent by
% 157.95/24.50  | | | | | | | | | | | | |            sub-proof #979.
% 157.95/24.50  | | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | End of split
% 157.95/24.50  | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | End of split
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | Case 2:
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | |   (198)  all_56_10 = e2 & op(e2, e0) = e2
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | ALPHA: (198) implies:
% 157.95/24.50  | | | | | | | | | | |   (199)  op(e2, e0) = e2
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | REF_CLOSE: (16), (51), (176), (199) are inconsistent by
% 157.95/24.50  | | | | | | | | | | |            sub-proof #996.
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | End of split
% 157.95/24.50  | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | End of split
% 157.95/24.50  | | | | | | | | | 
% 157.95/24.50  | | | | | | | | End of split
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | Case 2:
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | |   (200)  all_54_10 = e0
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | | REF_CLOSE: (41), (75), (200) are inconsistent by sub-proof #329.
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | End of split
% 157.95/24.50  | | | | | | | 
% 157.95/24.50  | | | | | | End of split
% 157.95/24.50  | | | | | | 
% 157.95/24.50  | | | | | End of split
% 157.95/24.50  | | | | | 
% 157.95/24.50  | | | | Case 2:
% 157.95/24.50  | | | | | 
% 157.95/24.50  | | | | |   (201)  all_22_2 = e0
% 157.95/24.50  | | | | | 
% 157.95/24.50  | | | | | COMBINE_EQS: (50), (201) imply:
% 157.95/24.50  | | | | |   (202)  all_10_2 = e0
% 157.95/24.50  | | | | | 
% 157.95/24.50  | | | | | SIMP: (202) implies:
% 157.95/24.50  | | | | |   (203)  all_10_2 = e0
% 157.95/24.50  | | | | | 
% 157.95/24.50  | | | | | REDUCE: (73), (203) imply:
% 157.95/24.50  | | | | |   (204)   ~ (e3 = e0)
% 157.95/24.50  | | | | | 
% 157.95/24.50  | | | | | REDUCE: (65), (203) imply:
% 157.95/24.50  | | | | |   (205)   ~ (e2 = e0)
% 157.95/24.50  | | | | | 
% 157.95/24.50  | | | | | REDUCE: (66), (203) imply:
% 157.95/24.50  | | | | |   (206)  op(e1, e1) = e0
% 157.95/24.50  | | | | | 
% 157.95/24.50  | | | | | BETA: splitting (11) gives:
% 157.95/24.50  | | | | | 
% 157.95/24.50  | | | | | Case 1:
% 157.95/24.50  | | | | | | 
% 157.95/24.50  | | | | | |   (207)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 &
% 157.95/24.50  | | | | | |                op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 157.95/24.50  | | | | | |                all_57_0 & $i(all_57_0))) & ((all_57_14 = e3 & op(e1,
% 157.95/24.50  | | | | | |                  e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 157.95/24.50  | | | | | |                all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 157.95/24.50  | | | | | |                  e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 157.95/24.50  | | | | | |                all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 157.95/24.50  | | | | | |              e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 157.95/24.50  | | | | | |                (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 157.95/24.50  | | | | | |                $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2)
% 157.95/24.50  | | | | | |              | ( ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 157.95/24.50  | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 157.95/24.50  | | | | | |              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 157.95/24.50  | | | | | |                $i(all_57_7))))
% 157.95/24.50  | | | | | | 
% 157.95/24.50  | | | | | | REF_CLOSE: (15), (16), (52), (54), (207) are inconsistent by
% 157.95/24.50  | | | | | |            sub-proof #42.
% 157.95/24.50  | | | | | | 
% 157.95/24.50  | | | | | Case 2:
% 157.95/24.50  | | | | | | 
% 157.95/24.50  | | | | | |   (208)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 &
% 157.95/24.50  | | | | | |                op(e3, e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) =
% 157.95/24.50  | | | | | |                all_57_4 & $i(all_57_4))) & ((all_57_12 = e1 & op(e2,
% 157.95/24.50  | | | | | |                  e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 157.95/24.50  | | | | | |                all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.95/24.50  | | | | | |                  e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 157.95/24.50  | | | | | |                all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 157.95/24.50  | | | | | |              e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 157.95/24.50  | | | | | |                (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 157.95/24.50  | | | | | |                $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0)
% 157.95/24.50  | | | | | |              | ( ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.95/24.50  | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 157.95/24.50  | | | | | |              | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 157.95/24.50  | | | | | |                $i(all_57_13))))
% 157.95/24.50  | | | | | | 
% 157.95/24.50  | | | | | | BETA: splitting (208) gives:
% 157.95/24.50  | | | | | | 
% 157.95/24.50  | | | | | | Case 1:
% 157.95/24.50  | | | | | | | 
% 157.95/24.50  | | | | | | |   (209)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 &
% 157.95/24.50  | | | | | | |              op(e3, e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) =
% 157.95/24.50  | | | | | | |              all_57_4 & $i(all_57_4))) & ((all_57_12 = e1 & op(e2,
% 157.95/24.50  | | | | | | |                e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 157.95/24.50  | | | | | | |              all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 157.95/24.50  | | | | | | |                e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 157.95/24.50  | | | | | | |              all_57_8 & $i(all_57_8)))
% 157.95/24.50  | | | | | | | 
% 157.95/24.50  | | | | | | | ALPHA: (209) implies:
% 157.95/24.50  | | | | | | |   (210)  op(e1, e1) = e1
% 157.95/24.50  | | | | | | | 
% 157.95/24.50  | | | | | | | REF_CLOSE: (16), (47), (206), (210) are inconsistent by sub-proof
% 157.95/24.50  | | | | | | |            #903.
% 157.95/24.50  | | | | | | | 
% 157.95/24.50  | | | | | | Case 2:
% 157.95/24.50  | | | | | | | 
% 157.95/24.50  | | | | | | |   (211)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 &
% 157.95/24.50  | | | | | | |              op(e3, e3) = e0) | ( ~ (all_57_9 = e3) & op(e3, e0) =
% 157.95/24.50  | | | | | | |              all_57_9 & $i(all_57_9))) & ((all_57_12 = e0 & op(e2,
% 157.95/24.50  | | | | | | |                e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 157.95/24.50  | | | | | | |              all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 &
% 157.95/24.50  | | | | | | |              op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0)
% 157.95/24.50  | | | | | | |              = all_57_13 & $i(all_57_13)))
% 157.95/24.50  | | | | | | | 
% 157.95/24.50  | | | | | | | ALPHA: (211) implies:
% 157.95/24.50  | | | | | | |   (212)  all_57_15 = e0
% 157.95/24.50  | | | | | | |   (213)  op(e0, e0) = e0
% 157.95/24.50  | | | | | | |   (214)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2)
% 157.95/24.50  | | | | | | |            & op(e2, e0) = all_57_11 & $i(all_57_11))
% 157.95/24.50  | | | | | | | 
% 157.95/24.50  | | | | | | | BETA: splitting (214) gives:
% 157.95/24.50  | | | | | | | 
% 157.95/24.50  | | | | | | | Case 1:
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | |   (215)  all_57_12 = e0 & op(e2, e2) = e0
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | | ALPHA: (215) implies:
% 157.95/24.50  | | | | | | | |   (216)  op(e2, e2) = e0
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | | REF_CLOSE: (16), (54), (68), (216) are inconsistent by sub-proof
% 157.95/24.50  | | | | | | | |            #945.
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | Case 2:
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | |   (217)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 157.95/24.50  | | | | | | | |          $i(all_57_11)
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | | ALPHA: (217) implies:
% 157.95/24.50  | | | | | | | |   (218)   ~ (all_57_11 = e2)
% 157.95/24.50  | | | | | | | |   (219)  op(e2, e0) = all_57_11
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | | BETA: splitting (63) gives:
% 157.95/24.50  | | | | | | | | 
% 157.95/24.50  | | | | | | | | Case 1:
% 157.95/24.50  | | | | | | | | | 
% 157.95/24.50  | | | | | | | | |   (220)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 157.95/24.50  | | | | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) =
% 157.95/24.50  | | | | | | | | |            e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.95/24.50  | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 157.95/24.50  | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 157.95/24.50  | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 157.95/24.50  | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 157.95/24.50  | | | | | | | | |            all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 157.95/24.50  | | | | | | | | |              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.95/24.50  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 157.95/24.50  | | | | | | | | |          | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.95/24.50  | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.95/24.50  | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3
% 157.95/24.50  | | | | | | | | |            & $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 157.95/24.50  | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 157.95/24.50  | | | | | | | | |            e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 157.95/24.50  | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.95/24.50  | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.95/24.50  | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 157.95/24.50  | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 157.95/24.50  | | | | | | | | |          | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.95/24.50  | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3
% 157.95/24.50  | | | | | | | | |            & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.95/24.50  | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 157.95/24.50  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 157.95/24.50  | | | | | | | | |          | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 157.95/24.50  | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) =
% 157.95/24.50  | | | | | | | | |            e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 157.95/24.50  | | | | | | | | |            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 &
% 157.95/24.50  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 157.95/24.50  | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 157.95/24.50  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 157.95/24.50  | | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 157.95/24.50  | | | | | | | | |            op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2
% 157.95/24.50  | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3)
% 157.95/24.50  | | | | | | | | |            = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 157.95/24.50  | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 157.95/24.50  | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 157.95/24.50  | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 157.95/24.50  | | | | | | | | |              e3) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.50  | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 &
% 157.95/24.50  | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.95/24.50  | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 157.95/24.50  | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 157.95/24.50  | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.95/24.50  | | | | | | | | |              e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 157.95/24.50  | | | | | | | | |              e3) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.50  | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 157.95/24.50  | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 157.95/24.50  | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 157.95/24.50  | | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.95/24.50  | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.95/24.50  | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 157.95/24.50  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 157.95/24.50  | | | | | | | | |          | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 157.95/24.50  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e1)
% 157.95/24.50  | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | BETA: splitting (220) gives:
% 157.95/24.50  | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | Case 1:
% 157.95/24.50  | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | |   (221)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.95/24.50  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 157.95/24.50  | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 157.95/24.50  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 157.95/24.50  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 157.95/24.50  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 157.95/24.50  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 157.95/24.50  | | | | | | | | | |            & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12
% 157.95/24.50  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 157.95/24.50  | | | | | | | | | |            all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 157.95/24.50  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 157.95/24.50  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 157.95/24.50  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 &
% 157.95/24.50  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 157.95/24.50  | | | | | | | | | |            & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12
% 157.95/24.50  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 157.95/24.50  | | | | | | | | | |            all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 157.95/24.50  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 157.95/24.50  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 157.95/24.50  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 157.95/24.50  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 157.95/24.50  | | | | | | | | | |            & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 157.95/24.50  | | | | | | | | | |            & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 157.95/24.50  | | | | | | | | | |            e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 157.95/24.50  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 157.95/24.50  | | | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 157.95/24.50  | | | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 157.95/24.50  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 157.95/24.50  | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 157.95/24.50  | | | | | | | | | |            $i(all_57_12))
% 157.95/24.50  | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | BETA: splitting (221) gives:
% 157.95/24.50  | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | Case 1:
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | |   (222)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 157.95/24.50  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 157.95/24.50  | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.95/24.50  | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.95/24.50  | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.95/24.50  | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 157.95/24.50  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.95/24.50  | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 157.95/24.50  | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 157.95/24.50  | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 157.95/24.50  | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.95/24.50  | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 157.95/24.50  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.95/24.50  | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 157.95/24.50  | | | | | | | | | | |            e3 & $i(all_57_10))
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | REF_CLOSE: (5), (16), (43), (222) are inconsistent by
% 157.95/24.50  | | | | | | | | | | |            sub-proof #1005.
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | Case 2:
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | |   (223)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.95/24.50  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.95/24.50  | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.95/24.50  | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.95/24.50  | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.95/24.50  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.95/24.50  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.95/24.50  | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 157.95/24.50  | | | | | | | | | | |            &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 157.95/24.50  | | | | | | | | | | |            e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 157.95/24.50  | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 157.95/24.50  | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 157.95/24.50  | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 157.95/24.50  | | | | | | | | | | |            e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 157.95/24.50  | | | | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 157.95/24.50  | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 157.95/24.50  | | | | | | | | | | |            & $i(all_57_12))
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | BETA: splitting (223) gives:
% 157.95/24.50  | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | Case 1:
% 157.95/24.50  | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | |   (224)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 157.95/24.50  | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 157.95/24.50  | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 157.95/24.50  | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 157.95/24.50  | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 157.95/24.50  | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.95/24.50  | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 157.95/24.50  | | | | | | | | | | | |            $i(all_57_10))
% 157.95/24.50  | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | | REF_CLOSE: (5), (16), (43), (224) are inconsistent by
% 157.95/24.50  | | | | | | | | | | | |            sub-proof #1004.
% 157.95/24.50  | | | | | | | | | | | | 
% 157.95/24.50  | | | | | | | | | | | Case 2:
% 157.95/24.50  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | |   (225)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.95/24.51  | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 157.95/24.51  | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 157.95/24.51  | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.95/24.51  | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.95/24.51  | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.95/24.51  | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.95/24.51  | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | BETA: splitting (225) gives:
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | Case 1:
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | |   (226)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 157.95/24.51  | | | | | | | | | | | | |          op(e2, e3) = e2 & op(e2, e2) = e2
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | ALPHA: (226) implies:
% 157.95/24.51  | | | | | | | | | | | | |   (227)  op(e2, e3) = e2
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | REF_CLOSE: (5), (16), (43), (227) are inconsistent by
% 157.95/24.51  | | | | | | | | | | | | |            sub-proof #1007.
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | Case 2:
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | |   (228)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 157.95/24.51  | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.95/24.51  | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 157.95/24.51  | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 157.95/24.51  | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.95/24.51  | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | BETA: splitting (228) gives:
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | Case 1:
% 157.95/24.51  | | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | |   (229)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 157.95/24.51  | | | | | | | | | | | | | |          ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.95/24.51  | | | | | | | | | | | | | |          op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 157.95/24.51  | | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | | ALPHA: (229) implies:
% 157.95/24.51  | | | | | | | | | | | | | |   (230)  op(e1, e1) = e3
% 157.95/24.51  | | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | | REF_CLOSE: (16), (68), (206), (230) are inconsistent by
% 157.95/24.51  | | | | | | | | | | | | | |            sub-proof #912.
% 157.95/24.51  | | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | Case 2:
% 157.95/24.51  | | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | |   (231)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 157.95/24.51  | | | | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 157.95/24.51  | | | | | | | | | | | | | |          = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 157.95/24.51  | | | | | | | | | | | | | |          $i(all_57_12)
% 157.95/24.51  | | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | | ALPHA: (231) implies:
% 157.95/24.51  | | | | | | | | | | | | | |   (232)  op(e3, e2) = e3
% 157.95/24.51  | | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (44), (232) are inconsistent by
% 157.95/24.51  | | | | | | | | | | | | | |            sub-proof #998.
% 157.95/24.51  | | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | End of split
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | End of split
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | End of split
% 157.95/24.51  | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | End of split
% 157.95/24.51  | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | Case 2:
% 157.95/24.51  | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | |   (233)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.95/24.51  | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.95/24.51  | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.95/24.51  | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.95/24.51  | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.95/24.51  | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.95/24.51  | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3)
% 157.95/24.51  | | | | | | | | | |            = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 157.95/24.51  | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1
% 157.95/24.51  | | | | | | | | | |            & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14
% 157.95/24.51  | | | | | | | | | |              = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.95/24.51  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.51  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 &
% 157.95/24.51  | | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 157.95/24.51  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 157.95/24.51  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 157.95/24.51  | | | | | | | | | |            & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14
% 157.95/24.51  | | | | | | | | | |              = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.95/24.51  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.51  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 157.95/24.51  | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3)
% 157.95/24.51  | | | | | | | | | |            = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 157.95/24.51  | | | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1
% 157.95/24.51  | | | | | | | | | |            & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10
% 157.95/24.51  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 157.95/24.51  | | | | | | | | | |            e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.95/24.51  | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.95/24.51  | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | |            e1)
% 157.95/24.51  | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | BETA: splitting (233) gives:
% 157.95/24.51  | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | Case 1:
% 157.95/24.51  | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | |   (234)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.95/24.51  | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.95/24.51  | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.95/24.51  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.95/24.51  | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.95/24.51  | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 157.95/24.51  | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 157.95/24.51  | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 157.95/24.51  | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 157.95/24.51  | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.95/24.51  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 157.95/24.51  | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 157.95/24.51  | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | BETA: splitting (234) gives:
% 157.95/24.51  | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | Case 1:
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | |   (235)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.95/24.51  | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 157.95/24.51  | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.95/24.51  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 157.95/24.51  | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 157.95/24.51  | | | | | | | | | | | |              e2) = e3)
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | REF_CLOSE: (16), (52), (68), (213), (235) are inconsistent by
% 157.95/24.51  | | | | | | | | | | | |            sub-proof #287.
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | Case 2:
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | |   (236)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 157.95/24.51  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 157.95/24.51  | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 157.95/24.51  | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 157.95/24.51  | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 157.95/24.51  | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 157.95/24.51  | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.51  | | | | | | | | | | | |            $i(all_57_14))
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | BETA: splitting (236) gives:
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | Case 1:
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | |   (237)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 157.95/24.51  | | | | | | | | | | | | |          ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 157.95/24.51  | | | | | | | | | | | | |          = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.95/24.51  | | | | | | | | | | | | |          $i(all_57_12)
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | ALPHA: (237) implies:
% 157.95/24.51  | | | | | | | | | | | | |   (238)  op(e2, e0) = e2
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | REF_CLOSE: (16), (51), (218), (219), (238) are inconsistent
% 157.95/24.51  | | | | | | | | | | | | |            by sub-proof #627.
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | Case 2:
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | |   (239)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.95/24.51  | | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 157.95/24.51  | | | | | | | | | | | | |          = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.51  | | | | | | | | | | | | |          $i(all_57_14)
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | ALPHA: (239) implies:
% 157.95/24.51  | | | | | | | | | | | | |   (240)  op(e3, e3) = e1
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | | REF_CLOSE: (16), (52), (56), (240) are inconsistent by
% 157.95/24.51  | | | | | | | | | | | | |            sub-proof #828.
% 157.95/24.51  | | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | End of split
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | End of split
% 157.95/24.51  | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | Case 2:
% 157.95/24.51  | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | |   (241)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.95/24.51  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.95/24.51  | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.95/24.51  | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.95/24.51  | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.95/24.51  | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 157.95/24.51  | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.95/24.51  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.95/24.51  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.95/24.51  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.95/24.51  | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.95/24.51  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.95/24.51  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.95/24.51  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.95/24.51  | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | | |            e1)
% 157.95/24.51  | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | BETA: splitting (241) gives:
% 157.95/24.51  | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | Case 1:
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | |   (242)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 157.95/24.51  | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.95/24.51  | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 157.95/24.51  | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 157.95/24.51  | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 157.95/24.51  | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | REF_CLOSE: (16), (54), (64), (68), (206), (242) are
% 157.95/24.51  | | | | | | | | | | | |            inconsistent by sub-proof #41.
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | Case 2:
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | |   (243)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.95/24.51  | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 157.95/24.51  | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.95/24.51  | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 157.95/24.51  | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 157.95/24.51  | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 157.95/24.51  | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 157.95/24.51  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 157.95/24.51  | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | | | |            e1)
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | | REF_CLOSE: (16), (42), (47), (68), (206), (213), (243) are
% 157.95/24.51  | | | | | | | | | | | |            inconsistent by sub-proof #240.
% 157.95/24.51  | | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | | End of split
% 157.95/24.51  | | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | End of split
% 157.95/24.51  | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | End of split
% 157.95/24.51  | | | | | | | | | 
% 157.95/24.51  | | | | | | | | Case 2:
% 157.95/24.51  | | | | | | | | | 
% 157.95/24.51  | | | | | | | | |   (244)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 157.95/24.51  | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) =
% 157.95/24.51  | | | | | | | | |            e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.51  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 157.95/24.51  | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 157.95/24.51  | | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 157.95/24.51  | | | | | | | | |            = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.95/24.51  | | | | | | | | |            all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 157.95/24.51  | | | | | | | | |              e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 157.95/24.51  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 157.95/24.51  | | | | | | | | |          | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.95/24.51  | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.95/24.51  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 157.95/24.51  | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 157.95/24.51  | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 157.95/24.51  | | | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 157.95/24.51  | | | | | | | | |            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 157.95/24.51  | | | | | | | | |            op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 157.95/24.51  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 157.95/24.51  | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.95/24.51  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 157.95/24.51  | | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 157.95/24.51  | | | | | | | | |            op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 157.95/24.51  | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3)
% 157.95/24.51  | | | | | | | | |            = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 157.95/24.51  | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 &
% 157.95/24.51  | | | | | | | | |            all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 157.95/24.51  | | | | | | | | |              e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 157.95/24.51  | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 157.95/24.51  | | | | | | | | |          | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 157.95/24.51  | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2
% 157.95/24.51  | | | | | | | | |            & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 157.95/24.51  | | | | | | | | |              e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 157.95/24.51  | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 &
% 157.95/24.51  | | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 157.95/24.51  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 157.95/24.51  | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 157.95/24.51  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 &
% 157.95/24.51  | | | | | | | | |            all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 157.95/24.51  | | | | | | | | |              e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 157.95/24.51  | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 157.95/24.51  | | | | | | | | |          | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 157.95/24.51  | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 157.95/24.51  | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 157.95/24.51  | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14
% 157.95/24.51  | | | | | | | | |            = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0)
% 157.95/24.51  | | | | | | | | |            = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 157.95/24.51  | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 157.95/24.51  | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 157.95/24.51  | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 157.95/24.51  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.95/24.51  | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 157.95/24.51  | | | | | | | | |                = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 157.95/24.51  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.95/24.51  | | | | | | | | |                  = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.95/24.51  | | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 157.95/24.51  | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 157.95/24.51  | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 157.95/24.51  | | | | | | | | |                 ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 157.95/24.51  | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 157.95/24.51  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.95/24.51  | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 157.95/24.51  | | | | | | | | |                = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 157.95/24.51  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.95/24.51  | | | | | | | | |                  = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.95/24.51  | | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 157.95/24.51  | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 157.95/24.51  | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 157.95/24.51  | | | | | | | | |                 ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 157.95/24.51  | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0
% 157.95/24.51  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 157.95/24.51  | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 157.95/24.51  | | | | | | | | |                = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 157.95/24.51  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 157.95/24.51  | | | | | | | | |                  = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 157.95/24.51  | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 157.95/24.51  | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 157.95/24.51  | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 157.95/24.51  | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 157.95/24.51  | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 157.95/24.51  | | | | | | | | |                = e0)))
% 157.95/24.51  | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | BETA: splitting (244) gives:
% 157.95/24.51  | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | Case 1:
% 157.95/24.51  | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | |   (245)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.95/24.51  | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 157.95/24.51  | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.51  | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 157.95/24.51  | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 157.95/24.51  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 157.95/24.51  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 157.95/24.51  | | | | | | | | | |            e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 157.95/24.51  | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.95/24.51  | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 =
% 157.95/24.51  | | | | | | | | | |            e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 157.95/24.51  | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 157.95/24.51  | | | | | | | | | |              e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 157.95/24.51  | | | | | | | | | |          (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 157.95/24.51  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.95/24.51  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.95/24.51  | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.95/24.51  | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 157.95/24.51  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 157.95/24.51  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 157.95/24.51  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3
% 157.95/24.51  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3
% 157.95/24.51  | | | | | | | | | |            & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 =
% 157.95/24.51  | | | | | | | | | |            e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 157.95/24.51  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 157.95/24.51  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 157.95/24.51  | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | BETA: splitting (245) gives:
% 157.95/24.51  | | | | | | | | | | 
% 157.95/24.51  | | | | | | | | | | Case 1:
% 157.95/24.51  | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | |   (246)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.95/24.52  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.95/24.52  | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.52  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.95/24.52  | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.95/24.52  | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.95/24.52  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.52  | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 157.95/24.52  | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 157.95/24.52  | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 157.95/24.52  | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 157.95/24.52  | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 157.95/24.52  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 157.95/24.52  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 157.95/24.52  | | | | | | | | | | |            = e1 & $i(all_57_14))
% 157.95/24.52  | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | BETA: splitting (246) gives:
% 157.95/24.52  | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | Case 1:
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | |   (247)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 157.95/24.52  | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 157.95/24.52  | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.52  | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 157.95/24.52  | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 157.95/24.52  | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 157.95/24.52  | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.52  | | | | | | | | | | | |            $i(all_57_14))
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | | REF_CLOSE: (16), (52), (54), (56), (64), (247) are
% 157.95/24.52  | | | | | | | | | | | |            inconsistent by sub-proof #44.
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | Case 2:
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | |   (248)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 157.95/24.52  | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 157.95/24.52  | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.52  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 157.95/24.52  | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 157.95/24.52  | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 157.95/24.52  | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 157.95/24.52  | | | | | | | | | | | |            $i(all_57_14))
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | | REF_CLOSE: (16), (42), (47), (67), (206), (213), (248) are
% 157.95/24.52  | | | | | | | | | | | |            inconsistent by sub-proof #491.
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | End of split
% 157.95/24.52  | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | Case 2:
% 157.95/24.52  | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | |   (249)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 157.95/24.52  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.95/24.52  | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.52  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.95/24.52  | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.95/24.52  | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 157.95/24.52  | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 157.95/24.52  | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 157.95/24.52  | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 157.95/24.52  | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 157.95/24.52  | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 157.95/24.52  | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 157.95/24.52  | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 157.95/24.52  | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 157.95/24.52  | | | | | | | | | | |            & $i(all_57_14))
% 157.95/24.52  | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | BETA: splitting (249) gives:
% 157.95/24.52  | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | Case 1:
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | |   (250)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 157.95/24.52  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 157.95/24.52  | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 157.95/24.52  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 157.95/24.52  | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 157.95/24.52  | | | | | | | | | | | |              e1) = e1)
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | | REF_CLOSE: (16), (47), (67), (206), (250) are inconsistent by
% 157.95/24.52  | | | | | | | | | | | |            sub-proof #701.
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | Case 2:
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | |   (251)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 157.95/24.52  | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 157.95/24.52  | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 157.95/24.52  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 157.95/24.52  | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 157.95/24.52  | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 157.95/24.52  | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 157.95/24.52  | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 157.95/24.52  | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | | REF_CLOSE: (15), (16), (52), (56), (68), (213), (251) are
% 157.95/24.52  | | | | | | | | | | | |            inconsistent by sub-proof #283.
% 157.95/24.52  | | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | | End of split
% 157.95/24.52  | | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | | End of split
% 157.95/24.52  | | | | | | | | | | 
% 157.95/24.52  | | | | | | | | | Case 2:
% 157.95/24.52  | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | |   (252)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.00/24.52  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.00/24.52  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.00/24.52  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.00/24.52  | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.00/24.52  | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.00/24.52  | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2)
% 158.00/24.52  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 &
% 158.00/24.52  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0
% 158.00/24.52  | | | | | | | | | |            & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10
% 158.00/24.52  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 158.00/24.52  | | | | | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.00/24.52  | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 158.00/24.52  | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 158.00/24.52  | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 158.00/24.52  | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.00/24.52  | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 158.00/24.52  | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 158.00/24.52  | | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 158.00/24.52  | | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 158.00/24.52  | | | | | | | | | |            all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.00/24.52  | | | | | | | | | |            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 158.00/24.52  | | | | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 158.00/24.52  | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3,
% 158.00/24.52  | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 158.00/24.52  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_11 = e2 &
% 158.00/24.52  | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2,
% 158.00/24.52  | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 158.00/24.52  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 158.00/24.52  | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 158.00/24.52  | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.00/24.52  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.00/24.52  | | | | | | | | | |                (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0
% 158.00/24.52  | | | | | | | | | |                & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.00/24.52  | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.00/24.52  | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.00/24.52  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.00/24.52  | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 158.00/24.52  | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.00/24.52  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.00/24.52  | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.00/24.52  | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.00/24.52  | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 158.00/24.52  | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 158.00/24.52  | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.00/24.52  | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.00/24.52  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 = e2
% 158.00/24.52  | | | | | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.00/24.52  | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.00/24.52  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 158.00/24.52  | | | | | | | | | |                & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.00/24.52  | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.00/24.52  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 158.00/24.52  | | | | | | | | | |                & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.00/24.52  | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.00/24.52  | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 158.00/24.52  | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0,
% 158.00/24.52  | | | | | | | | | |                  e1) = e0)))
% 158.00/24.52  | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | BETA: splitting (252) gives:
% 158.00/24.52  | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | Case 1:
% 158.00/24.52  | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | |   (253)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.00/24.52  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.00/24.52  | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.00/24.52  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.00/24.52  | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.00/24.52  | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.00/24.52  | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 158.00/24.52  | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 158.00/24.52  | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 158.00/24.52  | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 158.00/24.52  | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.00/24.52  | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.00/24.52  | | | | | | | | | | |            e3 & $i(all_57_10))
% 158.00/24.52  | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | BETA: splitting (253) gives:
% 158.00/24.52  | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | Case 1:
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | |   (254)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.00/24.52  | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.00/24.52  | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.00/24.52  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.00/24.52  | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.00/24.52  | | | | | | | | | | | |              e1) = e2)
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | | REF_CLOSE: (15), (16), (54), (67), (213), (254) are
% 158.00/24.52  | | | | | | | | | | | |            inconsistent by sub-proof #51.
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | Case 2:
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | |   (255)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 158.00/24.52  | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 158.00/24.52  | | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.00/24.52  | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 158.00/24.52  | | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 158.00/24.52  | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.00/24.52  | | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.00/24.52  | | | | | | | | | | | |            $i(all_57_10))
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | | REF_CLOSE: (16), (54), (64), (68), (213), (255) are
% 158.00/24.52  | | | | | | | | | | | |            inconsistent by sub-proof #50.
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | End of split
% 158.00/24.52  | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | Case 2:
% 158.00/24.52  | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | |   (256)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 158.00/24.52  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.00/24.52  | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.00/24.52  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.00/24.52  | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.00/24.52  | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 158.00/24.52  | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 158.00/24.52  | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 158.00/24.52  | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 158.00/24.52  | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.00/24.52  | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.00/24.52  | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 158.00/24.52  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.00/24.52  | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 158.00/24.52  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 158.00/24.52  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.00/24.52  | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 158.00/24.52  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 158.00/24.52  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 158.00/24.52  | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 158.00/24.52  | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.00/24.52  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.00/24.52  | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.00/24.52  | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.00/24.52  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.00/24.52  | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 158.00/24.52  | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.00/24.52  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.00/24.52  | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.00/24.52  | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.00/24.52  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 158.00/24.52  | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 158.00/24.52  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.00/24.52  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.00/24.52  | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 158.00/24.52  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.00/24.52  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.00/24.52  | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.00/24.52  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.00/24.52  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.00/24.52  | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.00/24.52  | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.00/24.52  | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.00/24.52  | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 158.00/24.52  | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.00/24.52  | | | | | | | | | | |                op(e0, e1) = e0)))
% 158.00/24.52  | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | BETA: splitting (256) gives:
% 158.00/24.52  | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | Case 1:
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | |   (257)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 158.00/24.52  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.00/24.52  | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.00/24.52  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.00/24.52  | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.00/24.52  | | | | | | | | | | | |              e0) = e3)
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | | REF_CLOSE: (15), (16), (52), (67), (213), (257) are
% 158.00/24.52  | | | | | | | | | | | |            inconsistent by sub-proof #282.
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | Case 2:
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | |   (258)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.00/24.52  | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 158.00/24.52  | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 158.00/24.52  | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.00/24.52  | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.00/24.52  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.00/24.52  | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.00/24.52  | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.00/24.52  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.00/24.52  | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.00/24.52  | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.00/24.52  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.00/24.52  | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.00/24.52  | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.00/24.52  | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.00/24.52  | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.00/24.52  | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.00/24.52  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.00/24.52  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.00/24.52  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.00/24.52  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.00/24.52  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.00/24.52  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.00/24.52  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.00/24.52  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.00/24.52  | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.00/24.52  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.00/24.52  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.00/24.52  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.00/24.52  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.00/24.52  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.00/24.52  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.00/24.52  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.00/24.52  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.00/24.52  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.00/24.52  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.00/24.52  | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.00/24.52  | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.00/24.52  | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.00/24.52  | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.00/24.52  | | | | | | | | | | | |                e0)))
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | | BETA: splitting (258) gives:
% 158.00/24.52  | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | | Case 1:
% 158.00/24.52  | | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | | |   (259)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.00/24.52  | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 158.00/24.52  | | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | | | ALPHA: (259) implies:
% 158.00/24.52  | | | | | | | | | | | | |   (260)  op(e2, e2) = e2
% 158.00/24.52  | | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | | | REF_CLOSE: (15), (16), (54), (260) are inconsistent by
% 158.00/24.52  | | | | | | | | | | | | |            sub-proof #54.
% 158.00/24.52  | | | | | | | | | | | | | 
% 158.00/24.52  | | | | | | | | | | | | Case 2:
% 158.00/24.52  | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | |   (261)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.00/24.53  | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.00/24.53  | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.00/24.53  | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.00/24.53  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.00/24.53  | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.00/24.53  | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.00/24.53  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.00/24.53  | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.00/24.53  | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.00/24.53  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.00/24.53  | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.00/24.53  | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.00/24.53  | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.00/24.53  | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.00/24.53  | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.00/24.53  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.00/24.53  | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.00/24.53  | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.00/24.53  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.00/24.53  | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.00/24.53  | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.00/24.53  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.00/24.53  | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.00/24.53  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.00/24.53  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.00/24.53  | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.00/24.53  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.00/24.53  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.00/24.53  | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.00/24.53  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.00/24.53  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.00/24.53  | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.00/24.53  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.00/24.53  | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.00/24.53  | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.00/24.53  | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.00/24.53  | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.00/24.53  | | | | | | | | | | | | |                e0)))
% 158.00/24.53  | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | BETA: splitting (261) gives:
% 158.00/24.53  | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | Case 1:
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | |   (262)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.00/24.53  | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | | ALPHA: (262) implies:
% 158.00/24.53  | | | | | | | | | | | | | |   (263)  op(e1, e1) = e1
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | | REF_CLOSE: (16), (47), (206), (263) are inconsistent by
% 158.00/24.53  | | | | | | | | | | | | | |            sub-proof #903.
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | Case 2:
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | |   (264)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.00/24.53  | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.00/24.53  | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.00/24.53  | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.00/24.53  | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.00/24.53  | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.00/24.53  | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.00/24.53  | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.00/24.53  | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.00/24.53  | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.00/24.53  | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.00/24.53  | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.00/24.53  | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 158.00/24.53  | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.00/24.53  | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.00/24.53  | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.00/24.53  | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.00/24.53  | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.00/24.53  | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.00/24.53  | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.00/24.53  | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 158.00/24.53  | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.00/24.53  | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.00/24.53  | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.00/24.53  | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.00/24.53  | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.00/24.53  | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 158.00/24.53  | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.00/24.53  | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 158.00/24.53  | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.00/24.53  | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.00/24.53  | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.00/24.53  | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.00/24.53  | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.00/24.53  | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.00/24.53  | | | | | | | | | | | | | |              e0))
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | | ALPHA: (264) implies:
% 158.00/24.53  | | | | | | | | | | | | | |   (265)  op(e0, e0) = all_57_15
% 158.00/24.53  | | | | | | | | | | | | | |   (266)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.00/24.53  | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.00/24.53  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.00/24.53  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.00/24.53  | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.00/24.53  | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.00/24.53  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.00/24.53  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.00/24.53  | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.00/24.53  | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.00/24.53  | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.00/24.53  | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.00/24.53  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.00/24.53  | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.00/24.53  | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.00/24.53  | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.00/24.53  | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.00/24.53  | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 158.00/24.53  | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.00/24.53  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.00/24.53  | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.00/24.53  | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.00/24.53  | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.00/24.53  | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 158.00/24.53  | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 158.00/24.53  | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 158.00/24.53  | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.00/24.53  | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.00/24.53  | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.00/24.53  | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.00/24.53  | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.00/24.53  | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.00/24.53  | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_14_2, e0, e0, e0,
% 158.00/24.53  | | | | | | | | | | | | | |              simplifying with (42), (213) gives:
% 158.00/24.53  | | | | | | | | | | | | | |   (267)  all_14_2 = e0
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | | REDUCE: (4), (267) imply:
% 158.00/24.53  | | | | | | | | | | | | | |   (268)   ~ (all_52_3 = e0)
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | | REDUCE: (1), (267) imply:
% 158.00/24.53  | | | | | | | | | | | | | |   (269)   ~ (all_52_7 = e0)
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | | REDUCE: (25), (267) imply:
% 158.00/24.53  | | | | | | | | | | | | | |   (270)   ~ (all_52_11 = e0)
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (17), (31), (266), (268), (269), (270)
% 158.00/24.53  | | | | | | | | | | | | | |            are inconsistent by sub-proof #97.
% 158.00/24.53  | | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | | End of split
% 158.00/24.53  | | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | | End of split
% 158.00/24.53  | | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | | End of split
% 158.00/24.53  | | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | | End of split
% 158.00/24.53  | | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | End of split
% 158.00/24.53  | | | | | | | | | 
% 158.00/24.53  | | | | | | | | End of split
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | End of split
% 158.00/24.53  | | | | | | | 
% 158.00/24.53  | | | | | | End of split
% 158.00/24.53  | | | | | | 
% 158.00/24.53  | | | | | End of split
% 158.00/24.53  | | | | | 
% 158.00/24.53  | | | | End of split
% 158.00/24.53  | | | | 
% 158.00/24.53  | | | Case 2:
% 158.00/24.53  | | | | 
% 158.00/24.53  | | | |   (271)  all_20_2 = e3
% 158.00/24.53  | | | | 
% 158.00/24.53  | | | | COMBINE_EQS: (53), (271) imply:
% 158.00/24.53  | | | |   (272)  all_10_2 = e3
% 158.00/24.53  | | | | 
% 158.00/24.53  | | | | SIMP: (272) implies:
% 158.00/24.53  | | | |   (273)  all_10_2 = e3
% 158.00/24.53  | | | | 
% 158.00/24.53  | | | | REDUCE: (62), (273) imply:
% 158.00/24.53  | | | |   (274)   ~ (all_52_8 = e3)
% 158.00/24.53  | | | | 
% 158.00/24.53  | | | | REDUCE: (66), (273) imply:
% 158.00/24.53  | | | |   (275)  op(e1, e1) = e3
% 158.00/24.53  | | | | 
% 158.00/24.53  | | | | BETA: splitting (38) gives:
% 158.00/24.53  | | | | 
% 158.00/24.53  | | | | Case 1:
% 158.00/24.53  | | | | | 
% 158.00/24.53  | | | | |   (276)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3,
% 158.00/24.53  | | | | |              e2) = e3)
% 158.00/24.53  | | | | | 
% 158.00/24.53  | | | | | REF_CLOSE: (8), (15), (16), (44), (52), (276) are inconsistent by
% 158.00/24.53  | | | | |            sub-proof #40.
% 158.00/24.53  | | | | | 
% 158.00/24.53  | | | | Case 2:
% 158.00/24.53  | | | | | 
% 158.00/24.53  | | | | |   (277)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3,
% 158.00/24.53  | | | | |              e0) = e3)
% 158.00/24.53  | | | | | 
% 158.00/24.53  | | | | | BETA: splitting (277) gives:
% 158.00/24.53  | | | | | 
% 158.00/24.53  | | | | | Case 1:
% 158.00/24.53  | | | | | | 
% 158.00/24.53  | | | | | |   (278)  all_56_4 = e3 & op(e3, e1) = e3
% 158.00/24.53  | | | | | | 
% 158.00/24.53  | | | | | | ALPHA: (278) implies:
% 158.00/24.53  | | | | | |   (279)  op(e3, e1) = e3
% 158.00/24.53  | | | | | | 
% 158.00/24.53  | | | | | | REF_CLOSE: (16), (18), (274), (279) are inconsistent by sub-proof
% 158.00/24.53  | | | | | |            #982.
% 158.00/24.53  | | | | | | 
% 158.00/24.53  | | | | | Case 2:
% 158.00/24.53  | | | | | | 
% 158.00/24.53  | | | | | |   (280)  all_56_9 = e3 & op(e3, e0) = e3
% 158.00/24.53  | | | | | | 
% 158.00/24.53  | | | | | | ALPHA: (280) implies:
% 158.00/24.53  | | | | | |   (281)  all_56_9 = e3
% 158.00/24.53  | | | | | |   (282)  op(e3, e0) = e3
% 158.00/24.53  | | | | | | 
% 158.00/24.53  | | | | | | BETA: splitting (11) gives:
% 158.00/24.53  | | | | | | 
% 158.00/24.53  | | | | | | Case 1:
% 158.00/24.53  | | | | | | | 
% 158.00/24.53  | | | | | | |   (283)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 &
% 158.00/24.53  | | | | | | |                op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3)
% 158.00/24.53  | | | | | | |                = all_57_0 & $i(all_57_0))) & ((all_57_14 = e3 &
% 158.00/24.53  | | | | | | |                op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.00/24.53  | | | | | | |                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 &
% 158.00/24.53  | | | | | | |                op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3)
% 158.00/24.53  | | | | | | |                = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 &
% 158.00/24.53  | | | | | | |            op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.00/24.53  | | | | | | |              ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.00/24.53  | | | | | | |                $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) =
% 158.00/24.53  | | | | | | |                e2) | ( ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 158.00/24.53  | | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 158.00/24.53  | | | | | | |                e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 158.00/24.53  | | | | | | |                $i(all_57_7))))
% 158.00/24.53  | | | | | | | 
% 158.00/24.53  | | | | | | | BETA: splitting (283) gives:
% 158.00/24.53  | | | | | | | 
% 158.00/24.53  | | | | | | | Case 1:
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | |   (284)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 &
% 158.00/24.53  | | | | | | | |              op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3)
% 158.00/24.53  | | | | | | | |              = all_57_0 & $i(all_57_0))) & ((all_57_14 = e3 &
% 158.00/24.53  | | | | | | | |              op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.00/24.53  | | | | | | | |              = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 &
% 158.00/24.53  | | | | | | | |              op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3)
% 158.00/24.53  | | | | | | | |              = all_57_6 & $i(all_57_6)))
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | | ALPHA: (284) implies:
% 158.00/24.53  | | | | | | | |   (285)  op(e3, e3) = e3
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | | REF_CLOSE: (6), (13), (15), (16), (45), (47), (56), (64), (67),
% 158.00/24.53  | | | | | | | |            (68), (281), (285) are inconsistent by sub-proof
% 158.00/24.53  | | | | | | | |            #632.
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | Case 2:
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | |   (286)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 &
% 158.00/24.53  | | | | | | | |              op(e3, e3) = e2) | ( ~ (all_57_1 = e3) & op(e3, e2)
% 158.00/24.53  | | | | | | | |              = all_57_1 & $i(all_57_1))) & ((all_57_14 = e2 &
% 158.00/24.53  | | | | | | | |              op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.00/24.53  | | | | | | | |              = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 &
% 158.00/24.53  | | | | | | | |              op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2)
% 158.00/24.53  | | | | | | | |              = all_57_7 & $i(all_57_7)))
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | | ALPHA: (286) implies:
% 158.00/24.53  | | | | | | | |   (287)  op(e2, e2) = e2
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | | REF_CLOSE: (15), (16), (54), (287) are inconsistent by sub-proof
% 158.00/24.53  | | | | | | | |            #54.
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | End of split
% 158.00/24.53  | | | | | | | 
% 158.00/24.53  | | | | | | Case 2:
% 158.00/24.53  | | | | | | | 
% 158.00/24.53  | | | | | | |   (288)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 &
% 158.00/24.53  | | | | | | |                op(e3, e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1)
% 158.00/24.53  | | | | | | |                = all_57_4 & $i(all_57_4))) & ((all_57_12 = e1 &
% 158.00/24.53  | | | | | | |                op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.00/24.53  | | | | | | |                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 &
% 158.00/24.53  | | | | | | |                op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1)
% 158.00/24.53  | | | | | | |                = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 &
% 158.00/24.53  | | | | | | |            op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.00/24.53  | | | | | | |              ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 158.00/24.53  | | | | | | |                $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) =
% 158.00/24.53  | | | | | | |                e0) | ( ~ (all_57_11 = e2) & op(e2, e0) = all_57_11
% 158.00/24.53  | | | | | | |                & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 158.00/24.53  | | | | | | |                e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13
% 158.00/24.53  | | | | | | |                & $i(all_57_13))))
% 158.00/24.53  | | | | | | | 
% 158.00/24.53  | | | | | | | BETA: splitting (288) gives:
% 158.00/24.53  | | | | | | | 
% 158.00/24.53  | | | | | | | Case 1:
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | |   (289)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 &
% 158.00/24.53  | | | | | | | |              op(e3, e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1)
% 158.00/24.53  | | | | | | | |              = all_57_4 & $i(all_57_4))) & ((all_57_12 = e1 &
% 158.00/24.53  | | | | | | | |              op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.00/24.53  | | | | | | | |              = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 &
% 158.00/24.53  | | | | | | | |              op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1)
% 158.00/24.53  | | | | | | | |              = all_57_8 & $i(all_57_8)))
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | | ALPHA: (289) implies:
% 158.00/24.53  | | | | | | | |   (290)  op(e1, e1) = e1
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | | REF_CLOSE: (16), (64), (275), (290) are inconsistent by
% 158.00/24.53  | | | | | | | |            sub-proof #1003.
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | Case 2:
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | |   (291)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 &
% 158.00/24.53  | | | | | | | |              op(e3, e3) = e0) | ( ~ (all_57_9 = e3) & op(e3, e0)
% 158.00/24.53  | | | | | | | |              = all_57_9 & $i(all_57_9))) & ((all_57_12 = e0 &
% 158.00/24.53  | | | | | | | |              op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 158.00/24.53  | | | | | | | |                e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 =
% 158.00/24.53  | | | | | | | |              e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) &
% 158.00/24.53  | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_13)))
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | | ALPHA: (291) implies:
% 158.00/24.53  | | | | | | | |   (292)  (all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 158.00/24.53  | | | | | | | |              e3) & op(e3, e0) = all_57_9 & $i(all_57_9))
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | | BETA: splitting (292) gives:
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | | Case 1:
% 158.00/24.53  | | | | | | | | | 
% 158.00/24.53  | | | | | | | | |   (293)  all_57_10 = e0 & op(e3, e3) = e0
% 158.00/24.53  | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | ALPHA: (293) implies:
% 158.00/24.53  | | | | | | | | |   (294)  op(e3, e3) = e0
% 158.00/24.53  | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | REF_CLOSE: (16), (52), (67), (294) are inconsistent by
% 158.00/24.53  | | | | | | | | |            sub-proof #281.
% 158.00/24.53  | | | | | | | | | 
% 158.00/24.53  | | | | | | | | Case 2:
% 158.00/24.53  | | | | | | | | | 
% 158.00/24.53  | | | | | | | | |   (295)   ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 158.00/24.53  | | | | | | | | |          $i(all_57_9)
% 158.00/24.53  | | | | | | | | | 
% 158.00/24.53  | | | | | | | | | REF_CLOSE: (16), (57), (282), (295) are inconsistent by
% 158.00/24.53  | | | | | | | | |            sub-proof #47.
% 158.00/24.53  | | | | | | | | | 
% 158.00/24.53  | | | | | | | | End of split
% 158.00/24.53  | | | | | | | | 
% 158.00/24.53  | | | | | | | End of split
% 158.00/24.53  | | | | | | | 
% 158.00/24.53  | | | | | | End of split
% 158.00/24.53  | | | | | | 
% 158.00/24.53  | | | | | End of split
% 158.00/24.53  | | | | | 
% 158.00/24.53  | | | | End of split
% 158.00/24.53  | | | | 
% 158.00/24.53  | | | End of split
% 158.00/24.53  | | | 
% 158.00/24.53  | | Case 2:
% 158.00/24.53  | | | 
% 158.00/24.53  | | |   (296)  all_18_2 = e3
% 158.00/24.53  | | | 
% 158.00/24.53  | | | COMBINE_EQS: (39), (296) imply:
% 158.00/24.53  | | |   (297)  all_14_2 = e3
% 158.00/24.53  | | | 
% 158.00/24.53  | | | SIMP: (297) implies:
% 158.00/24.53  | | |   (298)  all_14_2 = e3
% 158.00/24.53  | | | 
% 158.00/24.53  | | | REDUCE: (26), (298) imply:
% 158.00/24.53  | | |   (299)   ~ (all_52_12 = e3)
% 158.00/24.53  | | | 
% 158.00/24.53  | | | REDUCE: (42), (298) imply:
% 158.00/24.53  | | |   (300)  op(e0, e0) = e3
% 158.00/24.53  | | | 
% 158.00/24.53  | | | REF_CLOSE: (8), (11), (15), (16), (38), (44), (52), (54), (56), (57),
% 158.00/24.53  | | |            (68), (299), (300) are inconsistent by sub-proof #38.
% 158.00/24.53  | | | 
% 158.00/24.53  | | End of split
% 158.00/24.53  | | 
% 158.00/24.53  | Case 2:
% 158.00/24.53  | | 
% 158.00/24.53  | |   (301)  all_14_2 = e1
% 158.00/24.53  | | 
% 158.00/24.53  | | REDUCE: (26), (301) imply:
% 158.00/24.53  | |   (302)   ~ (all_52_12 = e1)
% 158.00/24.53  | | 
% 158.00/24.53  | | REDUCE: (12), (301) imply:
% 158.00/24.53  | |   (303)   ~ (all_52_13 = e1)
% 158.00/24.53  | | 
% 158.00/24.53  | | REDUCE: (42), (301) imply:
% 158.00/24.53  | |   (304)  op(e0, e0) = e1
% 158.00/24.53  | | 
% 158.00/24.53  | | BETA: splitting (11) gives:
% 158.00/24.53  | | 
% 158.00/24.53  | | Case 1:
% 158.00/24.53  | | | 
% 158.00/24.53  | | |   (305)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2)
% 158.00/24.53  | | |                = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.00/24.53  | | |                $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.00/24.53  | | |                (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.00/24.53  | | |            ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 158.00/24.53  | | |                op(e0, e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 &
% 158.00/24.53  | | |            op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 158.00/24.53  | | |                (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.00/24.53  | | |            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 158.00/24.53  | | |                op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 &
% 158.00/24.53  | | |                op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 158.00/24.53  | | |                all_57_7 & $i(all_57_7))))
% 158.00/24.53  | | | 
% 158.00/24.54  | | | REF_CLOSE: (15), (16), (52), (54), (305) are inconsistent by sub-proof
% 158.00/24.54  | | |            #42.
% 158.00/24.54  | | | 
% 158.00/24.54  | | Case 2:
% 158.00/24.54  | | | 
% 158.00/24.54  | | |   (306)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3)
% 158.00/24.54  | | |                = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 158.00/24.54  | | |                $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 158.00/24.54  | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 158.00/24.54  | | |            ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.00/24.54  | | |                op(e0, e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 &
% 158.00/24.54  | | |            op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 158.00/24.54  | | |                (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.00/24.54  | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 158.00/24.54  | | |                op(e2, e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0
% 158.00/24.54  | | |                & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) =
% 158.00/24.54  | | |                all_57_13 & $i(all_57_13))))
% 158.00/24.54  | | | 
% 158.00/24.54  | | | BETA: splitting (306) gives:
% 158.00/24.54  | | | 
% 158.00/24.54  | | | Case 1:
% 158.00/24.54  | | | | 
% 158.00/24.54  | | | |   (307)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 158.00/24.54  | | | |                e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 158.00/24.54  | | | |              $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 158.00/24.54  | | | |              (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 158.00/24.54  | | | |          ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.00/24.54  | | | |              op(e0, e1) = all_57_8 & $i(all_57_8)))
% 158.00/24.54  | | | | 
% 158.00/24.54  | | | | ALPHA: (307) implies:
% 158.00/24.54  | | | |   (308)  op(e1, e1) = e1
% 158.00/24.54  | | | |   (309)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) &
% 158.00/24.54  | | | |            op(e2, e1) = all_57_5 & $i(all_57_5))
% 158.00/24.54  | | | |   (310)  (all_57_10 = e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 158.00/24.54  | | | |            op(e3, e1) = all_57_4 & $i(all_57_4))
% 158.00/24.54  | | | | 
% 158.00/24.54  | | | | BETA: splitting (309) gives:
% 158.00/24.54  | | | | 
% 158.00/24.54  | | | | Case 1:
% 158.00/24.54  | | | | | 
% 158.00/24.54  | | | | |   (311)  all_57_12 = e1 & op(e2, e2) = e1
% 158.00/24.54  | | | | | 
% 158.00/24.54  | | | | | ALPHA: (311) implies:
% 158.00/24.54  | | | | |   (312)  op(e2, e2) = e1
% 158.00/24.54  | | | | | 
% 158.00/24.54  | | | | | REF_CLOSE: (16), (54), (64), (312) are inconsistent by sub-proof #847.
% 158.00/24.54  | | | | | 
% 158.00/24.54  | | | | Case 2:
% 158.00/24.54  | | | | | 
% 158.00/24.54  | | | | |   (313)   ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)
% 158.00/24.54  | | | | | 
% 158.00/24.54  | | | | | ALPHA: (313) implies:
% 158.00/24.54  | | | | |   (314)   ~ (all_57_5 = e2)
% 158.00/24.54  | | | | |   (315)  op(e2, e1) = all_57_5
% 158.00/24.54  | | | | | 
% 158.00/24.54  | | | | | BETA: splitting (310) gives:
% 158.00/24.54  | | | | | 
% 158.00/24.54  | | | | | Case 1:
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | |   (316)  all_57_10 = e1 & op(e3, e3) = e1
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | ALPHA: (316) implies:
% 158.00/24.54  | | | | | |   (317)  op(e3, e3) = e1
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | REF_CLOSE: (16), (52), (56), (317) are inconsistent by sub-proof
% 158.00/24.54  | | | | | |            #828.
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | Case 2:
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | |   (318)   ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4)
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | ALPHA: (318) implies:
% 158.00/24.54  | | | | | |   (319)   ~ (all_57_4 = e3)
% 158.00/24.54  | | | | | |   (320)  op(e3, e1) = all_57_4
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | GROUND_INST: instantiating (16) with all_10_2, e1, e1, e1,
% 158.00/24.54  | | | | | |              simplifying with (66), (308) gives:
% 158.00/24.54  | | | | | |   (321)  all_10_2 = e1
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | GROUND_INST: instantiating (16) with all_52_9, all_57_5, e1, e2,
% 158.00/24.54  | | | | | |              simplifying with (48), (315) gives:
% 158.00/24.54  | | | | | |   (322)  all_57_5 = all_52_9
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | GROUND_INST: instantiating (16) with all_52_8, all_57_4, e1, e3,
% 158.00/24.54  | | | | | |              simplifying with (18), (320) gives:
% 158.00/24.54  | | | | | |   (323)  all_57_4 = all_52_8
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | REDUCE: (319), (323) imply:
% 158.00/24.54  | | | | | |   (324)   ~ (all_52_8 = e3)
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | REDUCE: (314), (322) imply:
% 158.00/24.54  | | | | | |   (325)   ~ (all_52_9 = e2)
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | REDUCE: (10), (321) imply:
% 158.00/24.54  | | | | | |   (326)   ~ (all_52_2 = e1)
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | REDUCE: (33), (321) imply:
% 158.00/24.54  | | | | | |   (327)   ~ (all_52_6 = e1)
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | REDUCE: (62), (321) imply:
% 158.00/24.54  | | | | | |   (328)   ~ (all_52_8 = e1)
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | REDUCE: (7), (321) imply:
% 158.00/24.54  | | | | | |   (329)   ~ (all_52_9 = e1)
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | REDUCE: (32), (321) imply:
% 158.00/24.54  | | | | | |   (330)   ~ (all_52_14 = e1)
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | REDUCE: (65), (321) imply:
% 158.00/24.54  | | | | | |   (331)   ~ (e2 = e1)
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | BETA: splitting (46) gives:
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | | Case 1:
% 158.00/24.54  | | | | | | | 
% 158.00/24.54  | | | | | | |   (332)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 &
% 158.00/24.54  | | | | | | |            op(e2, e2) = e1)
% 158.00/24.54  | | | | | | | 
% 158.00/24.54  | | | | | | | BETA: splitting (332) gives:
% 158.00/24.54  | | | | | | | 
% 158.00/24.54  | | | | | | | Case 1:
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | |   (333)  all_56_2 = e1 & op(e2, e3) = e1
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | | ALPHA: (333) implies:
% 158.00/24.54  | | | | | | | |   (334)  all_56_2 = e1
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | | BETA: splitting (60) gives:
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | | Case 1:
% 158.00/24.54  | | | | | | | | | 
% 158.00/24.54  | | | | | | | | |   (335)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 &
% 158.00/24.54  | | | | | | | | |            op(e2, e2) = e2)
% 158.00/24.54  | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | REF_CLOSE: (5), (15), (16), (43), (54), (335) are inconsistent
% 158.00/24.54  | | | | | | | | |            by sub-proof #43.
% 158.00/24.54  | | | | | | | | | 
% 158.00/24.54  | | | | | | | | Case 2:
% 158.00/24.54  | | | | | | | | | 
% 158.00/24.54  | | | | | | | | |   (336)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 &
% 158.00/24.54  | | | | | | | | |            op(e2, e0) = e2)
% 158.00/24.54  | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | BETA: splitting (336) gives:
% 158.00/24.54  | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | Case 1:
% 158.00/24.54  | | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | |   (337)  all_56_5 = e2 & op(e2, e1) = e2
% 158.00/24.54  | | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | | ALPHA: (337) implies:
% 158.00/24.54  | | | | | | | | | |   (338)  op(e2, e1) = e2
% 158.00/24.54  | | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | | REF_CLOSE: (16), (48), (325), (338) are inconsistent by
% 158.00/24.54  | | | | | | | | | |            sub-proof #1002.
% 158.00/24.54  | | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | Case 2:
% 158.00/24.54  | | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | |   (339)  all_56_10 = e2 & op(e2, e0) = e2
% 158.00/24.54  | | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | | ALPHA: (339) implies:
% 158.00/24.54  | | | | | | | | | |   (340)  all_56_10 = e2
% 158.00/24.54  | | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | | REF_CLOSE: (3), (16), (23), (47), (48), (49), (54), (59),
% 158.00/24.54  | | | | | | | | | |            (61), (67), (68), (324), (328), (334), (340) are
% 158.00/24.54  | | | | | | | | | |            inconsistent by sub-proof #35.
% 158.00/24.54  | | | | | | | | | | 
% 158.00/24.54  | | | | | | | | | End of split
% 158.00/24.54  | | | | | | | | | 
% 158.00/24.54  | | | | | | | | End of split
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | Case 2:
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | |   (341)  all_56_3 = e1 & op(e2, e2) = e1
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | | ALPHA: (341) implies:
% 158.00/24.54  | | | | | | | |   (342)  op(e2, e2) = e1
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | | REF_CLOSE: (9), (11), (15), (16), (18), (24), (28), (30), (34),
% 158.00/24.54  | | | | | | | |            (36), (37), (42), (45), (47), (56), (57), (63), (64),
% 158.00/24.54  | | | | | | | |            (67), (68), (302), (304), (308), (326), (327), (328),
% 158.00/24.54  | | | | | | | |            (330), (342) are inconsistent by sub-proof #330.
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | End of split
% 158.00/24.54  | | | | | | | 
% 158.00/24.54  | | | | | | Case 2:
% 158.00/24.54  | | | | | | | 
% 158.00/24.54  | | | | | | |   (343)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 &
% 158.00/24.54  | | | | | | |            op(e2, e0) = e1)
% 158.00/24.54  | | | | | | | 
% 158.00/24.54  | | | | | | | BETA: splitting (343) gives:
% 158.00/24.54  | | | | | | | 
% 158.00/24.54  | | | | | | | Case 1:
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | |   (344)  all_56_5 = e1 & op(e2, e1) = e1
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | | REF_CLOSE: (16), (48), (329), (344) are inconsistent by
% 158.00/24.54  | | | | | | | |            sub-proof #423.
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | Case 2:
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | |   (345)  all_56_10 = e1 & op(e2, e0) = e1
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | | REF_CLOSE: (16), (51), (303), (345) are inconsistent by
% 158.00/24.54  | | | | | | | |            sub-proof #713.
% 158.00/24.54  | | | | | | | | 
% 158.00/24.54  | | | | | | | End of split
% 158.00/24.54  | | | | | | | 
% 158.00/24.54  | | | | | | End of split
% 158.00/24.54  | | | | | | 
% 158.00/24.54  | | | | | End of split
% 158.00/24.54  | | | | | 
% 158.00/24.54  | | | | End of split
% 158.00/24.54  | | | | 
% 158.00/24.54  | | | Case 2:
% 158.00/24.54  | | | | 
% 158.00/24.54  | | | |   (346)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3,
% 158.00/24.54  | | | |                e3) = e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 158.00/24.54  | | | |              $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 158.00/24.54  | | | |              (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11)))
% 158.00/24.54  | | | |          & ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) &
% 158.00/24.54  | | | |              op(e1, e0) = all_57_13 & $i(all_57_13)))
% 158.00/24.54  | | | | 
% 158.00/24.54  | | | | ALPHA: (346) implies:
% 158.00/24.54  | | | |   (347)  op(e0, e0) = e0
% 158.00/24.54  | | | | 
% 158.00/24.54  | | | | REF_CLOSE: (16), (42), (47), (304), (347) are inconsistent by sub-proof
% 158.00/24.54  | | | |            #991.
% 158.00/24.54  | | | | 
% 158.00/24.54  | | | End of split
% 158.00/24.54  | | | 
% 158.00/24.54  | | End of split
% 158.00/24.54  | | 
% 158.00/24.54  | End of split
% 158.00/24.54  | 
% 158.00/24.54  End of proof
% 158.00/24.54  
% 158.00/24.54  Sub-proof #35 shows that the following formulas are inconsistent:
% 158.00/24.54  ----------------------------------------------------------------
% 158.00/24.54    (1)  all_54_2 = all_52_8
% 158.00/24.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.00/24.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.00/24.54    (3)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.00/24.54    (4)  all_56_10 = e2
% 158.00/24.54    (5)   ~ (all_52_8 = e1)
% 158.00/24.54    (6)   ~ (e1 = e0)
% 158.00/24.54    (7)  op(e2, e1) = all_52_9
% 158.00/24.54    (8)   ~ (all_52_8 = all_52_9)
% 158.00/24.54    (9)  all_56_2 = e1
% 158.00/24.54    (10)  op(e2, e2) = e3
% 158.00/24.54    (11)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.00/24.54          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.00/24.54    (12)   ~ (all_52_8 = e2)
% 158.00/24.54    (13)   ~ (e2 = e0)
% 158.00/24.54    (14)   ~ (all_52_8 = e3)
% 158.00/24.54    (15)   ~ (e3 = e0)
% 158.00/24.54  
% 158.00/24.54  Begin of proof
% 158.00/24.54  | 
% 158.00/24.54  | BETA: splitting (11) gives:
% 158.00/24.54  | 
% 158.00/24.54  | Case 1:
% 158.00/24.54  | | 
% 158.00/24.54  | |   (16)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 158.00/24.54  | |           e0)
% 158.00/24.54  | | 
% 158.00/24.54  | | BETA: splitting (16) gives:
% 158.00/24.54  | | 
% 158.00/24.54  | | Case 1:
% 158.00/24.54  | | | 
% 158.00/24.54  | | |   (17)  all_56_2 = e0 & op(e2, e3) = e0
% 158.00/24.54  | | | 
% 158.00/24.54  | | | ALPHA: (17) implies:
% 158.00/24.54  | | |   (18)  all_56_2 = e0
% 158.00/24.54  | | | 
% 158.00/24.54  | | | REF_CLOSE: (6), (9), (18) are inconsistent by sub-proof #733.
% 158.00/24.54  | | | 
% 158.00/24.54  | | Case 2:
% 158.00/24.54  | | | 
% 158.00/24.54  | | |   (19)  all_56_3 = e0 & op(e2, e2) = e0
% 158.00/24.54  | | | 
% 158.00/24.54  | | | ALPHA: (19) implies:
% 158.00/24.54  | | |   (20)  op(e2, e2) = e0
% 158.00/24.54  | | | 
% 158.00/24.54  | | | REF_CLOSE: (2), (10), (15), (20) are inconsistent by sub-proof #945.
% 158.00/24.54  | | | 
% 158.00/24.54  | | End of split
% 158.00/24.54  | | 
% 158.00/24.54  | Case 2:
% 158.00/24.54  | | 
% 158.00/24.54  | |   (21)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 158.00/24.54  | |           e0)
% 158.00/24.54  | | 
% 158.00/24.54  | | BETA: splitting (21) gives:
% 158.00/24.54  | | 
% 158.00/24.54  | | Case 1:
% 158.00/24.54  | | | 
% 158.00/24.54  | | |   (22)  all_56_5 = e0 & op(e2, e1) = e0
% 158.00/24.54  | | | 
% 158.00/24.54  | | | ALPHA: (22) implies:
% 158.00/24.54  | | |   (23)  op(e2, e1) = e0
% 158.00/24.54  | | | 
% 158.00/24.54  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (12), (14), (23) are inconsistent
% 158.00/24.54  | | |            by sub-proof #36.
% 158.00/24.54  | | | 
% 158.00/24.54  | | Case 2:
% 158.00/24.54  | | | 
% 158.00/24.54  | | |   (24)  all_56_10 = e0 & op(e2, e0) = e0
% 158.00/24.54  | | | 
% 158.00/24.54  | | | ALPHA: (24) implies:
% 158.00/24.54  | | |   (25)  all_56_10 = e0
% 158.00/24.54  | | | 
% 158.00/24.54  | | | COMBINE_EQS: (4), (25) imply:
% 158.00/24.54  | | |   (26)  e2 = e0
% 158.00/24.54  | | | 
% 158.00/24.54  | | | REDUCE: (13), (26) imply:
% 158.00/24.54  | | |   (27)  $false
% 158.00/24.54  | | | 
% 158.00/24.54  | | | CLOSE: (27) is inconsistent.
% 158.00/24.54  | | | 
% 158.00/24.54  | | End of split
% 158.00/24.54  | | 
% 158.00/24.54  | End of split
% 158.00/24.54  | 
% 158.00/24.54  End of proof
% 158.00/24.54  
% 158.00/24.54  Sub-proof #36 shows that the following formulas are inconsistent:
% 158.00/24.54  ----------------------------------------------------------------
% 158.00/24.54    (1)  all_54_2 = all_52_8
% 158.00/24.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.00/24.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.00/24.54    (3)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.00/24.54    (4)   ~ (all_52_8 = e1)
% 158.00/24.54    (5)  op(e2, e1) = e0
% 158.00/24.54    (6)  op(e2, e1) = all_52_9
% 158.00/24.54    (7)   ~ (all_52_8 = all_52_9)
% 158.00/24.54    (8)   ~ (all_52_8 = e2)
% 158.00/24.54    (9)   ~ (all_52_8 = e3)
% 158.00/24.54  
% 158.00/24.54  Begin of proof
% 158.00/24.54  | 
% 158.00/24.54  | BETA: splitting (3) gives:
% 158.00/24.54  | 
% 158.00/24.54  | Case 1:
% 158.00/24.54  | | 
% 158.00/24.54  | |   (10)  all_54_2 = e3
% 158.00/24.54  | | 
% 158.00/24.54  | | COMBINE_EQS: (1), (10) imply:
% 158.00/24.54  | |   (11)  all_52_8 = e3
% 158.00/24.54  | | 
% 158.00/24.54  | | SIMP: (11) implies:
% 158.00/24.54  | |   (12)  all_52_8 = e3
% 158.00/24.54  | | 
% 158.00/24.54  | | REDUCE: (9), (12) imply:
% 158.00/24.54  | |   (13)  $false
% 158.00/24.54  | | 
% 158.00/24.54  | | CLOSE: (13) is inconsistent.
% 158.00/24.54  | | 
% 158.00/24.54  | Case 2:
% 158.00/24.54  | | 
% 158.00/24.54  | |   (14)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.00/24.54  | | 
% 158.00/24.54  | | BETA: splitting (14) gives:
% 158.00/24.54  | | 
% 158.00/24.54  | | Case 1:
% 158.00/24.54  | | | 
% 158.00/24.54  | | |   (15)  all_54_2 = e2
% 158.00/24.54  | | | 
% 158.00/24.54  | | | COMBINE_EQS: (1), (15) imply:
% 158.00/24.54  | | |   (16)  all_52_8 = e2
% 158.00/24.54  | | | 
% 158.00/24.54  | | | SIMP: (16) implies:
% 158.00/24.54  | | |   (17)  all_52_8 = e2
% 158.00/24.54  | | | 
% 158.00/24.54  | | | REDUCE: (8), (17) imply:
% 158.00/24.54  | | |   (18)  $false
% 158.00/24.54  | | | 
% 158.00/24.54  | | | CLOSE: (18) is inconsistent.
% 158.00/24.54  | | | 
% 158.00/24.54  | | Case 2:
% 158.00/24.54  | | | 
% 158.00/24.54  | | |   (19)  all_54_2 = e1 | all_54_2 = e0
% 158.00/24.54  | | | 
% 158.00/24.54  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (19) are inconsistent by
% 158.00/24.54  | | |            sub-proof #37.
% 158.00/24.54  | | | 
% 158.00/24.54  | | End of split
% 158.00/24.54  | | 
% 158.00/24.54  | End of split
% 158.00/24.54  | 
% 158.00/24.54  End of proof
% 158.00/24.54  
% 158.00/24.54  Sub-proof #37 shows that the following formulas are inconsistent:
% 158.00/24.54  ----------------------------------------------------------------
% 158.00/24.54    (1)  all_54_2 = all_52_8
% 158.00/24.54    (2)  all_54_2 = e1 | all_54_2 = e0
% 158.00/24.54    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.00/24.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.00/24.54    (4)   ~ (all_52_8 = e1)
% 158.00/24.54    (5)  op(e2, e1) = e0
% 158.00/24.54    (6)  op(e2, e1) = all_52_9
% 158.00/24.54    (7)   ~ (all_52_8 = all_52_9)
% 158.00/24.54  
% 158.00/24.54  Begin of proof
% 158.00/24.54  | 
% 158.00/24.54  | BETA: splitting (2) gives:
% 158.00/24.54  | 
% 158.00/24.54  | Case 1:
% 158.00/24.54  | | 
% 158.00/24.54  | |   (8)  all_54_2 = e1
% 158.00/24.54  | | 
% 158.00/24.54  | | COMBINE_EQS: (1), (8) imply:
% 158.00/24.54  | |   (9)  all_52_8 = e1
% 158.00/24.54  | | 
% 158.00/24.54  | | SIMP: (9) implies:
% 158.00/24.54  | |   (10)  all_52_8 = e1
% 158.00/24.54  | | 
% 158.00/24.54  | | REDUCE: (4), (10) imply:
% 158.00/24.54  | |   (11)  $false
% 158.00/24.54  | | 
% 158.00/24.54  | | CLOSE: (11) is inconsistent.
% 158.00/24.54  | | 
% 158.00/24.54  | Case 2:
% 158.00/24.54  | | 
% 158.00/24.54  | |   (12)  all_54_2 = e0
% 158.00/24.54  | | 
% 158.00/24.54  | | COMBINE_EQS: (1), (12) imply:
% 158.00/24.54  | |   (13)  all_52_8 = e0
% 158.00/24.54  | | 
% 158.00/24.54  | | SIMP: (13) implies:
% 158.00/24.54  | |   (14)  all_52_8 = e0
% 158.00/24.54  | | 
% 158.00/24.54  | | REDUCE: (7), (14) imply:
% 158.00/24.54  | |   (15)   ~ (all_52_9 = e0)
% 158.00/24.54  | | 
% 158.00/24.54  | | SIMP: (15) implies:
% 158.00/24.54  | |   (16)   ~ (all_52_9 = e0)
% 158.00/24.54  | | 
% 158.00/24.54  | | REF_CLOSE: (3), (5), (6), (16) are inconsistent by sub-proof #79.
% 158.00/24.54  | | 
% 158.00/24.54  | End of split
% 158.00/24.54  | 
% 158.00/24.54  End of proof
% 158.02/24.54  
% 158.02/24.54  Sub-proof #38 shows that the following formulas are inconsistent:
% 158.02/24.54  ----------------------------------------------------------------
% 158.02/24.54    (1)   ~ (all_52_4 = e3)
% 158.02/24.55    (2)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.02/24.55             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.02/24.55           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.02/24.55               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.02/24.55             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.02/24.55         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.02/24.55             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.02/24.55           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.02/24.55               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.02/24.55             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.02/24.55         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.02/24.55             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.02/24.55           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.02/24.55               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.02/24.55             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.02/24.55         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.02/24.55             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.02/24.55           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.02/24.55               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.02/24.55             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.02/24.55    (3)   ~ (e3 = e2)
% 158.02/24.55    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.55    (5)   ~ (all_52_12 = e3)
% 158.02/24.55    (6)  op(e0, e0) = e3
% 158.02/24.55    (7)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.02/24.55         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.02/24.55    (8)  op(e3, e2) = all_52_4
% 158.02/24.55    (9)  op(e3, e3) = e2
% 158.02/24.55    (10)  op(e2, e2) = e3
% 158.02/24.55    (11)   ~ (e2 = e1)
% 158.02/24.55    (12)  op(e3, e0) = all_52_12
% 158.02/24.55    (13)   ~ (e3 = e0)
% 158.02/24.55  
% 158.02/24.55  Begin of proof
% 158.02/24.55  | 
% 158.02/24.55  | BETA: splitting (7) gives:
% 158.02/24.55  | 
% 158.02/24.55  | Case 1:
% 158.02/24.55  | | 
% 158.02/24.55  | |   (14)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 158.02/24.55  | |           e3)
% 158.02/24.55  | | 
% 158.02/24.55  | | REF_CLOSE: (1), (3), (4), (8), (9), (14) are inconsistent by sub-proof #40.
% 158.02/24.55  | | 
% 158.02/24.55  | Case 2:
% 158.02/24.55  | | 
% 158.02/24.55  | |   (15)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 158.02/24.55  | |           e3)
% 158.02/24.55  | | 
% 158.02/24.55  | | BETA: splitting (15) gives:
% 158.02/24.55  | | 
% 158.02/24.55  | | Case 1:
% 158.02/24.55  | | | 
% 158.02/24.55  | | |   (16)  all_56_4 = e3 & op(e3, e1) = e3
% 158.02/24.55  | | | 
% 158.02/24.55  | | | ALPHA: (16) implies:
% 158.02/24.55  | | |   (17)  op(e3, e1) = e3
% 158.02/24.55  | | | 
% 158.02/24.55  | | | BETA: splitting (2) gives:
% 158.02/24.55  | | | 
% 158.02/24.55  | | | Case 1:
% 158.02/24.55  | | | | 
% 158.02/24.55  | | | |   (18)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2,
% 158.02/24.55  | | | |                 e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0
% 158.02/24.55  | | | |               & $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | (
% 158.02/24.55  | | | |               ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)))
% 158.02/24.55  | | | |           & ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 158.02/24.55  | | | |               op(e0, e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2
% 158.02/24.55  | | | |           & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 158.02/24.55  | | | |               (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.02/24.55  | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 158.02/24.55  | | | |               op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2
% 158.02/24.55  | | | |               & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 158.02/24.55  | | | |               all_57_7 & $i(all_57_7))))
% 158.02/24.55  | | | | 
% 158.02/24.55  | | | | REF_CLOSE: (3), (4), (9), (10), (18) are inconsistent by sub-proof #42.
% 158.02/24.55  | | | | 
% 158.02/24.55  | | | Case 2:
% 158.02/24.55  | | | | 
% 158.02/24.55  | | | |   (19)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 158.02/24.55  | | | |                 e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4
% 158.02/24.55  | | | |               & $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | (
% 158.02/24.55  | | | |               ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)))
% 158.02/24.55  | | | |           & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.02/24.55  | | | |               op(e0, e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0
% 158.02/24.55  | | | |           & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 158.02/24.55  | | | |               (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.02/24.55  | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 158.02/24.55  | | | |               op(e2, e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 =
% 158.02/24.55  | | | |               e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0)
% 158.02/24.55  | | | |               = all_57_13 & $i(all_57_13))))
% 158.02/24.55  | | | | 
% 158.02/24.55  | | | | BETA: splitting (19) gives:
% 158.02/24.55  | | | | 
% 158.02/24.55  | | | | Case 1:
% 158.02/24.55  | | | | | 
% 158.02/24.55  | | | | |   (20)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 158.02/24.55  | | | | |               e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4
% 158.02/24.55  | | | | |             & $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | (
% 158.02/24.55  | | | | |             ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)))
% 158.02/24.55  | | | | |         & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.02/24.55  | | | | |             op(e0, e1) = all_57_8 & $i(all_57_8)))
% 158.02/24.55  | | | | | 
% 158.02/24.55  | | | | | ALPHA: (20) implies:
% 158.02/24.55  | | | | |   (21)  (all_57_10 = e1 & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 158.02/24.55  | | | | |           op(e3, e1) = all_57_4 & $i(all_57_4))
% 158.02/24.55  | | | | | 
% 158.02/24.55  | | | | | BETA: splitting (21) gives:
% 158.02/24.55  | | | | | 
% 158.02/24.55  | | | | | Case 1:
% 158.02/24.55  | | | | | | 
% 158.02/24.55  | | | | | |   (22)  all_57_10 = e1 & op(e3, e3) = e1
% 158.02/24.55  | | | | | | 
% 158.02/24.55  | | | | | | ALPHA: (22) implies:
% 158.02/24.55  | | | | | |   (23)  op(e3, e3) = e1
% 158.02/24.55  | | | | | | 
% 158.02/24.55  | | | | | | REF_CLOSE: (4), (9), (11), (23) are inconsistent by sub-proof #828.
% 158.02/24.55  | | | | | | 
% 158.02/24.55  | | | | | Case 2:
% 158.02/24.55  | | | | | | 
% 158.02/24.55  | | | | | |   (24)   ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4)
% 158.02/24.55  | | | | | | 
% 158.02/24.55  | | | | | | REF_CLOSE: (4), (17), (24) are inconsistent by sub-proof #39.
% 158.02/24.55  | | | | | | 
% 158.02/24.55  | | | | | End of split
% 158.02/24.55  | | | | | 
% 158.02/24.55  | | | | Case 2:
% 158.02/24.55  | | | | | 
% 158.02/24.55  | | | | |   (25)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3,
% 158.02/24.55  | | | | |               e3) = e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9
% 158.02/24.55  | | | | |             & $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | (
% 158.02/24.55  | | | | |             ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 158.02/24.55  | | | | |             $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0) | (
% 158.02/24.55  | | | | |             ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.02/24.55  | | | | |             $i(all_57_13)))
% 158.02/24.55  | | | | | 
% 158.02/24.55  | | | | | ALPHA: (25) implies:
% 158.02/24.55  | | | | |   (26)  op(e0, e0) = e0
% 158.02/24.55  | | | | | 
% 158.02/24.55  | | | | | REF_CLOSE: (4), (6), (13), (26) are inconsistent by sub-proof #999.
% 158.02/24.55  | | | | | 
% 158.02/24.55  | | | | End of split
% 158.02/24.55  | | | | 
% 158.02/24.55  | | | End of split
% 158.02/24.55  | | | 
% 158.02/24.55  | | Case 2:
% 158.02/24.55  | | | 
% 158.02/24.55  | | |   (27)  all_56_9 = e3 & op(e3, e0) = e3
% 158.02/24.55  | | | 
% 158.02/24.55  | | | ALPHA: (27) implies:
% 158.02/24.55  | | |   (28)  op(e3, e0) = e3
% 158.02/24.55  | | | 
% 158.02/24.55  | | | REF_CLOSE: (4), (5), (12), (28) are inconsistent by sub-proof #976.
% 158.02/24.55  | | | 
% 158.02/24.55  | | End of split
% 158.02/24.55  | | 
% 158.02/24.55  | End of split
% 158.02/24.55  | 
% 158.02/24.55  End of proof
% 158.02/24.55  
% 158.02/24.55  Sub-proof #39 shows that the following formulas are inconsistent:
% 158.02/24.55  ----------------------------------------------------------------
% 158.02/24.55    (1)   ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4)
% 158.02/24.55    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.55    (3)  op(e3, e1) = e3
% 158.02/24.55  
% 158.02/24.55  Begin of proof
% 158.02/24.55  | 
% 158.02/24.55  | ALPHA: (1) implies:
% 158.02/24.55  |   (4)   ~ (all_57_4 = e3)
% 158.02/24.55  |   (5)  op(e3, e1) = all_57_4
% 158.02/24.55  | 
% 158.02/24.55  | GROUND_INST: instantiating (2) with e3, all_57_4, e1, e3, simplifying with
% 158.02/24.55  |              (3), (5) gives:
% 158.02/24.55  |   (6)  all_57_4 = e3
% 158.02/24.55  | 
% 158.02/24.55  | REDUCE: (4), (6) imply:
% 158.02/24.55  |   (7)  $false
% 158.02/24.55  | 
% 158.02/24.55  | CLOSE: (7) is inconsistent.
% 158.02/24.55  | 
% 158.02/24.55  End of proof
% 158.02/24.55  
% 158.02/24.55  Sub-proof #40 shows that the following formulas are inconsistent:
% 158.02/24.55  ----------------------------------------------------------------
% 158.02/24.55    (1)   ~ (all_52_4 = e3)
% 158.02/24.55    (2)   ~ (e3 = e2)
% 158.02/24.55    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.55    (4)  op(e3, e2) = all_52_4
% 158.02/24.55    (5)  op(e3, e3) = e2
% 158.02/24.55    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 158.02/24.55  
% 158.02/24.55  Begin of proof
% 158.02/24.55  | 
% 158.02/24.55  | BETA: splitting (6) gives:
% 158.02/24.55  | 
% 158.02/24.55  | Case 1:
% 158.02/24.55  | | 
% 158.02/24.55  | |   (7)  all_56_0 = e3 & op(e3, e3) = e3
% 158.02/24.55  | | 
% 158.02/24.55  | | ALPHA: (7) implies:
% 158.02/24.55  | |   (8)  op(e3, e3) = e3
% 158.02/24.55  | | 
% 158.02/24.55  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #958.
% 158.02/24.55  | | 
% 158.02/24.55  | Case 2:
% 158.02/24.55  | | 
% 158.02/24.55  | |   (9)  all_56_1 = e3 & op(e3, e2) = e3
% 158.02/24.55  | | 
% 158.02/24.55  | | ALPHA: (9) implies:
% 158.02/24.55  | |   (10)  op(e3, e2) = e3
% 158.02/24.55  | | 
% 158.02/24.55  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #998.
% 158.02/24.55  | | 
% 158.02/24.55  | End of split
% 158.02/24.55  | 
% 158.02/24.55  End of proof
% 158.02/24.55  
% 158.02/24.55  Sub-proof #41 shows that the following formulas are inconsistent:
% 158.02/24.55  ----------------------------------------------------------------
% 158.02/24.55    (1)  op(e1, e1) = e0
% 158.02/24.55    (2)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.02/24.55           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.02/24.55           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 158.02/24.55           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 158.02/24.55           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.02/24.55    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.55    (4)  op(e2, e2) = e3
% 158.02/24.55    (5)   ~ (e3 = e1)
% 158.02/24.55    (6)   ~ (e3 = e0)
% 158.02/24.55  
% 158.02/24.55  Begin of proof
% 158.02/24.55  | 
% 158.02/24.55  | BETA: splitting (2) gives:
% 158.02/24.55  | 
% 158.02/24.55  | Case 1:
% 158.02/24.55  | | 
% 158.02/24.55  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 158.02/24.55  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.02/24.55  | |          e1) = e3 & $i(all_57_10)
% 158.02/24.55  | | 
% 158.02/24.55  | | ALPHA: (7) implies:
% 158.02/24.55  | |   (8)  op(e1, e1) = e3
% 158.02/24.55  | | 
% 158.02/24.55  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #912.
% 158.02/24.55  | | 
% 158.02/24.55  | Case 2:
% 158.02/24.55  | | 
% 158.02/24.55  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 158.02/24.55  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.55  | |        all_57_14 & $i(all_57_14)
% 158.02/24.55  | | 
% 158.02/24.55  | | ALPHA: (9) implies:
% 158.02/24.55  | |   (10)  op(e2, e2) = e1
% 158.02/24.55  | | 
% 158.02/24.55  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #847.
% 158.02/24.55  | | 
% 158.02/24.55  | End of split
% 158.02/24.55  | 
% 158.02/24.55  End of proof
% 158.02/24.55  
% 158.02/24.55  Sub-proof #42 shows that the following formulas are inconsistent:
% 158.02/24.55  ----------------------------------------------------------------
% 158.02/24.55    (1)   ~ (e3 = e2)
% 158.02/24.55    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.55    (3)  op(e3, e3) = e2
% 158.02/24.55    (4)  op(e2, e2) = e3
% 158.02/24.55    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.02/24.55             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.02/24.55           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.02/24.55               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.02/24.55             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.02/24.55         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.02/24.55             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.02/24.55           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.02/24.55               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.02/24.55             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 158.02/24.55  
% 158.02/24.55  Begin of proof
% 158.02/24.55  | 
% 158.02/24.55  | BETA: splitting (5) gives:
% 158.02/24.55  | 
% 158.02/24.55  | Case 1:
% 158.02/24.55  | | 
% 158.02/24.56  | |   (6)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.02/24.56  | |            e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.02/24.56  | |            $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.02/24.56  | |            (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.02/24.56  | |        ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.02/24.56  | |              e3) = all_57_6 & $i(all_57_6)))
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (6) implies:
% 158.02/24.56  | |   (7)  op(e3, e3) = e3
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #958.
% 158.02/24.56  | | 
% 158.02/24.56  | Case 2:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (8)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 158.02/24.56  | |            e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.02/24.56  | |            $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 158.02/24.56  | |            (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 158.02/24.56  | |        ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 158.02/24.56  | |              e2) = all_57_7 & $i(all_57_7)))
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (8) implies:
% 158.02/24.56  | |   (9)  op(e2, e2) = e2
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #54.
% 158.02/24.56  | | 
% 158.02/24.56  | End of split
% 158.02/24.56  | 
% 158.02/24.56  End of proof
% 158.02/24.56  
% 158.02/24.56  Sub-proof #43 shows that the following formulas are inconsistent:
% 158.02/24.56  ----------------------------------------------------------------
% 158.02/24.56    (1)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 158.02/24.56    (2)   ~ (all_52_1 = e2)
% 158.02/24.56    (3)   ~ (e3 = e2)
% 158.02/24.56    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.56    (5)  op(e2, e3) = all_52_1
% 158.02/24.56    (6)  op(e2, e2) = e3
% 158.02/24.56  
% 158.02/24.56  Begin of proof
% 158.02/24.56  | 
% 158.02/24.56  | BETA: splitting (1) gives:
% 158.02/24.56  | 
% 158.02/24.56  | Case 1:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (7)  all_56_2 = e2 & op(e2, e3) = e2
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (7) implies:
% 158.02/24.56  | |   (8)  op(e2, e3) = e2
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #1007.
% 158.02/24.56  | | 
% 158.02/24.56  | Case 2:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (9)  all_56_3 = e2 & op(e2, e2) = e2
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (9) implies:
% 158.02/24.56  | |   (10)  op(e2, e2) = e2
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #54.
% 158.02/24.56  | | 
% 158.02/24.56  | End of split
% 158.02/24.56  | 
% 158.02/24.56  End of proof
% 158.02/24.56  
% 158.02/24.56  Sub-proof #44 shows that the following formulas are inconsistent:
% 158.02/24.56  ----------------------------------------------------------------
% 158.02/24.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.56    (2)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 158.02/24.56           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.56           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 158.02/24.56           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 158.02/24.56             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.02/24.56    (3)  op(e3, e3) = e2
% 158.02/24.56    (4)  op(e2, e2) = e3
% 158.02/24.56    (5)   ~ (e2 = e1)
% 158.02/24.56    (6)   ~ (e3 = e1)
% 158.02/24.56  
% 158.02/24.56  Begin of proof
% 158.02/24.56  | 
% 158.02/24.56  | BETA: splitting (2) gives:
% 158.02/24.56  | 
% 158.02/24.56  | Case 1:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (7)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 158.02/24.56  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.56  | |        all_57_14 & $i(all_57_14)
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (7) implies:
% 158.02/24.56  | |   (8)  op(e3, e3) = e1
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #828.
% 158.02/24.56  | | 
% 158.02/24.56  | Case 2:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 158.02/24.56  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.56  | |        all_57_14 & $i(all_57_14)
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (9) implies:
% 158.02/24.56  | |   (10)  op(e2, e2) = e1
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #847.
% 158.02/24.56  | | 
% 158.02/24.56  | End of split
% 158.02/24.56  | 
% 158.02/24.56  End of proof
% 158.02/24.56  
% 158.02/24.56  Sub-proof #45 shows that the following formulas are inconsistent:
% 158.02/24.56  ----------------------------------------------------------------
% 158.02/24.56    (1)  op(e0, e0) = e2
% 158.02/24.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.56    (3)  op(e1, e0) = all_52_14
% 158.02/24.56    (4)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.02/24.56    (5)   ~ (e2 = e1)
% 158.02/24.56    (6)   ~ (all_52_14 = e1)
% 158.02/24.56  
% 158.02/24.56  Begin of proof
% 158.02/24.56  | 
% 158.02/24.56  | BETA: splitting (4) gives:
% 158.02/24.56  | 
% 158.02/24.56  | Case 1:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (7)  all_56_11 = e1 & op(e1, e0) = e1
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (7) implies:
% 158.02/24.56  | |   (8)  op(e1, e0) = e1
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #974.
% 158.02/24.56  | | 
% 158.02/24.56  | Case 2:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (9)  all_56_15 = e1 & op(e0, e0) = e1
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (9) implies:
% 158.02/24.56  | |   (10)  op(e0, e0) = e1
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #875.
% 158.02/24.56  | | 
% 158.02/24.56  | End of split
% 158.02/24.56  | 
% 158.02/24.56  End of proof
% 158.02/24.56  
% 158.02/24.56  Sub-proof #46 shows that the following formulas are inconsistent:
% 158.02/24.56  ----------------------------------------------------------------
% 158.02/24.56    (1)  all_56_10 = e1 & op(e2, e0) = e1
% 158.02/24.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.56    (3)  op(e2, e0) = all_28_0
% 158.02/24.56    (4)   ~ (all_28_0 = e1)
% 158.02/24.56  
% 158.02/24.56  Begin of proof
% 158.02/24.56  | 
% 158.02/24.56  | ALPHA: (1) implies:
% 158.02/24.56  |   (5)  op(e2, e0) = e1
% 158.02/24.56  | 
% 158.02/24.56  | GROUND_INST: instantiating (2) with e1, all_28_0, e0, e2, simplifying with
% 158.02/24.56  |              (3), (5) gives:
% 158.02/24.56  |   (6)  all_28_0 = e1
% 158.02/24.56  | 
% 158.02/24.56  | REDUCE: (4), (6) imply:
% 158.02/24.56  |   (7)  $false
% 158.02/24.56  | 
% 158.02/24.56  | CLOSE: (7) is inconsistent.
% 158.02/24.56  | 
% 158.02/24.56  End of proof
% 158.02/24.56  
% 158.02/24.56  Sub-proof #47 shows that the following formulas are inconsistent:
% 158.02/24.56  ----------------------------------------------------------------
% 158.02/24.56    (1)   ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9)
% 158.02/24.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.56    (3)  op(e3, e0) = all_52_12
% 158.02/24.56    (4)  op(e3, e0) = e3
% 158.02/24.56  
% 158.02/24.56  Begin of proof
% 158.02/24.56  | 
% 158.02/24.56  | ALPHA: (1) implies:
% 158.02/24.56  |   (5)   ~ (all_57_9 = e3)
% 158.02/24.56  |   (6)  op(e3, e0) = all_57_9
% 158.02/24.56  | 
% 158.02/24.56  | GROUND_INST: instantiating (2) with all_52_12, all_57_9, e0, e3, simplifying
% 158.02/24.56  |              with (3), (6) gives:
% 158.02/24.56  |   (7)  all_57_9 = all_52_12
% 158.02/24.56  | 
% 158.02/24.56  | GROUND_INST: instantiating (2) with e3, all_57_9, e0, e3, simplifying with
% 158.02/24.56  |              (4), (6) gives:
% 158.02/24.56  |   (8)  all_57_9 = e3
% 158.02/24.56  | 
% 158.02/24.56  | COMBINE_EQS: (7), (8) imply:
% 158.02/24.56  |   (9)  all_52_12 = e3
% 158.02/24.56  | 
% 158.02/24.56  | REDUCE: (5), (8) imply:
% 158.02/24.56  |   (10)  $false
% 158.02/24.56  | 
% 158.02/24.56  | CLOSE: (10) is inconsistent.
% 158.02/24.56  | 
% 158.02/24.56  End of proof
% 158.02/24.56  
% 158.02/24.56  Sub-proof #48 shows that the following formulas are inconsistent:
% 158.02/24.56  ----------------------------------------------------------------
% 158.02/24.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.56    (2)  op(e3, e1) = all_52_8
% 158.02/24.56    (3)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3)
% 158.02/24.56    (4)  op(e2, e1) = all_52_9
% 158.02/24.56    (5)   ~ (all_52_9 = e3)
% 158.02/24.56    (6)   ~ (all_52_8 = e3)
% 158.02/24.56  
% 158.02/24.56  Begin of proof
% 158.02/24.56  | 
% 158.02/24.56  | BETA: splitting (3) gives:
% 158.02/24.56  | 
% 158.02/24.56  | Case 1:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (7)  all_56_4 = e3 & op(e3, e1) = e3
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (7) implies:
% 158.02/24.56  | |   (8)  op(e3, e1) = e3
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #982.
% 158.02/24.56  | | 
% 158.02/24.56  | Case 2:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (9)  all_56_5 = e3 & op(e2, e1) = e3
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (9) implies:
% 158.02/24.56  | |   (10)  op(e2, e1) = e3
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #763.
% 158.02/24.56  | | 
% 158.02/24.56  | End of split
% 158.02/24.56  | 
% 158.02/24.56  End of proof
% 158.02/24.56  
% 158.02/24.56  Sub-proof #49 shows that the following formulas are inconsistent:
% 158.02/24.56  ----------------------------------------------------------------
% 158.02/24.56    (1)   ~ (e3 = e2)
% 158.02/24.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.56    (3)  op(e3, e3) = e1
% 158.02/24.56    (4)  op(e2, e2) = e3
% 158.02/24.56    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.02/24.56             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.02/24.56           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.02/24.56               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.02/24.56             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.02/24.56         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.02/24.56             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.02/24.56           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.02/24.56               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.02/24.56             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 158.02/24.56    (6)   ~ (e3 = e1)
% 158.02/24.56  
% 158.02/24.56  Begin of proof
% 158.02/24.56  | 
% 158.02/24.56  | BETA: splitting (5) gives:
% 158.02/24.56  | 
% 158.02/24.56  | Case 1:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.02/24.56  | |            e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.02/24.56  | |            $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.02/24.56  | |            (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.02/24.56  | |        ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.02/24.56  | |              e3) = all_57_6 & $i(all_57_6)))
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (7) implies:
% 158.02/24.56  | |   (8)  op(e3, e3) = e3
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #995.
% 158.02/24.56  | | 
% 158.02/24.56  | Case 2:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 158.02/24.56  | |            e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.02/24.56  | |            $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 158.02/24.56  | |            (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 158.02/24.56  | |        ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 158.02/24.56  | |              e2) = all_57_7 & $i(all_57_7)))
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (9) implies:
% 158.02/24.56  | |   (10)  op(e2, e2) = e2
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #54.
% 158.02/24.56  | | 
% 158.02/24.56  | End of split
% 158.02/24.56  | 
% 158.02/24.56  End of proof
% 158.02/24.56  
% 158.02/24.56  Sub-proof #50 shows that the following formulas are inconsistent:
% 158.02/24.56  ----------------------------------------------------------------
% 158.02/24.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.56    (2)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.02/24.56           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.02/24.56           = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3
% 158.02/24.56           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.02/24.56           op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 158.02/24.56    (3)  op(e0, e0) = e0
% 158.02/24.56    (4)  op(e2, e2) = e3
% 158.02/24.56    (5)   ~ (e3 = e1)
% 158.02/24.56    (6)   ~ (e3 = e0)
% 158.02/24.56  
% 158.02/24.56  Begin of proof
% 158.02/24.56  | 
% 158.02/24.56  | BETA: splitting (2) gives:
% 158.02/24.56  | 
% 158.02/24.56  | Case 1:
% 158.02/24.56  | | 
% 158.02/24.56  | |   (7)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 158.02/24.56  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.02/24.56  | |          e0) = e1 & $i(all_57_14)
% 158.02/24.56  | | 
% 158.02/24.56  | | ALPHA: (7) implies:
% 158.02/24.56  | |   (8)  op(e2, e2) = e1
% 158.02/24.56  | | 
% 158.02/24.56  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #847.
% 158.02/24.56  | | 
% 158.02/24.56  | Case 2:
% 158.02/24.56  | | 
% 158.02/24.57  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0)
% 158.02/24.57  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 158.02/24.57  | |          e0) = e3 & $i(all_57_10)
% 158.02/24.57  | | 
% 158.02/24.57  | | ALPHA: (9) implies:
% 158.02/24.57  | |   (10)  op(e0, e0) = e3
% 158.02/24.57  | | 
% 158.02/24.57  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #999.
% 158.02/24.57  | | 
% 158.02/24.57  | End of split
% 158.02/24.57  | 
% 158.02/24.57  End of proof
% 158.02/24.57  
% 158.02/24.57  Sub-proof #51 shows that the following formulas are inconsistent:
% 158.02/24.57  ----------------------------------------------------------------
% 158.02/24.57    (1)   ~ (e3 = e2)
% 158.02/24.57    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.57    (3)  op(e0, e0) = e0
% 158.02/24.57    (4)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 158.02/24.57           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 158.02/24.57           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 158.02/24.57           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 158.02/24.57    (5)  op(e2, e2) = e3
% 158.02/24.57    (6)   ~ (e2 = e0)
% 158.02/24.57  
% 158.02/24.57  Begin of proof
% 158.02/24.57  | 
% 158.02/24.57  | BETA: splitting (4) gives:
% 158.02/24.57  | 
% 158.02/24.57  | Case 1:
% 158.02/24.57  | | 
% 158.02/24.57  | |   (7)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 158.02/24.57  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 158.02/24.57  | |          e0) = e2 & $i(all_57_12)
% 158.02/24.57  | | 
% 158.02/24.57  | | ALPHA: (7) implies:
% 158.02/24.57  | |   (8)  op(e0, e0) = e2
% 158.02/24.57  | | 
% 158.02/24.57  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #979.
% 158.02/24.57  | | 
% 158.02/24.57  | Case 2:
% 158.02/24.57  | | 
% 158.02/24.57  | |   (9)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 158.02/24.57  | |        op(e2, e1) = e2
% 158.02/24.57  | | 
% 158.02/24.57  | | ALPHA: (9) implies:
% 158.02/24.57  | |   (10)  op(e2, e2) = e2
% 158.02/24.57  | | 
% 158.02/24.57  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #54.
% 158.02/24.57  | | 
% 158.02/24.57  | End of split
% 158.02/24.57  | 
% 158.02/24.57  End of proof
% 158.02/24.57  
% 158.02/24.57  Sub-proof #52 shows that the following formulas are inconsistent:
% 158.02/24.57  ----------------------------------------------------------------
% 158.02/24.57    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.57    (2)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 158.02/24.57           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.57           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 158.02/24.57           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 158.02/24.57             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.02/24.57    (3)  op(e3, e3) = e3
% 158.02/24.57    (4)  op(e2, e2) = e3
% 158.02/24.57    (5)   ~ (e3 = e1)
% 158.02/24.57  
% 158.02/24.57  Begin of proof
% 158.02/24.57  | 
% 158.02/24.57  | BETA: splitting (2) gives:
% 158.02/24.57  | 
% 158.02/24.57  | Case 1:
% 158.02/24.57  | | 
% 158.02/24.57  | |   (6)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 158.02/24.57  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.57  | |        all_57_14 & $i(all_57_14)
% 158.02/24.57  | | 
% 158.02/24.57  | | ALPHA: (6) implies:
% 158.02/24.57  | |   (7)  op(e3, e3) = e1
% 158.02/24.57  | | 
% 158.02/24.57  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #995.
% 158.02/24.57  | | 
% 158.02/24.57  | Case 2:
% 158.02/24.57  | | 
% 158.02/24.57  | |   (8)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 158.02/24.57  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.57  | |        all_57_14 & $i(all_57_14)
% 158.02/24.57  | | 
% 158.02/24.57  | | ALPHA: (8) implies:
% 158.02/24.57  | |   (9)  op(e2, e2) = e1
% 158.02/24.57  | | 
% 158.02/24.57  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #847.
% 158.02/24.57  | | 
% 158.02/24.57  | End of split
% 158.02/24.57  | 
% 158.02/24.57  End of proof
% 158.02/24.57  
% 158.02/24.57  Sub-proof #53 shows that the following formulas are inconsistent:
% 158.02/24.57  ----------------------------------------------------------------
% 158.02/24.57    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.02/24.57           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.02/24.57           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 158.02/24.57           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 158.02/24.57           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.02/24.57    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.57    (3)  op(e1, e1) = e1
% 158.02/24.57    (4)  op(e2, e2) = e3
% 158.02/24.57    (5)   ~ (e3 = e1)
% 158.02/24.57  
% 158.02/24.57  Begin of proof
% 158.02/24.57  | 
% 158.02/24.57  | BETA: splitting (1) gives:
% 158.02/24.57  | 
% 158.02/24.57  | Case 1:
% 158.02/24.57  | | 
% 158.02/24.57  | |   (6)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 158.02/24.57  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.02/24.57  | |          e1) = e3 & $i(all_57_10)
% 158.02/24.57  | | 
% 158.02/24.57  | | ALPHA: (6) implies:
% 158.02/24.57  | |   (7)  op(e1, e1) = e3
% 158.02/24.57  | | 
% 158.02/24.57  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #1003.
% 158.02/24.57  | | 
% 158.02/24.57  | Case 2:
% 158.02/24.57  | | 
% 158.02/24.57  | |   (8)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 158.02/24.57  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.57  | |        all_57_14 & $i(all_57_14)
% 158.02/24.57  | | 
% 158.02/24.57  | | ALPHA: (8) implies:
% 158.02/24.57  | |   (9)  op(e2, e2) = e1
% 158.02/24.57  | | 
% 158.02/24.57  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #847.
% 158.02/24.57  | | 
% 158.02/24.57  | End of split
% 158.02/24.57  | 
% 158.02/24.57  End of proof
% 158.02/24.57  
% 158.02/24.57  Sub-proof #54 shows that the following formulas are inconsistent:
% 158.02/24.57  ----------------------------------------------------------------
% 158.02/24.57    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.57    (2)  op(e2, e2) = e3
% 158.02/24.57    (3)  op(e2, e2) = e2
% 158.02/24.57    (4)   ~ (e3 = e2)
% 158.02/24.57  
% 158.02/24.57  Begin of proof
% 158.02/24.57  | 
% 158.02/24.57  | GROUND_INST: instantiating (1) with e3, e2, e2, e2, simplifying with (2), (3)
% 158.02/24.57  |              gives:
% 158.02/24.57  |   (5)  e3 = e2
% 158.02/24.57  | 
% 158.02/24.57  | REDUCE: (4), (5) imply:
% 158.02/24.57  |   (6)  $false
% 158.02/24.57  | 
% 158.02/24.57  | CLOSE: (6) is inconsistent.
% 158.02/24.57  | 
% 158.02/24.57  End of proof
% 158.02/24.57  
% 158.02/24.57  Sub-proof #55 shows that the following formulas are inconsistent:
% 158.02/24.57  ----------------------------------------------------------------
% 158.02/24.57    (1)   ~ (all_8_1 = e1) & op(e0, e0) = all_8_1 & $i(all_8_1)
% 158.02/24.57    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.57    (3)  op(e0, e0) = e1
% 158.02/24.57  
% 158.02/24.57  Begin of proof
% 158.02/24.57  | 
% 158.02/24.57  | ALPHA: (1) implies:
% 158.02/24.57  |   (4)   ~ (all_8_1 = e1)
% 158.02/24.57  |   (5)  op(e0, e0) = all_8_1
% 158.02/24.57  | 
% 158.02/24.57  | GROUND_INST: instantiating (2) with e1, all_8_1, e0, e0, simplifying with (3),
% 158.02/24.57  |              (5) gives:
% 158.02/24.57  |   (6)  all_8_1 = e1
% 158.02/24.57  | 
% 158.02/24.57  | REDUCE: (4), (6) imply:
% 158.02/24.57  |   (7)  $false
% 158.02/24.57  | 
% 158.02/24.57  | CLOSE: (7) is inconsistent.
% 158.02/24.57  | 
% 158.02/24.57  End of proof
% 158.02/24.57  
% 158.02/24.57  Sub-proof #56 shows that the following formulas are inconsistent:
% 158.02/24.57  ----------------------------------------------------------------
% 158.02/24.57    (1)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.02/24.57    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.02/24.57         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.02/24.57    (3)  op(e0, e0) = e1
% 158.02/24.57    (4)  all_54_9 = all_52_6
% 158.02/24.57    (5)  all_54_13 = all_52_7
% 158.02/24.57    (6)  op(e1, e1) = e0
% 158.02/24.57    (7)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.02/24.57             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.02/24.57           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.02/24.57               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.02/24.57             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.02/24.57         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.02/24.57             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.02/24.57           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.02/24.57               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.02/24.57             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.02/24.57         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.02/24.57             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.02/24.57           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.02/24.57               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.02/24.57             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.02/24.57         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.02/24.57             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.02/24.57           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.02/24.57               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.02/24.57             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.02/24.57    (8)   ~ (all_52_6 = all_52_7)
% 158.02/24.57    (9)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/24.57    (10)   ~ (e3 = e2)
% 158.02/24.57    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.57    (12)   ~ (all_52_6 = e0)
% 158.02/24.57    (13)  op(e0, e2) = all_52_7
% 158.02/24.57    (14)  op(e1, e2) = all_52_6
% 158.02/24.57    (15)   ~ (all_52_6 = all_4_2)
% 158.02/24.57    (16)  op(e2, e2) = all_4_2
% 158.02/24.57    (17)  all_56_12 = e3
% 158.02/24.57    (18)  op(e0, e0) = all_14_2
% 158.02/24.57    (19)   ~ (all_52_7 = all_4_2)
% 158.02/24.57    (20)   ~ (e1 = e0)
% 158.02/24.57    (21)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.02/24.57          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.02/24.57    (22)   ~ (e2 = e1)
% 158.02/24.57    (23)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.02/24.57          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.02/24.57    (24)   ~ (all_52_7 = e1)
% 158.02/24.57    (25)   ~ (e3 = e1)
% 158.02/24.57    (26)   ~ (e2 = e0)
% 158.02/24.57    (27)   ~ (e3 = e0)
% 158.02/24.57  
% 158.02/24.57  Begin of proof
% 158.02/24.57  | 
% 158.02/24.57  | BETA: splitting (7) gives:
% 158.02/24.57  | 
% 158.02/24.57  | Case 1:
% 158.02/24.57  | | 
% 158.02/24.57  | |   (28)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.02/24.57  | |               e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.02/24.57  | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.02/24.57  | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.02/24.57  | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.02/24.57  | |                 e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 158.02/24.57  | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 158.02/24.57  | |                 e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 158.02/24.57  | |               e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 158.02/24.57  | |               all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 158.02/24.57  | |               e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 158.02/24.57  | |               $i(all_57_7))))
% 158.02/24.57  | | 
% 158.02/24.57  | | BETA: splitting (28) gives:
% 158.02/24.57  | | 
% 158.02/24.57  | | Case 1:
% 158.02/24.57  | | | 
% 158.02/24.57  | | |   (29)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.02/24.57  | | |             e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.02/24.57  | | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.02/24.57  | | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.02/24.57  | | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.02/24.57  | | |               e3) = all_57_6 & $i(all_57_6)))
% 158.02/24.57  | | | 
% 158.02/24.57  | | | ALPHA: (29) implies:
% 158.02/24.57  | | |   (30)  op(e3, e3) = e3
% 158.02/24.57  | | | 
% 158.02/24.57  | | | REF_CLOSE: (2), (10), (11), (17), (20), (21), (22), (23), (25), (26),
% 158.02/24.57  | | |            (27), (30) are inconsistent by sub-proof #729.
% 158.02/24.57  | | | 
% 158.02/24.57  | | Case 2:
% 158.02/24.57  | | | 
% 158.02/24.57  | | |   (31)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 158.02/24.57  | | |             e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.02/24.57  | | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 158.02/24.57  | | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 158.02/24.57  | | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 158.02/24.57  | | |               e2) = all_57_7 & $i(all_57_7)))
% 158.02/24.57  | | | 
% 158.02/24.57  | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 158.02/24.57  | | |            (15), (16), (19), (22), (24), (26), (31) are inconsistent by
% 158.02/24.57  | | |            sub-proof #201.
% 158.02/24.57  | | | 
% 158.02/24.57  | | End of split
% 158.02/24.57  | | 
% 158.02/24.57  | Case 2:
% 158.02/24.57  | | 
% 158.02/24.57  | |   (32)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 158.02/24.57  | |               e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 158.02/24.57  | |               $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 158.02/24.57  | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 158.02/24.57  | |           ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 158.02/24.57  | |                 e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 158.02/24.57  | |             e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 158.02/24.57  | |                 e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 =
% 158.02/24.57  | |               e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 158.02/24.57  | |               all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 158.02/24.57  | |               e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.02/24.57  | |               $i(all_57_13))))
% 158.02/24.57  | | 
% 158.02/24.57  | | REF_CLOSE: (3), (6), (11), (18), (20), (32) are inconsistent by sub-proof
% 158.02/24.57  | |            #629.
% 158.02/24.57  | | 
% 158.02/24.57  | End of split
% 158.02/24.57  | 
% 158.02/24.57  End of proof
% 158.02/24.57  
% 158.02/24.57  Sub-proof #57 shows that the following formulas are inconsistent:
% 158.02/24.57  ----------------------------------------------------------------
% 158.02/24.57    (1)   ~ (all_52_7 = e0)
% 158.02/24.57    (2)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.02/24.57         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.02/24.57    (3)   ~ (e3 = e2)
% 158.02/24.57    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.58    (5)  op(e0, e3) = all_52_3
% 158.02/24.58    (6)  op(e1, e1) = e1
% 158.02/24.58    (7)   ~ (all_52_3 = e0)
% 158.02/24.58    (8)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.02/24.58         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.02/24.58    (9)  op(e0, e2) = all_52_7
% 158.02/24.58    (10)  op(e1, e0) = e0
% 158.02/24.58    (11)  all_57_15 = e1
% 158.02/24.58    (12)  all_56_1 = e1
% 158.02/24.58    (13)  op(e2, e2) = e0
% 158.02/24.58    (14)  op(e1, e2) = e3
% 158.02/24.58    (15)  all_56_7 = e3
% 158.02/24.58    (16)   ~ (e1 = e0)
% 158.02/24.58    (17)   ~ (e2 = e1)
% 158.02/24.58    (18)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.58            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.02/24.58            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 158.02/24.58            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.02/24.58            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.02/24.58              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.02/24.58            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.02/24.58            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 158.02/24.58            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 158.02/24.58            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.02/24.58              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.02/24.58            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.02/24.58            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.02/24.58            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.02/24.58              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.02/24.58          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.58            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 158.02/24.58            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 158.02/24.58            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.02/24.58            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.02/24.58            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.02/24.58            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.02/24.58    (19)   ~ (e3 = e1)
% 158.02/24.58    (20)   ~ (e2 = e0)
% 158.02/24.58  
% 158.02/24.58  Begin of proof
% 158.02/24.58  | 
% 158.02/24.58  | BETA: splitting (18) gives:
% 158.02/24.58  | 
% 158.02/24.58  | Case 1:
% 158.02/24.58  | | 
% 158.02/24.58  | |   (21)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.02/24.58  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.02/24.58  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 158.02/24.58  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.02/24.58  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.02/24.58  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.02/24.58  | | 
% 158.02/24.58  | | BETA: splitting (21) gives:
% 158.02/24.58  | | 
% 158.02/24.58  | | Case 1:
% 158.02/24.58  | | | 
% 158.02/24.58  | | |   (22)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.02/24.58  | | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.02/24.58  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.02/24.58  | | | 
% 158.02/24.58  | | | REF_CLOSE: (4), (5), (6), (7), (16), (22) are inconsistent by sub-proof
% 158.02/24.58  | | |            #821.
% 158.02/24.58  | | | 
% 158.02/24.58  | | Case 2:
% 158.02/24.58  | | | 
% 158.02/24.58  | | |   (23)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0)
% 158.02/24.58  | | |         | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.02/24.58  | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.02/24.58  | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.02/24.58  | | | 
% 158.02/24.58  | | | REF_CLOSE: (1), (4), (5), (7), (9), (23) are inconsistent by sub-proof
% 158.02/24.58  | | |            #98.
% 158.02/24.58  | | | 
% 158.02/24.58  | | End of split
% 158.02/24.58  | | 
% 158.02/24.58  | Case 2:
% 158.02/24.58  | | 
% 158.02/24.58  | |   (24)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.02/24.58  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.02/24.58  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.02/24.58  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.02/24.58  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.02/24.58  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.02/24.58  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 158.02/24.58  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 158.02/24.58  | |           & op(e0, e1) = e0)
% 158.02/24.58  | | 
% 158.02/24.58  | | BETA: splitting (24) gives:
% 158.02/24.58  | | 
% 158.02/24.58  | | Case 1:
% 158.02/24.58  | | | 
% 158.02/24.58  | | |   (25)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.02/24.58  | | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.02/24.58  | | |         | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.02/24.58  | | |             = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.02/24.58  | | | 
% 158.02/24.58  | | | BETA: splitting (25) gives:
% 158.02/24.58  | | | 
% 158.02/24.58  | | | Case 1:
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | |   (26)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.02/24.58  | | | |           = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | | ALPHA: (26) implies:
% 158.02/24.58  | | | |   (27)  op(e1, e1) = e0
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | | REF_CLOSE: (4), (6), (16), (27) are inconsistent by sub-proof #903.
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | Case 2:
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | |   (28)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.02/24.58  | | | |           e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.02/24.58  | | | |           (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.02/24.58  | | | |             e1) = e0)
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | | BETA: splitting (28) gives:
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | | Case 1:
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | |   (29)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.02/24.58  | | | | |         e0
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | ALPHA: (29) implies:
% 158.02/24.58  | | | | |   (30)  op(e0, e2) = e0
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | REF_CLOSE: (1), (4), (9), (30) are inconsistent by sub-proof #969.
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | Case 2:
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | |   (31)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.02/24.58  | | | | |           = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | ALPHA: (31) implies:
% 158.02/24.58  | | | | |   (32)   ~ (all_57_15 = e1)
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | REDUCE: (11), (32) imply:
% 158.02/24.58  | | | | |   (33)  $false
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | CLOSE: (33) is inconsistent.
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | End of split
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | End of split
% 158.02/24.58  | | | 
% 158.02/24.58  | | Case 2:
% 158.02/24.58  | | | 
% 158.02/24.58  | | |   (34)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.02/24.58  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.58  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.02/24.58  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.02/24.58  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.02/24.58  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 158.02/24.58  | | |             e0) & op(e0, e1) = e0)
% 158.02/24.58  | | | 
% 158.02/24.58  | | | BETA: splitting (34) gives:
% 158.02/24.58  | | | 
% 158.02/24.58  | | | Case 1:
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | |   (35)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.02/24.58  | | | |             = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 158.02/24.58  | | | |         | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.02/24.58  | | | |           (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.02/24.58  | | | |             e1) = e0)
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | | REF_CLOSE: (4), (6), (11), (16), (35) are inconsistent by sub-proof
% 158.02/24.58  | | | |            #339.
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | Case 2:
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | |   (36)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.02/24.58  | | | |             = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.02/24.58  | | | |             e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 158.02/24.58  | | | |           &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | | BETA: splitting (36) gives:
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | | Case 1:
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | |   (37)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 158.02/24.58  | | | | |         (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.02/24.58  | | | | |         op(e0, e1) = e0 & $i(all_57_14)
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | ALPHA: (37) implies:
% 158.02/24.58  | | | | |   (38)  op(e1, e0) = e1
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | REF_CLOSE: (4), (10), (16), (38) are inconsistent by sub-proof #545.
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | Case 2:
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | |   (39)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.02/24.58  | | | | |         e0
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | ALPHA: (39) implies:
% 158.02/24.58  | | | | |   (40)  all_57_15 = e0
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | COMBINE_EQS: (11), (40) imply:
% 158.02/24.58  | | | | |   (41)  e1 = e0
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | COMBINE_EQS: (12), (41) imply:
% 158.02/24.58  | | | | |   (42)  all_56_1 = e0
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | | REF_CLOSE: (2), (3), (4), (8), (13), (14), (15), (16), (17), (19),
% 158.02/24.58  | | | | |            (20), (42) are inconsistent by sub-proof #937.
% 158.02/24.58  | | | | | 
% 158.02/24.58  | | | | End of split
% 158.02/24.58  | | | | 
% 158.02/24.58  | | | End of split
% 158.02/24.58  | | | 
% 158.02/24.58  | | End of split
% 158.02/24.58  | | 
% 158.02/24.58  | End of split
% 158.02/24.58  | 
% 158.02/24.58  End of proof
% 158.02/24.58  
% 158.02/24.58  Sub-proof #58 shows that the following formulas are inconsistent:
% 158.02/24.58  ----------------------------------------------------------------
% 158.02/24.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.58    (2)  all_56_14 = e0
% 158.02/24.58    (3)  op(e0, e0) = e3
% 158.02/24.58    (4)  all_56_13 = e2
% 158.02/24.58    (5)  all_56_12 = e3
% 158.02/24.58    (6)   ~ (e1 = e0)
% 158.02/24.58    (7)   ~ (e2 = e1)
% 158.02/24.58    (8)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1) |
% 158.02/24.58         (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.02/24.58    (9)   ~ (e3 = e1)
% 158.02/24.58  
% 158.02/24.58  Begin of proof
% 158.02/24.58  | 
% 158.02/24.58  | BETA: splitting (8) gives:
% 158.02/24.58  | 
% 158.02/24.58  | Case 1:
% 158.02/24.58  | | 
% 158.02/24.58  | |   (10)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 158.02/24.58  | |           e1)
% 158.02/24.58  | | 
% 158.02/24.58  | | BETA: splitting (10) gives:
% 158.02/24.58  | | 
% 158.02/24.58  | | Case 1:
% 158.02/24.58  | | | 
% 158.02/24.58  | | |   (11)  all_56_12 = e1 & op(e0, e3) = e1
% 158.02/24.58  | | | 
% 158.02/24.58  | | | ALPHA: (11) implies:
% 158.02/24.58  | | |   (12)  all_56_12 = e1
% 158.02/24.58  | | | 
% 158.02/24.58  | | | REF_CLOSE: (5), (9), (12) are inconsistent by sub-proof #498.
% 158.02/24.58  | | | 
% 158.02/24.58  | | Case 2:
% 158.02/24.58  | | | 
% 158.02/24.58  | | |   (13)  all_56_13 = e1 & op(e0, e2) = e1
% 158.02/24.58  | | | 
% 158.02/24.58  | | | ALPHA: (13) implies:
% 158.02/24.58  | | |   (14)  all_56_13 = e1
% 158.02/24.58  | | | 
% 158.02/24.58  | | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #907.
% 158.02/24.58  | | | 
% 158.02/24.58  | | End of split
% 158.02/24.58  | | 
% 158.02/24.58  | Case 2:
% 158.02/24.58  | | 
% 158.02/24.58  | |   (15)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.02/24.58  | |           e1)
% 158.02/24.58  | | 
% 158.02/24.58  | | BETA: splitting (15) gives:
% 158.02/24.58  | | 
% 158.02/24.58  | | Case 1:
% 158.02/24.58  | | | 
% 158.02/24.58  | | |   (16)  all_56_14 = e1 & op(e0, e1) = e1
% 158.02/24.58  | | | 
% 158.02/24.58  | | | ALPHA: (16) implies:
% 158.02/24.58  | | |   (17)  all_56_14 = e1
% 158.02/24.58  | | | 
% 158.02/24.58  | | | COMBINE_EQS: (2), (17) imply:
% 158.02/24.58  | | |   (18)  e1 = e0
% 158.02/24.58  | | | 
% 158.02/24.58  | | | REDUCE: (6), (18) imply:
% 158.02/24.58  | | |   (19)  $false
% 158.02/24.58  | | | 
% 158.02/24.58  | | | CLOSE: (19) is inconsistent.
% 158.02/24.58  | | | 
% 158.02/24.58  | | Case 2:
% 158.02/24.58  | | | 
% 158.02/24.58  | | |   (20)  all_56_15 = e1 & op(e0, e0) = e1
% 158.02/24.58  | | | 
% 158.02/24.58  | | | ALPHA: (20) implies:
% 158.02/24.58  | | |   (21)  op(e0, e0) = e1
% 158.02/24.58  | | | 
% 158.02/24.58  | | | REF_CLOSE: (1), (3), (9), (21) are inconsistent by sub-proof #473.
% 158.02/24.58  | | | 
% 158.02/24.58  | | End of split
% 158.02/24.58  | | 
% 158.02/24.58  | End of split
% 158.02/24.58  | 
% 158.02/24.58  End of proof
% 158.02/24.58  
% 158.02/24.58  Sub-proof #59 shows that the following formulas are inconsistent:
% 158.02/24.58  ----------------------------------------------------------------
% 158.02/24.58    (1)  op(e0, e0) = e1
% 158.02/24.58    (2)  op(e0, e1) = all_52_11
% 158.02/24.58    (3)   ~ (e3 = e2)
% 158.02/24.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.58    (5)  all_56_6 = e2
% 158.02/24.58    (6)  all_56_13 = e2
% 158.02/24.58    (7)  op(e3, e3) = e3
% 158.02/24.58    (8)   ~ (e1 = e0)
% 158.02/24.58    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.02/24.58         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.02/24.58    (10)   ~ (e2 = e1)
% 158.02/24.58    (11)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.02/24.58          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.02/24.58            e3)
% 158.02/24.58    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.02/24.58          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.02/24.58    (13)   ~ (e3 = e1)
% 158.02/24.58    (14)   ~ (e2 = e0)
% 158.02/24.58    (15)   ~ (all_52_11 = e3)
% 158.02/24.58    (16)   ~ (e3 = e0)
% 158.02/24.58  
% 158.02/24.58  Begin of proof
% 158.02/24.58  | 
% 158.02/24.58  | BETA: splitting (11) gives:
% 158.02/24.58  | 
% 158.02/24.58  | Case 1:
% 158.02/24.58  | | 
% 158.02/24.58  | |   (17)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 158.02/24.58  | |           e3)
% 158.02/24.58  | | 
% 158.02/24.58  | | BETA: splitting (17) gives:
% 158.02/24.58  | | 
% 158.02/24.58  | | Case 1:
% 158.02/24.58  | | | 
% 158.02/24.58  | | |   (18)  all_56_12 = e3 & op(e0, e3) = e3
% 158.02/24.58  | | | 
% 158.02/24.58  | | | ALPHA: (18) implies:
% 158.02/24.58  | | |   (19)  all_56_12 = e3
% 158.02/24.58  | | | 
% 158.02/24.58  | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (12), (13), (14), (16), (19) are
% 158.02/24.58  | | |            inconsistent by sub-proof #731.
% 158.02/24.58  | | | 
% 158.02/24.58  | | Case 2:
% 158.02/24.58  | | | 
% 158.02/24.58  | | |   (20)  all_56_13 = e3 & op(e0, e2) = e3
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REF_CLOSE: (3), (6), (20) are inconsistent by sub-proof #906.
% 158.02/24.59  | | | 
% 158.02/24.59  | | End of split
% 158.02/24.59  | | 
% 158.02/24.59  | Case 2:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (21)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.02/24.59  | |           e3)
% 158.02/24.59  | | 
% 158.02/24.59  | | REF_CLOSE: (1), (2), (4), (13), (15), (21) are inconsistent by sub-proof
% 158.02/24.59  | |            #290.
% 158.02/24.59  | | 
% 158.02/24.59  | End of split
% 158.02/24.59  | 
% 158.02/24.59  End of proof
% 158.02/24.59  
% 158.02/24.59  Sub-proof #60 shows that the following formulas are inconsistent:
% 158.02/24.59  ----------------------------------------------------------------
% 158.02/24.59    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.59    (2)  op(e1, e1) = e1
% 158.02/24.59    (3)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 158.02/24.59           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.02/24.59           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1)
% 158.02/24.59           & op(e1, e2) = e1 & op(e1, e1) = e1)
% 158.02/24.59    (4)  op(e1, e2) = e3
% 158.02/24.59    (5)   ~ (e2 = e1)
% 158.02/24.59    (6)   ~ (e3 = e1)
% 158.02/24.59  
% 158.02/24.59  Begin of proof
% 158.02/24.59  | 
% 158.02/24.59  | BETA: splitting (3) gives:
% 158.02/24.59  | 
% 158.02/24.59  | Case 1:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (7)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0)
% 158.02/24.59  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1,
% 158.02/24.59  | |          e1) = e2 & $i(all_57_12)
% 158.02/24.59  | | 
% 158.02/24.59  | | ALPHA: (7) implies:
% 158.02/24.59  | |   (8)  op(e1, e1) = e2
% 158.02/24.59  | | 
% 158.02/24.59  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #986.
% 158.02/24.59  | | 
% 158.02/24.59  | Case 2:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (9)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.02/24.59  | |        op(e1, e1) = e1
% 158.02/24.59  | | 
% 158.02/24.59  | | ALPHA: (9) implies:
% 158.02/24.59  | |   (10)  op(e1, e2) = e1
% 158.02/24.59  | | 
% 158.02/24.59  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #939.
% 158.02/24.59  | | 
% 158.02/24.59  | End of split
% 158.02/24.59  | 
% 158.02/24.59  End of proof
% 158.02/24.59  
% 158.02/24.59  Sub-proof #61 shows that the following formulas are inconsistent:
% 158.02/24.59  ----------------------------------------------------------------
% 158.02/24.59    (1)   ~ (all_52_9 = all_52_11)
% 158.02/24.59    (2)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.02/24.59    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.59    (4)   ~ (all_52_11 = e1)
% 158.02/24.59    (5)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.02/24.59         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.02/24.59    (6)  op(e2, e2) = e1
% 158.02/24.59    (7)   ~ (e1 = e0)
% 158.02/24.59    (8)  op(e2, e1) = all_52_9
% 158.02/24.59    (9)  all_54_14 = all_52_11
% 158.02/24.59    (10)  all_56_2 = e1
% 158.02/24.59    (11)   ~ (all_52_11 = e0)
% 158.02/24.59    (12)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.02/24.59          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.02/24.59    (13)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.02/24.59          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.02/24.59    (14)   ~ (e3 = e1)
% 158.02/24.59    (15)   ~ (all_52_11 = e3)
% 158.02/24.59    (16)   ~ (e3 = e0)
% 158.02/24.59  
% 158.02/24.59  Begin of proof
% 158.02/24.59  | 
% 158.02/24.59  | BETA: splitting (2) gives:
% 158.02/24.59  | 
% 158.02/24.59  | Case 1:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (17)  all_54_14 = e3
% 158.02/24.59  | | 
% 158.02/24.59  | | REF_CLOSE: (9), (15), (17) are inconsistent by sub-proof #587.
% 158.02/24.59  | | 
% 158.02/24.59  | Case 2:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (18)   ~ (all_54_14 = e3)
% 158.02/24.59  | |   (19)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.02/24.59  | | 
% 158.02/24.59  | | BETA: splitting (19) gives:
% 158.02/24.59  | | 
% 158.02/24.59  | | Case 1:
% 158.02/24.59  | | | 
% 158.02/24.59  | | |   (20)  all_54_14 = e2
% 158.02/24.59  | | | 
% 158.02/24.59  | | | COMBINE_EQS: (9), (20) imply:
% 158.02/24.59  | | |   (21)  all_52_11 = e2
% 158.02/24.59  | | | 
% 158.02/24.59  | | | SIMP: (21) implies:
% 158.02/24.59  | | |   (22)  all_52_11 = e2
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REDUCE: (1), (22) imply:
% 158.02/24.59  | | |   (23)   ~ (all_52_9 = e2)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REDUCE: (15), (22) imply:
% 158.02/24.59  | | |   (24)   ~ (e3 = e2)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | SIMP: (24) implies:
% 158.02/24.59  | | |   (25)   ~ (e3 = e2)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REDUCE: (4), (22) imply:
% 158.02/24.59  | | |   (26)   ~ (e2 = e1)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REDUCE: (11), (22) imply:
% 158.02/24.59  | | |   (27)   ~ (e2 = e0)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REF_CLOSE: (3), (5), (6), (7), (8), (10), (12), (13), (14), (16), (23),
% 158.02/24.59  | | |            (25), (26), (27) are inconsistent by sub-proof #355.
% 158.02/24.59  | | | 
% 158.02/24.59  | | Case 2:
% 158.02/24.59  | | | 
% 158.02/24.59  | | |   (28)  all_54_14 = e1 | all_54_14 = e0
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REF_CLOSE: (4), (9), (11), (28) are inconsistent by sub-proof #585.
% 158.02/24.59  | | | 
% 158.02/24.59  | | End of split
% 158.02/24.59  | | 
% 158.02/24.59  | End of split
% 158.02/24.59  | 
% 158.02/24.59  End of proof
% 158.02/24.59  
% 158.02/24.59  Sub-proof #62 shows that the following formulas are inconsistent:
% 158.02/24.59  ----------------------------------------------------------------
% 158.02/24.59    (1)  all_56_9 = e2
% 158.02/24.59    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.02/24.59         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.02/24.59    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.59    (4)  all_56_1 = e1
% 158.02/24.59    (5)  all_56_4 = e3
% 158.02/24.59    (6)  op(e3, e3) = e1
% 158.02/24.59    (7)   ~ (e1 = e0)
% 158.02/24.59    (8)   ~ (e2 = e0)
% 158.02/24.59    (9)   ~ (e3 = e0)
% 158.02/24.59  
% 158.02/24.59  Begin of proof
% 158.02/24.59  | 
% 158.02/24.59  | BETA: splitting (2) gives:
% 158.02/24.59  | 
% 158.02/24.59  | Case 1:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 158.02/24.59  | |           e0)
% 158.02/24.59  | | 
% 158.02/24.59  | | BETA: splitting (10) gives:
% 158.02/24.59  | | 
% 158.02/24.59  | | Case 1:
% 158.02/24.59  | | | 
% 158.02/24.59  | | |   (11)  all_56_0 = e0 & op(e3, e3) = e0
% 158.02/24.59  | | | 
% 158.02/24.59  | | | ALPHA: (11) implies:
% 158.02/24.59  | | |   (12)  op(e3, e3) = e0
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REF_CLOSE: (3), (6), (7), (12) are inconsistent by sub-proof #834.
% 158.02/24.59  | | | 
% 158.02/24.59  | | Case 2:
% 158.02/24.59  | | | 
% 158.02/24.59  | | |   (13)  all_56_1 = e0 & op(e3, e2) = e0
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REF_CLOSE: (4), (7), (13) are inconsistent by sub-proof #760.
% 158.02/24.59  | | | 
% 158.02/24.59  | | End of split
% 158.02/24.59  | | 
% 158.02/24.59  | Case 2:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (14)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 158.02/24.59  | |           e0)
% 158.02/24.59  | | 
% 158.02/24.59  | | BETA: splitting (14) gives:
% 158.02/24.59  | | 
% 158.02/24.59  | | Case 1:
% 158.02/24.59  | | | 
% 158.02/24.59  | | |   (15)  all_56_4 = e0 & op(e3, e1) = e0
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REF_CLOSE: (5), (9), (15) are inconsistent by sub-proof #248.
% 158.02/24.59  | | | 
% 158.02/24.59  | | Case 2:
% 158.02/24.59  | | | 
% 158.02/24.59  | | |   (16)  all_56_9 = e0 & op(e3, e0) = e0
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REF_CLOSE: (1), (8), (16) are inconsistent by sub-proof #950.
% 158.02/24.59  | | | 
% 158.02/24.59  | | End of split
% 158.02/24.59  | | 
% 158.02/24.59  | End of split
% 158.02/24.59  | 
% 158.02/24.59  End of proof
% 158.02/24.59  
% 158.02/24.59  Sub-proof #63 shows that the following formulas are inconsistent:
% 158.02/24.59  ----------------------------------------------------------------
% 158.02/24.59    (1)   ~ (e3 = e2)
% 158.02/24.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.59    (3)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.02/24.59         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.02/24.59    (4)  op(e1, e0) = all_52_14
% 158.02/24.59    (5)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.02/24.59         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.02/24.59    (6)  op(e1, e2) = e3
% 158.02/24.59    (7)  all_56_7 = e3
% 158.02/24.59    (8)   ~ (e1 = e0)
% 158.02/24.59    (9)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 158.02/24.59           all_57_5 & $i(all_57_5))
% 158.02/24.59    (10)   ~ (e2 = e1)
% 158.02/24.59    (11)   ~ (all_52_14 = e1)
% 158.02/24.59    (12)   ~ (e3 = e1)
% 158.02/24.59    (13)   ~ (e2 = e0)
% 158.02/24.59    (14)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 158.02/24.59          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 158.02/24.59    (15)   ~ (e3 = e0)
% 158.02/24.59    (16)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.02/24.59            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 158.02/24.59              e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 158.02/24.59            all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) =
% 158.02/24.59            e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.02/24.59  
% 158.02/24.59  Begin of proof
% 158.02/24.59  | 
% 158.02/24.59  | BETA: splitting (16) gives:
% 158.02/24.59  | 
% 158.02/24.59  | Case 1:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (17)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 158.02/24.59  | |         & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 158.02/24.59  | |         op(e1, e1) = e3 & $i(all_57_10)
% 158.02/24.59  | | 
% 158.02/24.59  | | ALPHA: (17) implies:
% 158.02/24.59  | |   (18)  op(e1, e1) = e3
% 158.02/24.59  | | 
% 158.02/24.59  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 158.02/24.59  | |            (14), (15), (18) are inconsistent by sub-proof #457.
% 158.02/24.59  | | 
% 158.02/24.59  | Case 2:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (19)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 158.02/24.59  | |         & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.02/24.59  | |         op(e2, e1) = e2 & $i(all_57_12)
% 158.02/24.59  | | 
% 158.02/24.59  | | ALPHA: (19) implies:
% 158.02/24.59  | |   (20)  all_57_5 = e2
% 158.02/24.59  | |   (21)   ~ (all_57_12 = e1)
% 158.02/24.59  | |   (22)  op(e2, e2) = all_57_12
% 158.02/24.59  | | 
% 158.02/24.59  | | REF_CLOSE: (2), (9), (20), (21), (22) are inconsistent by sub-proof #274.
% 158.02/24.59  | | 
% 158.02/24.59  | End of split
% 158.02/24.59  | 
% 158.02/24.59  End of proof
% 158.02/24.59  
% 158.02/24.59  Sub-proof #64 shows that the following formulas are inconsistent:
% 158.02/24.59  ----------------------------------------------------------------
% 158.02/24.59    (1)   ~ (all_52_3 = all_52_7)
% 158.02/24.59    (2)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 158.02/24.59           all_57_7 & $i(all_57_7))
% 158.02/24.59    (3)  op(e0, e0) = e1
% 158.02/24.59    (4)  all_54_13 = all_52_7
% 158.02/24.59    (5)  all_54_12 = all_52_3
% 158.02/24.59    (6)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/24.59    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.59    (8)  op(e0, e3) = all_52_3
% 158.02/24.59    (9)  op(e2, e2) = e2
% 158.02/24.59    (10)   ~ (all_52_3 = e0)
% 158.02/24.59    (11)  op(e0, e2) = all_52_7
% 158.02/24.59    (12)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 158.02/24.59    (13)  all_54_1 = all_52_4
% 158.02/24.59    (14)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.02/24.59    (15)   ~ (all_52_3 = e1)
% 158.02/24.59    (16)  op(e2, e2) = all_4_2
% 158.02/24.59    (17)  op(e0, e3) = all_8_0
% 158.02/24.59    (18)   ~ (all_8_0 = e2)
% 158.02/24.59    (19)   ~ (all_52_4 = all_4_2)
% 158.02/24.59    (20)  op(e3, e3) = e0
% 158.02/24.59    (21)   ~ (all_52_4 = all_52_7)
% 158.02/24.59    (22)  op(e3, e2) = all_52_4
% 158.02/24.59    (23)   ~ (all_52_7 = all_4_2)
% 158.02/24.59    (24)   ~ (e2 = e1)
% 158.02/24.59    (25)   ~ (all_52_4 = e0)
% 158.02/24.59    (26)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) & op(e3, e2) =
% 158.02/24.59            all_57_1 & $i(all_57_1))
% 158.02/24.59    (27)   ~ (e2 = e0)
% 158.02/24.59  
% 158.02/24.59  Begin of proof
% 158.02/24.59  | 
% 158.02/24.59  | BETA: splitting (2) gives:
% 158.02/24.59  | 
% 158.02/24.59  | Case 1:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (28)  all_57_15 = e2 & op(e0, e0) = e2
% 158.02/24.59  | | 
% 158.02/24.59  | | ALPHA: (28) implies:
% 158.02/24.59  | |   (29)  op(e0, e0) = e2
% 158.02/24.59  | | 
% 158.02/24.59  | | REF_CLOSE: (3), (7), (24), (29) are inconsistent by sub-proof #875.
% 158.02/24.59  | | 
% 158.02/24.59  | Case 2:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (30)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)
% 158.02/24.59  | | 
% 158.02/24.59  | | ALPHA: (30) implies:
% 158.02/24.59  | |   (31)   ~ (all_57_7 = e0)
% 158.02/24.59  | |   (32)  op(e0, e2) = all_57_7
% 158.02/24.59  | | 
% 158.02/24.59  | | BETA: splitting (26) gives:
% 158.02/24.59  | | 
% 158.02/24.59  | | Case 1:
% 158.02/24.59  | | | 
% 158.02/24.59  | | |   (33)  all_57_10 = e2 & op(e3, e3) = e2
% 158.02/24.59  | | | 
% 158.02/24.59  | | | ALPHA: (33) implies:
% 158.02/24.59  | | |   (34)  op(e3, e3) = e2
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REF_CLOSE: (7), (20), (27), (34) are inconsistent by sub-proof #281.
% 158.02/24.59  | | | 
% 158.02/24.59  | | Case 2:
% 158.02/24.59  | | | 
% 158.02/24.59  | | |   (35)   ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | ALPHA: (35) implies:
% 158.02/24.59  | | |   (36)   ~ (all_57_1 = e3)
% 158.02/24.59  | | |   (37)  op(e3, e2) = all_57_1
% 158.02/24.59  | | | 
% 158.02/24.59  | | | GROUND_INST: instantiating (7) with all_52_7, all_57_7, e2, e0,
% 158.02/24.59  | | |              simplifying with (11), (32) gives:
% 158.02/24.59  | | |   (38)  all_57_7 = all_52_7
% 158.02/24.59  | | | 
% 158.02/24.59  | | | GROUND_INST: instantiating (7) with all_52_3, all_8_0, e3, e0, simplifying
% 158.02/24.59  | | |              with (8), (17) gives:
% 158.02/24.59  | | |   (39)  all_52_3 = all_8_0
% 158.02/24.59  | | | 
% 158.02/24.59  | | | GROUND_INST: instantiating (7) with all_4_2, e2, e2, e2, simplifying with
% 158.02/24.59  | | |              (9), (16) gives:
% 158.02/24.59  | | |   (40)  all_4_2 = e2
% 158.02/24.59  | | | 
% 158.02/24.59  | | | GROUND_INST: instantiating (7) with all_52_4, all_57_1, e2, e3,
% 158.02/24.59  | | |              simplifying with (22), (37) gives:
% 158.02/24.59  | | |   (41)  all_57_1 = all_52_4
% 158.02/24.59  | | | 
% 158.02/24.59  | | | COMBINE_EQS: (5), (39) imply:
% 158.02/24.59  | | |   (42)  all_54_12 = all_8_0
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REDUCE: (36), (41) imply:
% 158.02/24.59  | | |   (43)   ~ (all_52_4 = e3)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REDUCE: (31), (38) imply:
% 158.02/24.59  | | |   (44)   ~ (all_52_7 = e0)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REDUCE: (1), (39) imply:
% 158.02/24.59  | | |   (45)   ~ (all_52_7 = all_8_0)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | SIMP: (45) implies:
% 158.02/24.59  | | |   (46)   ~ (all_52_7 = all_8_0)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REDUCE: (19), (40) imply:
% 158.02/24.59  | | |   (47)   ~ (all_52_4 = e2)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | REDUCE: (23), (40) imply:
% 158.02/24.59  | | |   (48)   ~ (all_52_7 = e2)
% 158.02/24.59  | | | 
% 158.02/24.59  | | | BETA: splitting (12) gives:
% 158.02/24.59  | | | 
% 158.02/24.59  | | | Case 1:
% 158.02/24.59  | | | | 
% 158.02/24.59  | | | |   (49)  all_54_12 = e3
% 158.02/24.59  | | | | 
% 158.02/24.59  | | | | COMBINE_EQS: (42), (49) imply:
% 158.02/24.59  | | | |   (50)  all_8_0 = e3
% 158.02/24.59  | | | | 
% 158.02/24.59  | | | | SIMP: (50) implies:
% 158.02/24.59  | | | |   (51)  all_8_0 = e3
% 158.02/24.59  | | | | 
% 158.02/24.59  | | | | REDUCE: (46), (51) imply:
% 158.02/24.59  | | | |   (52)   ~ (all_52_7 = e3)
% 158.02/24.59  | | | | 
% 158.02/24.59  | | | | REF_CLOSE: (4), (6), (13), (14), (21), (25), (43), (44), (47), (48),
% 158.02/24.59  | | | |            (52) are inconsistent by sub-proof #94.
% 158.02/24.59  | | | | 
% 158.02/24.59  | | | Case 2:
% 158.02/24.59  | | | | 
% 158.02/24.59  | | | |   (53)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 158.02/24.59  | | | | 
% 158.02/24.59  | | | | REF_CLOSE: (5), (10), (15), (18), (42), (53) are inconsistent by
% 158.02/24.59  | | | |            sub-proof #65.
% 158.02/24.59  | | | | 
% 158.02/24.59  | | | End of split
% 158.02/24.59  | | | 
% 158.02/24.59  | | End of split
% 158.02/24.59  | | 
% 158.02/24.59  | End of split
% 158.02/24.59  | 
% 158.02/24.59  End of proof
% 158.02/24.59  
% 158.02/24.59  Sub-proof #65 shows that the following formulas are inconsistent:
% 158.02/24.59  ----------------------------------------------------------------
% 158.02/24.59    (1)  all_54_12 = all_52_3
% 158.02/24.59    (2)   ~ (all_52_3 = e0)
% 158.02/24.59    (3)   ~ (all_52_3 = e1)
% 158.02/24.59    (4)   ~ (all_8_0 = e2)
% 158.02/24.59    (5)  all_54_12 = all_8_0
% 158.02/24.59    (6)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 158.02/24.59  
% 158.02/24.59  Begin of proof
% 158.02/24.59  | 
% 158.02/24.59  | BETA: splitting (6) gives:
% 158.02/24.59  | 
% 158.02/24.59  | Case 1:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (7)  all_54_12 = e2
% 158.02/24.59  | | 
% 158.02/24.59  | | COMBINE_EQS: (5), (7) imply:
% 158.02/24.59  | |   (8)  all_8_0 = e2
% 158.02/24.59  | | 
% 158.02/24.59  | | SIMP: (8) implies:
% 158.02/24.59  | |   (9)  all_8_0 = e2
% 158.02/24.59  | | 
% 158.02/24.59  | | REDUCE: (4), (9) imply:
% 158.02/24.59  | |   (10)  $false
% 158.02/24.59  | | 
% 158.02/24.59  | | CLOSE: (10) is inconsistent.
% 158.02/24.59  | | 
% 158.02/24.59  | Case 2:
% 158.02/24.59  | | 
% 158.02/24.59  | |   (11)  all_54_12 = e1 | all_54_12 = e0
% 158.02/24.59  | | 
% 158.02/24.59  | | REF_CLOSE: (1), (2), (3), (11) are inconsistent by sub-proof #619.
% 158.02/24.59  | | 
% 158.02/24.59  | End of split
% 158.02/24.59  | 
% 158.02/24.59  End of proof
% 158.02/24.59  
% 158.02/24.59  Sub-proof #66 shows that the following formulas are inconsistent:
% 158.02/24.59  ----------------------------------------------------------------
% 158.02/24.59    (1)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 158.02/24.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.59    (3)  op(e0, e3) = all_52_3
% 158.02/24.59    (4)   ~ (all_4_2 = e3)
% 158.02/24.59    (5)  all_56_6 = e2
% 158.02/24.59    (6)   ~ (all_52_3 = e1)
% 158.02/24.59    (7)  op(e2, e2) = all_4_2
% 158.02/24.59    (8)  op(e3, e3) = e0
% 158.02/24.59    (9)   ~ (e1 = e0)
% 158.02/24.59    (10)   ~ (e2 = e1)
% 158.02/24.59    (11)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.02/24.59          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.02/24.59    (12)   ~ (e3 = e1)
% 158.02/24.59  
% 158.02/24.59  Begin of proof
% 158.02/24.59  | 
% 158.02/24.59  | BETA: splitting (1) gives:
% 158.02/24.59  | 
% 158.02/24.59  | Case 1:
% 158.02/24.59  | | 
% 158.02/24.60  | |   (13)  all_56_2 = e3 & op(e2, e3) = e3
% 158.02/24.60  | | 
% 158.02/24.60  | | ALPHA: (13) implies:
% 158.02/24.60  | |   (14)  all_56_2 = e3
% 158.02/24.60  | | 
% 158.02/24.60  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (12), (14) are
% 158.02/24.60  | |            inconsistent by sub-proof #69.
% 158.02/24.60  | | 
% 158.02/24.60  | Case 2:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (15)  all_56_3 = e3 & op(e2, e2) = e3
% 158.02/24.60  | | 
% 158.02/24.60  | | ALPHA: (15) implies:
% 158.02/24.60  | |   (16)  op(e2, e2) = e3
% 158.02/24.60  | | 
% 158.02/24.60  | | REF_CLOSE: (2), (4), (7), (16) are inconsistent by sub-proof #711.
% 158.02/24.60  | | 
% 158.02/24.60  | End of split
% 158.02/24.60  | 
% 158.02/24.60  End of proof
% 158.02/24.60  
% 158.02/24.60  Sub-proof #67 shows that the following formulas are inconsistent:
% 158.02/24.60  ----------------------------------------------------------------
% 158.02/24.60    (1)   ~ (all_52_1 = e2)
% 158.02/24.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.60    (3)  op(e3, e3) = e0
% 158.02/24.60    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 158.02/24.60    (5)  op(e2, e3) = all_52_1
% 158.02/24.60    (6)   ~ (e2 = e0)
% 158.02/24.60  
% 158.02/24.60  Begin of proof
% 158.02/24.60  | 
% 158.02/24.60  | BETA: splitting (4) gives:
% 158.02/24.60  | 
% 158.02/24.60  | Case 1:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 158.02/24.60  | | 
% 158.02/24.60  | | ALPHA: (7) implies:
% 158.02/24.60  | |   (8)  op(e3, e3) = e2
% 158.02/24.60  | | 
% 158.02/24.60  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #281.
% 158.02/24.60  | | 
% 158.02/24.60  | Case 2:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 158.02/24.60  | | 
% 158.02/24.60  | | ALPHA: (9) implies:
% 158.02/24.60  | |   (10)  op(e2, e3) = e2
% 158.02/24.60  | | 
% 158.02/24.60  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1007.
% 158.02/24.60  | | 
% 158.02/24.60  | End of split
% 158.02/24.60  | 
% 158.02/24.60  End of proof
% 158.02/24.60  
% 158.02/24.60  Sub-proof #68 shows that the following formulas are inconsistent:
% 158.02/24.60  ----------------------------------------------------------------
% 158.02/24.60    (1)  op(e0, e0) = e1
% 158.02/24.60    (2)  op(e0, e1) = all_52_11
% 158.02/24.60    (3)   ~ (e3 = e2)
% 158.02/24.60    (4)   ~ (all_52_7 = e3)
% 158.02/24.60    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.60    (6)  all_56_12 = e2
% 158.02/24.60    (7)  op(e0, e2) = all_52_7
% 158.02/24.60    (8)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3) |
% 158.02/24.60         (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.02/24.60    (9)   ~ (e3 = e1)
% 158.02/24.60    (10)   ~ (all_52_11 = e3)
% 158.02/24.60  
% 158.02/24.60  Begin of proof
% 158.02/24.60  | 
% 158.02/24.60  | BETA: splitting (8) gives:
% 158.02/24.60  | 
% 158.02/24.60  | Case 1:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (11)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 158.02/24.60  | |           e3)
% 158.02/24.60  | | 
% 158.02/24.60  | | BETA: splitting (11) gives:
% 158.02/24.60  | | 
% 158.02/24.60  | | Case 1:
% 158.02/24.60  | | | 
% 158.02/24.60  | | |   (12)  all_56_12 = e3 & op(e0, e3) = e3
% 158.02/24.60  | | | 
% 158.02/24.60  | | | ALPHA: (12) implies:
% 158.02/24.60  | | |   (13)  all_56_12 = e3
% 158.02/24.60  | | | 
% 158.02/24.60  | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #616.
% 158.02/24.60  | | | 
% 158.02/24.60  | | Case 2:
% 158.02/24.60  | | | 
% 158.02/24.60  | | |   (14)  all_56_13 = e3 & op(e0, e2) = e3
% 158.02/24.60  | | | 
% 158.02/24.60  | | | REF_CLOSE: (4), (5), (7), (14) are inconsistent by sub-proof #429.
% 158.02/24.60  | | | 
% 158.02/24.60  | | End of split
% 158.02/24.60  | | 
% 158.02/24.60  | Case 2:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (15)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.02/24.60  | |           e3)
% 158.02/24.60  | | 
% 158.02/24.60  | | REF_CLOSE: (1), (2), (5), (9), (10), (15) are inconsistent by sub-proof
% 158.02/24.60  | |            #290.
% 158.02/24.60  | | 
% 158.02/24.60  | End of split
% 158.02/24.60  | 
% 158.02/24.60  End of proof
% 158.02/24.60  
% 158.02/24.60  Sub-proof #69 shows that the following formulas are inconsistent:
% 158.02/24.60  ----------------------------------------------------------------
% 158.02/24.60    (1)  all_56_2 = e3
% 158.02/24.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.60    (3)  op(e0, e3) = all_52_3
% 158.02/24.60    (4)  all_56_6 = e2
% 158.02/24.60    (5)   ~ (all_52_3 = e1)
% 158.02/24.60    (6)  op(e3, e3) = e0
% 158.02/24.60    (7)   ~ (e1 = e0)
% 158.02/24.60    (8)   ~ (e2 = e1)
% 158.02/24.60    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.02/24.60         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.02/24.60    (10)   ~ (e3 = e1)
% 158.02/24.60  
% 158.02/24.60  Begin of proof
% 158.02/24.60  | 
% 158.02/24.60  | BETA: splitting (9) gives:
% 158.02/24.60  | 
% 158.02/24.60  | Case 1:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (11)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 158.02/24.60  | |           e1)
% 158.02/24.60  | | 
% 158.02/24.60  | | BETA: splitting (11) gives:
% 158.02/24.60  | | 
% 158.02/24.60  | | Case 1:
% 158.02/24.60  | | | 
% 158.02/24.60  | | |   (12)  all_56_0 = e1 & op(e3, e3) = e1
% 158.02/24.60  | | | 
% 158.02/24.60  | | | ALPHA: (12) implies:
% 158.02/24.60  | | |   (13)  op(e3, e3) = e1
% 158.02/24.60  | | | 
% 158.02/24.60  | | | REF_CLOSE: (2), (6), (7), (13) are inconsistent by sub-proof #834.
% 158.02/24.60  | | | 
% 158.02/24.60  | | Case 2:
% 158.02/24.60  | | | 
% 158.02/24.60  | | |   (14)  all_56_2 = e1 & op(e2, e3) = e1
% 158.02/24.60  | | | 
% 158.02/24.60  | | | REF_CLOSE: (1), (10), (14) are inconsistent by sub-proof #774.
% 158.02/24.60  | | | 
% 158.02/24.60  | | End of split
% 158.02/24.60  | | 
% 158.02/24.60  | Case 2:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (15)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 158.02/24.60  | |           e1)
% 158.02/24.60  | | 
% 158.02/24.60  | | REF_CLOSE: (2), (3), (4), (5), (8), (15) are inconsistent by sub-proof #304.
% 158.02/24.60  | | 
% 158.02/24.60  | End of split
% 158.02/24.60  | 
% 158.02/24.60  End of proof
% 158.02/24.60  
% 158.02/24.60  Sub-proof #70 shows that the following formulas are inconsistent:
% 158.02/24.60  ----------------------------------------------------------------
% 158.02/24.60    (1)  all_54_13 = all_52_7
% 158.02/24.60    (2)  op(e1, e1) = e3
% 158.02/24.60    (3)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.02/24.60             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.02/24.60           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.02/24.60               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.02/24.60             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.02/24.60         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.02/24.60             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.02/24.60           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.02/24.60               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.02/24.60             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.02/24.60         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.02/24.60             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.02/24.60           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.02/24.60               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.02/24.60             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.02/24.60         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.02/24.60             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.02/24.60           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.02/24.60               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.02/24.60             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.02/24.60    (4)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/24.60    (5)   ~ (e3 = e2)
% 158.02/24.60    (6)   ~ (all_52_7 = e3)
% 158.02/24.60    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.60    (8)  op(e0, e0) = e3
% 158.02/24.60    (9)  op(e0, e2) = all_52_7
% 158.02/24.60    (10)  all_54_1 = all_52_4
% 158.02/24.60    (11)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.02/24.60    (12)  op(e2, e2) = all_4_2
% 158.02/24.60    (13)   ~ (all_52_4 = all_4_2)
% 158.02/24.60    (14)  op(e3, e3) = e0
% 158.02/24.60    (15)   ~ (all_52_4 = all_52_7)
% 158.02/24.60    (16)  op(e3, e2) = all_52_4
% 158.02/24.60    (17)   ~ (all_52_7 = all_4_2)
% 158.02/24.60    (18)   ~ (all_52_4 = e0)
% 158.02/24.60    (19)   ~ (e3 = e1)
% 158.02/24.60    (20)   ~ (e2 = e0)
% 158.02/24.60    (21)   ~ (e3 = e0)
% 158.02/24.60  
% 158.02/24.60  Begin of proof
% 158.02/24.60  | 
% 158.02/24.60  | BETA: splitting (3) gives:
% 158.02/24.60  | 
% 158.02/24.60  | Case 1:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (22)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.02/24.60  | |               e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.02/24.60  | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.02/24.60  | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.02/24.60  | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.02/24.60  | |                 e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 158.02/24.60  | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 158.02/24.60  | |                 e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 158.02/24.60  | |               e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 158.02/24.60  | |               all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 158.02/24.60  | |               e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 158.02/24.60  | |               $i(all_57_7))))
% 158.02/24.60  | | 
% 158.02/24.60  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 158.02/24.60  | |            (15), (16), (17), (18), (20), (21), (22) are inconsistent by
% 158.02/24.60  | |            sub-proof #71.
% 158.02/24.60  | | 
% 158.02/24.60  | Case 2:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (23)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 158.02/24.60  | |               e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 158.02/24.60  | |               $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 158.02/24.60  | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 158.02/24.60  | |           ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 158.02/24.60  | |                 e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 158.02/24.60  | |             e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 158.02/24.60  | |                 e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 =
% 158.02/24.60  | |               e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 158.02/24.60  | |               all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 158.02/24.60  | |               e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.02/24.60  | |               $i(all_57_13))))
% 158.02/24.60  | | 
% 158.02/24.60  | | REF_CLOSE: (2), (7), (8), (19), (21), (23) are inconsistent by sub-proof
% 158.02/24.60  | |            #389.
% 158.02/24.60  | | 
% 158.02/24.60  | End of split
% 158.02/24.60  | 
% 158.02/24.60  End of proof
% 158.02/24.60  
% 158.02/24.60  Sub-proof #71 shows that the following formulas are inconsistent:
% 158.02/24.60  ----------------------------------------------------------------
% 158.02/24.60    (1)  all_54_13 = all_52_7
% 158.02/24.60    (2)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/24.60    (3)   ~ (e3 = e2)
% 158.02/24.60    (4)   ~ (all_52_7 = e3)
% 158.02/24.60    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.60    (6)  op(e0, e0) = e3
% 158.02/24.60    (7)  op(e0, e2) = all_52_7
% 158.02/24.60    (8)  all_54_1 = all_52_4
% 158.02/24.60    (9)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.02/24.60    (10)  op(e2, e2) = all_4_2
% 158.02/24.60    (11)   ~ (all_52_4 = all_4_2)
% 158.02/24.60    (12)  op(e3, e3) = e0
% 158.02/24.60    (13)   ~ (all_52_4 = all_52_7)
% 158.02/24.60    (14)  op(e3, e2) = all_52_4
% 158.02/24.60    (15)   ~ (all_52_7 = all_4_2)
% 158.02/24.60    (16)   ~ (all_52_4 = e0)
% 158.02/24.60    (17)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 158.02/24.60              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.02/24.60            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.02/24.60                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 158.02/24.60              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.02/24.60          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 158.02/24.60              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.02/24.60            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.02/24.60                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 158.02/24.60              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 158.02/24.60    (18)   ~ (e2 = e0)
% 158.02/24.60    (19)   ~ (e3 = e0)
% 158.02/24.60  
% 158.02/24.60  Begin of proof
% 158.02/24.60  | 
% 158.02/24.60  | BETA: splitting (17) gives:
% 158.02/24.60  | 
% 158.02/24.60  | Case 1:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (20)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.02/24.60  | |             e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.02/24.60  | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.02/24.60  | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.02/24.60  | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.02/24.60  | |               e3) = all_57_6 & $i(all_57_6)))
% 158.02/24.60  | | 
% 158.02/24.60  | | ALPHA: (20) implies:
% 158.02/24.60  | |   (21)  op(e3, e3) = e3
% 158.02/24.60  | | 
% 158.02/24.60  | | REF_CLOSE: (5), (12), (19), (21) are inconsistent by sub-proof #971.
% 158.02/24.60  | | 
% 158.02/24.60  | Case 2:
% 158.02/24.60  | | 
% 158.02/24.60  | |   (22)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 158.02/24.60  | |             e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.02/24.60  | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 158.02/24.60  | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 158.02/24.60  | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 158.02/24.60  | |               e2) = all_57_7 & $i(all_57_7)))
% 158.02/24.60  | | 
% 158.02/24.60  | | ALPHA: (22) implies:
% 158.02/24.60  | |   (23)  op(e2, e2) = e2
% 158.02/24.60  | |   (24)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 158.02/24.60  | |             e2) = all_57_7 & $i(all_57_7))
% 158.02/24.60  | |   (25)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) & op(e3,
% 158.02/24.60  | |             e2) = all_57_1 & $i(all_57_1))
% 158.02/24.60  | | 
% 158.02/24.60  | | BETA: splitting (24) gives:
% 158.02/24.60  | | 
% 158.02/24.60  | | Case 1:
% 158.02/24.60  | | | 
% 158.02/24.60  | | |   (26)  all_57_15 = e2 & op(e0, e0) = e2
% 158.02/24.60  | | | 
% 158.02/24.60  | | | ALPHA: (26) implies:
% 158.02/24.60  | | |   (27)  op(e0, e0) = e2
% 158.02/24.60  | | | 
% 158.02/24.60  | | | REF_CLOSE: (3), (5), (6), (27) are inconsistent by sub-proof #878.
% 158.02/24.60  | | | 
% 158.02/24.60  | | Case 2:
% 158.02/24.60  | | | 
% 158.02/24.60  | | |   (28)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)
% 158.02/24.60  | | | 
% 158.02/24.60  | | | ALPHA: (28) implies:
% 158.02/24.60  | | |   (29)   ~ (all_57_7 = e0)
% 158.02/24.60  | | |   (30)  op(e0, e2) = all_57_7
% 158.02/24.60  | | | 
% 158.02/24.60  | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 158.02/24.60  | | |            (14), (15), (16), (18), (23), (25), (29), (30) are inconsistent
% 158.02/24.60  | | |            by sub-proof #82.
% 158.02/24.60  | | | 
% 158.02/24.60  | | End of split
% 158.02/24.60  | | 
% 158.02/24.60  | End of split
% 158.02/24.60  | 
% 158.02/24.60  End of proof
% 158.02/24.60  
% 158.02/24.60  Sub-proof #72 shows that the following formulas are inconsistent:
% 158.02/24.60  ----------------------------------------------------------------
% 158.02/24.60    (1)  op(e1, e1) = e3
% 158.02/24.60    (2)  op(e0, e1) = all_52_11
% 158.02/24.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.60    (4)   ~ (e1 = e0)
% 158.02/24.60    (5)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.60           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.02/24.60           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.02/24.60           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 158.02/24.60           & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.02/24.60    (6)  op(e0, e2) = e1
% 158.02/24.60    (7)   ~ (all_52_11 = e0)
% 158.02/24.60    (8)   ~ (e3 = e0)
% 158.02/24.60  
% 158.02/24.60  Begin of proof
% 158.02/24.60  | 
% 158.02/24.60  | BETA: splitting (5) gives:
% 158.02/24.60  | 
% 158.02/24.60  | Case 1:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (9)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 158.02/24.61  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 158.02/24.61  | | 
% 158.02/24.61  | | ALPHA: (9) implies:
% 158.02/24.61  | |   (10)  op(e1, e1) = e0
% 158.02/24.61  | | 
% 158.02/24.61  | | REF_CLOSE: (1), (3), (8), (10) are inconsistent by sub-proof #912.
% 158.02/24.61  | | 
% 158.02/24.61  | Case 2:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (11)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.02/24.61  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.61  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.02/24.61  | | 
% 158.02/24.61  | | BETA: splitting (11) gives:
% 158.02/24.61  | | 
% 158.02/24.61  | | Case 1:
% 158.02/24.61  | | | 
% 158.02/24.61  | | |   (12)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 158.02/24.61  | | | 
% 158.02/24.61  | | | ALPHA: (12) implies:
% 158.02/24.61  | | |   (13)  op(e0, e2) = e0
% 158.02/24.61  | | | 
% 158.02/24.61  | | | REF_CLOSE: (3), (4), (6), (13) are inconsistent by sub-proof #832.
% 158.02/24.61  | | | 
% 158.02/24.61  | | Case 2:
% 158.02/24.61  | | | 
% 158.02/24.61  | | |   (14)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.61  | | |           e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 158.02/24.61  | | | 
% 158.02/24.61  | | | ALPHA: (14) implies:
% 158.02/24.61  | | |   (15)  op(e0, e1) = e0
% 158.02/24.61  | | | 
% 158.02/24.61  | | | REF_CLOSE: (2), (3), (7), (15) are inconsistent by sub-proof #966.
% 158.02/24.61  | | | 
% 158.02/24.61  | | End of split
% 158.02/24.61  | | 
% 158.02/24.61  | End of split
% 158.02/24.61  | 
% 158.02/24.61  End of proof
% 158.02/24.61  
% 158.02/24.61  Sub-proof #73 shows that the following formulas are inconsistent:
% 158.02/24.61  ----------------------------------------------------------------
% 158.02/24.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.61    (2)  op(e0, e3) = all_52_3
% 158.02/24.61    (3)   ~ (all_52_12 = e3)
% 158.02/24.61    (4)   ~ (all_52_3 = e0)
% 158.02/24.61    (5)  op(e2, e0) = all_52_13
% 158.02/24.61    (6)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.02/24.61         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.61           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.02/24.61           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 158.02/24.61           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.02/24.61    (7)  op(e3, e0) = all_52_12
% 158.02/24.61    (8)   ~ (all_52_13 = e2)
% 158.02/24.61  
% 158.02/24.61  Begin of proof
% 158.02/24.61  | 
% 158.02/24.61  | BETA: splitting (6) gives:
% 158.02/24.61  | 
% 158.02/24.61  | Case 1:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (9)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 158.02/24.61  | | 
% 158.02/24.61  | | ALPHA: (9) implies:
% 158.02/24.61  | |   (10)  op(e0, e3) = e0
% 158.02/24.61  | | 
% 158.02/24.61  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #973.
% 158.02/24.61  | | 
% 158.02/24.61  | Case 2:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (11)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.61  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.02/24.61  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.61  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.02/24.61  | | 
% 158.02/24.61  | | REF_CLOSE: (1), (3), (5), (7), (8), (11) are inconsistent by sub-proof #167.
% 158.02/24.61  | | 
% 158.02/24.61  | End of split
% 158.02/24.61  | 
% 158.02/24.61  End of proof
% 158.02/24.61  
% 158.02/24.61  Sub-proof #74 shows that the following formulas are inconsistent:
% 158.02/24.61  ----------------------------------------------------------------
% 158.02/24.61    (1)  op(e0, e0) = e2
% 158.02/24.61    (2)   ~ (e3 = e2)
% 158.02/24.61    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.61    (4)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.02/24.61             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 158.02/24.61               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.02/24.61               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.02/24.61    (5)   ~ (e1 = e0)
% 158.02/24.61    (6)  op(e0, e2) = e1
% 158.02/24.61    (7)  all_56_14 = e2
% 158.02/24.61    (8)   ~ (e2 = e1)
% 158.02/24.61    (9)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3) |
% 158.02/24.61         (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.02/24.61    (10)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.02/24.61          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.02/24.61            e1)
% 158.02/24.61    (11)   ~ (e3 = e1)
% 158.02/24.61    (12)   ~ (e2 = e0)
% 158.02/24.61    (13)   ~ (e3 = e0)
% 158.02/24.61  
% 158.02/24.61  Begin of proof
% 158.02/24.61  | 
% 158.02/24.61  | BETA: splitting (9) gives:
% 158.02/24.61  | 
% 158.02/24.61  | Case 1:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (14)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 158.02/24.61  | |           e3)
% 158.02/24.61  | | 
% 158.02/24.61  | | BETA: splitting (14) gives:
% 158.02/24.61  | | 
% 158.02/24.61  | | Case 1:
% 158.02/24.61  | | | 
% 158.02/24.61  | | |   (15)  all_56_12 = e3 & op(e0, e3) = e3
% 158.02/24.61  | | | 
% 158.02/24.61  | | | ALPHA: (15) implies:
% 158.02/24.61  | | |   (16)  all_56_12 = e3
% 158.02/24.61  | | | 
% 158.02/24.61  | | | BETA: splitting (4) gives:
% 158.02/24.61  | | | 
% 158.02/24.61  | | | Case 1:
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | |   (17)  all_56_15 = e0 & op(e0, e0) = e0
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | ALPHA: (17) implies:
% 158.02/24.61  | | | |   (18)  op(e0, e0) = e0
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | REF_CLOSE: (1), (3), (12), (18) are inconsistent by sub-proof #979.
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | Case 2:
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | |   (19)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 158.02/24.61  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 158.02/24.61  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 158.02/24.61  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | ALPHA: (19) implies:
% 158.02/24.61  | | | |   (20)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 158.02/24.61  | | | |             e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | BETA: splitting (20) gives:
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | Case 1:
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | |   (21)  all_56_12 = e0 & op(e0, e3) = e0
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | | REF_CLOSE: (13), (16), (21) are inconsistent by sub-proof #735.
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | Case 2:
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | |   (22)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 158.02/24.61  | | | | |             e1) = e0)
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | | BETA: splitting (22) gives:
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | | Case 1:
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | |   (23)  all_56_13 = e0 & op(e0, e2) = e0
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | | ALPHA: (23) implies:
% 158.02/24.61  | | | | | |   (24)  op(e0, e2) = e0
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | | REF_CLOSE: (3), (5), (6), (24) are inconsistent by sub-proof #832.
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | Case 2:
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | |   (25)  all_56_14 = e0 & op(e0, e1) = e0
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | | REF_CLOSE: (7), (12), (25) are inconsistent by sub-proof #725.
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | End of split
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | End of split
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | End of split
% 158.02/24.61  | | | 
% 158.02/24.61  | | Case 2:
% 158.02/24.61  | | | 
% 158.02/24.61  | | |   (26)  all_56_13 = e3 & op(e0, e2) = e3
% 158.02/24.61  | | | 
% 158.02/24.61  | | | ALPHA: (26) implies:
% 158.02/24.61  | | |   (27)  all_56_13 = e3
% 158.02/24.61  | | |   (28)  op(e0, e2) = e3
% 158.02/24.61  | | | 
% 158.02/24.61  | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11), (12), (13), (27),
% 158.02/24.61  | | |            (28) are inconsistent by sub-proof #724.
% 158.02/24.61  | | | 
% 158.02/24.61  | | End of split
% 158.02/24.61  | | 
% 158.02/24.61  | Case 2:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (29)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.02/24.61  | |           e3)
% 158.02/24.61  | | 
% 158.02/24.61  | | REF_CLOSE: (1), (2), (3), (7), (29) are inconsistent by sub-proof #722.
% 158.02/24.61  | | 
% 158.02/24.61  | End of split
% 158.02/24.61  | 
% 158.02/24.61  End of proof
% 158.02/24.61  
% 158.02/24.61  Sub-proof #75 shows that the following formulas are inconsistent:
% 158.02/24.61  ----------------------------------------------------------------
% 158.02/24.61    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.02/24.61         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.02/24.61    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 158.02/24.61         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 158.02/24.61    (3)   ~ (e3 = e2)
% 158.02/24.61    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.61    (5)  op(e1, e3) = all_52_2
% 158.02/24.61    (6)   ~ (all_52_2 = e3)
% 158.02/24.61    (7)  op(e3, e3) = e1
% 158.02/24.61    (8)   ~ (e1 = e0)
% 158.02/24.61    (9)  all_56_2 = e1
% 158.02/24.61    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.02/24.61          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.02/24.61    (11)  op(e2, e3) = e1
% 158.02/24.61    (12)   ~ (e2 = e1)
% 158.02/24.61    (13)   ~ (e3 = e1)
% 158.02/24.61    (14)   ~ (e2 = e0)
% 158.02/24.61    (15)   ~ (e3 = e0)
% 158.02/24.61  
% 158.02/24.61  Begin of proof
% 158.02/24.61  | 
% 158.02/24.61  | BETA: splitting (2) gives:
% 158.02/24.61  | 
% 158.02/24.61  | Case 1:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (16)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 158.02/24.61  | |           e3)
% 158.02/24.61  | | 
% 158.02/24.61  | | REF_CLOSE: (4), (7), (9), (13), (16) are inconsistent by sub-proof #483.
% 158.02/24.61  | | 
% 158.02/24.61  | Case 2:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (17)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 158.02/24.61  | |           e3)
% 158.02/24.61  | | 
% 158.02/24.61  | | BETA: splitting (17) gives:
% 158.02/24.61  | | 
% 158.02/24.61  | | Case 1:
% 158.02/24.61  | | | 
% 158.02/24.61  | | |   (18)  all_56_6 = e3 & op(e1, e3) = e3
% 158.02/24.61  | | | 
% 158.02/24.61  | | | REF_CLOSE: (4), (5), (6), (18) are inconsistent by sub-proof #681.
% 158.02/24.61  | | | 
% 158.02/24.61  | | Case 2:
% 158.02/24.61  | | | 
% 158.02/24.61  | | |   (19)  all_56_12 = e3 & op(e0, e3) = e3
% 158.02/24.61  | | | 
% 158.02/24.61  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13),
% 158.02/24.61  | | |            (14), (15), (19) are inconsistent by sub-proof #426.
% 158.02/24.61  | | | 
% 158.02/24.61  | | End of split
% 158.02/24.61  | | 
% 158.02/24.61  | End of split
% 158.02/24.61  | 
% 158.02/24.61  End of proof
% 158.02/24.61  
% 158.02/24.61  Sub-proof #76 shows that the following formulas are inconsistent:
% 158.02/24.61  ----------------------------------------------------------------
% 158.02/24.61    (1)   ~ (all_52_12 = e1)
% 158.02/24.61    (2)   ~ (all_52_14 = e3)
% 158.02/24.61    (3)   ~ (all_52_14 = e0)
% 158.02/24.61    (4)   ~ (all_52_4 = all_52_12)
% 158.02/24.61    (5)   ~ (all_52_2 = all_52_14)
% 158.02/24.61    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.61    (7)   ~ (all_52_12 = all_52_14)
% 158.02/24.61    (8)  op(e1, e3) = all_52_2
% 158.02/24.61    (9)  all_54_3 = all_52_12
% 158.02/24.61    (10)  all_54_1 = all_52_4
% 158.02/24.61    (11)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.02/24.61    (12)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.02/24.61    (13)  op(e3, e2) = all_52_4
% 158.02/24.61    (14)  op(e1, e3) = e1
% 158.02/24.61    (15)   ~ (all_52_12 = e0)
% 158.02/24.61    (16)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 158.02/24.61    (17)  all_54_11 = all_52_14
% 158.02/24.61    (18)  op(e3, e2) = e3
% 158.02/24.61  
% 158.02/24.61  Begin of proof
% 158.02/24.61  | 
% 158.02/24.61  | BETA: splitting (11) gives:
% 158.02/24.61  | 
% 158.02/24.61  | Case 1:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (19)  all_54_1 = e3
% 158.02/24.61  | | 
% 158.02/24.61  | | COMBINE_EQS: (10), (19) imply:
% 158.02/24.61  | |   (20)  all_52_4 = e3
% 158.02/24.61  | | 
% 158.02/24.61  | | REDUCE: (4), (20) imply:
% 158.02/24.61  | |   (21)   ~ (all_52_12 = e3)
% 158.02/24.61  | | 
% 158.02/24.61  | | SIMP: (21) implies:
% 158.02/24.61  | |   (22)   ~ (all_52_12 = e3)
% 158.02/24.61  | | 
% 158.02/24.61  | | BETA: splitting (16) gives:
% 158.02/24.61  | | 
% 158.02/24.61  | | Case 1:
% 158.02/24.61  | | | 
% 158.02/24.61  | | |   (23)  all_54_3 = e3
% 158.02/24.61  | | | 
% 158.02/24.61  | | | COMBINE_EQS: (9), (23) imply:
% 158.02/24.61  | | |   (24)  all_52_12 = e3
% 158.02/24.61  | | | 
% 158.02/24.61  | | | REDUCE: (22), (24) imply:
% 158.02/24.61  | | |   (25)  $false
% 158.02/24.61  | | | 
% 158.02/24.61  | | | CLOSE: (25) is inconsistent.
% 158.02/24.61  | | | 
% 158.02/24.61  | | Case 2:
% 158.02/24.61  | | | 
% 158.02/24.61  | | |   (26)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 158.02/24.61  | | | 
% 158.02/24.61  | | | BETA: splitting (26) gives:
% 158.02/24.61  | | | 
% 158.02/24.61  | | | Case 1:
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | |   (27)  all_54_3 = e2
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | COMBINE_EQS: (9), (27) imply:
% 158.02/24.61  | | | |   (28)  all_52_12 = e2
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | REDUCE: (7), (28) imply:
% 158.02/24.61  | | | |   (29)   ~ (all_52_14 = e2)
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | SIMP: (29) implies:
% 158.02/24.61  | | | |   (30)   ~ (all_52_14 = e2)
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | BETA: splitting (12) gives:
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | Case 1:
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | |   (31)  all_54_11 = e3
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | | REF_CLOSE: (2), (17), (31) are inconsistent by sub-proof #655.
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | Case 2:
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | |   (32)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | | BETA: splitting (32) gives:
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | | Case 1:
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | |   (33)  all_54_11 = e2
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | | REF_CLOSE: (17), (30), (33) are inconsistent by sub-proof #588.
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | Case 2:
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | |   (34)  all_54_11 = e1 | all_54_11 = e0
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | | BETA: splitting (34) gives:
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | | Case 1:
% 158.02/24.61  | | | | | | | 
% 158.02/24.61  | | | | | | |   (35)  all_54_11 = e1
% 158.02/24.61  | | | | | | | 
% 158.02/24.61  | | | | | | | COMBINE_EQS: (17), (35) imply:
% 158.02/24.61  | | | | | | |   (36)  all_52_14 = e1
% 158.02/24.61  | | | | | | | 
% 158.02/24.61  | | | | | | | SIMP: (36) implies:
% 158.02/24.61  | | | | | | |   (37)  all_52_14 = e1
% 158.02/24.61  | | | | | | | 
% 158.02/24.61  | | | | | | | REDUCE: (5), (37) imply:
% 158.02/24.61  | | | | | | |   (38)   ~ (all_52_2 = e1)
% 158.02/24.61  | | | | | | | 
% 158.02/24.61  | | | | | | | REF_CLOSE: (6), (8), (14), (38) are inconsistent by sub-proof
% 158.02/24.61  | | | | | | |            #990.
% 158.02/24.61  | | | | | | | 
% 158.02/24.61  | | | | | | Case 2:
% 158.02/24.61  | | | | | | | 
% 158.02/24.61  | | | | | | |   (39)  all_54_11 = e0
% 158.02/24.61  | | | | | | | 
% 158.02/24.61  | | | | | | | REF_CLOSE: (3), (17), (39) are inconsistent by sub-proof #624.
% 158.02/24.61  | | | | | | | 
% 158.02/24.61  | | | | | | End of split
% 158.02/24.61  | | | | | | 
% 158.02/24.61  | | | | | End of split
% 158.02/24.61  | | | | | 
% 158.02/24.61  | | | | End of split
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | Case 2:
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | |   (40)  all_54_3 = e1 | all_54_3 = e0
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | | REF_CLOSE: (1), (9), (15), (40) are inconsistent by sub-proof #582.
% 158.02/24.61  | | | | 
% 158.02/24.61  | | | End of split
% 158.02/24.61  | | | 
% 158.02/24.61  | | End of split
% 158.02/24.61  | | 
% 158.02/24.61  | Case 2:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (41)   ~ (all_54_1 = e3)
% 158.02/24.61  | | 
% 158.02/24.61  | | REDUCE: (10), (41) imply:
% 158.02/24.61  | |   (42)   ~ (all_52_4 = e3)
% 158.02/24.61  | | 
% 158.02/24.61  | | REF_CLOSE: (6), (13), (18), (42) are inconsistent by sub-proof #998.
% 158.02/24.61  | | 
% 158.02/24.61  | End of split
% 158.02/24.61  | 
% 158.02/24.61  End of proof
% 158.02/24.61  
% 158.02/24.61  Sub-proof #77 shows that the following formulas are inconsistent:
% 158.02/24.61  ----------------------------------------------------------------
% 158.02/24.61    (1)  all_54_2 = all_52_8
% 158.02/24.61    (2)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2)
% 158.02/24.61    (3)   ~ (all_52_9 = all_52_11)
% 158.02/24.61    (4)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.02/24.61    (5)  all_54_2 = e1 | all_54_2 = e0
% 158.02/24.61    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.61    (7)   ~ (all_52_8 = e0)
% 158.02/24.61    (8)   ~ (all_52_8 = all_52_11)
% 158.02/24.61    (9)  op(e2, e1) = all_52_9
% 158.02/24.61    (10)  all_54_14 = all_52_11
% 158.02/24.61    (11)   ~ (all_52_11 = e0)
% 158.02/24.61    (12)   ~ (e2 = e1)
% 158.02/24.61    (13)  all_56_4 = e1
% 158.02/24.61    (14)   ~ (all_52_11 = e3)
% 158.02/24.61  
% 158.02/24.61  Begin of proof
% 158.02/24.61  | 
% 158.02/24.61  | BETA: splitting (2) gives:
% 158.02/24.61  | 
% 158.02/24.61  | Case 1:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (15)  all_56_4 = e2 & op(e3, e1) = e2
% 158.02/24.61  | | 
% 158.02/24.61  | | REF_CLOSE: (12), (13), (15) are inconsistent by sub-proof #317.
% 158.02/24.61  | | 
% 158.02/24.61  | Case 2:
% 158.02/24.61  | | 
% 158.02/24.61  | |   (16)  all_56_5 = e2 & op(e2, e1) = e2
% 158.02/24.61  | | 
% 158.02/24.61  | | ALPHA: (16) implies:
% 158.02/24.61  | |   (17)  op(e2, e1) = e2
% 158.02/24.61  | | 
% 158.02/24.61  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), (17)
% 158.02/24.61  | |            are inconsistent by sub-proof #583.
% 158.02/24.61  | | 
% 158.02/24.61  | End of split
% 158.02/24.61  | 
% 158.02/24.61  End of proof
% 158.02/24.61  
% 158.02/24.61  Sub-proof #78 shows that the following formulas are inconsistent:
% 158.02/24.61  ----------------------------------------------------------------
% 158.02/24.61    (1)   ~ (all_52_13 = all_14_2)
% 158.02/24.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.61    (3)   ~ (all_52_9 = e0)
% 158.02/24.62    (4)  op(e0, e0) = e0
% 158.02/24.62    (5)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.02/24.62    (6)  op(e0, e0) = all_14_2
% 158.02/24.62    (7)  op(e2, e1) = all_52_9
% 158.02/24.62    (8)  op(e2, e0) = all_52_13
% 158.02/24.62    (9)  op(e2, e0) = all_57_11
% 158.02/24.62  
% 158.02/24.62  Begin of proof
% 158.02/24.62  | 
% 158.02/24.62  | BETA: splitting (5) gives:
% 158.02/24.62  | 
% 158.02/24.62  | Case 1:
% 158.02/24.62  | | 
% 158.02/24.62  | |   (10)  all_56_5 = e0 & op(e2, e1) = e0
% 158.02/24.62  | | 
% 158.02/24.62  | | ALPHA: (10) implies:
% 158.02/24.62  | |   (11)  op(e2, e1) = e0
% 158.02/24.62  | | 
% 158.02/24.62  | | REF_CLOSE: (2), (3), (7), (11) are inconsistent by sub-proof #79.
% 158.02/24.62  | | 
% 158.02/24.62  | Case 2:
% 158.02/24.62  | | 
% 158.02/24.62  | |   (12)  all_56_10 = e0 & op(e2, e0) = e0
% 158.02/24.62  | | 
% 158.02/24.62  | | ALPHA: (12) implies:
% 158.02/24.62  | |   (13)  op(e2, e0) = e0
% 158.02/24.62  | | 
% 158.02/24.62  | | GROUND_INST: instantiating (2) with all_14_2, e0, e0, e0, simplifying with
% 158.02/24.62  | |              (4), (6) gives:
% 158.02/24.62  | |   (14)  all_14_2 = e0
% 158.02/24.62  | | 
% 158.02/24.62  | | GROUND_INST: instantiating (2) with all_52_13, all_57_11, e0, e2,
% 158.02/24.62  | |              simplifying with (8), (9) gives:
% 158.02/24.62  | |   (15)  all_57_11 = all_52_13
% 158.02/24.62  | | 
% 158.02/24.62  | | GROUND_INST: instantiating (2) with e0, all_57_11, e0, e2, simplifying with
% 158.02/24.62  | |              (9), (13) gives:
% 158.02/24.62  | |   (16)  all_57_11 = e0
% 158.02/24.62  | | 
% 158.02/24.62  | | COMBINE_EQS: (15), (16) imply:
% 158.02/24.62  | |   (17)  all_52_13 = e0
% 158.02/24.62  | | 
% 158.02/24.62  | | SIMP: (17) implies:
% 158.02/24.62  | |   (18)  all_52_13 = e0
% 158.02/24.62  | | 
% 158.02/24.62  | | REDUCE: (1), (14), (18) imply:
% 158.02/24.62  | |   (19)  $false
% 158.02/24.62  | | 
% 158.02/24.62  | | CLOSE: (19) is inconsistent.
% 158.02/24.62  | | 
% 158.02/24.62  | End of split
% 158.02/24.62  | 
% 158.02/24.62  End of proof
% 158.02/24.62  
% 158.02/24.62  Sub-proof #79 shows that the following formulas are inconsistent:
% 158.02/24.62  ----------------------------------------------------------------
% 158.02/24.62    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.62    (2)  op(e2, e1) = all_52_9
% 158.02/24.62    (3)  op(e2, e1) = e0
% 158.02/24.62    (4)   ~ (all_52_9 = e0)
% 158.02/24.62  
% 158.02/24.62  Begin of proof
% 158.02/24.62  | 
% 158.02/24.62  | GROUND_INST: instantiating (1) with all_52_9, e0, e1, e2, simplifying with
% 158.02/24.62  |              (2), (3) gives:
% 158.02/24.62  |   (5)  all_52_9 = e0
% 158.02/24.62  | 
% 158.02/24.62  | REDUCE: (4), (5) imply:
% 158.02/24.62  |   (6)  $false
% 158.02/24.62  | 
% 158.02/24.62  | CLOSE: (6) is inconsistent.
% 158.02/24.62  | 
% 158.02/24.62  End of proof
% 158.02/24.62  
% 158.02/24.62  Sub-proof #80 shows that the following formulas are inconsistent:
% 158.02/24.62  ----------------------------------------------------------------
% 158.02/24.62    (1)  all_56_2 = e0 & op(e2, e3) = e0
% 158.02/24.62    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.62    (3)  op(e2, e3) = all_52_1
% 158.02/24.62    (4)   ~ (all_52_1 = e0)
% 158.02/24.62  
% 158.02/24.62  Begin of proof
% 158.02/24.62  | 
% 158.02/24.62  | ALPHA: (1) implies:
% 158.02/24.62  |   (5)  op(e2, e3) = e0
% 158.02/24.62  | 
% 158.02/24.62  | GROUND_INST: instantiating (2) with all_52_1, e0, e3, e2, simplifying with
% 158.02/24.62  |              (3), (5) gives:
% 158.02/24.62  |   (6)  all_52_1 = e0
% 158.02/24.62  | 
% 158.02/24.62  | REDUCE: (4), (6) imply:
% 158.02/24.62  |   (7)  $false
% 158.02/24.62  | 
% 158.02/24.62  | CLOSE: (7) is inconsistent.
% 158.02/24.62  | 
% 158.02/24.62  End of proof
% 158.02/24.62  
% 158.02/24.62  Sub-proof #81 shows that the following formulas are inconsistent:
% 158.02/24.62  ----------------------------------------------------------------
% 158.02/24.62    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.62    (2)  op(e3, e3) = e0
% 158.02/24.62    (3)  op(e2, e2) = e1
% 158.02/24.62    (4)   ~ (e2 = e1)
% 158.02/24.62    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.02/24.62             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.02/24.62           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.02/24.62               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.02/24.62             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.02/24.62         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.02/24.62             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.02/24.62           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.02/24.62               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.02/24.62             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 158.02/24.62    (6)   ~ (e3 = e0)
% 158.02/24.62  
% 158.02/24.62  Begin of proof
% 158.02/24.62  | 
% 158.02/24.62  | BETA: splitting (5) gives:
% 158.02/24.62  | 
% 158.02/24.62  | Case 1:
% 158.02/24.62  | | 
% 158.02/24.62  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.02/24.62  | |            e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.02/24.62  | |            $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.02/24.62  | |            (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.02/24.62  | |        ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.02/24.62  | |              e3) = all_57_6 & $i(all_57_6)))
% 158.02/24.62  | | 
% 158.02/24.62  | | ALPHA: (7) implies:
% 158.02/24.62  | |   (8)  op(e3, e3) = e3
% 158.02/24.62  | | 
% 158.02/24.62  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #971.
% 158.02/24.62  | | 
% 158.02/24.62  | Case 2:
% 158.02/24.62  | | 
% 158.02/24.62  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 158.02/24.62  | |            e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.02/24.62  | |            $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 158.02/24.62  | |            (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 158.02/24.62  | |        ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 158.02/24.62  | |              e2) = all_57_7 & $i(all_57_7)))
% 158.02/24.62  | | 
% 158.02/24.62  | | ALPHA: (9) implies:
% 158.02/24.62  | |   (10)  op(e2, e2) = e2
% 158.02/24.62  | | 
% 158.02/24.62  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #993.
% 158.02/24.62  | | 
% 158.02/24.62  | End of split
% 158.02/24.62  | 
% 158.02/24.62  End of proof
% 158.02/24.62  
% 158.02/24.62  Sub-proof #82 shows that the following formulas are inconsistent:
% 158.02/24.62  ----------------------------------------------------------------
% 158.02/24.62    (1)  all_54_13 = all_52_7
% 158.02/24.62    (2)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/24.62    (3)   ~ (all_52_7 = e3)
% 158.02/24.62    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.62    (5)  op(e2, e2) = e2
% 158.02/24.62    (6)  op(e0, e2) = all_52_7
% 158.02/24.62    (7)  all_54_1 = all_52_4
% 158.02/24.62    (8)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.02/24.62    (9)  op(e2, e2) = all_4_2
% 158.02/24.62    (10)   ~ (all_52_4 = all_4_2)
% 158.02/24.62    (11)  op(e3, e3) = e0
% 158.02/24.62    (12)   ~ (all_52_4 = all_52_7)
% 158.02/24.62    (13)  op(e3, e2) = all_52_4
% 158.02/24.62    (14)   ~ (all_52_7 = all_4_2)
% 158.02/24.62    (15)   ~ (all_57_7 = e0)
% 158.02/24.62    (16)   ~ (all_52_4 = e0)
% 158.02/24.62    (17)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) & op(e3, e2) =
% 158.02/24.62            all_57_1 & $i(all_57_1))
% 158.02/24.62    (18)   ~ (e2 = e0)
% 158.02/24.62    (19)  op(e0, e2) = all_57_7
% 158.02/24.62  
% 158.02/24.62  Begin of proof
% 158.02/24.62  | 
% 158.02/24.62  | BETA: splitting (17) gives:
% 158.02/24.62  | 
% 158.02/24.62  | Case 1:
% 158.02/24.62  | | 
% 158.02/24.62  | |   (20)  all_57_10 = e2 & op(e3, e3) = e2
% 158.02/24.62  | | 
% 158.02/24.62  | | ALPHA: (20) implies:
% 158.02/24.62  | |   (21)  op(e3, e3) = e2
% 158.02/24.62  | | 
% 158.02/24.62  | | REF_CLOSE: (4), (11), (18), (21) are inconsistent by sub-proof #281.
% 158.02/24.62  | | 
% 158.02/24.62  | Case 2:
% 158.02/24.62  | | 
% 158.02/24.62  | |   (22)   ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1)
% 158.02/24.62  | | 
% 158.02/24.62  | | ALPHA: (22) implies:
% 158.02/24.62  | |   (23)   ~ (all_57_1 = e3)
% 158.02/24.62  | |   (24)  op(e3, e2) = all_57_1
% 158.02/24.62  | | 
% 158.02/24.62  | | GROUND_INST: instantiating (4) with all_52_7, all_57_7, e2, e0, simplifying
% 158.02/24.62  | |              with (6), (19) gives:
% 158.02/24.62  | |   (25)  all_57_7 = all_52_7
% 158.02/24.62  | | 
% 158.02/24.62  | | GROUND_INST: instantiating (4) with all_4_2, e2, e2, e2, simplifying with
% 158.02/24.62  | |              (5), (9) gives:
% 158.02/24.62  | |   (26)  all_4_2 = e2
% 158.02/24.62  | | 
% 158.02/24.62  | | GROUND_INST: instantiating (4) with all_52_4, all_57_1, e2, e3, simplifying
% 158.02/24.62  | |              with (13), (24) gives:
% 158.02/24.62  | |   (27)  all_57_1 = all_52_4
% 158.02/24.62  | | 
% 158.02/24.62  | | REDUCE: (23), (27) imply:
% 158.02/24.62  | |   (28)   ~ (all_52_4 = e3)
% 158.02/24.62  | | 
% 158.02/24.62  | | REDUCE: (15), (25) imply:
% 158.02/24.62  | |   (29)   ~ (all_52_7 = e0)
% 158.02/24.62  | | 
% 158.02/24.62  | | REDUCE: (10), (26) imply:
% 158.02/24.62  | |   (30)   ~ (all_52_4 = e2)
% 158.02/24.62  | | 
% 158.02/24.62  | | REDUCE: (14), (26) imply:
% 158.02/24.62  | |   (31)   ~ (all_52_7 = e2)
% 158.02/24.62  | | 
% 158.02/24.62  | | REF_CLOSE: (1), (2), (3), (7), (8), (12), (16), (28), (29), (30), (31) are
% 158.02/24.62  | |            inconsistent by sub-proof #94.
% 158.02/24.62  | | 
% 158.02/24.62  | End of split
% 158.02/24.62  | 
% 158.02/24.62  End of proof
% 158.02/24.62  
% 158.02/24.62  Sub-proof #83 shows that the following formulas are inconsistent:
% 158.02/24.62  ----------------------------------------------------------------
% 158.02/24.62    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.62    (2)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.02/24.62           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 158.02/24.62           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 158.02/24.62           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 158.02/24.62    (3)  op(e0, e0) = e0
% 158.02/24.62    (4)  op(e3, e3) = e0
% 158.02/24.62    (5)   ~ (e2 = e0)
% 158.02/24.62  
% 158.02/24.62  Begin of proof
% 158.02/24.62  | 
% 158.02/24.62  | BETA: splitting (2) gives:
% 158.02/24.62  | 
% 158.02/24.62  | Case 1:
% 158.02/24.62  | | 
% 158.02/24.62  | |   (6)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 158.02/24.62  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.02/24.62  | |          e0) = e2 & $i(all_57_12)
% 158.02/24.62  | | 
% 158.02/24.62  | | ALPHA: (6) implies:
% 158.02/24.62  | |   (7)  op(e0, e0) = e2
% 158.02/24.62  | | 
% 158.02/24.62  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #979.
% 158.02/24.62  | | 
% 158.02/24.62  | Case 2:
% 158.02/24.62  | | 
% 158.02/24.62  | |   (8)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 158.02/24.62  | |        op(e3, e0) = e3
% 158.02/24.62  | | 
% 158.02/24.62  | | ALPHA: (8) implies:
% 158.02/24.62  | |   (9)   ~ (e3 = e0)
% 158.02/24.62  | |   (10)  op(e3, e3) = e3
% 158.02/24.62  | | 
% 158.02/24.62  | | REF_CLOSE: (1), (4), (9), (10) are inconsistent by sub-proof #971.
% 158.02/24.62  | | 
% 158.02/24.62  | End of split
% 158.02/24.62  | 
% 158.02/24.62  End of proof
% 158.02/24.62  
% 158.02/24.62  Sub-proof #84 shows that the following formulas are inconsistent:
% 158.02/24.62  ----------------------------------------------------------------
% 158.02/24.62    (1)  all_56_1 = e0 & op(e3, e2) = e0
% 158.02/24.62    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.62    (3)  op(e3, e2) = all_52_4
% 158.02/24.62    (4)   ~ (all_52_4 = e0)
% 158.02/24.62  
% 158.02/24.62  Begin of proof
% 158.02/24.62  | 
% 158.02/24.62  | ALPHA: (1) implies:
% 158.02/24.62  |   (5)  op(e3, e2) = e0
% 158.02/24.62  | 
% 158.02/24.62  | GROUND_INST: instantiating (2) with all_52_4, e0, e2, e3, simplifying with
% 158.02/24.62  |              (3), (5) gives:
% 158.02/24.62  |   (6)  all_52_4 = e0
% 158.02/24.62  | 
% 158.02/24.62  | REDUCE: (4), (6) imply:
% 158.02/24.62  |   (7)  $false
% 158.02/24.62  | 
% 158.02/24.62  | CLOSE: (7) is inconsistent.
% 158.02/24.62  | 
% 158.02/24.62  End of proof
% 158.02/24.62  
% 158.02/24.62  Sub-proof #85 shows that the following formulas are inconsistent:
% 158.02/24.62  ----------------------------------------------------------------
% 158.02/24.62    (1)   ~ (all_52_7 = all_14_2)
% 158.02/24.62    (2)   ~ (all_52_6 = e1)
% 158.02/24.62    (3)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.02/24.62         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 158.02/24.62    (4)  op(e0, e1) = all_52_11
% 158.02/24.62    (5)   ~ (e3 = e2)
% 158.02/24.62    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.62    (7)  op(e0, e3) = all_52_3
% 158.02/24.62    (8)  op(e3, e1) = all_52_8
% 158.02/24.62    (9)  op(e1, e1) = e1
% 158.02/24.62    (10)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.02/24.62    (11)   ~ (all_52_11 = all_14_2)
% 158.02/24.62    (12)   ~ (all_52_12 = all_14_2)
% 158.02/24.62    (13)   ~ (all_52_3 = e0)
% 158.02/24.62    (14)   ~ (all_52_12 = all_52_14)
% 158.02/24.62    (15)  op(e1, e3) = all_52_2
% 158.02/24.62    (16)  all_54_15 = all_14_2
% 158.02/24.62    (17)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.02/24.62          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.02/24.62    (18)  op(e0, e2) = all_52_7
% 158.02/24.62    (19)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.02/24.62          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.02/24.62    (20)   ~ (all_52_2 = all_52_3)
% 158.02/24.62    (21)   ~ (all_52_2 = e1)
% 158.02/24.62    (22)  op(e1, e2) = all_52_6
% 158.02/24.62    (23)  op(e1, e0) = all_52_14
% 158.02/24.62    (24)   ~ (all_52_8 = e1)
% 158.02/24.62    (25)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.02/24.62          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.02/24.62    (26)  op(e3, e3) = e0
% 158.02/24.62    (27)  op(e0, e0) = all_14_2
% 158.02/24.62    (28)  op(e2, e2) = e1
% 158.02/24.62    (29)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.02/24.62          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.02/24.62    (30)   ~ (e1 = e0)
% 158.02/24.62    (31)  ( ~ (all_6_0 = e1) & op(e0, e3) = all_6_0 & $i(all_6_0)) | ( ~ (all_6_1
% 158.02/24.62              = e2) & op(e0, e0) = all_6_1 & $i(all_6_1))
% 158.02/24.62    (32)   ~ (all_52_12 = e0)
% 158.02/24.62    (33)   ~ (e2 = e1)
% 158.02/24.62    (34)  op(e3, e0) = all_52_12
% 158.02/24.62    (35)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.02/24.62          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.02/24.62    (36)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.02/24.62          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.02/24.62    (37)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.02/24.62          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.02/24.63    (38)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.02/24.63            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.63            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.02/24.63            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.63              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.02/24.63          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.02/24.63            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.02/24.63              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.02/24.63            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.63              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.02/24.63          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.02/24.63            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.02/24.63              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.02/24.63            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.63              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.02/24.63          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.02/24.63            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.02/24.63            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.02/24.63              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.02/24.63            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.02/24.63            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.02/24.63            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.02/24.63            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.02/24.63              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.02/24.63            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.02/24.63          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.02/24.63            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.02/24.63              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.02/24.63            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.02/24.63            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.02/24.63          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.02/24.63            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.02/24.63              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.02/24.63            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.02/24.63            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.02/24.63          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.02/24.63            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.02/24.63              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.02/24.63            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.63              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.02/24.63          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.02/24.63            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.02/24.63            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.02/24.63            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.02/24.63            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.02/24.63            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.63            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.02/24.63            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.02/24.63              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.02/24.63            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.02/24.63            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.02/24.63            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.02/24.63            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.02/24.63              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.02/24.63            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.02/24.63          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.02/24.63            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.02/24.63              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.02/24.63              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.02/24.63            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.02/24.63            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.02/24.63            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.02/24.63            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.02/24.63              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.02/24.63            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.02/24.63          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.02/24.63            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.02/24.63              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.02/24.63            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.63              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.02/24.63          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.02/24.63            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.02/24.63              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.02/24.63              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.02/24.63            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.02/24.63          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.02/24.63            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.02/24.63            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.02/24.63                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.02/24.63                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.63                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.02/24.63                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.63                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.02/24.63                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.02/24.63                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.63                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.02/24.63                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.63                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.02/24.63                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.63                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.02/24.63                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.02/24.63                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.63                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.02/24.63                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.63                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.02/24.63                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.63                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.02/24.63                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.02/24.63                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.02/24.63                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.02/24.63                op(e0, e1) = e0)))
% 158.02/24.63    (39)   ~ (e3 = e1)
% 158.02/24.63    (40)   ~ (e2 = e0)
% 158.02/24.63    (41)   ~ (all_14_2 = e3)
% 158.02/24.63    (42)   ~ (e3 = e0)
% 158.02/24.63  
% 158.02/24.63  Begin of proof
% 158.02/24.63  | 
% 158.02/24.63  | BETA: splitting (37) gives:
% 158.02/24.63  | 
% 158.02/24.63  | Case 1:
% 158.02/24.63  | | 
% 158.02/24.63  | |   (43)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 158.02/24.63  | |           e1)
% 158.02/24.63  | | 
% 158.02/24.63  | | BETA: splitting (43) gives:
% 158.02/24.63  | | 
% 158.02/24.63  | | Case 1:
% 158.02/24.63  | | | 
% 158.02/24.63  | | |   (44)  all_56_0 = e1 & op(e3, e3) = e1
% 158.02/24.63  | | | 
% 158.02/24.63  | | | ALPHA: (44) implies:
% 158.02/24.63  | | |   (45)  op(e3, e3) = e1
% 158.02/24.63  | | | 
% 158.02/24.63  | | | REF_CLOSE: (6), (26), (30), (45) are inconsistent by sub-proof #834.
% 158.02/24.63  | | | 
% 158.02/24.63  | | Case 2:
% 158.02/24.63  | | | 
% 158.02/24.63  | | |   (46)  all_56_2 = e1 & op(e2, e3) = e1
% 158.02/24.63  | | | 
% 158.02/24.63  | | | ALPHA: (46) implies:
% 158.02/24.63  | | |   (47)  all_56_2 = e1
% 158.02/24.63  | | |   (48)  op(e2, e3) = e1
% 158.02/24.63  | | | 
% 158.02/24.63  | | | REF_CLOSE: (5), (6), (19), (28), (30), (33), (35), (36), (39), (40), (42),
% 158.02/24.63  | | |            (47), (48) are inconsistent by sub-proof #259.
% 158.02/24.63  | | | 
% 158.02/24.63  | | End of split
% 158.02/24.63  | | 
% 158.02/24.63  | Case 2:
% 158.02/24.63  | | 
% 158.02/24.63  | |   (49)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 158.02/24.63  | |           e1)
% 158.02/24.63  | | 
% 158.02/24.63  | | BETA: splitting (49) gives:
% 158.02/24.63  | | 
% 158.02/24.63  | | Case 1:
% 158.02/24.63  | | | 
% 158.02/24.63  | | |   (50)  all_56_6 = e1 & op(e1, e3) = e1
% 158.02/24.63  | | | 
% 158.02/24.63  | | | ALPHA: (50) implies:
% 158.02/24.63  | | |   (51)  op(e1, e3) = e1
% 158.02/24.63  | | | 
% 158.02/24.63  | | | REF_CLOSE: (6), (15), (21), (51) are inconsistent by sub-proof #990.
% 158.02/24.63  | | | 
% 158.02/24.63  | | Case 2:
% 158.02/24.63  | | | 
% 158.02/24.63  | | |   (52)  all_56_12 = e1 & op(e0, e3) = e1
% 158.02/24.63  | | | 
% 158.02/24.63  | | | ALPHA: (52) implies:
% 158.02/24.63  | | |   (53)  op(e0, e3) = e1
% 158.02/24.63  | | | 
% 158.02/24.63  | | | BETA: splitting (29) gives:
% 158.02/24.63  | | | 
% 158.02/24.63  | | | Case 1:
% 158.02/24.63  | | | | 
% 158.02/24.63  | | | |   (54)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2)
% 158.02/24.63  | | | |           = e1)
% 158.02/24.63  | | | | 
% 158.02/24.63  | | | | BETA: splitting (54) gives:
% 158.02/24.63  | | | | 
% 158.02/24.63  | | | | Case 1:
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | |   (55)  all_56_0 = e1 & op(e3, e3) = e1
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | ALPHA: (55) implies:
% 158.02/24.63  | | | | |   (56)  op(e3, e3) = e1
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | REF_CLOSE: (6), (26), (30), (56) are inconsistent by sub-proof #834.
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | Case 2:
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | |   (57)  all_56_1 = e1 & op(e3, e2) = e1
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | ALPHA: (57) implies:
% 158.02/24.63  | | | | |   (58)  all_56_1 = e1
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | REF_CLOSE: (3), (5), (6), (17), (25), (28), (30), (33), (39), (40),
% 158.02/24.63  | | | | |            (42), (58) are inconsistent by sub-proof #332.
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | End of split
% 158.02/24.63  | | | | 
% 158.02/24.63  | | | Case 2:
% 158.02/24.63  | | | | 
% 158.02/24.63  | | | |   (59)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0)
% 158.02/24.63  | | | |           = e1)
% 158.02/24.63  | | | | 
% 158.02/24.63  | | | | BETA: splitting (59) gives:
% 158.02/24.63  | | | | 
% 158.02/24.63  | | | | Case 1:
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | |   (60)  all_56_4 = e1 & op(e3, e1) = e1
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | REF_CLOSE: (6), (8), (24), (60) are inconsistent by sub-proof #331.
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | Case 2:
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | |   (61)  all_56_9 = e1 & op(e3, e0) = e1
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | ALPHA: (61) implies:
% 158.02/24.63  | | | | |   (62)  op(e3, e0) = e1
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | GROUND_INST: instantiating (6) with all_52_3, e1, e3, e0, simplifying
% 158.02/24.63  | | | | |              with (7), (53) gives:
% 158.02/24.63  | | | | |   (63)  all_52_3 = e1
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | GROUND_INST: instantiating (6) with all_52_12, e1, e0, e3, simplifying
% 158.02/24.63  | | | | |              with (34), (62) gives:
% 158.02/24.63  | | | | |   (64)  all_52_12 = e1
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | REDUCE: (14), (64) imply:
% 158.02/24.63  | | | | |   (65)   ~ (all_52_14 = e1)
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | SIMP: (65) implies:
% 158.02/24.63  | | | | |   (66)   ~ (all_52_14 = e1)
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | REDUCE: (12), (64) imply:
% 158.02/24.63  | | | | |   (67)   ~ (all_14_2 = e1)
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | SIMP: (67) implies:
% 158.02/24.63  | | | | |   (68)   ~ (all_14_2 = e1)
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | BETA: splitting (31) gives:
% 158.02/24.63  | | | | | 
% 158.02/24.63  | | | | | Case 1:
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | |   (69)   ~ (all_6_0 = e1) & op(e0, e3) = all_6_0 & $i(all_6_0)
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | ALPHA: (69) implies:
% 158.02/24.63  | | | | | |   (70)   ~ (all_6_0 = e1)
% 158.02/24.63  | | | | | |   (71)  op(e0, e3) = all_6_0
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | GROUND_INST: instantiating (6) with e1, all_6_0, e3, e0, simplifying
% 158.02/24.63  | | | | | |              with (53), (71) gives:
% 158.02/24.63  | | | | | |   (72)  all_6_0 = e1
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | REDUCE: (70), (72) imply:
% 158.02/24.63  | | | | | |   (73)  $false
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | CLOSE: (73) is inconsistent.
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | Case 2:
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | |   (74)   ~ (all_6_1 = e2) & op(e0, e0) = all_6_1 & $i(all_6_1)
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | ALPHA: (74) implies:
% 158.02/24.63  | | | | | |   (75)   ~ (all_6_1 = e2)
% 158.02/24.63  | | | | | |   (76)  op(e0, e0) = all_6_1
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | GROUND_INST: instantiating (6) with all_14_2, all_6_1, e0, e0,
% 158.02/24.63  | | | | | |              simplifying with (27), (76) gives:
% 158.02/24.63  | | | | | |   (77)  all_14_2 = all_6_1
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | COMBINE_EQS: (16), (77) imply:
% 158.02/24.63  | | | | | |   (78)  all_54_15 = all_6_1
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | REDUCE: (1), (77) imply:
% 158.02/24.63  | | | | | |   (79)   ~ (all_52_7 = all_6_1)
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | REDUCE: (11), (77) imply:
% 158.02/24.63  | | | | | |   (80)   ~ (all_52_11 = all_6_1)
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | REDUCE: (41), (77) imply:
% 158.02/24.63  | | | | | |   (81)   ~ (all_6_1 = e3)
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | REDUCE: (68), (77) imply:
% 158.02/24.63  | | | | | |   (82)   ~ (all_6_1 = e1)
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | BETA: splitting (38) gives:
% 158.02/24.63  | | | | | | 
% 158.02/24.63  | | | | | | Case 1:
% 158.02/24.63  | | | | | | | 
% 158.02/24.63  | | | | | | |   (83)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.02/24.63  | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.02/24.63  | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.02/24.63  | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.02/24.63  | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.02/24.63  | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 158.02/24.63  | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_3
% 158.02/24.63  | | | | | | |           = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3)
% 158.02/24.63  | | | | | | |           = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.02/24.63  | | | | | | |             e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4
% 158.02/24.63  | | | | | | |           = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.02/24.63  | | | | | | |           = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 158.02/24.63  | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 158.02/24.63  | | | | | | |           = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3)
% 158.02/24.63  | | | | | | |           = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.02/24.63  | | | | | | |             e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9
% 158.02/24.63  | | | | | | |           = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.02/24.63  | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.02/24.64  | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_12
% 158.02/24.64  | | | | | | |           = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2)
% 158.02/24.64  | | | | | | |         | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.02/24.64  | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.02/24.64  | | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 158.02/24.64  | | | | | | |         | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 158.02/24.64  | | | | | | |           (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.02/24.64  | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.02/24.64  | | | | | | |           $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 &
% 158.02/24.64  | | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.02/24.64  | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 158.02/24.64  | | | | | | |             e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.02/24.64  | | | | | | |           = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 158.02/24.64  | | | | | | |         | (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.02/24.64  | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.02/24.64  | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.02/24.64  | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.02/24.64  | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 158.02/24.64  | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.64  | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_4 =
% 158.02/24.64  | | | | | | |           e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.02/24.64  | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.02/24.64  | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 158.02/24.64  | | | | | | |           = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2)
% 158.02/24.64  | | | | | | |           = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.64  | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_8 =
% 158.02/24.64  | | | | | | |           e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 158.02/24.64  | | | | | | |           e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.02/24.64  | | | | | | |             e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9
% 158.02/24.64  | | | | | | |           = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.02/24.64  | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 158.02/24.64  | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 158.02/24.64  | | | | | | |           = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.02/24.64  | | | | | | | 
% 158.02/24.64  | | | | | | | BETA: splitting (83) gives:
% 158.02/24.64  | | | | | | | 
% 158.02/24.64  | | | | | | | Case 1:
% 158.02/24.64  | | | | | | | | 
% 158.02/24.64  | | | | | | | |   (84)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.02/24.64  | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.02/24.64  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.02/24.64  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.02/24.64  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.02/24.64  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 158.02/24.64  | | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.02/24.64  | | | | | | | |           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.02/24.64  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 158.02/24.64  | | | | | | | |           = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 =
% 158.02/24.64  | | | | | | | |           e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.02/24.64  | | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 158.02/24.64  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.02/24.64  | | | | | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.02/24.64  | | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.64  | | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.02/24.64  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.02/24.64  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.02/24.64  | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.02/24.64  | | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.02/24.64  | | | | | | | |           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.02/24.64  | | | | | | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 158.02/24.64  | | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.02/24.64  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 158.02/24.64  | | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.02/24.64  | | | | | | | |           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.02/24.64  | | | | | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.02/24.64  | | | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.02/24.64  | | | | | | | | 
% 158.02/24.64  | | | | | | | | BETA: splitting (84) gives:
% 158.02/24.64  | | | | | | | | 
% 158.02/24.64  | | | | | | | | Case 1:
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | |   (85)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.02/24.64  | | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.02/24.64  | | | | | | | | |           & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.02/24.64  | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.02/24.64  | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.02/24.64  | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.02/24.64  | | | | | | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.02/24.64  | | | | | | | | |           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 158.02/24.64  | | | | | | | | |           & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1,
% 158.02/24.64  | | | | | | | | |             e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.02/24.64  | | | | | | | | |         (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.02/24.64  | | | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.64  | | | | | | | | |             e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.02/24.64  | | | | | | | | |           $i(all_57_10))
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | BETA: splitting (85) gives:
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | Case 1:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | |   (86)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.02/24.64  | | | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) =
% 158.02/24.64  | | | | | | | | | |           e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.02/24.64  | | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.02/24.64  | | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 158.02/24.64  | | | | | | | | | |           = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.02/24.64  | | | | | | | | | |           op(e2, e2) = e3 & $i(all_57_10))
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | REF_CLOSE: (6), (26), (28), (39), (40), (86) are inconsistent
% 158.02/24.64  | | | | | | | | | |            by sub-proof #88.
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | Case 2:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | |   (87)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.02/24.64  | | | | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.64  | | | | | | | | | |           all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.02/24.64  | | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.02/24.64  | | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.02/24.64  | | | | | | | | | |           = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 &
% 158.02/24.64  | | | | | | | | | |           op(e2, e2) = e3 & $i(all_57_10))
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | REF_CLOSE: (6), (9), (28), (33), (39), (87) are inconsistent
% 158.02/24.64  | | | | | | | | | |            by sub-proof #800.
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | End of split
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | Case 2:
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | |   (88)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.02/24.64  | | | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.64  | | | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.02/24.64  | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.02/24.64  | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.02/24.64  | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 158.02/24.64  | | | | | | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.02/24.64  | | | | | | | | |           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.02/24.64  | | | | | | | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 158.02/24.64  | | | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.02/24.64  | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 158.02/24.64  | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.02/24.64  | | | | | | | | |           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 158.02/24.64  | | | | | | | | |           & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.02/24.64  | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | BETA: splitting (88) gives:
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | Case 1:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | |   (89)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.02/24.64  | | | | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.64  | | | | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.02/24.64  | | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.02/24.64  | | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.02/24.64  | | | | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 158.02/24.64  | | | | | | | | | |           op(e2, e2) = e3 & $i(all_57_10))
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | BETA: splitting (89) gives:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | Case 1:
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | |   (90)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.02/24.64  | | | | | | | | | | |         ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 158.02/24.64  | | | | | | | | | | |         = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.02/24.64  | | | | | | | | | | |         $i(all_57_12)
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | | ALPHA: (90) implies:
% 158.02/24.64  | | | | | | | | | | |   (91)  op(e0, e0) = e2
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | | REF_CLOSE: (6), (75), (76), (91) are inconsistent by
% 158.02/24.64  | | | | | | | | | | |            sub-proof #89.
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | Case 2:
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | |   (92)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 & 
% 158.02/24.64  | | | | | | | | | | |         ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.02/24.64  | | | | | | | | | | |         op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.64  | | | | | | | | | | |         e3 & $i(all_57_10)
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | | ALPHA: (92) implies:
% 158.02/24.64  | | | | | | | | | | |   (93)  op(e3, e0) = e3
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | | REF_CLOSE: (6), (39), (62), (93) are inconsistent by
% 158.02/24.64  | | | | | | | | | | |            sub-proof #796.
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | End of split
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | Case 2:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | |   (94)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.02/24.64  | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 158.02/24.64  | | | | | | | | | |           e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.02/24.64  | | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.64  | | | | | | | | | |             e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.02/24.64  | | | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 158.02/24.64  | | | | | | | | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3)
% 158.02/24.64  | | | | | | | | | |           = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.02/24.64  | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_12))
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | REF_CLOSE: (6), (9), (28), (33), (39), (94) are inconsistent
% 158.02/24.64  | | | | | | | | | |            by sub-proof #793.
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | End of split
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | End of split
% 158.02/24.64  | | | | | | | | 
% 158.02/24.64  | | | | | | | Case 2:
% 158.02/24.64  | | | | | | | | 
% 158.02/24.64  | | | | | | | |   (95)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.02/24.64  | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2)
% 158.02/24.64  | | | | | | | |           = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.02/24.64  | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~
% 158.02/24.64  | | | | | | | |           (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.02/24.64  | | | | | | | |         (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.02/24.64  | | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.02/24.64  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.02/24.64  | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.02/24.64  | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1
% 158.02/24.64  | | | | | | | |           & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.64  | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_4
% 158.02/24.64  | | | | | | | |           = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 158.02/24.64  | | | | | | | |             e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1
% 158.02/24.64  | | | | | | | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 158.02/24.64  | | | | | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.02/24.64  | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 158.02/24.64  | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2 =
% 158.02/24.64  | | | | | | | |           e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.02/24.64  | | | | | | | |             e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.64  | | | | | | | |           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 158.02/24.64  | | | | | | | |         (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~
% 158.02/24.64  | | | | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0)
% 158.02/24.64  | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.02/24.64  | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~
% 158.02/24.64  | | | | | | | |           (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.02/24.64  | | | | | | | | 
% 158.02/24.64  | | | | | | | | BETA: splitting (95) gives:
% 158.02/24.64  | | | | | | | | 
% 158.02/24.64  | | | | | | | | Case 1:
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | |   (96)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.02/24.64  | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.64  | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.02/24.64  | | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 & 
% 158.02/24.64  | | | | | | | | |           ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.02/24.64  | | | | | | | | |         (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.02/24.64  | | | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.02/24.64  | | | | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.02/24.64  | | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.02/24.64  | | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) =
% 158.02/24.64  | | | | | | | | |           e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.02/24.64  | | | | | | | | |           = all_57_14 & $i(all_57_14))
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | BETA: splitting (96) gives:
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | Case 1:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | |   (97)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.02/24.64  | | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.64  | | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.02/24.64  | | | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &
% 158.02/24.64  | | | | | | | | | |            ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | BETA: splitting (97) gives:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | Case 1:
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | |   (98)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.02/24.64  | | | | | | | | | | |         ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.02/24.64  | | | | | | | | | | |         op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.02/24.64  | | | | | | | | | | |         e3 & $i(all_57_10)
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | | ALPHA: (98) implies:
% 158.02/24.64  | | | | | | | | | | |   (99)  op(e0, e0) = e3
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | | REF_CLOSE: (6), (27), (41), (99) are inconsistent by
% 158.02/24.64  | | | | | | | | | | |            sub-proof #245.
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | Case 2:
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | |   (100)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 158.02/24.64  | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e2) = e3
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | | ALPHA: (100) implies:
% 158.02/24.64  | | | | | | | | | | |   (101)  op(e3, e3) = e3
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | | REF_CLOSE: (6), (26), (42), (101) are inconsistent by
% 158.02/24.64  | | | | | | | | | | |            sub-proof #971.
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | End of split
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | Case 2:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | |   (102)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 158.02/24.64  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 158.02/24.64  | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.02/24.64  | | | | | | | | | |            $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.02/24.64  | | | | | | | | | |            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3)
% 158.02/24.64  | | | | | | | | | |            = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.02/24.64  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_14))
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | REF_CLOSE: (6), (26), (30), (40), (102) are inconsistent by
% 158.02/24.64  | | | | | | | | | |            sub-proof #87.
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | End of split
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | Case 2:
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | |   (103)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.02/24.64  | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.64  | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.02/24.64  | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.02/24.64  | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) =
% 158.02/24.64  | | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1)
% 158.02/24.64  | | | | | | | | |            = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.02/24.64  | | | | | | | | |            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.02/24.64  | | | | | | | | |              e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.64  | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 158.02/24.64  | | | | | | | | |          | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 158.02/24.64  | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.02/24.64  | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3
% 158.02/24.64  | | | | | | | | |            & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.02/24.64  | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | BETA: splitting (103) gives:
% 158.02/24.64  | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | Case 1:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | |   (104)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 158.02/24.64  | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.02/24.64  | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.64  | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 =
% 158.02/24.64  | | | | | | | | | |            e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.02/24.64  | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 158.02/24.64  | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | REF_CLOSE: (6), (9), (15), (21), (39), (104) are inconsistent
% 158.02/24.64  | | | | | | | | | |            by sub-proof #791.
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | Case 2:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | |   (105)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.02/24.64  | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 158.02/24.64  | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.02/24.64  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.02/24.64  | | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.02/24.64  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 158.02/24.64  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 158.02/24.64  | | | | | | | | | |            & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1
% 158.02/24.64  | | | | | | | | | |            & op(e1, e1) = e1)
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | BETA: splitting (105) gives:
% 158.02/24.64  | | | | | | | | | | 
% 158.02/24.64  | | | | | | | | | | Case 1:
% 158.02/24.64  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | |   (106)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.02/24.65  | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 158.02/24.65  | | | | | | | | | | |          = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.02/24.65  | | | | | | | | | | |          $i(all_57_14)
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | | ALPHA: (106) implies:
% 158.02/24.65  | | | | | | | | | | |   (107)  op(e0, e0) = e1
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | | REF_CLOSE: (6), (27), (68), (107) are inconsistent by
% 158.02/24.65  | | | | | | | | | | |            sub-proof #805.
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | Case 2:
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | |   (108)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 158.02/24.65  | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.02/24.65  | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.65  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 158.02/24.65  | | | | | | | | | | |            = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 158.02/24.65  | | | | | | | | | | |              e1) = e1)
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | | REF_CLOSE: (6), (9), (15), (21), (39), (108) are inconsistent
% 158.02/24.65  | | | | | | | | | | |            by sub-proof #989.
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | End of split
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | End of split
% 158.02/24.65  | | | | | | | | | 
% 158.02/24.65  | | | | | | | | End of split
% 158.02/24.65  | | | | | | | | 
% 158.02/24.65  | | | | | | | End of split
% 158.02/24.65  | | | | | | | 
% 158.02/24.65  | | | | | | Case 2:
% 158.02/24.65  | | | | | | | 
% 158.02/24.65  | | | | | | |   (109)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.02/24.65  | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.02/24.65  | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.65  | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.02/24.65  | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.02/24.65  | | | | | | |            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.65  | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5
% 158.02/24.65  | | | | | | |            = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 158.02/24.65  | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 &
% 158.02/24.65  | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.02/24.65  | | | | | | |            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.02/24.65  | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) =
% 158.02/24.65  | | | | | | |            e0 & op(e0, e0) = e1 & $i(all_57_14)) | (all_57_3 = e1
% 158.02/24.65  | | | | | | |            & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0)
% 158.02/24.65  | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2)
% 158.02/24.65  | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 =
% 158.02/24.65  | | | | | | |            e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.02/24.65  | | | | | | |            op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.02/24.65  | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.02/24.65  | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.02/24.65  | | | | | | |              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 158.02/24.65  | | | | | | |            all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.02/24.65  | | | | | | |            op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.02/24.65  | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1
% 158.02/24.65  | | | | | | |            & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.02/24.65  | | | | | | |            = e1 & $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0
% 158.02/24.65  | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) =
% 158.02/24.65  | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 158.02/24.65  | | | | | | |              e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.02/24.65  | | | | | | |            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 158.02/24.65  | | | | | | |            op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.02/24.65  | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1
% 158.02/24.65  | | | | | | |            & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.02/24.65  | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3
% 158.02/24.65  | | | | | | |            & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.02/24.65  | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 158.02/24.65  | | | | | | |              e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 &
% 158.02/24.65  | | | | | | |            all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.02/24.65  | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) =
% 158.02/24.65  | | | | | | |            e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_9 = e3
% 158.02/24.65  | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 158.02/24.65  | | | | | | |            op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 & 
% 158.02/24.65  | | | | | | |            ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.02/24.65  | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 158.02/24.65  | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 158.02/24.65  | | | | | | |            & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 158.02/24.65  | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) =
% 158.02/24.65  | | | | | | |                e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.02/24.65  | | | | | | |                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.02/24.65  | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) =
% 158.02/24.65  | | | | | | |                e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13
% 158.02/24.65  | | | | | | |                = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.65  | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.02/24.65  | | | | | | |                e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.02/24.65  | | | | | | |                  e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.02/24.65  | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.65  | | | | | | |                  e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.02/24.65  | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.02/24.65  | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) =
% 158.02/24.65  | | | | | | |                e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7
% 158.02/24.65  | | | | | | |                = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.02/24.65  | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) =
% 158.02/24.65  | | | | | | |                e1 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15
% 158.02/24.65  | | | | | | |                = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.02/24.65  | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.02/24.65  | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) =
% 158.02/24.65  | | | | | | |                e3 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.02/24.65  | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.65  | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) =
% 158.02/24.65  | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.02/24.65  | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.02/24.65  | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.02/24.65  | | | | | | |                all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.02/24.65  | | | | | | |                  e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.02/24.65  | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.02/24.65  | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.02/24.65  | | | | | | | 
% 158.02/24.65  | | | | | | | BETA: splitting (109) gives:
% 158.02/24.65  | | | | | | | 
% 158.02/24.65  | | | | | | | Case 1:
% 158.02/24.65  | | | | | | | | 
% 158.02/24.65  | | | | | | | |   (110)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.02/24.65  | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3
% 158.02/24.65  | | | | | | | |            & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.65  | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.02/24.65  | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 158.02/24.65  | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.65  | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.02/24.65  | | | | | | | |            all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 158.02/24.65  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.02/24.65  | | | | | | | |              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.02/24.65  | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.02/24.65  | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.65  | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.02/24.65  | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 158.02/24.65  | | | | | | | |            all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 158.02/24.65  | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 158.02/24.65  | | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.02/24.65  | | | | | | | |            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.02/24.65  | | | | | | | |            op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.02/24.65  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.02/24.65  | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.02/24.65  | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 158.02/24.65  | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.02/24.65  | | | | | | | |            op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.02/24.65  | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.02/24.65  | | | | | | | |            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.02/24.65  | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14))
% 158.02/24.65  | | | | | | | | 
% 158.02/24.65  | | | | | | | | BETA: splitting (110) gives:
% 158.02/24.65  | | | | | | | | 
% 158.02/24.65  | | | | | | | | Case 1:
% 158.02/24.65  | | | | | | | | | 
% 158.02/24.65  | | | | | | | | |   (111)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.02/24.65  | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) =
% 158.02/24.65  | | | | | | | | |            e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.65  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.02/24.65  | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 158.02/24.65  | | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.02/24.65  | | | | | | | | |            = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.02/24.65  | | | | | | | | |            all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 158.02/24.65  | | | | | | | | |              e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.02/24.65  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 158.02/24.65  | | | | | | | | |          | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.02/24.65  | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.65  | | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.02/24.65  | | | | | | | | |            $i(all_57_14))
% 158.02/24.65  | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | BETA: splitting (111) gives:
% 158.02/24.65  | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | Case 1:
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | |   (112)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.02/24.65  | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 158.02/24.65  | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.65  | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.02/24.65  | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 158.02/24.65  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 158.02/24.65  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_14))
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | REF_CLOSE: (2), (6), (22), (26), (30), (112) are inconsistent
% 158.02/24.65  | | | | | | | | | |            by sub-proof #86.
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | Case 2:
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | |   (113)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 158.02/24.65  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.02/24.65  | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.65  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 =
% 158.02/24.65  | | | | | | | | | |            e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.02/24.65  | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 158.02/24.65  | | | | | | | | | |              e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | BETA: splitting (113) gives:
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | Case 1:
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | |   (114)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 158.02/24.65  | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.02/24.65  | | | | | | | | | | |          op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.65  | | | | | | | | | | |          e2 & $i(all_57_12)
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | | ALPHA: (114) implies:
% 158.02/24.65  | | | | | | | | | | |   (115)  op(e1, e1) = e2
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | | REF_CLOSE: (6), (9), (33), (115) are inconsistent by
% 158.02/24.65  | | | | | | | | | | |            sub-proof #986.
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | Case 2:
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | |   (116)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.02/24.65  | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 158.02/24.65  | | | | | | | | | | |          = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.02/24.65  | | | | | | | | | | |          $i(all_57_14)
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | | ALPHA: (116) implies:
% 158.02/24.65  | | | | | | | | | | |   (117)  op(e0, e0) = e1
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | | REF_CLOSE: (6), (27), (68), (117) are inconsistent by
% 158.02/24.65  | | | | | | | | | | |            sub-proof #805.
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | End of split
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | End of split
% 158.02/24.65  | | | | | | | | | 
% 158.02/24.65  | | | | | | | | Case 2:
% 158.02/24.65  | | | | | | | | | 
% 158.02/24.65  | | | | | | | | |   (118)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.02/24.65  | | | | | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 158.02/24.65  | | | | | | | | |              e0) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.02/24.65  | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 & 
% 158.02/24.65  | | | | | | | | |            ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.02/24.65  | | | | | | | | |          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.02/24.65  | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.65  | | | | | | | | |              e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.02/24.65  | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 & 
% 158.02/24.65  | | | | | | | | |            ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) |
% 158.02/24.65  | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.02/24.65  | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 158.02/24.65  | | | | | | | | |            e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.02/24.65  | | | | | | | | |            $i(all_57_14))
% 158.02/24.65  | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | BETA: splitting (118) gives:
% 158.02/24.65  | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | Case 1:
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | |   (119)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 158.02/24.65  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.02/24.65  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.65  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.02/24.65  | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.02/24.65  | | | | | | | | | |              e1) = e1)
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | REF_CLOSE: (2), (6), (9), (22), (33), (119) are inconsistent
% 158.02/24.65  | | | | | | | | | |            by sub-proof #983.
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | Case 2:
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | |   (120)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.02/24.65  | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.02/24.65  | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.02/24.65  | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 158.02/24.65  | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 158.02/24.65  | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.02/24.65  | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3)
% 158.02/24.65  | | | | | | | | | |            = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.02/24.65  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14))
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | BETA: splitting (120) gives:
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | Case 1:
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | |   (121)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.02/24.65  | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.02/24.65  | | | | | | | | | | |          op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.02/24.65  | | | | | | | | | | |          e3 & $i(all_57_10)
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | | ALPHA: (121) implies:
% 158.02/24.65  | | | | | | | | | | |   (122)  op(e0, e0) = e3
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | | REF_CLOSE: (6), (27), (41), (122) are inconsistent by
% 158.02/24.65  | | | | | | | | | | |            sub-proof #245.
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | Case 2:
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | |   (123)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 158.02/24.65  | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 158.02/24.65  | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.02/24.65  | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 158.02/24.65  | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 158.02/24.65  | | | | | | | | | | |            & $i(all_57_14))
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | | REF_CLOSE: (6), (26), (30), (42), (123) are inconsistent by
% 158.02/24.65  | | | | | | | | | | |            sub-proof #101.
% 158.02/24.65  | | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | | End of split
% 158.02/24.65  | | | | | | | | | | 
% 158.02/24.65  | | | | | | | | | End of split
% 158.02/24.65  | | | | | | | | | 
% 158.02/24.65  | | | | | | | | End of split
% 158.02/24.65  | | | | | | | | 
% 158.02/24.65  | | | | | | | Case 2:
% 158.02/24.65  | | | | | | | | 
% 158.02/24.66  | | | | | | | |   (124)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.02/24.66  | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.02/24.66  | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.02/24.66  | | | | | | | |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~
% 158.02/24.66  | | | | | | | |            (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.02/24.66  | | | | | | | |          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 158.02/24.66  | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2
% 158.02/24.66  | | | | | | | |            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.02/24.66  | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.02/24.66  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.02/24.66  | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 158.02/24.66  | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 &
% 158.02/24.66  | | | | | | | |            all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 158.02/24.66  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0,
% 158.02/24.66  | | | | | | | |              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.02/24.66  | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3,
% 158.02/24.66  | | | | | | | |              e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.02/24.66  | | | | | | | |            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 &
% 158.02/24.66  | | | | | | | |            op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1 &
% 158.02/24.66  | | | | | | | |             ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 158.02/24.66  | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 =
% 158.02/24.66  | | | | | | | |                e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.02/24.66  | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 158.02/24.66  | | | | | | | |                e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.02/24.66  | | | | | | | |                all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.66  | | | | | | | |                  e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.02/24.66  | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.02/24.66  | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.66  | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.02/24.66  | | | | | | | |                e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.02/24.66  | | | | | | | |                  e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.02/24.66  | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.66  | | | | | | | |                  e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.02/24.66  | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.02/24.66  | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.66  | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.02/24.66  | | | | | | | |                e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14
% 158.02/24.66  | | | | | | | |                = e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 158.02/24.66  | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.02/24.66  | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.02/24.66  | | | | | | | |                e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10
% 158.02/24.66  | | | | | | | |                = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.02/24.66  | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.02/24.66  | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.02/24.66  | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 158.02/24.66  | | | | | | | |                e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.02/24.66  | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.66  | | | | | | | |                  e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.02/24.66  | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.02/24.66  | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.02/24.66  | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.02/24.66  | | | | | | | |                  e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.02/24.66  | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.02/24.66  | | | | | | | |                e0)))
% 158.02/24.66  | | | | | | | | 
% 158.02/24.66  | | | | | | | | BETA: splitting (124) gives:
% 158.02/24.66  | | | | | | | | 
% 158.02/24.66  | | | | | | | | Case 1:
% 158.02/24.66  | | | | | | | | | 
% 158.02/24.66  | | | | | | | | |   (125)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.02/24.66  | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.02/24.66  | | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.02/24.66  | | | | | | | | |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 & 
% 158.02/24.66  | | | | | | | | |            ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.02/24.66  | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 158.02/24.66  | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 158.02/24.66  | | | | | | | | |            e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.02/24.66  | | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.02/24.66  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.02/24.66  | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 158.02/24.66  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10))
% 158.02/24.66  | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | BETA: splitting (125) gives:
% 158.02/24.66  | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | Case 1:
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | |   (126)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.02/24.66  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.02/24.66  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.02/24.66  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.02/24.66  | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.02/24.66  | | | | | | | | | |              e1) = e2)
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | BETA: splitting (126) gives:
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | Case 1:
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | |   (127)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.02/24.66  | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.02/24.66  | | | | | | | | | | |          op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.02/24.66  | | | | | | | | | | |          e2 & $i(all_57_12)
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | ALPHA: (127) implies:
% 158.02/24.66  | | | | | | | | | | |   (128)  op(e0, e0) = e2
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | REF_CLOSE: (6), (75), (76), (128) are inconsistent by
% 158.02/24.66  | | | | | | | | | | |            sub-proof #89.
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | Case 2:
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | |   (129)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 158.02/24.66  | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e1) = e2
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | ALPHA: (129) implies:
% 158.02/24.66  | | | | | | | | | | |   (130)  op(e2, e2) = e2
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | REF_CLOSE: (6), (28), (33), (130) are inconsistent by
% 158.02/24.66  | | | | | | | | | | |            sub-proof #993.
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | End of split
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | Case 2:
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | |   (131)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 158.02/24.66  | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 158.02/24.66  | | | | | | | | | |            = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.02/24.66  | | | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.02/24.66  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.02/24.66  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 158.02/24.66  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10))
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | BETA: splitting (131) gives:
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | Case 1:
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | |   (132)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 158.02/24.66  | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 158.02/24.66  | | | | | | | | | | |          = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.02/24.66  | | | | | | | | | | |          $i(all_57_14)
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | ALPHA: (132) implies:
% 158.02/24.66  | | | | | | | | | | |   (133)  op(e1, e0) = e1
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | REF_CLOSE: (6), (23), (66), (133) are inconsistent by
% 158.02/24.66  | | | | | | | | | | |            sub-proof #974.
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | Case 2:
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | |   (134)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 158.02/24.66  | | | | | | | | | | |          ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.02/24.66  | | | | | | | | | | |          op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.02/24.66  | | | | | | | | | | |          e3 & $i(all_57_10)
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | ALPHA: (134) implies:
% 158.02/24.66  | | | | | | | | | | |   (135)  op(e0, e0) = e3
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | REF_CLOSE: (6), (27), (41), (135) are inconsistent by
% 158.02/24.66  | | | | | | | | | | |            sub-proof #245.
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | End of split
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | End of split
% 158.02/24.66  | | | | | | | | | 
% 158.02/24.66  | | | | | | | | Case 2:
% 158.02/24.66  | | | | | | | | | 
% 158.02/24.66  | | | | | | | | |   (136)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 158.02/24.66  | | | | | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 158.02/24.66  | | | | | | | | |              e0) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.02/24.66  | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 & 
% 158.02/24.66  | | | | | | | | |            ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) |
% 158.02/24.66  | | | | | | | | |          (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.02/24.66  | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13 =
% 158.02/24.66  | | | | | | | | |            e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 158.02/24.66  | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 158.02/24.66  | | | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 158.02/24.66  | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3,
% 158.02/24.66  | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0)
% 158.02/24.66  | | | | | | | | |              | (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 158.02/24.66  | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 158.02/24.66  | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6
% 158.02/24.66  | | | | | | | | |                = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.02/24.66  | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 158.02/24.66  | | | | | | | | |                = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.02/24.66  | | | | | | | | |                all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.02/24.66  | | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.02/24.66  | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 158.02/24.66  | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0)
% 158.02/24.66  | | | | | | | | |              | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 158.02/24.66  | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 158.02/24.66  | | | | | | | | |                op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7
% 158.02/24.66  | | | | | | | | |                = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.02/24.66  | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 158.02/24.66  | | | | | | | | |                = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.02/24.66  | | | | | | | | |                all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.02/24.66  | | | | | | | | |                e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 158.02/24.66  | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3,
% 158.02/24.66  | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.02/24.66  | | | | | | | | |              | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.02/24.66  | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.02/24.66  | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8
% 158.02/24.66  | | | | | | | | |                = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.02/24.66  | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 158.02/24.66  | | | | | | | | |                = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.02/24.66  | | | | | | | | |                all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.02/24.66  | | | | | | | | |                  = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.02/24.66  | | | | | | | | |                e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.02/24.66  | | | | | | | | |              (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.02/24.66  | | | | | | | | |                op(e0, e1) = e0)))
% 158.02/24.66  | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | BETA: splitting (136) gives:
% 158.02/24.66  | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | Case 1:
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | |   (137)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 158.02/24.66  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.02/24.66  | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.02/24.66  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.02/24.66  | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.02/24.66  | | | | | | | | | |              e0) = e3)
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | BETA: splitting (137) gives:
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | Case 1:
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | |   (138)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 158.02/24.66  | | | | | | | | | | |          ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.02/24.66  | | | | | | | | | | |          op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.02/24.66  | | | | | | | | | | |          e2 & $i(all_57_12)
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | ALPHA: (138) implies:
% 158.02/24.66  | | | | | | | | | | |   (139)  op(e0, e0) = e2
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | REF_CLOSE: (6), (75), (76), (139) are inconsistent by
% 158.02/24.66  | | | | | | | | | | |            sub-proof #89.
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | Case 2:
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | |   (140)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 158.02/24.66  | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e0) = e3
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | ALPHA: (140) implies:
% 158.02/24.66  | | | | | | | | | | |   (141)  op(e3, e3) = e3
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | REF_CLOSE: (6), (26), (42), (141) are inconsistent by
% 158.02/24.66  | | | | | | | | | | |            sub-proof #971.
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | End of split
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | Case 2:
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | |   (142)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.02/24.66  | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13 =
% 158.02/24.66  | | | | | | | | | |            e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 158.02/24.66  | | | | | | | | | |            e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 158.02/24.66  | | | | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 158.02/24.66  | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3,
% 158.02/24.66  | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 158.02/24.66  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_11 = e2 &
% 158.02/24.66  | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2,
% 158.02/24.66  | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 158.02/24.66  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 158.02/24.66  | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 158.02/24.66  | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.02/24.66  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.02/24.66  | | | | | | | | | |                (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0
% 158.02/24.66  | | | | | | | | | |                & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.02/24.66  | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.02/24.66  | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.02/24.66  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.02/24.66  | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 158.02/24.66  | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.02/24.66  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.02/24.66  | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.02/24.66  | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.02/24.66  | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 158.02/24.66  | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 158.02/24.66  | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.66  | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.02/24.66  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 = e2
% 158.02/24.66  | | | | | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.66  | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.02/24.66  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 158.02/24.66  | | | | | | | | | |                & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.66  | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.02/24.66  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 158.02/24.66  | | | | | | | | | |                & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.02/24.66  | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.02/24.66  | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 158.02/24.66  | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0,
% 158.02/24.66  | | | | | | | | | |                  e1) = e0)))
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | BETA: splitting (142) gives:
% 158.02/24.66  | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | Case 1:
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | |   (143)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.02/24.66  | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | ALPHA: (143) implies:
% 158.02/24.66  | | | | | | | | | | |   (144)  op(e2, e2) = e2
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | REF_CLOSE: (6), (28), (33), (144) are inconsistent by
% 158.02/24.66  | | | | | | | | | | |            sub-proof #993.
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | Case 2:
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | |   (145)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.02/24.66  | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.02/24.66  | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.02/24.66  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.02/24.66  | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.02/24.66  | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.02/24.66  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.02/24.66  | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.02/24.66  | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.02/24.66  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.02/24.66  | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.02/24.66  | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.02/24.66  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.02/24.66  | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.02/24.66  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.66  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.02/24.66  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.02/24.66  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.66  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.02/24.66  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.02/24.66  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.66  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.02/24.66  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.02/24.66  | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.02/24.66  | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.02/24.66  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.02/24.66  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.02/24.66  | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.02/24.66  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.02/24.66  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.02/24.66  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.02/24.66  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.02/24.66  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.02/24.66  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.02/24.66  | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.02/24.66  | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.02/24.66  | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.02/24.66  | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.02/24.66  | | | | | | | | | | |                e0)))
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | BETA: splitting (145) gives:
% 158.02/24.66  | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | Case 1:
% 158.02/24.66  | | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | |   (146)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.02/24.66  | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 158.02/24.66  | | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | | ALPHA: (146) implies:
% 158.02/24.66  | | | | | | | | | | | |   (147)  op(e1, e0) = e1
% 158.02/24.66  | | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | | REF_CLOSE: (6), (23), (66), (147) are inconsistent by
% 158.02/24.66  | | | | | | | | | | | |            sub-proof #974.
% 158.02/24.66  | | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | Case 2:
% 158.02/24.66  | | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | |   (148)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.02/24.66  | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.02/24.66  | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.02/24.66  | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.02/24.66  | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.02/24.66  | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.02/24.66  | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.02/24.66  | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.02/24.66  | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.02/24.66  | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.02/24.66  | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.02/24.66  | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.02/24.66  | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 158.02/24.66  | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.02/24.66  | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.02/24.66  | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.02/24.66  | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.02/24.66  | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.02/24.66  | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.02/24.66  | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.02/24.66  | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 158.02/24.66  | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.02/24.66  | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.02/24.66  | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.02/24.66  | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.02/24.66  | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.66  | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 158.02/24.66  | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.02/24.66  | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 158.02/24.66  | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.02/24.66  | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.02/24.66  | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.02/24.66  | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.02/24.66  | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.02/24.66  | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.02/24.66  | | | | | | | | | | | |              e0))
% 158.02/24.66  | | | | | | | | | | | | 
% 158.02/24.66  | | | | | | | | | | | | ALPHA: (148) implies:
% 158.02/24.67  | | | | | | | | | | | |   (149)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.02/24.67  | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.02/24.67  | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.02/24.67  | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.02/24.67  | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.02/24.67  | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.02/24.67  | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.67  | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.02/24.67  | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.02/24.67  | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.02/24.67  | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.67  | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.02/24.67  | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.02/24.67  | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.67  | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.02/24.67  | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.02/24.67  | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.02/24.67  | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 158.02/24.67  | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.02/24.67  | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.02/24.67  | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.67  | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.02/24.67  | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.02/24.67  | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 158.02/24.67  | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 158.02/24.67  | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 158.02/24.67  | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.02/24.67  | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.02/24.67  | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.02/24.67  | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.02/24.67  | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.02/24.67  | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.02/24.67  | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.02/24.67  | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | BETA: splitting (10) gives:
% 158.02/24.67  | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | Case 1:
% 158.02/24.67  | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | |   (150)  all_54_15 = e3
% 158.02/24.67  | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | COMBINE_EQS: (78), (150) imply:
% 158.02/24.67  | | | | | | | | | | | | |   (151)  all_6_1 = e3
% 158.02/24.67  | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | SIMP: (151) implies:
% 158.02/24.67  | | | | | | | | | | | | |   (152)  all_6_1 = e3
% 158.02/24.67  | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | REDUCE: (81), (152) imply:
% 158.02/24.67  | | | | | | | | | | | | |   (153)  $false
% 158.02/24.67  | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 158.02/24.67  | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | Case 2:
% 158.02/24.67  | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | |   (154)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.02/24.67  | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | BETA: splitting (154) gives:
% 158.02/24.67  | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | Case 1:
% 158.02/24.67  | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | |   (155)  all_54_15 = e2
% 158.02/24.67  | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | COMBINE_EQS: (78), (155) imply:
% 158.02/24.67  | | | | | | | | | | | | | |   (156)  all_6_1 = e2
% 158.02/24.67  | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | SIMP: (156) implies:
% 158.02/24.67  | | | | | | | | | | | | | |   (157)  all_6_1 = e2
% 158.02/24.67  | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | REDUCE: (75), (157) imply:
% 158.02/24.67  | | | | | | | | | | | | | |   (158)  $false
% 158.02/24.67  | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | CLOSE: (158) is inconsistent.
% 158.02/24.67  | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | Case 2:
% 158.02/24.67  | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | |   (159)  all_54_15 = e1 | all_54_15 = e0
% 158.02/24.67  | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 158.02/24.67  | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | Case 1:
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | |   (160)  all_54_15 = e1
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | | COMBINE_EQS: (78), (160) imply:
% 158.02/24.67  | | | | | | | | | | | | | | |   (161)  all_6_1 = e1
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | | SIMP: (161) implies:
% 158.02/24.67  | | | | | | | | | | | | | | |   (162)  all_6_1 = e1
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | | REDUCE: (82), (162) imply:
% 158.02/24.67  | | | | | | | | | | | | | | |   (163)  $false
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | | CLOSE: (163) is inconsistent.
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | Case 2:
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | |   (164)  all_54_15 = e0
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | | COMBINE_EQS: (78), (164) imply:
% 158.02/24.67  | | | | | | | | | | | | | | |   (165)  all_6_1 = e0
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | | SIMP: (165) implies:
% 158.02/24.67  | | | | | | | | | | | | | | |   (166)  all_6_1 = e0
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | | REDUCE: (79), (166) imply:
% 158.02/24.67  | | | | | | | | | | | | | | |   (167)   ~ (all_52_7 = e0)
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | | REDUCE: (80), (166) imply:
% 158.02/24.67  | | | | | | | | | | | | | | |   (168)   ~ (all_52_11 = e0)
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (13), (18), (149), (167), (168) are
% 158.02/24.67  | | | | | | | | | | | | | | |            inconsistent by sub-proof #97.
% 158.02/24.67  | | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | | End of split
% 158.02/24.67  | | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | | End of split
% 158.02/24.67  | | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | | End of split
% 158.02/24.67  | | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | | End of split
% 158.02/24.67  | | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | | End of split
% 158.02/24.67  | | | | | | | | | | 
% 158.02/24.67  | | | | | | | | | End of split
% 158.02/24.67  | | | | | | | | | 
% 158.02/24.67  | | | | | | | | End of split
% 158.02/24.67  | | | | | | | | 
% 158.02/24.67  | | | | | | | End of split
% 158.02/24.67  | | | | | | | 
% 158.02/24.67  | | | | | | End of split
% 158.02/24.67  | | | | | | 
% 158.02/24.67  | | | | | End of split
% 158.02/24.67  | | | | | 
% 158.02/24.67  | | | | End of split
% 158.02/24.67  | | | | 
% 158.02/24.67  | | | End of split
% 158.02/24.67  | | | 
% 158.02/24.67  | | End of split
% 158.02/24.67  | | 
% 158.02/24.67  | End of split
% 158.02/24.67  | 
% 158.02/24.67  End of proof
% 158.02/24.67  
% 158.02/24.67  Sub-proof #86 shows that the following formulas are inconsistent:
% 158.02/24.67  ----------------------------------------------------------------
% 158.02/24.67    (1)   ~ (all_52_6 = e1)
% 158.02/24.67    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.67    (3)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 158.02/24.67           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.67           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 158.02/24.67           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 158.02/24.67             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.02/24.67    (4)  op(e1, e2) = all_52_6
% 158.02/24.67    (5)  op(e3, e3) = e0
% 158.02/24.67    (6)   ~ (e1 = e0)
% 158.02/24.67  
% 158.02/24.67  Begin of proof
% 158.02/24.67  | 
% 158.02/24.67  | BETA: splitting (3) gives:
% 158.02/24.67  | 
% 158.02/24.67  | Case 1:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (7)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 158.02/24.67  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.67  | |        all_57_14 & $i(all_57_14)
% 158.02/24.67  | | 
% 158.02/24.67  | | ALPHA: (7) implies:
% 158.02/24.67  | |   (8)  op(e3, e3) = e1
% 158.02/24.67  | | 
% 158.02/24.67  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #834.
% 158.02/24.67  | | 
% 158.02/24.67  | Case 2:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 158.02/24.67  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.67  | |        all_57_14 & $i(all_57_14)
% 158.02/24.67  | | 
% 158.02/24.67  | | ALPHA: (9) implies:
% 158.02/24.67  | |   (10)  op(e1, e2) = e1
% 158.02/24.67  | | 
% 158.02/24.67  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #984.
% 158.02/24.67  | | 
% 158.02/24.67  | End of split
% 158.02/24.67  | 
% 158.02/24.67  End of proof
% 158.02/24.67  
% 158.02/24.67  Sub-proof #87 shows that the following formulas are inconsistent:
% 158.02/24.67  ----------------------------------------------------------------
% 158.02/24.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.67    (2)  op(e3, e3) = e0
% 158.02/24.67    (3)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.02/24.67           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.02/24.67           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 158.02/24.67           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 158.02/24.67           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.02/24.67    (4)   ~ (e1 = e0)
% 158.02/24.67    (5)   ~ (e2 = e0)
% 158.02/24.67  
% 158.02/24.67  Begin of proof
% 158.02/24.67  | 
% 158.02/24.67  | BETA: splitting (3) gives:
% 158.02/24.67  | 
% 158.02/24.67  | Case 1:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (6)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 158.02/24.67  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.02/24.67  | |          e0) = e2 & $i(all_57_12)
% 158.02/24.67  | | 
% 158.02/24.67  | | ALPHA: (6) implies:
% 158.02/24.67  | |   (7)  op(e3, e3) = e2
% 158.02/24.67  | | 
% 158.02/24.67  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #281.
% 158.02/24.67  | | 
% 158.02/24.67  | Case 2:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (8)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 158.02/24.67  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.67  | |        all_57_14 & $i(all_57_14)
% 158.02/24.67  | | 
% 158.02/24.67  | | ALPHA: (8) implies:
% 158.02/24.67  | |   (9)  op(e3, e3) = e1
% 158.02/24.67  | | 
% 158.02/24.67  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #834.
% 158.02/24.67  | | 
% 158.02/24.67  | End of split
% 158.02/24.67  | 
% 158.02/24.67  End of proof
% 158.02/24.67  
% 158.02/24.67  Sub-proof #88 shows that the following formulas are inconsistent:
% 158.02/24.67  ----------------------------------------------------------------
% 158.02/24.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.67    (2)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.02/24.67           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.67           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 158.02/24.67           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 158.02/24.67           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 158.02/24.67    (3)  op(e3, e3) = e0
% 158.02/24.67    (4)  op(e2, e2) = e1
% 158.02/24.67    (5)   ~ (e3 = e1)
% 158.02/24.67    (6)   ~ (e2 = e0)
% 158.02/24.67  
% 158.02/24.67  Begin of proof
% 158.02/24.67  | 
% 158.02/24.67  | BETA: splitting (2) gives:
% 158.02/24.67  | 
% 158.02/24.67  | Case 1:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (7)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 158.02/24.67  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.67  | |        all_57_12 & $i(all_57_12)
% 158.02/24.67  | | 
% 158.02/24.67  | | ALPHA: (7) implies:
% 158.02/24.67  | |   (8)  op(e3, e3) = e2
% 158.02/24.67  | | 
% 158.02/24.67  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #281.
% 158.02/24.67  | | 
% 158.02/24.67  | Case 2:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (9)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2)
% 158.02/24.67  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 158.02/24.67  | |          e2) = e3 & $i(all_57_10)
% 158.02/24.67  | | 
% 158.02/24.67  | | ALPHA: (9) implies:
% 158.02/24.67  | |   (10)  op(e2, e2) = e3
% 158.02/24.67  | | 
% 158.02/24.67  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #847.
% 158.02/24.67  | | 
% 158.02/24.67  | End of split
% 158.02/24.67  | 
% 158.02/24.67  End of proof
% 158.02/24.67  
% 158.02/24.67  Sub-proof #89 shows that the following formulas are inconsistent:
% 158.02/24.67  ----------------------------------------------------------------
% 158.02/24.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.67    (2)  op(e0, e0) = all_6_1
% 158.02/24.67    (3)  op(e0, e0) = e2
% 158.02/24.67    (4)   ~ (all_6_1 = e2)
% 158.02/24.67  
% 158.02/24.67  Begin of proof
% 158.02/24.67  | 
% 158.02/24.67  | GROUND_INST: instantiating (1) with e2, all_6_1, e0, e0, simplifying with (2),
% 158.02/24.67  |              (3) gives:
% 158.02/24.67  |   (5)  all_6_1 = e2
% 158.02/24.67  | 
% 158.02/24.67  | REDUCE: (4), (5) imply:
% 158.02/24.67  |   (6)  $false
% 158.02/24.67  | 
% 158.02/24.67  | CLOSE: (6) is inconsistent.
% 158.02/24.67  | 
% 158.02/24.67  End of proof
% 158.02/24.67  
% 158.02/24.67  Sub-proof #90 shows that the following formulas are inconsistent:
% 158.02/24.67  ----------------------------------------------------------------
% 158.02/24.67    (1)  all_56_12 = e1
% 158.02/24.67    (2)  op(e0, e0) = e2
% 158.02/24.67    (3)  op(e0, e1) = all_52_11
% 158.02/24.67    (4)   ~ (e3 = e2)
% 158.02/24.67    (5)   ~ (all_52_7 = e3)
% 158.02/24.67    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.67    (7)  op(e0, e2) = all_52_7
% 158.02/24.67    (8)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3) |
% 158.02/24.67         (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.02/24.67    (9)   ~ (e3 = e1)
% 158.02/24.67    (10)   ~ (all_52_11 = e3)
% 158.02/24.67  
% 158.02/24.67  Begin of proof
% 158.02/24.67  | 
% 158.02/24.67  | BETA: splitting (8) gives:
% 158.02/24.67  | 
% 158.02/24.67  | Case 1:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (11)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 158.02/24.67  | |           e3)
% 158.02/24.67  | | 
% 158.02/24.67  | | BETA: splitting (11) gives:
% 158.02/24.67  | | 
% 158.02/24.67  | | Case 1:
% 158.02/24.67  | | | 
% 158.02/24.67  | | |   (12)  all_56_12 = e3 & op(e0, e3) = e3
% 158.02/24.67  | | | 
% 158.02/24.67  | | | ALPHA: (12) implies:
% 158.02/24.67  | | |   (13)  all_56_12 = e3
% 158.02/24.67  | | | 
% 158.02/24.67  | | | REF_CLOSE: (1), (9), (13) are inconsistent by sub-proof #498.
% 158.02/24.67  | | | 
% 158.02/24.67  | | Case 2:
% 158.02/24.67  | | | 
% 158.02/24.67  | | |   (14)  all_56_13 = e3 & op(e0, e2) = e3
% 158.02/24.67  | | | 
% 158.02/24.67  | | | REF_CLOSE: (5), (6), (7), (14) are inconsistent by sub-proof #429.
% 158.02/24.67  | | | 
% 158.02/24.67  | | End of split
% 158.02/24.67  | | 
% 158.02/24.67  | Case 2:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (15)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.02/24.67  | |           e3)
% 158.02/24.67  | | 
% 158.02/24.67  | | REF_CLOSE: (2), (3), (4), (6), (10), (15) are inconsistent by sub-proof
% 158.02/24.67  | |            #719.
% 158.02/24.67  | | 
% 158.02/24.67  | End of split
% 158.02/24.67  | 
% 158.02/24.67  End of proof
% 158.02/24.67  
% 158.02/24.67  Sub-proof #91 shows that the following formulas are inconsistent:
% 158.02/24.67  ----------------------------------------------------------------
% 158.02/24.67    (1)   ~ (all_6_0 = e1)
% 158.02/24.67    (2)   ~ (all_6_0 = e0)
% 158.02/24.67    (3)  all_54_12 = all_6_0
% 158.02/24.67    (4)   ~ (all_6_0 = e2)
% 158.02/24.67    (5)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 158.02/24.67  
% 158.02/24.67  Begin of proof
% 158.02/24.67  | 
% 158.02/24.67  | BETA: splitting (5) gives:
% 158.02/24.67  | 
% 158.02/24.67  | Case 1:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (6)  all_54_12 = e2
% 158.02/24.67  | | 
% 158.02/24.67  | | COMBINE_EQS: (3), (6) imply:
% 158.02/24.67  | |   (7)  all_6_0 = e2
% 158.02/24.67  | | 
% 158.02/24.67  | | SIMP: (7) implies:
% 158.02/24.67  | |   (8)  all_6_0 = e2
% 158.02/24.67  | | 
% 158.02/24.67  | | REDUCE: (4), (8) imply:
% 158.02/24.67  | |   (9)  $false
% 158.02/24.67  | | 
% 158.02/24.67  | | CLOSE: (9) is inconsistent.
% 158.02/24.67  | | 
% 158.02/24.67  | Case 2:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (10)  all_54_12 = e1 | all_54_12 = e0
% 158.02/24.67  | | 
% 158.02/24.67  | | BETA: splitting (10) gives:
% 158.02/24.67  | | 
% 158.02/24.67  | | Case 1:
% 158.02/24.67  | | | 
% 158.02/24.67  | | |   (11)  all_54_12 = e1
% 158.02/24.67  | | | 
% 158.02/24.67  | | | COMBINE_EQS: (3), (11) imply:
% 158.02/24.67  | | |   (12)  all_6_0 = e1
% 158.02/24.67  | | | 
% 158.02/24.67  | | | SIMP: (12) implies:
% 158.02/24.67  | | |   (13)  all_6_0 = e1
% 158.02/24.67  | | | 
% 158.02/24.67  | | | REDUCE: (1), (13) imply:
% 158.02/24.67  | | |   (14)  $false
% 158.02/24.67  | | | 
% 158.02/24.67  | | | CLOSE: (14) is inconsistent.
% 158.02/24.67  | | | 
% 158.02/24.67  | | Case 2:
% 158.02/24.67  | | | 
% 158.02/24.67  | | |   (15)  all_54_12 = e0
% 158.02/24.67  | | | 
% 158.02/24.67  | | | COMBINE_EQS: (3), (15) imply:
% 158.02/24.67  | | |   (16)  all_6_0 = e0
% 158.02/24.67  | | | 
% 158.02/24.67  | | | SIMP: (16) implies:
% 158.02/24.67  | | |   (17)  all_6_0 = e0
% 158.02/24.67  | | | 
% 158.02/24.67  | | | REDUCE: (2), (17) imply:
% 158.02/24.67  | | |   (18)  $false
% 158.02/24.67  | | | 
% 158.02/24.67  | | | CLOSE: (18) is inconsistent.
% 158.02/24.67  | | | 
% 158.02/24.67  | | End of split
% 158.02/24.67  | | 
% 158.02/24.67  | End of split
% 158.02/24.67  | 
% 158.02/24.67  End of proof
% 158.02/24.67  
% 158.02/24.67  Sub-proof #92 shows that the following formulas are inconsistent:
% 158.02/24.67  ----------------------------------------------------------------
% 158.02/24.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.67    (2)  op(e0, e3) = all_52_3
% 158.02/24.67    (3)  op(e1, e1) = e1
% 158.02/24.67    (4)   ~ (all_52_3 = e0)
% 158.02/24.67    (5)   ~ (e1 = e0)
% 158.02/24.67    (6)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.67           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.02/24.67           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 158.02/24.67           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 158.02/24.67           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 158.02/24.67           e1 & op(e0, e3) = e0)
% 158.02/24.67    (7)  op(e2, e0) = all_52_13
% 158.02/24.67    (8)   ~ (all_52_13 = e2)
% 158.02/24.67  
% 158.02/24.67  Begin of proof
% 158.02/24.67  | 
% 158.02/24.67  | BETA: splitting (6) gives:
% 158.02/24.67  | 
% 158.02/24.67  | Case 1:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.02/24.67  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 158.02/24.67  | | 
% 158.02/24.67  | | ALPHA: (9) implies:
% 158.02/24.67  | |   (10)  op(e0, e3) = e0
% 158.02/24.67  | | 
% 158.02/24.67  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #973.
% 158.02/24.67  | | 
% 158.02/24.67  | Case 2:
% 158.02/24.67  | | 
% 158.02/24.67  | |   (11)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.67  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.02/24.67  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.67  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.02/24.67  | | 
% 158.02/24.67  | | REF_CLOSE: (1), (3), (5), (7), (8), (11) are inconsistent by sub-proof #867.
% 158.02/24.67  | | 
% 158.02/24.67  | End of split
% 158.02/24.67  | 
% 158.02/24.67  End of proof
% 158.02/24.67  
% 158.02/24.67  Sub-proof #93 shows that the following formulas are inconsistent:
% 158.02/24.67  ----------------------------------------------------------------
% 158.02/24.67    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.02/24.67           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.02/24.67           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 158.02/24.67           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 158.02/24.67           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.02/24.67    (2)   ~ (e3 = e2)
% 158.02/24.67    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.68    (4)  op(e1, e1) = e1
% 158.02/24.68    (5)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.02/24.68         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.02/24.68    (6)   ~ (e1 = e0)
% 158.02/24.68    (7)  all_56_2 = e1
% 158.02/24.68    (8)  op(e2, e3) = e1
% 158.02/24.68    (9)   ~ (e2 = e1)
% 158.02/24.68    (10)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.02/24.68          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.02/24.68    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.02/24.68          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.02/24.68    (12)   ~ (e3 = e1)
% 158.02/24.68    (13)   ~ (e2 = e0)
% 158.02/24.68    (14)   ~ (e3 = e0)
% 158.02/24.68  
% 158.02/24.68  Begin of proof
% 158.02/24.68  | 
% 158.02/24.68  | BETA: splitting (1) gives:
% 158.02/24.68  | 
% 158.02/24.68  | Case 1:
% 158.02/24.68  | | 
% 158.02/24.68  | |   (15)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 158.02/24.68  | |         & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 158.02/24.68  | |         op(e1, e1) = e3 & $i(all_57_10)
% 158.02/24.68  | | 
% 158.02/24.68  | | ALPHA: (15) implies:
% 158.02/24.68  | |   (16)  op(e1, e1) = e3
% 158.02/24.68  | | 
% 158.02/24.68  | | REF_CLOSE: (3), (4), (12), (16) are inconsistent by sub-proof #1003.
% 158.02/24.68  | | 
% 158.02/24.68  | Case 2:
% 158.02/24.68  | | 
% 158.02/24.68  | |   (17)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 158.02/24.68  | |         & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.68  | |         all_57_14 & $i(all_57_14)
% 158.02/24.68  | | 
% 158.02/24.68  | | ALPHA: (17) implies:
% 158.02/24.68  | |   (18)  op(e2, e2) = e1
% 158.02/24.68  | | 
% 158.02/24.68  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 158.02/24.68  | |            (18) are inconsistent by sub-proof #259.
% 158.02/24.68  | | 
% 158.02/24.68  | End of split
% 158.02/24.68  | 
% 158.02/24.68  End of proof
% 158.02/24.68  
% 158.02/24.68  Sub-proof #94 shows that the following formulas are inconsistent:
% 158.02/24.68  ----------------------------------------------------------------
% 158.02/24.68    (1)   ~ (all_52_7 = e0)
% 158.02/24.68    (2)   ~ (all_52_4 = e3)
% 158.02/24.68    (3)  all_54_13 = all_52_7
% 158.02/24.68    (4)   ~ (all_52_7 = e2)
% 158.02/24.68    (5)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/24.68    (6)   ~ (all_52_7 = e3)
% 158.02/24.68    (7)  all_54_1 = all_52_4
% 158.02/24.68    (8)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.02/24.68    (9)   ~ (all_52_4 = all_52_7)
% 158.02/24.68    (10)   ~ (all_52_4 = e0)
% 158.02/24.68    (11)   ~ (all_52_4 = e2)
% 158.02/24.68  
% 158.02/24.68  Begin of proof
% 158.02/24.68  | 
% 158.02/24.68  | BETA: splitting (8) gives:
% 158.02/24.68  | 
% 158.02/24.68  | Case 1:
% 158.02/24.68  | | 
% 158.02/24.68  | |   (12)  all_54_1 = e3
% 158.02/24.68  | | 
% 158.02/24.68  | | REF_CLOSE: (2), (7), (12) are inconsistent by sub-proof #299.
% 158.02/24.68  | | 
% 158.02/24.68  | Case 2:
% 158.02/24.68  | | 
% 158.02/24.68  | |   (13)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.02/24.68  | | 
% 158.02/24.68  | | BETA: splitting (13) gives:
% 158.02/24.68  | | 
% 158.02/24.68  | | Case 1:
% 158.02/24.68  | | | 
% 158.02/24.68  | | |   (14)  all_54_1 = e2
% 158.02/24.68  | | | 
% 158.02/24.68  | | | REF_CLOSE: (7), (11), (14) are inconsistent by sub-proof #609.
% 158.02/24.68  | | | 
% 158.02/24.68  | | Case 2:
% 158.02/24.68  | | | 
% 158.02/24.68  | | |   (15)  all_54_1 = e1 | all_54_1 = e0
% 158.02/24.68  | | | 
% 158.02/24.68  | | | BETA: splitting (15) gives:
% 158.02/24.68  | | | 
% 158.02/24.68  | | | Case 1:
% 158.02/24.68  | | | | 
% 158.02/24.68  | | | |   (16)  all_54_1 = e1
% 158.02/24.68  | | | | 
% 158.02/24.68  | | | | COMBINE_EQS: (7), (16) imply:
% 158.02/24.68  | | | |   (17)  all_52_4 = e1
% 158.02/24.68  | | | | 
% 158.02/24.68  | | | | SIMP: (17) implies:
% 158.02/24.68  | | | |   (18)  all_52_4 = e1
% 158.02/24.68  | | | | 
% 158.02/24.68  | | | | REDUCE: (9), (18) imply:
% 158.02/24.68  | | | |   (19)   ~ (all_52_7 = e1)
% 158.02/24.68  | | | | 
% 158.02/24.68  | | | | SIMP: (19) implies:
% 158.02/24.68  | | | |   (20)   ~ (all_52_7 = e1)
% 158.02/24.68  | | | | 
% 158.02/24.68  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (20) are inconsistent by sub-proof
% 158.02/24.68  | | | |            #207.
% 158.02/24.68  | | | | 
% 158.02/24.68  | | | Case 2:
% 158.02/24.68  | | | | 
% 158.02/24.68  | | | |   (21)  all_54_1 = e0
% 158.02/24.68  | | | | 
% 158.02/24.68  | | | | REF_CLOSE: (7), (10), (21) are inconsistent by sub-proof #418.
% 158.02/24.68  | | | | 
% 158.02/24.68  | | | End of split
% 158.02/24.68  | | | 
% 158.02/24.68  | | End of split
% 158.02/24.68  | | 
% 158.02/24.68  | End of split
% 158.02/24.68  | 
% 158.02/24.68  End of proof
% 158.02/24.68  
% 158.02/24.68  Sub-proof #95 shows that the following formulas are inconsistent:
% 158.02/24.68  ----------------------------------------------------------------
% 158.02/24.68    (1)  all_54_14 = all_52_11
% 158.02/24.68    (2)  all_54_14 = e2
% 158.02/24.68    (3)   ~ (all_52_11 = e2)
% 158.02/24.68  
% 158.02/24.68  Begin of proof
% 158.02/24.68  | 
% 158.02/24.68  | COMBINE_EQS: (1), (2) imply:
% 158.02/24.68  |   (4)  all_52_11 = e2
% 158.02/24.68  | 
% 158.02/24.68  | SIMP: (4) implies:
% 158.02/24.68  |   (5)  all_52_11 = e2
% 158.02/24.68  | 
% 158.02/24.68  | REDUCE: (3), (5) imply:
% 158.02/24.68  |   (6)  $false
% 158.02/24.68  | 
% 158.02/24.68  | CLOSE: (6) is inconsistent.
% 158.02/24.68  | 
% 158.02/24.68  End of proof
% 158.02/24.68  
% 158.02/24.68  Sub-proof #96 shows that the following formulas are inconsistent:
% 158.02/24.68  ----------------------------------------------------------------
% 158.02/24.68    (1)   ~ (all_52_7 = e0)
% 158.02/24.68    (2)  op(e0, e1) = all_52_11
% 158.02/24.68    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.68    (4)  op(e0, e3) = all_52_3
% 158.02/24.68    (5)   ~ (all_52_3 = e0)
% 158.02/24.68    (6)  op(e0, e2) = all_52_7
% 158.02/24.68    (7)  op(e1, e0) = all_52_14
% 158.02/24.68    (8)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.02/24.68           op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6
% 158.02/24.68               = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.68               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.02/24.68               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2,
% 158.02/24.68                 e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.02/24.68               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1)
% 158.02/24.68               = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.02/24.68               all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.02/24.68               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) =
% 158.02/24.68               e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.02/24.68               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2)
% 158.02/24.68               = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.02/24.68               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1, e1)
% 158.02/24.68               = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.02/24.68               all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.02/24.68               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) =
% 158.02/24.68               e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.02/24.68               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2)
% 158.02/24.68               = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.02/24.68               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1)
% 158.02/24.68               = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.02/24.68               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1)
% 158.02/24.68               = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.02/24.68             (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.02/24.68    (9)   ~ (all_52_11 = e0)
% 158.02/24.68    (10)   ~ (all_52_14 = e1)
% 158.02/24.68  
% 158.02/24.68  Begin of proof
% 158.02/24.68  | 
% 158.02/24.68  | BETA: splitting (8) gives:
% 158.02/24.68  | 
% 158.02/24.68  | Case 1:
% 158.02/24.68  | | 
% 158.02/24.68  | |   (11)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.02/24.68  | |         op(e1, e0) = e1
% 158.02/24.68  | | 
% 158.02/24.68  | | ALPHA: (11) implies:
% 158.02/24.68  | |   (12)  op(e1, e0) = e1
% 158.02/24.68  | | 
% 158.02/24.68  | | REF_CLOSE: (3), (7), (10), (12) are inconsistent by sub-proof #974.
% 158.02/24.68  | | 
% 158.02/24.68  | Case 2:
% 158.02/24.68  | | 
% 158.02/24.68  | |   (13)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9
% 158.02/24.68  | |             = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 158.02/24.68  | |             op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 158.02/24.68  | |             = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 158.02/24.68  | |             op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13
% 158.02/24.68  | |             = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 158.02/24.68  | |             op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15
% 158.02/24.68  | |             = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.02/24.68  | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 158.02/24.68  | |               e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 158.02/24.68  | |             & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.02/24.68  | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0
% 158.02/24.68  | |             & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.02/24.68  | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0
% 158.02/24.68  | |             & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 =
% 158.02/24.68  | |             e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.68  | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8
% 158.02/24.68  | |             = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.68  | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8
% 158.02/24.68  | |             = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.68  | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8
% 158.02/24.68  | |             = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.02/24.68  | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.02/24.68  | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 158.02/24.68  | |             & op(e0, e1) = e0))
% 158.02/24.68  | | 
% 158.02/24.68  | | ALPHA: (13) implies:
% 158.02/24.68  | |   (14)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.02/24.68  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.02/24.68  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 158.02/24.68  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.02/24.68  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.02/24.68  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) |
% 158.02/24.68  | |         (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.02/24.68  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.02/24.68  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.02/24.68  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.02/24.68  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.02/24.68  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.02/24.68  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 158.02/24.68  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 158.02/24.68  | |           & op(e0, e1) = e0)
% 158.02/24.68  | | 
% 158.02/24.68  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (14) are inconsistent by
% 158.02/24.68  | |            sub-proof #97.
% 158.02/24.68  | | 
% 158.02/24.68  | End of split
% 158.02/24.68  | 
% 158.02/24.68  End of proof
% 158.02/24.68  
% 158.02/24.68  Sub-proof #97 shows that the following formulas are inconsistent:
% 158.02/24.68  ----------------------------------------------------------------
% 158.02/24.68    (1)   ~ (all_52_7 = e0)
% 158.02/24.68    (2)  op(e0, e1) = all_52_11
% 158.02/24.68    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.68    (4)  op(e0, e3) = all_52_3
% 158.02/24.68    (5)   ~ (all_52_3 = e0)
% 158.02/24.68    (6)  op(e0, e2) = all_52_7
% 158.02/24.68    (7)   ~ (all_52_11 = e0)
% 158.02/24.68    (8)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.68           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.02/24.68           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 158.02/24.68           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 158.02/24.68           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 158.02/24.68           e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 158.02/24.68           & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.02/24.68           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.02/24.68           e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.02/24.68             = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) |
% 158.02/24.68         (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.68           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.02/24.68           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.02/24.68           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 158.02/24.68           & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 = e2
% 158.02/24.68           & all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 158.02/24.68           e2 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.02/24.68           e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.02/24.68             e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 158.02/24.68           (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.02/24.68             e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1
% 158.02/24.68             = e0) & op(e0, e1) = e0)
% 158.02/24.68  
% 158.02/24.68  Begin of proof
% 158.02/24.68  | 
% 158.02/24.68  | BETA: splitting (8) gives:
% 158.02/24.68  | 
% 158.02/24.68  | Case 1:
% 158.02/24.68  | | 
% 158.02/24.68  | |   (9)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.02/24.68  | |          & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.02/24.68  | |          = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.68  | |          op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.02/24.68  | |          e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 158.02/24.68  | |            e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.02/24.68  | |          all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.02/24.68  | |          all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) =
% 158.02/24.68  | |          e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.02/24.68  | |          all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2)
% 158.02/24.68  | |          = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.02/24.68  | | 
% 158.02/24.68  | | BETA: splitting (9) gives:
% 158.02/24.68  | | 
% 158.02/24.68  | | Case 1:
% 158.02/24.68  | | | 
% 158.02/24.68  | | |   (10)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.02/24.68  | | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.02/24.68  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.02/24.68  | | | 
% 158.02/24.68  | | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #99.
% 158.02/24.68  | | | 
% 158.02/24.68  | | Case 2:
% 158.02/24.68  | | | 
% 158.02/24.68  | | |   (11)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0)
% 158.02/24.68  | | |         | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.02/24.68  | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.02/24.68  | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.68  | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.02/24.68  | | | 
% 158.02/24.68  | | | REF_CLOSE: (1), (3), (4), (5), (6), (11) are inconsistent by sub-proof
% 158.02/24.68  | | |            #98.
% 158.02/24.68  | | | 
% 158.02/24.68  | | End of split
% 158.02/24.68  | | 
% 158.02/24.68  | Case 2:
% 158.02/24.68  | | 
% 158.02/24.69  | |   (12)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.02/24.69  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.02/24.69  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.02/24.69  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.02/24.69  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.02/24.69  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.02/24.69  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 158.02/24.69  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 158.02/24.69  | |           & op(e0, e1) = e0)
% 158.02/24.69  | | 
% 158.02/24.69  | | BETA: splitting (12) gives:
% 158.02/24.69  | | 
% 158.02/24.69  | | Case 1:
% 158.02/24.69  | | | 
% 158.02/24.69  | | |   (13)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.02/24.69  | | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.02/24.69  | | |         | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.02/24.69  | | |             = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.02/24.69  | | | 
% 158.02/24.69  | | | BETA: splitting (13) gives:
% 158.02/24.69  | | | 
% 158.02/24.69  | | | Case 1:
% 158.02/24.69  | | | | 
% 158.02/24.69  | | | |   (14)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.02/24.69  | | | |           = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 158.02/24.69  | | | | 
% 158.02/24.69  | | | | ALPHA: (14) implies:
% 158.02/24.69  | | | |   (15)  op(e0, e2) = e0
% 158.02/24.69  | | | | 
% 158.02/24.69  | | | | REF_CLOSE: (1), (3), (6), (15) are inconsistent by sub-proof #969.
% 158.02/24.69  | | | | 
% 158.02/24.69  | | | Case 2:
% 158.02/24.69  | | | | 
% 158.02/24.69  | | | |   (16)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.02/24.69  | | | |           e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.02/24.69  | | | |           (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.02/24.69  | | | |             e1) = e0)
% 158.02/24.69  | | | | 
% 158.02/24.69  | | | | REF_CLOSE: (1), (2), (3), (6), (7), (16) are inconsistent by sub-proof
% 158.02/24.69  | | | |            #166.
% 158.02/24.69  | | | | 
% 158.02/24.69  | | | End of split
% 158.02/24.69  | | | 
% 158.02/24.69  | | Case 2:
% 158.02/24.69  | | | 
% 158.02/24.69  | | |   (17)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.02/24.69  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.02/24.69  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.02/24.69  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.02/24.69  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 158.02/24.69  | | |             e0) & op(e0, e1) = e0)
% 158.02/24.69  | | | 
% 158.02/24.69  | | | REF_CLOSE: (2), (3), (7), (17) are inconsistent by sub-proof #744.
% 158.02/24.69  | | | 
% 158.02/24.69  | | End of split
% 158.02/24.69  | | 
% 158.02/24.69  | End of split
% 158.02/24.69  | 
% 158.02/24.69  End of proof
% 158.02/24.69  
% 158.02/24.69  Sub-proof #98 shows that the following formulas are inconsistent:
% 158.02/24.69  ----------------------------------------------------------------
% 158.02/24.69    (1)   ~ (all_52_7 = e0)
% 158.02/24.69    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.69    (3)  op(e0, e3) = all_52_3
% 158.02/24.69    (4)   ~ (all_52_3 = e0)
% 158.02/24.69    (5)  op(e0, e2) = all_52_7
% 158.02/24.69    (6)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.02/24.69         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.69           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.02/24.69           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 158.02/24.69           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.02/24.69  
% 158.02/24.69  Begin of proof
% 158.02/24.69  | 
% 158.02/24.69  | BETA: splitting (6) gives:
% 158.02/24.69  | 
% 158.02/24.69  | Case 1:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (7)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 158.02/24.69  | | 
% 158.02/24.69  | | ALPHA: (7) implies:
% 158.02/24.69  | |   (8)  op(e0, e3) = e0
% 158.02/24.69  | | 
% 158.02/24.69  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #973.
% 158.02/24.69  | | 
% 158.02/24.69  | Case 2:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (9)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 158.02/24.69  | |          & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7
% 158.02/24.69  | |          = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.69  | |          op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.02/24.69  | | 
% 158.02/24.69  | | BETA: splitting (9) gives:
% 158.02/24.69  | | 
% 158.02/24.69  | | Case 1:
% 158.02/24.69  | | | 
% 158.02/24.69  | | |   (10)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | | |           e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 158.02/24.69  | | | 
% 158.02/24.69  | | | ALPHA: (10) implies:
% 158.02/24.69  | | |   (11)  op(e0, e2) = e0
% 158.02/24.69  | | | 
% 158.02/24.69  | | | REF_CLOSE: (1), (2), (5), (11) are inconsistent by sub-proof #969.
% 158.02/24.69  | | | 
% 158.02/24.69  | | Case 2:
% 158.02/24.69  | | | 
% 158.02/24.69  | | |   (12)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | | |           e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 158.02/24.69  | | | 
% 158.02/24.69  | | | ALPHA: (12) implies:
% 158.02/24.69  | | |   (13)  op(e0, e2) = e0
% 158.02/24.69  | | | 
% 158.02/24.69  | | | REF_CLOSE: (1), (2), (5), (13) are inconsistent by sub-proof #969.
% 158.02/24.69  | | | 
% 158.02/24.69  | | End of split
% 158.02/24.69  | | 
% 158.02/24.69  | End of split
% 158.02/24.69  | 
% 158.02/24.69  End of proof
% 158.02/24.69  
% 158.02/24.69  Sub-proof #99 shows that the following formulas are inconsistent:
% 158.02/24.69  ----------------------------------------------------------------
% 158.02/24.69    (1)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.69           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.02/24.69           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 158.02/24.69           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 158.02/24.69           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 158.02/24.69           e1 & op(e0, e3) = e0)
% 158.02/24.69    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.69    (3)  op(e0, e3) = all_52_3
% 158.02/24.69    (4)   ~ (all_52_3 = e0)
% 158.02/24.69  
% 158.02/24.69  Begin of proof
% 158.02/24.69  | 
% 158.02/24.69  | BETA: splitting (1) gives:
% 158.02/24.69  | 
% 158.02/24.69  | Case 1:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (5)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.02/24.69  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 158.02/24.69  | | 
% 158.02/24.69  | | ALPHA: (5) implies:
% 158.02/24.69  | |   (6)  op(e0, e3) = e0
% 158.02/24.69  | | 
% 158.02/24.69  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #973.
% 158.02/24.69  | | 
% 158.02/24.69  | Case 2:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (7)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | |            e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.02/24.69  | |        (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | |            e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.02/24.69  | | 
% 158.02/24.69  | | BETA: splitting (7) gives:
% 158.02/24.69  | | 
% 158.02/24.69  | | Case 1:
% 158.02/24.69  | | | 
% 158.02/24.69  | | |   (8)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | | |          e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 158.02/24.69  | | | 
% 158.02/24.69  | | | ALPHA: (8) implies:
% 158.02/24.69  | | |   (9)  op(e0, e3) = e0
% 158.02/24.69  | | | 
% 158.02/24.69  | | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #973.
% 158.02/24.69  | | | 
% 158.02/24.69  | | Case 2:
% 158.02/24.69  | | | 
% 158.02/24.69  | | |   (10)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.02/24.69  | | |           e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 158.02/24.69  | | | 
% 158.02/24.69  | | | ALPHA: (10) implies:
% 158.02/24.69  | | |   (11)  op(e0, e3) = e0
% 158.02/24.69  | | | 
% 158.02/24.69  | | | REF_CLOSE: (2), (3), (4), (11) are inconsistent by sub-proof #973.
% 158.02/24.69  | | | 
% 158.02/24.69  | | End of split
% 158.02/24.69  | | 
% 158.02/24.69  | End of split
% 158.02/24.69  | 
% 158.02/24.69  End of proof
% 158.02/24.69  
% 158.02/24.69  Sub-proof #100 shows that the following formulas are inconsistent:
% 158.02/24.69  ----------------------------------------------------------------
% 158.02/24.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.69    (2)  op(e0, e0) = e0
% 158.02/24.69    (3)  op(e3, e3) = e0
% 158.02/24.69    (4)   ~ (e1 = e0)
% 158.02/24.69    (5)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.02/24.69           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.02/24.69           = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1)
% 158.02/24.69           & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 158.02/24.69           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 158.02/24.69           e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.02/24.69    (6)   ~ (e3 = e0)
% 158.02/24.69  
% 158.02/24.69  Begin of proof
% 158.02/24.69  | 
% 158.02/24.69  | BETA: splitting (5) gives:
% 158.02/24.69  | 
% 158.02/24.69  | Case 1:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (7)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1)
% 158.02/24.69  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.02/24.69  | |          e0) = e3 & $i(all_57_10)
% 158.02/24.69  | | 
% 158.02/24.69  | | ALPHA: (7) implies:
% 158.02/24.69  | |   (8)  op(e0, e0) = e3
% 158.02/24.69  | | 
% 158.02/24.69  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #999.
% 158.02/24.69  | | 
% 158.02/24.69  | Case 2:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (9)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.02/24.69  | |          op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1
% 158.02/24.69  | |          &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 158.02/24.69  | |            e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.02/24.69  | | 
% 158.02/24.69  | | REF_CLOSE: (1), (3), (4), (6), (9) are inconsistent by sub-proof #101.
% 158.02/24.69  | | 
% 158.02/24.69  | End of split
% 158.02/24.69  | 
% 158.02/24.69  End of proof
% 158.02/24.69  
% 158.02/24.69  Sub-proof #101 shows that the following formulas are inconsistent:
% 158.02/24.69  ----------------------------------------------------------------
% 158.02/24.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.69    (2)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 158.02/24.69             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.02/24.69           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.02/24.69           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.02/24.69    (3)  op(e3, e3) = e0
% 158.02/24.69    (4)   ~ (e1 = e0)
% 158.02/24.69    (5)   ~ (e3 = e0)
% 158.02/24.69  
% 158.02/24.69  Begin of proof
% 158.02/24.69  | 
% 158.02/24.69  | BETA: splitting (2) gives:
% 158.02/24.69  | 
% 158.02/24.69  | Case 1:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (6)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.02/24.69  | |        op(e3, e1) = e3
% 158.02/24.69  | | 
% 158.02/24.69  | | ALPHA: (6) implies:
% 158.02/24.69  | |   (7)  op(e3, e3) = e3
% 158.02/24.69  | | 
% 158.02/24.69  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #971.
% 158.02/24.69  | | 
% 158.02/24.69  | Case 2:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (8)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 158.02/24.69  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 158.02/24.69  | |          e0) = e1 & $i(all_57_14)
% 158.02/24.69  | | 
% 158.02/24.69  | | ALPHA: (8) implies:
% 158.02/24.69  | |   (9)  op(e3, e3) = e1
% 158.02/24.69  | | 
% 158.02/24.69  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #834.
% 158.02/24.69  | | 
% 158.02/24.69  | End of split
% 158.02/24.69  | 
% 158.02/24.69  End of proof
% 158.02/24.69  
% 158.02/24.69  Sub-proof #102 shows that the following formulas are inconsistent:
% 158.02/24.69  ----------------------------------------------------------------
% 158.02/24.69    (1)  all_54_15 = e1 | all_54_15 = e0
% 158.02/24.69    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.69    (3)  op(e1, e1) = e1
% 158.02/24.69    (4)  all_54_15 = all_14_2
% 158.02/24.69    (5)  op(e0, e0) = all_14_2
% 158.02/24.69    (6)   ~ (all_14_2 = e1)
% 158.02/24.69    (7)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 158.02/24.69           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.02/24.69           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 158.02/24.69           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.69           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 158.02/24.69    (8)   ~ (e2 = e1)
% 158.02/24.69  
% 158.02/24.69  Begin of proof
% 158.02/24.69  | 
% 158.02/24.69  | BETA: splitting (7) gives:
% 158.02/24.69  | 
% 158.02/24.69  | Case 1:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 158.02/24.69  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 158.02/24.69  | |          e1) = e2 & $i(all_57_12)
% 158.02/24.69  | | 
% 158.02/24.69  | | ALPHA: (9) implies:
% 158.02/24.69  | |   (10)  op(e1, e1) = e2
% 158.02/24.69  | | 
% 158.02/24.69  | | REF_CLOSE: (2), (3), (8), (10) are inconsistent by sub-proof #986.
% 158.02/24.69  | | 
% 158.02/24.69  | Case 2:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (11)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 158.02/24.69  | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.02/24.69  | |         op(e0, e0) = e1 & $i(all_57_14)
% 158.02/24.69  | | 
% 158.02/24.69  | | ALPHA: (11) implies:
% 158.02/24.69  | |   (12)  op(e0, e0) = e1
% 158.02/24.69  | | 
% 158.02/24.69  | | REF_CLOSE: (1), (2), (4), (5), (6), (12) are inconsistent by sub-proof #790.
% 158.02/24.69  | | 
% 158.02/24.69  | End of split
% 158.02/24.69  | 
% 158.02/24.69  End of proof
% 158.02/24.69  
% 158.02/24.69  Sub-proof #103 shows that the following formulas are inconsistent:
% 158.02/24.69  ----------------------------------------------------------------
% 158.02/24.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.69    (2)  op(e2, e2) = e2
% 158.02/24.69    (3)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 158.02/24.69           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.69           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 158.02/24.69           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 158.02/24.69             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.02/24.69    (4)  op(e3, e3) = e0
% 158.02/24.69    (5)   ~ (e1 = e0)
% 158.02/24.69    (6)   ~ (e2 = e1)
% 158.02/24.69  
% 158.02/24.69  Begin of proof
% 158.02/24.69  | 
% 158.02/24.69  | BETA: splitting (3) gives:
% 158.02/24.69  | 
% 158.02/24.69  | Case 1:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (7)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 158.02/24.69  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.69  | |        all_57_14 & $i(all_57_14)
% 158.02/24.69  | | 
% 158.02/24.69  | | ALPHA: (7) implies:
% 158.02/24.69  | |   (8)  op(e3, e3) = e1
% 158.02/24.69  | | 
% 158.02/24.69  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #834.
% 158.02/24.69  | | 
% 158.02/24.69  | Case 2:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 158.02/24.69  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.02/24.69  | |        all_57_14 & $i(all_57_14)
% 158.02/24.69  | | 
% 158.02/24.69  | | ALPHA: (9) implies:
% 158.02/24.69  | |   (10)  op(e2, e2) = e1
% 158.02/24.69  | | 
% 158.02/24.69  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #993.
% 158.02/24.69  | | 
% 158.02/24.69  | End of split
% 158.02/24.69  | 
% 158.02/24.69  End of proof
% 158.02/24.69  
% 158.02/24.69  Sub-proof #104 shows that the following formulas are inconsistent:
% 158.02/24.69  ----------------------------------------------------------------
% 158.02/24.69    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.69    (2)  op(e3, e3) = e0
% 158.02/24.69    (3)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.02/24.69           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.02/24.69           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 158.02/24.69           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 158.02/24.69           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.02/24.69    (4)   ~ (e1 = e0)
% 158.02/24.69    (5)  op(e2, e0) = all_52_13
% 158.02/24.69    (6)   ~ (all_52_13 = e2)
% 158.02/24.69  
% 158.02/24.69  Begin of proof
% 158.02/24.69  | 
% 158.02/24.69  | BETA: splitting (3) gives:
% 158.02/24.69  | 
% 158.02/24.69  | Case 1:
% 158.02/24.69  | | 
% 158.02/24.69  | |   (7)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 158.02/24.69  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.02/24.69  | |          e0) = e2 & $i(all_57_12)
% 158.02/24.69  | | 
% 158.02/24.69  | | ALPHA: (7) implies:
% 158.02/24.70  | |   (8)  op(e2, e0) = e2
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #996.
% 158.02/24.70  | | 
% 158.02/24.70  | Case 2:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (9)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 158.02/24.70  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.70  | |        all_57_14 & $i(all_57_14)
% 158.02/24.70  | | 
% 158.02/24.70  | | ALPHA: (9) implies:
% 158.02/24.70  | |   (10)  op(e3, e3) = e1
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #834.
% 158.02/24.70  | | 
% 158.02/24.70  | End of split
% 158.02/24.70  | 
% 158.02/24.70  End of proof
% 158.02/24.70  
% 158.02/24.70  Sub-proof #105 shows that the following formulas are inconsistent:
% 158.02/24.70  ----------------------------------------------------------------
% 158.02/24.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.70    (2)  op(e0, e0) = e0
% 158.02/24.70    (3)  op(e3, e3) = e0
% 158.02/24.70    (4)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 158.02/24.70           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.02/24.70           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 158.02/24.70           & op(e3, e3) = e3 & op(e3, e2) = e3)
% 158.02/24.70    (5)   ~ (e3 = e0)
% 158.02/24.70  
% 158.02/24.70  Begin of proof
% 158.02/24.70  | 
% 158.02/24.70  | BETA: splitting (4) gives:
% 158.02/24.70  | 
% 158.02/24.70  | Case 1:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (6)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 158.02/24.70  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 158.02/24.70  | |          e0) = e3 & $i(all_57_10)
% 158.02/24.70  | | 
% 158.02/24.70  | | ALPHA: (6) implies:
% 158.02/24.70  | |   (7)  op(e0, e0) = e3
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #999.
% 158.02/24.70  | | 
% 158.02/24.70  | Case 2:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (8)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 158.02/24.70  | |        op(e3, e2) = e3
% 158.02/24.70  | | 
% 158.02/24.70  | | ALPHA: (8) implies:
% 158.02/24.70  | |   (9)  op(e3, e3) = e3
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #971.
% 158.02/24.70  | | 
% 158.02/24.70  | End of split
% 158.02/24.70  | 
% 158.02/24.70  End of proof
% 158.02/24.70  
% 158.02/24.70  Sub-proof #106 shows that the following formulas are inconsistent:
% 158.02/24.70  ----------------------------------------------------------------
% 158.02/24.70    (1)  op(e0, e0) = e2
% 158.02/24.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.70    (3)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 158.02/24.70           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.02/24.70           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 158.02/24.70           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.70           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 158.02/24.70    (4)  op(e2, e1) = all_52_9
% 158.02/24.70    (5)   ~ (e2 = e1)
% 158.02/24.70    (6)   ~ (all_52_9 = e2)
% 158.02/24.70  
% 158.02/24.70  Begin of proof
% 158.02/24.70  | 
% 158.02/24.70  | BETA: splitting (3) gives:
% 158.02/24.70  | 
% 158.02/24.70  | Case 1:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (7)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 158.02/24.70  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 158.02/24.70  | |          e1) = e2 & $i(all_57_12)
% 158.02/24.70  | | 
% 158.02/24.70  | | ALPHA: (7) implies:
% 158.02/24.70  | |   (8)  op(e2, e1) = e2
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1002.
% 158.02/24.70  | | 
% 158.02/24.70  | Case 2:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (9)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 158.02/24.70  | |        & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.02/24.70  | |          e0) = e1 & $i(all_57_14)
% 158.02/24.70  | | 
% 158.02/24.70  | | ALPHA: (9) implies:
% 158.02/24.70  | |   (10)  op(e0, e0) = e1
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #875.
% 158.02/24.70  | | 
% 158.02/24.70  | End of split
% 158.02/24.70  | 
% 158.02/24.70  End of proof
% 158.02/24.70  
% 158.02/24.70  Sub-proof #107 shows that the following formulas are inconsistent:
% 158.02/24.70  ----------------------------------------------------------------
% 158.02/24.70    (1)  op(e0, e0) = e2
% 158.02/24.70    (2)   ~ (e3 = e2)
% 158.02/24.70    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.70    (4)  op(e1, e1) = e2
% 158.02/24.70    (5)   ~ (e2 = e1)
% 158.02/24.70    (6)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.02/24.70           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.02/24.70           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 158.02/24.70           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.02/24.70           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 158.02/24.70           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.02/24.70  
% 158.02/24.70  Begin of proof
% 158.02/24.70  | 
% 158.02/24.70  | BETA: splitting (6) gives:
% 158.02/24.70  | 
% 158.02/24.70  | Case 1:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (7)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 158.02/24.70  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.02/24.70  | |          e0) = e1 & $i(all_57_14)
% 158.02/24.70  | | 
% 158.02/24.70  | | ALPHA: (7) implies:
% 158.02/24.70  | |   (8)  op(e0, e0) = e1
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #875.
% 158.02/24.70  | | 
% 158.02/24.70  | Case 2:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (9)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 158.02/24.70  | |          & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 158.02/24.70  | |          op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.02/24.70  | |          &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (2), (3), (4), (5), (9) are inconsistent by sub-proof #139.
% 158.02/24.70  | | 
% 158.02/24.70  | End of split
% 158.02/24.70  | 
% 158.02/24.70  End of proof
% 158.02/24.70  
% 158.02/24.70  Sub-proof #108 shows that the following formulas are inconsistent:
% 158.02/24.70  ----------------------------------------------------------------
% 158.02/24.70    (1)   ~ (e3 = e2)
% 158.02/24.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.70    (3)  op(e1, e1) = e2
% 158.02/24.70    (4)  op(e0, e0) = e0
% 158.02/24.70    (5)  op(e0, e0) = all_14_2
% 158.02/24.70    (6)   ~ (e1 = e0)
% 158.02/24.70    (7)   ~ (e2 = e1)
% 158.02/24.70    (8)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.02/24.70           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.02/24.70           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 158.02/24.70           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.02/24.70           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 158.02/24.70           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.02/24.70  
% 158.02/24.70  Begin of proof
% 158.02/24.70  | 
% 158.02/24.70  | BETA: splitting (8) gives:
% 158.02/24.70  | 
% 158.02/24.70  | Case 1:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (9)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 158.02/24.70  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.02/24.70  | |          e0) = e1 & $i(all_57_14)
% 158.02/24.70  | | 
% 158.02/24.70  | | ALPHA: (9) implies:
% 158.02/24.70  | |   (10)  op(e0, e0) = e1
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #991.
% 158.02/24.70  | | 
% 158.02/24.70  | Case 2:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (11)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.02/24.70  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 158.02/24.70  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 158.02/24.70  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (1), (2), (3), (7), (11) are inconsistent by sub-proof #139.
% 158.02/24.70  | | 
% 158.02/24.70  | End of split
% 158.02/24.70  | 
% 158.02/24.70  End of proof
% 158.02/24.70  
% 158.02/24.70  Sub-proof #109 shows that the following formulas are inconsistent:
% 158.02/24.70  ----------------------------------------------------------------
% 158.02/24.70    (1)  all_54_5 = all_4_2
% 158.02/24.70    (2)  ( ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 & $i(all_10_0)) | ( ~
% 158.02/24.70           (all_10_1 = e0) & op(e2, e2) = all_10_1 & $i(all_10_1))
% 158.02/24.70    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.70    (4)  op(e2, e2) = all_57_12
% 158.02/24.70    (5)  op(e2, e2) = all_4_2
% 158.02/24.70    (6)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.02/24.70    (7)   ~ (all_4_2 = e2)
% 158.02/24.70    (8)   ~ (all_4_2 = e1)
% 158.02/24.70    (9)  op(e2, e1) = all_52_9
% 158.02/24.70    (10)  op(e2, e1) = e2
% 158.02/24.70    (11)   ~ (all_52_9 = e2)
% 158.02/24.70  
% 158.02/24.70  Begin of proof
% 158.02/24.70  | 
% 158.02/24.70  | BETA: splitting (6) gives:
% 158.02/24.70  | 
% 158.02/24.70  | Case 1:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (12)  all_54_5 = e2
% 158.02/24.70  | | 
% 158.02/24.70  | | REF_CLOSE: (1), (7), (12) are inconsistent by sub-proof #268.
% 158.02/24.70  | | 
% 158.02/24.70  | Case 2:
% 158.02/24.70  | | 
% 158.02/24.70  | |   (13)  all_54_5 = e1 | all_54_5 = e0
% 158.02/24.70  | | 
% 158.02/24.70  | | BETA: splitting (13) gives:
% 158.02/24.70  | | 
% 158.02/24.70  | | Case 1:
% 158.02/24.70  | | | 
% 158.02/24.70  | | |   (14)  all_54_5 = e1
% 158.02/24.70  | | | 
% 158.02/24.70  | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #693.
% 158.02/24.70  | | | 
% 158.02/24.70  | | Case 2:
% 158.02/24.70  | | | 
% 158.02/24.70  | | |   (15)  all_54_5 = e0
% 158.02/24.70  | | | 
% 158.02/24.70  | | | COMBINE_EQS: (1), (15) imply:
% 158.02/24.70  | | |   (16)  all_4_2 = e0
% 158.02/24.70  | | | 
% 158.02/24.70  | | | SIMP: (16) implies:
% 158.02/24.70  | | |   (17)  all_4_2 = e0
% 158.02/24.70  | | | 
% 158.02/24.70  | | | REDUCE: (5), (17) imply:
% 158.02/24.70  | | |   (18)  op(e2, e2) = e0
% 158.02/24.70  | | | 
% 158.02/24.70  | | | BETA: splitting (2) gives:
% 158.02/24.70  | | | 
% 158.02/24.70  | | | Case 1:
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | |   (19)   ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 & $i(all_10_0)
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | | ALPHA: (19) implies:
% 158.02/24.70  | | | |   (20)  op(e2, e1) = all_10_0
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | | REF_CLOSE: (3), (9), (10), (11), (20) are inconsistent by sub-proof
% 158.02/24.70  | | | |            #194.
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | Case 2:
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | |   (21)   ~ (all_10_1 = e0) & op(e2, e2) = all_10_1 & $i(all_10_1)
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | | ALPHA: (21) implies:
% 158.02/24.70  | | | |   (22)   ~ (all_10_1 = e0)
% 158.02/24.70  | | | |   (23)  op(e2, e2) = all_10_1
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | | GROUND_INST: instantiating (3) with all_10_1, all_57_12, e2, e2,
% 158.02/24.70  | | | |              simplifying with (4), (23) gives:
% 158.02/24.70  | | | |   (24)  all_57_12 = all_10_1
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | | GROUND_INST: instantiating (3) with e0, all_57_12, e2, e2, simplifying
% 158.02/24.70  | | | |              with (4), (18) gives:
% 158.02/24.70  | | | |   (25)  all_57_12 = e0
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | | COMBINE_EQS: (24), (25) imply:
% 158.02/24.70  | | | |   (26)  all_10_1 = e0
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | | REDUCE: (22), (26) imply:
% 158.02/24.70  | | | |   (27)  $false
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | | CLOSE: (27) is inconsistent.
% 158.02/24.70  | | | | 
% 158.02/24.70  | | | End of split
% 158.02/24.70  | | | 
% 158.02/24.70  | | End of split
% 158.02/24.70  | | 
% 158.02/24.70  | End of split
% 158.02/24.70  | 
% 158.02/24.70  End of proof
% 158.02/24.70  
% 158.02/24.70  Sub-proof #110 shows that the following formulas are inconsistent:
% 158.02/24.70  ----------------------------------------------------------------
% 158.02/24.70    (1)   ~ (all_52_13 = e1)
% 158.02/24.70    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.02/24.70         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.02/24.70    (3)   ~ (all_52_1 = all_52_3)
% 158.02/24.70    (4)  op(e0, e0) = e1
% 158.02/24.70    (5)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.02/24.70         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.02/24.70    (6)   ~ (e3 = e2)
% 158.02/24.70    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.02/24.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.02/24.70    (8)  all_56_11 = e0
% 158.02/24.70    (9)  op(e0, e3) = all_52_3
% 158.02/24.70    (10)   ~ (all_4_2 = e3)
% 158.02/24.70    (11)  op(e2, e2) = e2
% 158.02/24.70    (12)  op(e1, e3) = all_52_2
% 158.02/24.70    (13)  op(e0, e2) = all_52_7
% 158.02/24.70    (14)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.02/24.70          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.02/24.70    (15)  op(e1, e0) = e0
% 158.02/24.70    (16)  all_56_5 = e1
% 158.02/24.70    (17)   ~ (all_52_2 = e2)
% 158.02/24.70    (18)   ~ (all_52_2 = e1)
% 158.02/24.70    (19)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 158.02/24.70          (all_56_11 = e0 & op(e1, e0) = e0)
% 158.02/24.70    (20)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 158.02/24.70    (21)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.02/24.70          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.02/24.70    (22)  op(e2, e2) = all_4_2
% 158.02/24.70    (23)  op(e2, e1) = e1
% 158.02/24.70    (24)  op(e0, e0) = all_14_2
% 158.02/24.70    (25)  op(e3, e3) = e1
% 158.02/24.70    (26)  op(e2, e3) = all_52_1
% 158.02/24.70    (27)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 158.02/24.70            all_57_3 & $i(all_57_3))
% 158.02/24.70    (28)   ~ (all_4_2 = e1)
% 158.02/24.70    (29)  op(e1, e3) = e3
% 158.02/24.70    (30)   ~ (all_52_1 = all_52_9)
% 158.02/24.70    (31)  all_56_0 = e1
% 158.02/24.70    (32)   ~ (e1 = e0)
% 158.02/24.70    (33)  op(e2, e1) = all_52_9
% 158.02/24.70    (34)  all_54_4 = all_52_1
% 158.02/24.70    (35)   ~ (all_57_7 = e0)
% 158.02/24.70    (36)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.02/24.70          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.02/24.70    (37)  op(e2, e0) = all_52_13
% 158.02/24.70    (38)   ~ (e2 = e1)
% 158.02/24.71    (39)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.02/24.71            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.71            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.02/24.71            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.71              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.02/24.71          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.02/24.71            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.02/24.71              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.02/24.71            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.71              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.02/24.71          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.02/24.71            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.02/24.71              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.02/24.71            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.71              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.02/24.71          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.02/24.71            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.02/24.71            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.02/24.71              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.02/24.71            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.02/24.71            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.02/24.71            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.02/24.71            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.02/24.71              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.02/24.71            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.02/24.71          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.02/24.71            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.02/24.71              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.02/24.71            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.02/24.71            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.02/24.71          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.02/24.71            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.02/24.71              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.02/24.71            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.02/24.71            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.02/24.71          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.02/24.71            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.02/24.71              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.02/24.71            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.71              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.02/24.71          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.02/24.71            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.02/24.71            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.02/24.71            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.02/24.71            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.02/24.71            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.71            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.02/24.71            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.02/24.71              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.02/24.71            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.02/24.71            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.02/24.71            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.02/24.71            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.02/24.71              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.02/24.71            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.02/24.71          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.02/24.71            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.02/24.71              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.02/24.71              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.02/24.71            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.02/24.71            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.02/24.71            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.02/24.71            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.02/24.71              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.02/24.71            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.02/24.71          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.02/24.71            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.02/24.71              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.02/24.71            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.02/24.71              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.02/24.71          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.02/24.71            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.02/24.71              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.02/24.71              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.02/24.71            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.02/24.71          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.02/24.71            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.02/24.71            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.02/24.71                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.02/24.71                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.71                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.02/24.71                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.02/24.71                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.02/24.71                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.02/24.71                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.71                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.02/24.71                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.71                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.02/24.71                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.02/24.71                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.02/24.71                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.02/24.71                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.71                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.02/24.71                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.71                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.02/24.71                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.02/24.71                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.02/24.71                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.02/24.71                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.02/24.71                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.02/24.71                op(e0, e1) = e0)))
% 158.02/24.71    (40)   ~ (all_52_9 = e2)
% 158.02/24.71    (41)   ~ (e3 = e1)
% 158.02/24.71    (42)   ~ (all_52_1 = all_4_2)
% 158.02/24.71    (43)   ~ (e2 = e0)
% 158.02/24.71    (44)  op(e1, e2) = e1
% 158.02/24.71    (45)   ~ (all_52_1 = all_52_13)
% 158.02/24.71    (46)  op(e0, e2) = all_57_7
% 158.02/24.71    (47)   ~ (e3 = e0)
% 158.02/24.71  
% 158.02/24.71  Begin of proof
% 158.02/24.71  | 
% 158.02/24.71  | BETA: splitting (27) gives:
% 158.02/24.71  | 
% 158.02/24.71  | Case 1:
% 158.02/24.71  | | 
% 158.02/24.71  | |   (48)  all_57_14 = e2 & op(e1, e1) = e2
% 158.02/24.71  | | 
% 158.02/24.71  | | ALPHA: (48) implies:
% 158.02/24.71  | |   (49)  all_57_14 = e2
% 158.02/24.71  | |   (50)  op(e1, e1) = e2
% 158.02/24.71  | | 
% 158.02/24.71  | | BETA: splitting (14) gives:
% 158.02/24.71  | | 
% 158.02/24.71  | | Case 1:
% 158.02/24.71  | | | 
% 158.02/24.71  | | |   (51)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 158.02/24.71  | | |           e3)
% 158.02/24.71  | | | 
% 158.02/24.71  | | | BETA: splitting (51) gives:
% 158.02/24.71  | | | 
% 158.02/24.71  | | | Case 1:
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | |   (52)  all_56_2 = e3 & op(e2, e3) = e3
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | | ALPHA: (52) implies:
% 158.02/24.71  | | | |   (53)  all_56_2 = e3
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | | BETA: splitting (36) gives:
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | | Case 1:
% 158.02/24.71  | | | | | 
% 158.02/24.71  | | | | |   (54)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2,
% 158.02/24.71  | | | | |             e3) = e0)
% 158.02/24.71  | | | | | 
% 158.02/24.71  | | | | | REF_CLOSE: (7), (25), (32), (47), (53), (54) are inconsistent by
% 158.02/24.71  | | | | |            sub-proof #618.
% 158.02/24.71  | | | | | 
% 158.02/24.71  | | | | Case 2:
% 158.02/24.71  | | | | | 
% 158.02/24.71  | | | | |   (55)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0,
% 158.02/24.71  | | | | |             e3) = e0)
% 158.02/24.71  | | | | | 
% 158.02/24.71  | | | | | BETA: splitting (55) gives:
% 158.02/24.71  | | | | | 
% 158.02/24.71  | | | | | Case 1:
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | |   (56)  all_56_6 = e0 & op(e1, e3) = e0
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | ALPHA: (56) implies:
% 158.02/24.71  | | | | | |   (57)  op(e1, e3) = e0
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | REF_CLOSE: (7), (29), (47), (57) are inconsistent by sub-proof #913.
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | Case 2:
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | |   (58)  all_56_12 = e0 & op(e0, e3) = e0
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | ALPHA: (58) implies:
% 158.02/24.71  | | | | | |   (59)  op(e0, e3) = e0
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | REF_CLOSE: (2), (6), (7), (9), (12), (17), (31), (38), (43), (53),
% 158.02/24.71  | | | | | |            (59) are inconsistent by sub-proof #203.
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | End of split
% 158.02/24.71  | | | | | 
% 158.02/24.71  | | | | End of split
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | Case 2:
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | |   (60)  all_56_3 = e3 & op(e2, e2) = e3
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | | ALPHA: (60) implies:
% 158.02/24.71  | | | |   (61)  op(e2, e2) = e3
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | | REF_CLOSE: (7), (10), (22), (61) are inconsistent by sub-proof #711.
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | End of split
% 158.02/24.71  | | | 
% 158.02/24.71  | | Case 2:
% 158.02/24.71  | | | 
% 158.02/24.71  | | |   (62)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 158.02/24.71  | | |           e3)
% 158.02/24.71  | | | 
% 158.02/24.71  | | | BETA: splitting (62) gives:
% 158.02/24.71  | | | 
% 158.02/24.71  | | | Case 1:
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | |   (63)  all_56_5 = e3 & op(e2, e1) = e3
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | | ALPHA: (63) implies:
% 158.02/24.71  | | | |   (64)  all_56_5 = e3
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | | REF_CLOSE: (16), (41), (64) are inconsistent by sub-proof #531.
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | Case 2:
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | |   (65)  all_56_10 = e3 & op(e2, e0) = e3
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | | ALPHA: (65) implies:
% 158.02/24.71  | | | |   (66)  all_56_10 = e3
% 158.02/24.71  | | | |   (67)  op(e2, e0) = e3
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | | BETA: splitting (21) gives:
% 158.02/24.71  | | | | 
% 158.02/24.71  | | | | Case 1:
% 158.02/24.71  | | | | | 
% 158.02/24.71  | | | | |   (68)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2,
% 158.02/24.71  | | | | |             e0) = e2)
% 158.02/24.71  | | | | | 
% 158.02/24.71  | | | | | BETA: splitting (68) gives:
% 158.02/24.71  | | | | | 
% 158.02/24.71  | | | | | Case 1:
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | |   (69)  all_56_9 = e2 & op(e3, e0) = e2
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | ALPHA: (69) implies:
% 158.02/24.71  | | | | | |   (70)  all_56_9 = e2
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | GROUND_INST: instantiating (7) with all_52_7, all_57_7, e2, e0,
% 158.02/24.71  | | | | | |              simplifying with (13), (46) gives:
% 158.02/24.71  | | | | | |   (71)  all_57_7 = all_52_7
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | GROUND_INST: instantiating (7) with all_52_13, e3, e0, e2,
% 158.02/24.71  | | | | | |              simplifying with (37), (67) gives:
% 158.02/24.71  | | | | | |   (72)  all_52_13 = e3
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | GROUND_INST: instantiating (7) with all_52_9, e1, e1, e2,
% 158.02/24.71  | | | | | |              simplifying with (23), (33) gives:
% 158.02/24.71  | | | | | |   (73)  all_52_9 = e1
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | GROUND_INST: instantiating (7) with all_4_2, e2, e2, e2, simplifying
% 158.02/24.71  | | | | | |              with (11), (22) gives:
% 158.02/24.71  | | | | | |   (74)  all_4_2 = e2
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | REDUCE: (35), (71) imply:
% 158.02/24.71  | | | | | |   (75)   ~ (all_52_7 = e0)
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | REDUCE: (30), (73) imply:
% 158.02/24.71  | | | | | |   (76)   ~ (all_52_1 = e1)
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | REDUCE: (45), (72) imply:
% 158.02/24.71  | | | | | |   (77)   ~ (all_52_1 = e3)
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | REDUCE: (42), (74) imply:
% 158.02/24.71  | | | | | |   (78)   ~ (all_52_1 = e2)
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | REDUCE: (10), (74) imply:
% 158.02/24.71  | | | | | |   (79)   ~ (e3 = e2)
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | BETA: splitting (20) gives:
% 158.02/24.71  | | | | | | 
% 158.02/24.71  | | | | | | Case 1:
% 158.02/24.71  | | | | | | | 
% 158.02/24.71  | | | | | | |   (80)  all_54_4 = e3
% 158.02/24.71  | | | | | | | 
% 158.02/24.71  | | | | | | | COMBINE_EQS: (34), (80) imply:
% 158.02/24.71  | | | | | | |   (81)  all_52_1 = e3
% 158.02/24.71  | | | | | | | 
% 158.02/24.71  | | | | | | | REDUCE: (77), (81) imply:
% 158.02/24.71  | | | | | | |   (82)  $false
% 158.02/24.71  | | | | | | | 
% 158.02/24.71  | | | | | | | CLOSE: (82) is inconsistent.
% 158.02/24.71  | | | | | | | 
% 158.02/24.71  | | | | | | Case 2:
% 158.02/24.71  | | | | | | | 
% 158.02/24.71  | | | | | | |   (83)   ~ (all_54_4 = e3)
% 158.02/24.71  | | | | | | |   (84)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 158.02/24.71  | | | | | | | 
% 158.02/24.71  | | | | | | | BETA: splitting (84) gives:
% 158.02/24.71  | | | | | | | 
% 158.02/24.71  | | | | | | | Case 1:
% 158.02/24.71  | | | | | | | | 
% 158.02/24.71  | | | | | | | |   (85)  all_54_4 = e2
% 158.02/24.71  | | | | | | | | 
% 158.02/24.71  | | | | | | | | COMBINE_EQS: (34), (85) imply:
% 158.02/24.71  | | | | | | | |   (86)  all_52_1 = e2
% 158.02/24.71  | | | | | | | | 
% 158.02/24.71  | | | | | | | | REDUCE: (78), (86) imply:
% 158.02/24.71  | | | | | | | |   (87)  $false
% 158.02/24.71  | | | | | | | | 
% 158.02/24.71  | | | | | | | | CLOSE: (87) is inconsistent.
% 158.02/24.71  | | | | | | | | 
% 158.02/24.71  | | | | | | | Case 2:
% 158.02/24.71  | | | | | | | | 
% 158.02/24.71  | | | | | | | |   (88)   ~ (all_54_4 = e2)
% 158.02/24.71  | | | | | | | |   (89)  all_54_4 = e1 | all_54_4 = e0
% 158.02/24.71  | | | | | | | | 
% 158.02/24.71  | | | | | | | | BETA: splitting (89) gives:
% 158.02/24.71  | | | | | | | | 
% 158.02/24.71  | | | | | | | | Case 1:
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | |   (90)  all_54_4 = e1
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | COMBINE_EQS: (34), (90) imply:
% 158.02/24.71  | | | | | | | | |   (91)  all_52_1 = e1
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | REDUCE: (76), (91) imply:
% 158.02/24.71  | | | | | | | | |   (92)  $false
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | CLOSE: (92) is inconsistent.
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | Case 2:
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | |   (93)  all_54_4 = e0
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | COMBINE_EQS: (34), (93) imply:
% 158.02/24.71  | | | | | | | | |   (94)  all_52_1 = e0
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | REDUCE: (3), (94) imply:
% 158.02/24.71  | | | | | | | | |   (95)   ~ (all_52_3 = e0)
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | SIMP: (95) implies:
% 158.02/24.71  | | | | | | | | |   (96)   ~ (all_52_3 = e0)
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | REDUCE: (77), (94) imply:
% 158.02/24.71  | | | | | | | | |   (97)   ~ (e3 = e0)
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | REDUCE: (78), (94) imply:
% 158.02/24.71  | | | | | | | | |   (98)   ~ (e2 = e0)
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | REDUCE: (76), (94) imply:
% 158.02/24.71  | | | | | | | | |   (99)   ~ (e1 = e0)
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | BETA: splitting (39) gives:
% 158.02/24.71  | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | Case 1:
% 158.02/24.71  | | | | | | | | | | 
% 158.02/24.71  | | | | | | | | | |   (100)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 158.02/24.71  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 158.02/24.71  | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.02/24.71  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.02/24.71  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 158.02/24.71  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.02/24.71  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 158.02/24.71  | | | | | | | | | |            & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12
% 158.02/24.71  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.71  | | | | | | | | | |            all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.02/24.71  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.02/24.71  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.02/24.71  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 &
% 158.02/24.71  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 158.02/24.71  | | | | | | | | | |            & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12
% 158.02/24.71  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.71  | | | | | | | | | |            all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.02/24.71  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.02/24.71  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.02/24.71  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 158.02/24.71  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 158.02/24.71  | | | | | | | | | |            & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 158.02/24.71  | | | | | | | | | |            & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 158.02/24.71  | | | | | | | | | |            e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.02/24.71  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.02/24.71  | | | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.02/24.71  | | | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 158.02/24.71  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 158.02/24.71  | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.02/24.71  | | | | | | | | | |            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 &
% 158.02/24.71  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 158.02/24.71  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 158.02/24.71  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 158.02/24.71  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3
% 158.02/24.71  | | | | | | | | | |            & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 =
% 158.02/24.71  | | | | | | | | | |            e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.02/24.71  | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.02/24.71  | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 158.02/24.72  | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.02/24.72  | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 158.02/24.72  | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.72  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.02/24.72  | | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.02/24.72  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 158.02/24.72  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 158.02/24.72  | | | | | | | | | |            & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14
% 158.02/24.72  | | | | | | | | | |              = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.02/24.72  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.72  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 158.02/24.72  | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3)
% 158.02/24.72  | | | | | | | | | |            = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.02/24.72  | | | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1
% 158.02/24.72  | | | | | | | | | |            & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10
% 158.02/24.72  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 158.02/24.72  | | | | | | | | | |            e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.02/24.72  | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.02/24.72  | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.72  | | | | | | | | | |            e1)
% 158.02/24.72  | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | BETA: splitting (100) gives:
% 158.02/24.72  | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | Case 1:
% 158.02/24.72  | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | |   (101)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 158.02/24.72  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 158.02/24.72  | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.72  | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.02/24.72  | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.02/24.72  | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 158.02/24.72  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.02/24.72  | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 158.02/24.72  | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 158.02/24.72  | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 158.02/24.72  | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.02/24.72  | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 158.02/24.72  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.02/24.72  | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.02/24.72  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 158.02/24.72  | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.02/24.72  | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.02/24.72  | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.02/24.72  | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 158.02/24.72  | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 158.02/24.72  | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 158.02/24.72  | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.02/24.72  | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.02/24.72  | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 158.02/24.72  | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.02/24.72  | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.02/24.72  | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.72  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 158.02/24.72  | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.02/24.72  | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.02/24.72  | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.02/24.72  | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | REF_CLOSE: (6), (7), (26), (33), (40), (50), (78), (101) are
% 158.02/24.72  | | | | | | | | | | |            inconsistent by sub-proof #114.
% 158.02/24.72  | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | Case 2:
% 158.02/24.72  | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | |   (102)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.02/24.72  | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.02/24.72  | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.02/24.72  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.02/24.72  | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 158.02/24.72  | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 158.02/24.72  | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 158.02/24.72  | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.02/24.72  | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 158.02/24.72  | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.02/24.72  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 158.02/24.72  | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.72  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.02/24.72  | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.02/24.72  | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 158.02/24.72  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.02/24.72  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 158.02/24.72  | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 158.02/24.72  | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 158.02/24.72  | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.02/24.72  | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.02/24.72  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 158.02/24.72  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.02/24.72  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.02/24.72  | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.02/24.72  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.02/24.72  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.02/24.72  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.02/24.72  | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.72  | | | | | | | | | | |            e1)
% 158.02/24.72  | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | BETA: splitting (102) gives:
% 158.02/24.72  | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | Case 1:
% 158.02/24.72  | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | |   (103)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.02/24.72  | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.02/24.72  | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.02/24.72  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.02/24.72  | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 158.02/24.72  | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 158.02/24.72  | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 158.02/24.72  | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.02/24.72  | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 158.02/24.72  | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.02/24.72  | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 158.02/24.72  | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.02/24.72  | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 158.02/24.72  | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | BETA: splitting (103) gives:
% 158.02/24.72  | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | Case 1:
% 158.02/24.72  | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | |   (104)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.02/24.72  | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.02/24.72  | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.02/24.72  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.02/24.72  | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 158.02/24.72  | | | | | | | | | | | | |              e2) = e3)
% 158.02/24.72  | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | BETA: splitting (104) gives:
% 158.02/24.72  | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | Case 1:
% 158.02/24.72  | | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | |   (105)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.02/24.72  | | | | | | | | | | | | | |          ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.02/24.72  | | | | | | | | | | | | | |          op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.02/24.72  | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 158.02/24.72  | | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | | ALPHA: (105) implies:
% 158.02/24.72  | | | | | | | | | | | | | |   (106)  op(e0, e0) = e3
% 158.02/24.72  | | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (19), (32), (38), (41), (43), (47),
% 158.02/24.72  | | | | | | | | | | | | | |            (66), (70), (106) are inconsistent by sub-proof
% 158.02/24.72  | | | | | | | | | | | | | |            #472.
% 158.02/24.72  | | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | Case 2:
% 158.02/24.72  | | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | |   (107)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 158.02/24.72  | | | | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e2) = e3
% 158.02/24.72  | | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | | ALPHA: (107) implies:
% 158.02/24.72  | | | | | | | | | | | | | |   (108)  op(e3, e3) = e3
% 158.02/24.72  | | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | | REF_CLOSE: (7), (25), (41), (108) are inconsistent by
% 158.02/24.72  | | | | | | | | | | | | | |            sub-proof #995.
% 158.02/24.72  | | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | End of split
% 158.02/24.72  | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | Case 2:
% 158.02/24.72  | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | |   (109)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 158.02/24.72  | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 158.02/24.72  | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.02/24.72  | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 158.02/24.72  | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 158.02/24.72  | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.02/24.72  | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.02/24.72  | | | | | | | | | | | | |            $i(all_57_14))
% 158.02/24.72  | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | BETA: splitting (109) gives:
% 158.02/24.72  | | | | | | | | | | | | | 
% 158.02/24.72  | | | | | | | | | | | | | Case 1:
% 158.02/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | |   (110)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 158.19/24.72  | | | | | | | | | | | | | |          ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 158.19/24.72  | | | | | | | | | | | | | |          = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.19/24.72  | | | | | | | | | | | | | |          $i(all_57_12)
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | | ALPHA: (110) implies:
% 158.19/24.72  | | | | | | | | | | | | | |   (111)  op(e2, e0) = e2
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (67), (111) are inconsistent by
% 158.19/24.72  | | | | | | | | | | | | | |            sub-proof #580.
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | Case 2:
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | |   (112)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.19/24.72  | | | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 158.19/24.72  | | | | | | | | | | | | | |          = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.19/24.72  | | | | | | | | | | | | | |          $i(all_57_14)
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | | ALPHA: (112) implies:
% 158.19/24.72  | | | | | | | | | | | | | |   (113)  op(e1, e3) = e1
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (18), (113) are inconsistent by
% 158.19/24.72  | | | | | | | | | | | | | |            sub-proof #990.
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | End of split
% 158.19/24.72  | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | End of split
% 158.19/24.72  | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | Case 2:
% 158.19/24.72  | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | |   (114)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 158.19/24.72  | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.19/24.72  | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.19/24.72  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 158.19/24.72  | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.19/24.72  | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 158.19/24.72  | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.19/24.72  | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.19/24.72  | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 158.19/24.72  | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.19/24.72  | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.19/24.72  | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.19/24.72  | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.19/24.72  | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.19/24.72  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.19/24.72  | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.19/24.72  | | | | | | | | | | | |            e1)
% 158.19/24.72  | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | BETA: splitting (114) gives:
% 158.19/24.72  | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | Case 1:
% 158.19/24.72  | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | |   (115)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 158.19/24.72  | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.19/24.72  | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.19/24.72  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 158.19/24.72  | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.19/24.72  | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 158.19/24.72  | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.19/24.72  | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (11), (38), (50), (115) are inconsistent
% 158.19/24.72  | | | | | | | | | | | | |            by sub-proof #113.
% 158.19/24.72  | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | Case 2:
% 158.19/24.72  | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | |   (116)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.19/24.72  | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 158.19/24.72  | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.19/24.72  | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.19/24.72  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.19/24.72  | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.19/24.72  | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.19/24.72  | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.19/24.72  | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.19/24.72  | | | | | | | | | | | | |            e1)
% 158.19/24.72  | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | BETA: splitting (116) gives:
% 158.19/24.72  | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | Case 1:
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | |   (117)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.19/24.72  | | | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 158.19/24.72  | | | | | | | | | | | | | |          = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.19/24.72  | | | | | | | | | | | | | |          $i(all_57_14)
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | | ALPHA: (117) implies:
% 158.19/24.72  | | | | | | | | | | | | | |   (118)  op(e1, e3) = e1
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (18), (118) are inconsistent by
% 158.19/24.72  | | | | | | | | | | | | | |            sub-proof #990.
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | Case 2:
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | |   (119)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 158.19/24.72  | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.19/24.72  | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.19/24.72  | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 158.19/24.72  | | | | | | | | | | | | | |            = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 158.19/24.72  | | | | | | | | | | | | | |              e1) = e1)
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (38), (50), (119) are inconsistent by
% 158.19/24.72  | | | | | | | | | | | | | |            sub-proof #139.
% 158.19/24.72  | | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | | End of split
% 158.19/24.72  | | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | | End of split
% 158.19/24.72  | | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | | End of split
% 158.19/24.72  | | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | | End of split
% 158.19/24.72  | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | Case 2:
% 158.19/24.72  | | | | | | | | | | 
% 158.19/24.72  | | | | | | | | | |   (120)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.19/24.72  | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 158.19/24.72  | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.19/24.72  | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.19/24.72  | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 158.19/24.72  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 158.19/24.72  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 158.19/24.72  | | | | | | | | | |            e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.19/24.72  | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.19/24.72  | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.72  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 =
% 158.19/24.72  | | | | | | | | | |            e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.19/24.72  | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 158.19/24.72  | | | | | | | | | |              e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 158.19/24.72  | | | | | | | | | |          (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 158.19/24.72  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.19/24.72  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.72  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.19/24.72  | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.19/24.72  | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.19/24.72  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.19/24.72  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.19/24.72  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3
% 158.19/24.72  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3
% 158.19/24.72  | | | | | | | | | |            & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 =
% 158.19/24.72  | | | | | | | | | |            e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.19/24.72  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.19/24.72  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 158.19/24.72  | | | | | | | | | |          (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.19/24.72  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.19/24.72  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.19/24.72  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.19/24.72  | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.19/24.72  | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.19/24.72  | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2)
% 158.19/24.72  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 &
% 158.19/24.72  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0
% 158.19/24.72  | | | | | | | | | |            & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10
% 158.19/24.72  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 158.19/24.72  | | | | | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.19/24.72  | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 158.19/24.72  | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 158.19/24.72  | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 158.19/24.72  | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.19/24.72  | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 158.19/24.72  | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 158.19/24.72  | | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 158.19/24.72  | | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 158.19/24.72  | | | | | | | | | |            all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.19/24.72  | | | | | | | | | |            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 158.19/24.72  | | | | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 158.19/24.72  | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3,
% 158.19/24.72  | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 158.19/24.72  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_11 = e2 &
% 158.19/24.72  | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2,
% 158.19/24.72  | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 158.19/24.72  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 158.19/24.72  | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 158.19/24.72  | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.19/24.72  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.19/24.72  | | | | | | | | | |                (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0
% 158.19/24.72  | | | | | | | | | |                & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.19/24.72  | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.19/24.72  | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.19/24.72  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.19/24.72  | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 158.19/24.72  | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.19/24.72  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.19/24.72  | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.19/24.72  | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.19/24.72  | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 158.19/24.72  | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 158.19/24.72  | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.72  | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.19/24.72  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 = e2
% 158.19/24.72  | | | | | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.72  | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.19/24.72  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 158.19/24.72  | | | | | | | | | |                & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.72  | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.19/24.72  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 158.19/24.72  | | | | | | | | | |                & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.19/24.72  | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.19/24.72  | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 158.19/24.72  | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0,
% 158.19/24.72  | | | | | | | | | |                  e1) = e0)))
% 158.19/24.72  | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | BETA: splitting (120) gives:
% 158.19/24.73  | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | |   (121)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.19/24.73  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 158.19/24.73  | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.19/24.73  | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 158.19/24.73  | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.19/24.73  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.19/24.73  | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 158.19/24.73  | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 158.19/24.73  | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 158.19/24.73  | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.19/24.73  | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.19/24.73  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 158.19/24.73  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.19/24.73  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.19/24.73  | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 158.19/24.73  | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 158.19/24.73  | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.19/24.73  | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 158.19/24.73  | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 158.19/24.73  | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.19/24.73  | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.19/24.73  | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 158.19/24.73  | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 158.19/24.73  | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.19/24.73  | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 158.19/24.73  | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.19/24.73  | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.19/24.73  | | | | | | | | | | |            $i(all_57_14))
% 158.19/24.73  | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | BETA: splitting (121) gives:
% 158.19/24.73  | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | |   (122)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.19/24.73  | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 158.19/24.73  | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.19/24.73  | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 158.19/24.73  | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.19/24.73  | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.19/24.73  | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 158.19/24.73  | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 158.19/24.73  | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 158.19/24.73  | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.19/24.73  | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.19/24.73  | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 158.19/24.73  | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.19/24.73  | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | BETA: splitting (122) gives:
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | |   (123)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.19/24.73  | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 158.19/24.73  | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.19/24.73  | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 158.19/24.73  | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.19/24.73  | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.19/24.73  | | | | | | | | | | | | |            $i(all_57_14))
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | BETA: splitting (123) gives:
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | |   (124)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.19/24.73  | | | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 158.19/24.73  | | | | | | | | | | | | | |          = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.19/24.73  | | | | | | | | | | | | | |          $i(all_57_14)
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | ALPHA: (124) implies:
% 158.19/24.73  | | | | | | | | | | | | | |   (125)   ~ (all_57_14 = e2)
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | REDUCE: (49), (125) imply:
% 158.19/24.73  | | | | | | | | | | | | | |   (126)  $false
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | CLOSE: (126) is inconsistent.
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | Case 2:
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | |   (127)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 158.19/24.73  | | | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 158.19/24.73  | | | | | | | | | | | | | |          = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.19/24.73  | | | | | | | | | | | | | |          $i(all_57_14)
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | ALPHA: (127) implies:
% 158.19/24.73  | | | | | | | | | | | | | |   (128)  op(e2, e2) = e1
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (38), (128) are inconsistent by
% 158.19/24.73  | | | | | | | | | | | | | |            sub-proof #993.
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | End of split
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | Case 2:
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | |   (129)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 158.19/24.73  | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.19/24.73  | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 158.19/24.73  | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.19/24.73  | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.19/24.73  | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.19/24.73  | | | | | | | | | | | | |            $i(all_57_14))
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | BETA: splitting (129) gives:
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | |   (130)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 158.19/24.73  | | | | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.19/24.73  | | | | | | | | | | | | | |          op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | | | | |          e2 & $i(all_57_12)
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | ALPHA: (130) implies:
% 158.19/24.73  | | | | | | | | | | | | | |   (131)  op(e2, e1) = e2
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | REF_CLOSE: (7), (33), (40), (131) are inconsistent by
% 158.19/24.73  | | | | | | | | | | | | | |            sub-proof #1002.
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | Case 2:
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | |   (132)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.19/24.73  | | | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 158.19/24.73  | | | | | | | | | | | | | |          = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.19/24.73  | | | | | | | | | | | | | |          $i(all_57_14)
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | ALPHA: (132) implies:
% 158.19/24.73  | | | | | | | | | | | | | |   (133)   ~ (all_57_14 = e2)
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | REDUCE: (49), (133) imply:
% 158.19/24.73  | | | | | | | | | | | | | |   (134)  $false
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | End of split
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | End of split
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | Case 2:
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | |   (135)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 158.19/24.73  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.19/24.73  | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.19/24.73  | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.19/24.73  | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.19/24.73  | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 158.19/24.73  | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 158.19/24.73  | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.19/24.73  | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 158.19/24.73  | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 158.19/24.73  | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.19/24.73  | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 158.19/24.73  | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 158.19/24.73  | | | | | | | | | | | |            & $i(all_57_14))
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | BETA: splitting (135) gives:
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | |   (136)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 158.19/24.73  | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.19/24.73  | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.19/24.73  | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.19/24.73  | | | | | | | | | | | | |              e1) = e1)
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | BETA: splitting (136) gives:
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | |   (137)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 158.19/24.73  | | | | | | | | | | | | | |          ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.19/24.73  | | | | | | | | | | | | | |          op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | | | | |          e2 & $i(all_57_12)
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | ALPHA: (137) implies:
% 158.19/24.73  | | | | | | | | | | | | | |   (138)  op(e2, e0) = e2
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e3, e2, e0, e2, simplifying
% 158.19/24.73  | | | | | | | | | | | | | |              with (67), (138) gives:
% 158.19/24.73  | | | | | | | | | | | | | |   (139)  e3 = e2
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | REDUCE: (6), (139) imply:
% 158.19/24.73  | | | | | | | | | | | | | |   (140)  $false
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | Case 2:
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | |   (141)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) &
% 158.19/24.73  | | | | | | | | | | | | | |          op(e1, e2) = e1 & op(e1, e1) = e1
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | ALPHA: (141) implies:
% 158.19/24.73  | | | | | | | | | | | | | |   (142)  op(e1, e1) = e1
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | REF_CLOSE: (7), (38), (50), (142) are inconsistent by
% 158.19/24.73  | | | | | | | | | | | | | |            sub-proof #986.
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | End of split
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | Case 2:
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | |   (143)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.19/24.73  | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.19/24.73  | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.19/24.73  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 158.19/24.73  | | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 158.19/24.73  | | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.19/24.73  | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 158.19/24.73  | | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | BETA: splitting (143) gives:
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | |   (144)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.19/24.73  | | | | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.19/24.73  | | | | | | | | | | | | | |          op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.19/24.73  | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | ALPHA: (144) implies:
% 158.19/24.73  | | | | | | | | | | | | | |   (145)  op(e0, e0) = e3
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (19), (32), (38), (41), (43), (47),
% 158.19/24.73  | | | | | | | | | | | | | |            (66), (70), (145) are inconsistent by sub-proof
% 158.19/24.73  | | | | | | | | | | | | | |            #472.
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | Case 2:
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | |   (146)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 158.19/24.73  | | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 158.19/24.73  | | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.19/24.73  | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 158.19/24.73  | | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 158.19/24.73  | | | | | | | | | | | | | |            & $i(all_57_14))
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | |   (147)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 158.19/24.73  | | | | | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e1) = e3
% 158.19/24.73  | | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 158.19/24.73  | | | | | | | | | | | | | | |   (148)  op(e3, e3) = e3
% 158.19/24.73  | | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | | REF_CLOSE: (7), (25), (41), (148) are inconsistent by
% 158.19/24.73  | | | | | | | | | | | | | | |            sub-proof #995.
% 158.19/24.73  | | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | Case 2:
% 158.19/24.73  | | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | |   (149)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 158.19/24.73  | | | | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 158.19/24.73  | | | | | | | | | | | | | | |          = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.19/24.73  | | | | | | | | | | | | | | |          $i(all_57_14)
% 158.19/24.73  | | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 158.19/24.73  | | | | | | | | | | | | | | |   (150)  op(e1, e0) = e1
% 158.19/24.73  | | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e0, e1, e0, e1, simplifying
% 158.19/24.73  | | | | | | | | | | | | | | |              with (15), (150) gives:
% 158.19/24.73  | | | | | | | | | | | | | | |   (151)  e1 = e0
% 158.19/24.73  | | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | | REDUCE: (32), (151) imply:
% 158.19/24.73  | | | | | | | | | | | | | | |   (152)  $false
% 158.19/24.73  | | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | | CLOSE: (152) is inconsistent.
% 158.19/24.73  | | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | | End of split
% 158.19/24.73  | | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | End of split
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | End of split
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | End of split
% 158.19/24.73  | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | Case 2:
% 158.19/24.73  | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | |   (153)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.19/24.73  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.19/24.73  | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.19/24.73  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.19/24.73  | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.19/24.73  | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.19/24.73  | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 158.19/24.73  | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 158.19/24.73  | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 158.19/24.73  | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.19/24.73  | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.19/24.73  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 158.19/24.73  | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.19/24.73  | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.19/24.73  | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.19/24.73  | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 158.19/24.73  | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 158.19/24.73  | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 158.19/24.73  | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.19/24.73  | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.19/24.73  | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.19/24.73  | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.19/24.73  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.19/24.73  | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.19/24.73  | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.19/24.73  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.19/24.73  | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.19/24.73  | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.19/24.73  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.19/24.73  | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.19/24.73  | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.19/24.73  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.19/24.73  | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.19/24.73  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.73  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.19/24.73  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.19/24.73  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.73  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.19/24.73  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.19/24.73  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.73  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.19/24.73  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.19/24.73  | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.19/24.73  | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.19/24.73  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.19/24.73  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.19/24.73  | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.19/24.73  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.19/24.73  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.19/24.73  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.19/24.73  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.19/24.73  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.19/24.73  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.19/24.73  | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.19/24.73  | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.19/24.73  | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.19/24.73  | | | | | | | | | | |                e0)))
% 158.19/24.73  | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | BETA: splitting (153) gives:
% 158.19/24.73  | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | |   (154)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.19/24.73  | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.19/24.73  | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.19/24.73  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.19/24.73  | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.19/24.73  | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.19/24.73  | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 158.19/24.73  | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 158.19/24.73  | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 158.19/24.73  | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 158.19/24.73  | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.19/24.73  | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.19/24.73  | | | | | | | | | | | |            e3 & $i(all_57_10))
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | BETA: splitting (154) gives:
% 158.19/24.73  | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | Case 1:
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | |   (155)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.19/24.73  | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.19/24.73  | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.19/24.73  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.19/24.73  | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.19/24.73  | | | | | | | | | | | | |              e1) = e2)
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (33), (38), (40), (155) are inconsistent
% 158.19/24.73  | | | | | | | | | | | | |            by sub-proof #374.
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.73  | | | | | | | | | | | | Case 2:
% 158.19/24.73  | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | |   (156)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 158.19/24.74  | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 158.19/24.74  | | | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.19/24.74  | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 158.19/24.74  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 158.19/24.74  | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.19/24.74  | | | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.19/24.74  | | | | | | | | | | | | |            $i(all_57_10))
% 158.19/24.74  | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | BETA: splitting (156) gives:
% 158.19/24.74  | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | Case 1:
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | |   (157)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 158.19/24.74  | | | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 158.19/24.74  | | | | | | | | | | | | | |          = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.19/24.74  | | | | | | | | | | | | | |          $i(all_57_14)
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | ALPHA: (157) implies:
% 158.19/24.74  | | | | | | | | | | | | | |   (158)  op(e2, e2) = e1
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (38), (158) are inconsistent by
% 158.19/24.74  | | | | | | | | | | | | | |            sub-proof #993.
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | Case 2:
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | |   (159)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 158.19/24.74  | | | | | | | | | | | | | |          ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.19/24.74  | | | | | | | | | | | | | |          op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.19/24.74  | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | ALPHA: (159) implies:
% 158.19/24.74  | | | | | | | | | | | | | |   (160)  op(e0, e0) = e3
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (19), (32), (38), (41), (43), (47),
% 158.19/24.74  | | | | | | | | | | | | | |            (66), (70), (160) are inconsistent by sub-proof
% 158.19/24.74  | | | | | | | | | | | | | |            #472.
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | End of split
% 158.19/24.74  | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | End of split
% 158.19/24.74  | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | Case 2:
% 158.19/24.74  | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | |   (161)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 158.19/24.74  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.19/24.74  | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.19/24.74  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.19/24.74  | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.19/24.74  | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 158.19/24.74  | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 158.19/24.74  | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 158.19/24.74  | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 158.19/24.74  | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.19/24.74  | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.19/24.74  | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 158.19/24.74  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.19/24.74  | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 158.19/24.74  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 158.19/24.74  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.19/24.74  | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 158.19/24.74  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 158.19/24.74  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 158.19/24.74  | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 158.19/24.74  | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.19/24.74  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.19/24.74  | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.19/24.74  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 158.19/24.74  | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.19/24.74  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.19/24.74  | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.19/24.74  | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 158.19/24.74  | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 158.19/24.74  | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.74  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.19/24.74  | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 158.19/24.74  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.74  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.19/24.74  | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.19/24.74  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.74  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.19/24.74  | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.19/24.74  | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.19/24.74  | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.19/24.74  | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 158.19/24.74  | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.19/24.74  | | | | | | | | | | | |                op(e0, e1) = e0)))
% 158.19/24.74  | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | BETA: splitting (161) gives:
% 158.19/24.74  | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | Case 1:
% 158.19/24.74  | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | |   (162)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 158.19/24.74  | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.19/24.74  | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.19/24.74  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.19/24.74  | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.19/24.74  | | | | | | | | | | | | |              e0) = e3)
% 158.19/24.74  | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (25), (38), (41), (162) are inconsistent
% 158.19/24.74  | | | | | | | | | | | | |            by sub-proof #336.
% 158.19/24.74  | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | Case 2:
% 158.19/24.74  | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | |   (163)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.19/24.74  | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 158.19/24.74  | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 158.19/24.74  | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.19/24.74  | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.19/24.74  | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.19/24.74  | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.19/24.74  | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.19/24.74  | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.19/24.74  | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.19/24.74  | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.19/24.74  | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.19/24.74  | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.19/24.74  | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.74  | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.19/24.74  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.19/24.74  | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.74  | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.19/24.74  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.19/24.74  | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.74  | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.19/24.74  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.19/24.74  | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.19/24.74  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.19/24.74  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.19/24.74  | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.19/24.74  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.19/24.74  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.19/24.74  | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.19/24.74  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.19/24.74  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.19/24.74  | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.19/24.74  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.19/24.74  | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.19/24.74  | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.19/24.74  | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.19/24.74  | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.19/24.74  | | | | | | | | | | | | |                e0)))
% 158.19/24.74  | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | BETA: splitting (163) gives:
% 158.19/24.74  | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | Case 1:
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | |   (164)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.19/24.74  | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | ALPHA: (164) implies:
% 158.19/24.74  | | | | | | | | | | | | | |   (165)  op(e2, e0) = e2
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (67), (165) are inconsistent by
% 158.19/24.74  | | | | | | | | | | | | | |            sub-proof #580.
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | Case 2:
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | |   (166)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.19/24.74  | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.19/24.74  | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.19/24.74  | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.19/24.74  | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.19/24.74  | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.19/24.74  | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.19/24.74  | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.19/24.74  | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.19/24.74  | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.19/24.74  | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.74  | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.19/24.74  | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.19/24.74  | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.74  | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.19/24.74  | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.19/24.74  | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.74  | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.19/24.74  | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.19/24.74  | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.19/24.74  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.19/24.74  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.19/24.74  | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.19/24.74  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.19/24.74  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.19/24.74  | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.19/24.74  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.19/24.74  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.19/24.74  | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.19/24.74  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.19/24.74  | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.19/24.74  | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.19/24.74  | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.19/24.74  | | | | | | | | | | | | | |                e0)))
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 158.19/24.74  | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | Case 1:
% 158.19/24.74  | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | |   (167)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.19/24.74  | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 158.19/24.74  | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 158.19/24.74  | | | | | | | | | | | | | | |   (168)  op(e1, e1) = e1
% 158.19/24.74  | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | | REF_CLOSE: (7), (38), (50), (168) are inconsistent by
% 158.19/24.74  | | | | | | | | | | | | | | |            sub-proof #986.
% 158.19/24.74  | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | Case 2:
% 158.19/24.74  | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | |   (169)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.19/24.74  | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.19/24.74  | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.19/24.74  | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.19/24.74  | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.19/24.74  | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.19/24.74  | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.19/24.74  | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.19/24.74  | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.19/24.74  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.19/24.74  | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 158.19/24.74  | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.19/24.74  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.19/24.74  | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.19/24.74  | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.19/24.74  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.19/24.74  | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.19/24.74  | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.19/24.74  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 158.19/24.74  | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.19/24.74  | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.19/24.74  | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.19/24.74  | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.74  | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 158.19/24.74  | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.19/24.74  | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 158.19/24.74  | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.19/24.74  | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.19/24.74  | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.19/24.74  | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.19/24.74  | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.19/24.74  | | | | | | | | | | | | | | |              e0))
% 158.19/24.74  | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 158.19/24.74  | | | | | | | | | | | | | | |   (170)  op(e0, e0) = all_57_15
% 158.19/24.74  | | | | | | | | | | | | | | |   (171)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.19/24.74  | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.19/24.74  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.19/24.74  | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.19/24.74  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.19/24.74  | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.19/24.74  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.19/24.74  | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.19/24.74  | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.19/24.74  | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.19/24.74  | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.19/24.74  | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.74  | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.19/24.74  | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.19/24.74  | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.19/24.74  | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 158.19/24.74  | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.19/24.74  | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.19/24.74  | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.74  | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.19/24.74  | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.19/24.74  | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 158.19/24.74  | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 158.19/24.74  | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 158.19/24.74  | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.19/24.74  | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.19/24.74  | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.19/24.74  | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.19/24.74  | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.19/24.74  | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.19/24.74  | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 158.19/24.74  | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | | Case 1:
% 158.19/24.74  | | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | | |   (172)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.19/24.74  | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.19/24.74  | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.19/24.74  | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.19/24.74  | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.19/24.74  | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.19/24.74  | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.19/24.74  | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.19/24.74  | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.19/24.74  | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.19/24.74  | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.19/24.74  | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.74  | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.19/24.74  | | | | | | | | | | | | | | | |            e0)
% 158.19/24.74  | | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 158.19/24.74  | | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | | | Case 1:
% 158.19/24.74  | | | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | | | |   (173)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.19/24.74  | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.19/24.74  | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.19/24.74  | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.19/24.74  | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.19/24.74  | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.19/24.74  | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.19/24.74  | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.19/24.74  | | | | | | | | | | | | | | | | |            e0)
% 158.19/24.74  | | | | | | | | | | | | | | | | | 
% 158.19/24.74  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (43), (50), (67), (96), (173) are
% 158.19/24.74  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #112.
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | Case 2:
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | |   (174)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.19/24.75  | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 158.19/24.75  | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.19/24.75  | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.19/24.75  | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.19/24.75  | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.19/24.75  | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | Case 1:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | |   (175)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |          op(e0, e3) = e0
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 158.19/24.75  | | | | | | | | | | | | | | | | | |   (176)  op(e0, e3) = e0
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (96), (176) are inconsistent by
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            sub-proof #973.
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | Case 2:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | |   (177)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.19/24.75  | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.19/24.75  | | | | | | | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | Case 1:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | |   (178)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | | | |          = e3 & op(e0, e2) = e0
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | |   (179)  op(e3, e3) = e0
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (25), (32), (179) are inconsistent by
% 158.19/24.75  | | | | | | | | | | | | | | | | | | |            sub-proof #834.
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | Case 2:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | |   (180)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | | | |          = e2 & op(e0, e2) = e0
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | |   (181)  op(e2, e0) = e2
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (67), (181) are inconsistent by
% 158.19/24.75  | | | | | | | | | | | | | | | | | | |            sub-proof #580.
% 158.19/24.75  | | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | Case 2:
% 158.19/24.75  | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | |   (182)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.19/24.75  | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.19/24.75  | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.19/24.75  | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.19/24.75  | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.19/24.75  | | | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.19/24.75  | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.19/24.75  | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.75  | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.19/24.75  | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.19/24.75  | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.19/24.75  | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 158.19/24.75  | | | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 158.19/24.75  | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | Case 1:
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | |   (183)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.19/24.75  | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.19/24.75  | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.19/24.75  | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | Case 1:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | |   (184)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 158.19/24.75  | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | | |          = e1 & op(e0, e2) = e0
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 158.19/24.75  | | | | | | | | | | | | | | | | | |   (185)  op(e1, e1) = e0
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (43), (50), (185) are inconsistent by
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            sub-proof #914.
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | Case 2:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | |   (186)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (25), (32), (75), (186) are
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #641.
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | Case 2:
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | |   (187)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.19/24.75  | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.19/24.75  | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.19/24.75  | | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.19/24.75  | | | | | | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.19/24.75  | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.19/24.75  | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 158.19/24.75  | | | | | | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 158.19/24.75  | | | | | | | | | | | | | | | | |            = e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | Case 1:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | |   (188)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.19/24.75  | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.19/24.75  | | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (43), (50), (67), (188) are inconsistent
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            by sub-proof #111.
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | Case 2:
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | |   (189)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (15), (24), (32), (170), (189) are
% 158.19/24.75  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #289.
% 158.19/24.75  | | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | | 
% 158.19/24.75  | | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | | 
% 158.19/24.75  | | | | | | | | End of split
% 158.19/24.75  | | | | | | | | 
% 158.19/24.75  | | | | | | | End of split
% 158.19/24.75  | | | | | | | 
% 158.19/24.75  | | | | | | End of split
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | Case 2:
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | |   (190)  all_56_10 = e2 & op(e2, e0) = e2
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | | REF_CLOSE: (6), (66), (190) are inconsistent by sub-proof #470.
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | End of split
% 158.19/24.75  | | | | | 
% 158.19/24.75  | | | | Case 2:
% 158.19/24.75  | | | | | 
% 158.19/24.75  | | | | |   (191)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0,
% 158.19/24.75  | | | | |              e0) = e2)
% 158.19/24.75  | | | | | 
% 158.19/24.75  | | | | | BETA: splitting (191) gives:
% 158.19/24.75  | | | | | 
% 158.19/24.75  | | | | | Case 1:
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | |   (192)  all_56_11 = e2 & op(e1, e0) = e2
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | | ALPHA: (192) implies:
% 158.19/24.75  | | | | | |   (193)  all_56_11 = e2
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | | COMBINE_EQS: (8), (193) imply:
% 158.19/24.75  | | | | | |   (194)  e2 = e0
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | | REDUCE: (43), (194) imply:
% 158.19/24.75  | | | | | |   (195)  $false
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | | CLOSE: (195) is inconsistent.
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | Case 2:
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | |   (196)  all_56_15 = e2 & op(e0, e0) = e2
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | | ALPHA: (196) implies:
% 158.19/24.75  | | | | | |   (197)  op(e0, e0) = e2
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | | REF_CLOSE: (4), (7), (38), (197) are inconsistent by sub-proof #875.
% 158.19/24.75  | | | | | | 
% 158.19/24.75  | | | | | End of split
% 158.19/24.75  | | | | | 
% 158.19/24.75  | | | | End of split
% 158.19/24.75  | | | | 
% 158.19/24.75  | | | End of split
% 158.19/24.75  | | | 
% 158.19/24.75  | | End of split
% 158.19/24.75  | | 
% 158.19/24.75  | Case 2:
% 158.19/24.75  | | 
% 158.19/24.75  | |   (198)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3)
% 158.19/24.75  | | 
% 158.19/24.75  | | ALPHA: (198) implies:
% 158.19/24.75  | |   (199)   ~ (all_57_3 = e1)
% 158.19/24.75  | |   (200)  op(e1, e2) = all_57_3
% 158.19/24.75  | | 
% 158.19/24.75  | | REF_CLOSE: (7), (44), (199), (200) are inconsistent by sub-proof #631.
% 158.19/24.75  | | 
% 158.19/24.75  | End of split
% 158.19/24.75  | 
% 158.19/24.75  End of proof
% 158.19/24.75  
% 158.19/24.75  Sub-proof #111 shows that the following formulas are inconsistent:
% 158.19/24.75  ----------------------------------------------------------------
% 158.19/24.75    (1)   ~ (e3 = e2)
% 158.19/24.75    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.19/24.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.19/24.75    (3)  op(e1, e1) = e2
% 158.19/24.75    (4)  op(e2, e0) = e3
% 158.19/24.75    (5)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.19/24.75           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.19/24.75           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 158.19/24.75           & op(e1, e0) = e1 & op(e0, e1) = e0)
% 158.19/24.75    (6)   ~ (e2 = e0)
% 158.19/24.75  
% 158.19/24.75  Begin of proof
% 158.19/24.75  | 
% 158.19/24.75  | BETA: splitting (5) gives:
% 158.19/24.75  | 
% 158.19/24.75  | Case 1:
% 158.19/24.75  | | 
% 158.19/24.75  | |   (7)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1)
% 158.19/24.75  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 158.19/24.75  | | 
% 158.19/24.75  | | ALPHA: (7) implies:
% 158.19/24.75  | |   (8)  op(e2, e0) = e2
% 158.19/24.75  | | 
% 158.19/24.75  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #580.
% 158.19/24.75  | | 
% 158.19/24.75  | Case 2:
% 158.19/24.75  | | 
% 158.19/24.75  | |   (9)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1)
% 158.19/24.75  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 158.19/24.75  | | 
% 158.19/24.75  | | ALPHA: (9) implies:
% 158.19/24.75  | |   (10)  op(e1, e1) = e0
% 158.19/24.75  | | 
% 158.19/24.75  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #914.
% 158.19/24.75  | | 
% 158.19/24.75  | End of split
% 158.19/24.75  | 
% 158.19/24.75  End of proof
% 158.19/24.75  
% 158.19/24.75  Sub-proof #112 shows that the following formulas are inconsistent:
% 158.19/24.75  ----------------------------------------------------------------
% 158.19/24.75    (1)   ~ (e3 = e2)
% 158.19/24.75    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.19/24.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.19/24.75    (3)  op(e0, e3) = all_52_3
% 158.19/24.75    (4)  op(e1, e1) = e2
% 158.19/24.75    (5)   ~ (all_52_3 = e0)
% 158.19/24.75    (6)  op(e2, e0) = e3
% 158.19/24.75    (7)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.19/24.75           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.19/24.75           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 158.19/24.75           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 158.19/24.75           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 158.19/24.75           e1 & op(e0, e3) = e0)
% 158.19/24.75    (8)   ~ (e2 = e0)
% 158.19/24.75  
% 158.19/24.75  Begin of proof
% 158.19/24.75  | 
% 158.19/24.75  | BETA: splitting (7) gives:
% 158.19/24.75  | 
% 158.19/24.75  | Case 1:
% 158.19/24.75  | | 
% 158.19/24.75  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.19/24.75  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 158.19/24.75  | | 
% 158.19/24.75  | | ALPHA: (9) implies:
% 158.19/24.75  | |   (10)  op(e0, e3) = e0
% 158.19/24.75  | | 
% 158.19/24.75  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #973.
% 158.19/24.75  | | 
% 158.19/24.75  | Case 2:
% 158.19/24.75  | | 
% 158.19/24.75  | |   (11)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.19/24.75  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.19/24.75  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.19/24.75  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.19/24.75  | | 
% 158.19/24.75  | | BETA: splitting (11) gives:
% 158.19/24.75  | | 
% 158.19/24.75  | | Case 1:
% 158.19/24.75  | | | 
% 158.19/24.75  | | |   (12)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.19/24.75  | | |           e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 158.19/24.75  | | | 
% 158.19/24.75  | | | ALPHA: (12) implies:
% 158.19/24.75  | | |   (13)  op(e2, e0) = e2
% 158.19/24.75  | | | 
% 158.19/24.75  | | | REF_CLOSE: (1), (2), (6), (13) are inconsistent by sub-proof #580.
% 158.19/24.75  | | | 
% 158.19/24.75  | | Case 2:
% 158.19/24.75  | | | 
% 158.19/24.75  | | |   (14)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.19/24.75  | | |           e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 158.19/24.75  | | | 
% 158.19/24.75  | | | ALPHA: (14) implies:
% 158.19/24.75  | | |   (15)  op(e1, e1) = e0
% 158.19/24.75  | | | 
% 158.19/24.75  | | | REF_CLOSE: (2), (4), (8), (15) are inconsistent by sub-proof #914.
% 158.19/24.75  | | | 
% 158.19/24.75  | | End of split
% 158.19/24.75  | | 
% 158.19/24.75  | End of split
% 158.19/24.75  | 
% 158.19/24.75  End of proof
% 158.19/24.75  
% 158.19/24.75  Sub-proof #113 shows that the following formulas are inconsistent:
% 158.19/24.75  ----------------------------------------------------------------
% 158.19/24.75    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.19/24.75           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.19/24.75           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 158.19/24.75           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 158.19/24.75           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.19/24.75    (2)   ~ (e3 = e2)
% 158.19/24.75    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.19/24.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.19/24.75    (4)  op(e1, e1) = e2
% 158.19/24.75    (5)  op(e2, e2) = e2
% 158.19/24.75    (6)   ~ (e2 = e1)
% 158.19/24.75  
% 158.19/24.75  Begin of proof
% 158.19/24.75  | 
% 158.19/24.75  | BETA: splitting (1) gives:
% 158.19/24.75  | 
% 158.19/24.75  | Case 1:
% 158.19/24.75  | | 
% 158.19/24.75  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 158.19/24.75  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.19/24.75  | |          e1) = e3 & $i(all_57_10)
% 158.19/24.75  | | 
% 158.19/24.75  | | ALPHA: (7) implies:
% 158.19/24.75  | |   (8)  op(e1, e1) = e3
% 158.19/24.75  | | 
% 158.19/24.75  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #646.
% 158.19/24.75  | | 
% 158.19/24.75  | Case 2:
% 158.19/24.75  | | 
% 158.19/24.75  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 158.19/24.75  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 158.19/24.75  | |        all_57_14 & $i(all_57_14)
% 158.19/24.75  | | 
% 158.19/24.75  | | ALPHA: (9) implies:
% 158.19/24.75  | |   (10)  op(e2, e2) = e1
% 158.19/24.75  | | 
% 158.19/24.75  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #993.
% 158.19/24.75  | | 
% 158.19/24.75  | End of split
% 158.19/24.75  | 
% 158.19/24.75  End of proof
% 158.19/24.75  
% 158.19/24.75  Sub-proof #114 shows that the following formulas are inconsistent:
% 158.19/24.75  ----------------------------------------------------------------
% 158.19/24.75    (1)   ~ (all_52_1 = e2)
% 158.19/24.75    (2)   ~ (e3 = e2)
% 158.19/24.75    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.19/24.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.19/24.75    (4)  op(e1, e1) = e2
% 158.19/24.76    (5)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.19/24.76           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.19/24.76           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 158.19/24.76           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 158.19/24.76           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.19/24.76           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 158.19/24.76           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.19/24.76           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.19/24.76           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 158.19/24.76             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.19/24.76           all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 158.19/24.76           & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.19/24.76           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 158.19/24.76           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 158.19/24.76             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.19/24.76           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 158.19/24.76         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.19/24.76           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.19/24.76           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 158.19/24.76           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 158.19/24.76           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.19/24.76    (6)  op(e2, e3) = all_52_1
% 158.19/24.76    (7)  op(e2, e1) = all_52_9
% 158.19/24.76    (8)   ~ (all_52_9 = e2)
% 158.19/24.76  
% 158.19/24.76  Begin of proof
% 158.19/24.76  | 
% 158.19/24.76  | BETA: splitting (5) gives:
% 158.19/24.76  | 
% 158.19/24.76  | Case 1:
% 158.19/24.76  | | 
% 158.19/24.76  | |   (9)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 158.19/24.76  | |          & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 158.19/24.76  | |          = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.19/24.76  | |          all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.19/24.76  | |          op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.19/24.76  | |          $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 158.19/24.76  | |          ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.19/24.76  | |          op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 158.19/24.76  | |          & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.19/24.76  | |          = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.19/24.76  | |          $i(all_57_10))
% 158.19/24.76  | | 
% 158.19/24.76  | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #1005.
% 158.19/24.76  | | 
% 158.19/24.76  | Case 2:
% 158.19/24.76  | | 
% 158.19/24.76  | |   (10)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 158.19/24.76  | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0
% 158.19/24.76  | |           & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 =
% 158.19/24.76  | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 158.19/24.76  | |           & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.19/24.76  | |           $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.19/24.76  | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 158.19/24.76  | |           e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 158.19/24.76  | |           & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.19/24.76  | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &
% 158.19/24.76  | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2,
% 158.19/24.76  | |             e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.19/24.76  | | 
% 158.19/24.76  | | BETA: splitting (10) gives:
% 158.19/24.76  | | 
% 158.19/24.76  | | Case 1:
% 158.19/24.76  | | | 
% 158.19/24.76  | | |   (11)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 158.19/24.76  | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) =
% 158.19/24.76  | | |           e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.19/24.76  | | |           all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 158.19/24.76  | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.19/24.76  | | |             e2) = e3 & $i(all_57_10))
% 158.19/24.76  | | | 
% 158.19/24.76  | | | REF_CLOSE: (1), (3), (6), (11) are inconsistent by sub-proof #1004.
% 158.19/24.76  | | | 
% 158.19/24.76  | | Case 2:
% 158.19/24.76  | | | 
% 158.19/24.76  | | |   (12)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.19/24.76  | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 =
% 158.19/24.76  | | |           e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.19/24.76  | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.19/24.76  | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 =
% 158.19/24.76  | | |             e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.19/24.76  | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.19/24.76  | | | 
% 158.19/24.76  | | | BETA: splitting (12) gives:
% 158.19/24.76  | | | 
% 158.19/24.76  | | | Case 1:
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | |   (13)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 158.19/24.76  | | | |         & op(e2, e2) = e2
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | | ALPHA: (13) implies:
% 158.19/24.76  | | | |   (14)  op(e2, e3) = e2
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | | REF_CLOSE: (1), (3), (6), (14) are inconsistent by sub-proof #1007.
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | Case 2:
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | |   (15)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 158.19/24.76  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.19/24.76  | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 158.19/24.76  | | | |           & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.19/24.76  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.19/24.76  | | | |           op(e2, e1) = e2 & $i(all_57_12))
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | | REF_CLOSE: (2), (3), (4), (7), (8), (15) are inconsistent by sub-proof
% 158.19/24.76  | | | |            #140.
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | End of split
% 158.19/24.76  | | | 
% 158.19/24.76  | | End of split
% 158.19/24.76  | | 
% 158.19/24.76  | End of split
% 158.19/24.76  | 
% 158.19/24.76  End of proof
% 158.19/24.76  
% 158.19/24.76  Sub-proof #115 shows that the following formulas are inconsistent:
% 158.19/24.76  ----------------------------------------------------------------
% 158.19/24.76    (1)   ~ (e3 = e2)
% 158.19/24.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.19/24.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.19/24.76    (3)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.19/24.76         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.19/24.76    (4)  op(e1, e3) = all_52_2
% 158.19/24.76    (5)   ~ (all_52_2 = e3)
% 158.19/24.76    (6)  all_56_8 = e2
% 158.19/24.76    (7)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.19/24.76         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.19/24.76    (8)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.19/24.76         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.19/24.76    (9)  all_56_11 = e2 & op(e1, e0) = e2
% 158.19/24.76    (10)   ~ (e1 = e0)
% 158.19/24.76    (11)   ~ (e2 = e1)
% 158.19/24.76    (12)   ~ (e3 = e1)
% 158.19/24.76    (13)   ~ (e2 = e0)
% 158.19/24.76    (14)   ~ (e3 = e0)
% 158.19/24.76  
% 158.19/24.76  Begin of proof
% 158.19/24.76  | 
% 158.19/24.76  | ALPHA: (9) implies:
% 158.19/24.76  |   (15)  all_56_11 = e2
% 158.19/24.76  | 
% 158.19/24.76  | BETA: splitting (8) gives:
% 158.19/24.76  | 
% 158.19/24.76  | Case 1:
% 158.19/24.76  | | 
% 158.19/24.76  | |   (16)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) =
% 158.19/24.76  | |           e3)
% 158.19/24.76  | | 
% 158.19/24.76  | | BETA: splitting (16) gives:
% 158.19/24.76  | | 
% 158.19/24.76  | | Case 1:
% 158.19/24.76  | | | 
% 158.19/24.76  | | |   (17)  all_56_6 = e3 & op(e1, e3) = e3
% 158.19/24.76  | | | 
% 158.19/24.76  | | | REF_CLOSE: (2), (4), (5), (17) are inconsistent by sub-proof #681.
% 158.19/24.76  | | | 
% 158.19/24.76  | | Case 2:
% 158.19/24.76  | | | 
% 158.19/24.76  | | |   (18)  all_56_7 = e3 & op(e1, e2) = e3
% 158.19/24.76  | | | 
% 158.19/24.76  | | | ALPHA: (18) implies:
% 158.19/24.76  | | |   (19)  all_56_7 = e3
% 158.19/24.76  | | | 
% 158.19/24.76  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 158.19/24.76  | | |            (14), (15), (19) are inconsistent by sub-proof #183.
% 158.19/24.76  | | | 
% 158.19/24.76  | | End of split
% 158.19/24.76  | | 
% 158.19/24.76  | Case 2:
% 158.19/24.76  | | 
% 158.19/24.76  | |   (20)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) =
% 158.19/24.76  | |           e3)
% 158.19/24.76  | | 
% 158.19/24.76  | | BETA: splitting (20) gives:
% 158.19/24.76  | | 
% 158.19/24.76  | | Case 1:
% 158.19/24.76  | | | 
% 158.19/24.76  | | |   (21)  all_56_8 = e3 & op(e1, e1) = e3
% 158.19/24.76  | | | 
% 158.19/24.76  | | | REF_CLOSE: (1), (6), (21) are inconsistent by sub-proof #193.
% 158.19/24.76  | | | 
% 158.19/24.76  | | Case 2:
% 158.19/24.76  | | | 
% 158.19/24.76  | | |   (22)  all_56_11 = e3 & op(e1, e0) = e3
% 158.19/24.76  | | | 
% 158.19/24.76  | | | ALPHA: (22) implies:
% 158.19/24.76  | | |   (23)  all_56_11 = e3
% 158.19/24.76  | | | 
% 158.19/24.76  | | | REF_CLOSE: (1), (15), (23) are inconsistent by sub-proof #319.
% 158.19/24.76  | | | 
% 158.19/24.76  | | End of split
% 158.19/24.76  | | 
% 158.19/24.76  | End of split
% 158.19/24.76  | 
% 158.19/24.76  End of proof
% 158.19/24.76  
% 158.19/24.76  Sub-proof #116 shows that the following formulas are inconsistent:
% 158.19/24.76  ----------------------------------------------------------------
% 158.19/24.76    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.19/24.76         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.19/24.76    (2)  op(e0, e0) = e1
% 158.19/24.76    (3)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 158.19/24.76         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.19/24.76    (4)  all_56_9 = e2
% 158.19/24.76    (5)   ~ (e3 = e2)
% 158.19/24.76    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.19/24.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.19/24.76    (7)  op(e0, e3) = all_52_3
% 158.19/24.76    (8)  op(e3, e1) = all_52_8
% 158.19/24.76    (9)  all_56_13 = e1
% 158.19/24.76    (10)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 158.19/24.76          | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.19/24.76    (11)  op(e1, e1) = e2
% 158.19/24.76    (12)   ~ (all_4_2 = e3)
% 158.19/24.76    (13)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.19/24.76          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.19/24.76    (14)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 158.19/24.76          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.19/24.76    (15)  op(e1, e3) = all_52_2
% 158.19/24.76    (16)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.19/24.76          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.19/24.76    (17)  op(e1, e0) = e0
% 158.19/24.76    (18)  all_56_5 = e1
% 158.19/24.76    (19)  all_56_10 = e3
% 158.19/24.76    (20)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.19/24.76          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.19/24.76    (21)  op(e2, e2) = all_4_2
% 158.19/24.76    (22)  op(e3, e3) = e3
% 158.19/24.76    (23)   ~ (all_52_2 = e3)
% 158.19/24.76    (24)  all_56_8 = e2
% 158.19/24.76    (25)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.19/24.76          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.19/24.76    (26)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.19/24.76          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.19/24.76    (27)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.19/24.76          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 158.19/24.76            e2)
% 158.19/24.76    (28)   ~ (e1 = e0)
% 158.19/24.76    (29)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.19/24.76          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.19/24.76    (30)  op(e2, e0) = all_52_13
% 158.19/24.76    (31)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.19/24.76          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.19/24.76    (32)   ~ (e2 = e1)
% 158.19/24.76    (33)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.19/24.76          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.19/24.76    (34)   ~ (e3 = e1)
% 158.19/24.76    (35)   ~ (e2 = e0)
% 158.19/24.76    (36)   ~ (all_52_8 = e3)
% 158.19/24.76    (37)   ~ (e3 = e0)
% 158.19/24.76    (38)   ~ (all_52_13 = e2)
% 158.19/24.76  
% 158.19/24.76  Begin of proof
% 158.19/24.76  | 
% 158.19/24.76  | BETA: splitting (26) gives:
% 158.19/24.76  | 
% 158.19/24.76  | Case 1:
% 158.19/24.76  | | 
% 158.19/24.76  | |   (39)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) =
% 158.19/24.76  | |           e3)
% 158.19/24.76  | | 
% 158.19/24.76  | | BETA: splitting (39) gives:
% 158.19/24.76  | | 
% 158.19/24.76  | | Case 1:
% 158.19/24.76  | | | 
% 158.19/24.76  | | |   (40)  all_56_6 = e3 & op(e1, e3) = e3
% 158.19/24.76  | | | 
% 158.19/24.76  | | | REF_CLOSE: (6), (15), (23), (40) are inconsistent by sub-proof #681.
% 158.19/24.76  | | | 
% 158.19/24.76  | | Case 2:
% 158.19/24.76  | | | 
% 158.19/24.76  | | |   (41)  all_56_7 = e3 & op(e1, e2) = e3
% 158.19/24.76  | | | 
% 158.19/24.76  | | | ALPHA: (41) implies:
% 158.19/24.76  | | |   (42)  all_56_7 = e3
% 158.19/24.76  | | | 
% 158.19/24.76  | | | BETA: splitting (14) gives:
% 158.19/24.76  | | | 
% 158.19/24.76  | | | Case 1:
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | |   (43)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1)
% 158.19/24.76  | | | |           = e3)
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | | BETA: splitting (43) gives:
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | | Case 1:
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | |   (44)  all_56_4 = e3 & op(e3, e1) = e3
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | ALPHA: (44) implies:
% 158.19/24.76  | | | | |   (45)  op(e3, e1) = e3
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | REF_CLOSE: (6), (8), (36), (45) are inconsistent by sub-proof #982.
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | Case 2:
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | |   (46)  all_56_5 = e3 & op(e2, e1) = e3
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | ALPHA: (46) implies:
% 158.19/24.76  | | | | |   (47)  all_56_5 = e3
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | COMBINE_EQS: (18), (47) imply:
% 158.19/24.76  | | | | |   (48)  e3 = e1
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | SIMP: (48) implies:
% 158.19/24.76  | | | | |   (49)  e3 = e1
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | COMBINE_EQS: (19), (49) imply:
% 158.19/24.76  | | | | |   (50)  all_56_10 = e1
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | REF_CLOSE: (1), (5), (6), (12), (16), (18), (21), (22), (28), (29),
% 158.19/24.76  | | | | |            (32), (33), (34), (35), (37), (50) are inconsistent by
% 158.19/24.76  | | | | |            sub-proof #126.
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | End of split
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | Case 2:
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | |   (51)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1)
% 158.19/24.76  | | | |           = e3)
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | | BETA: splitting (51) gives:
% 158.19/24.76  | | | | 
% 158.19/24.76  | | | | Case 1:
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | |   (52)  all_56_8 = e3 & op(e1, e1) = e3
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | ALPHA: (52) implies:
% 158.19/24.76  | | | | |   (53)  op(e1, e1) = e3
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | REF_CLOSE: (5), (6), (11), (53) are inconsistent by sub-proof #646.
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | Case 2:
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | |   (54)  all_56_14 = e3 & op(e0, e1) = e3
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | ALPHA: (54) implies:
% 158.19/24.76  | | | | |   (55)  all_56_14 = e3
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | BETA: splitting (27) gives:
% 158.19/24.76  | | | | | 
% 158.19/24.76  | | | | | Case 1:
% 158.19/24.76  | | | | | | 
% 158.19/24.76  | | | | | |   (56)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 &
% 158.19/24.76  | | | | | |           op(e0, e2) = e2)
% 158.19/24.76  | | | | | | 
% 158.19/24.76  | | | | | | BETA: splitting (56) gives:
% 158.19/24.76  | | | | | | 
% 158.19/24.76  | | | | | | Case 1:
% 158.19/24.76  | | | | | | | 
% 158.19/24.76  | | | | | | |   (57)  all_56_12 = e2 & op(e0, e3) = e2
% 158.19/24.76  | | | | | | | 
% 158.19/24.76  | | | | | | | ALPHA: (57) implies:
% 158.19/24.76  | | | | | | |   (58)  op(e0, e3) = e2
% 158.19/24.76  | | | | | | | 
% 158.19/24.76  | | | | | | | REF_CLOSE: (6), (7), (9), (10), (28), (35), (37), (55), (58) are
% 158.19/24.76  | | | | | | |            inconsistent by sub-proof #130.
% 158.19/24.76  | | | | | | | 
% 158.19/24.76  | | | | | | Case 2:
% 158.19/24.76  | | | | | | | 
% 158.19/24.76  | | | | | | |   (59)  all_56_13 = e2 & op(e0, e2) = e2
% 158.19/24.76  | | | | | | | 
% 158.19/24.76  | | | | | | | ALPHA: (59) implies:
% 158.19/24.76  | | | | | | |   (60)  all_56_13 = e2
% 158.19/24.76  | | | | | | | 
% 158.19/24.76  | | | | | | | COMBINE_EQS: (9), (60) imply:
% 158.19/24.76  | | | | | | |   (61)  e2 = e1
% 158.19/24.76  | | | | | | | 
% 158.19/24.76  | | | | | | | COMBINE_EQS: (4), (61) imply:
% 158.19/24.76  | | | | | | |   (62)  all_56_9 = e1
% 158.19/24.76  | | | | | | | 
% 158.19/24.76  | | | | | | | BETA: splitting (20) gives:
% 158.19/24.76  | | | | | | | 
% 158.19/24.76  | | | | | | | Case 1:
% 158.19/24.76  | | | | | | | | 
% 158.19/24.76  | | | | | | | |   (63)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 &
% 158.19/24.76  | | | | | | | |           op(e2, e0) = e2)
% 158.19/24.76  | | | | | | | | 
% 158.19/24.76  | | | | | | | | BETA: splitting (63) gives:
% 158.19/24.76  | | | | | | | | 
% 158.19/24.76  | | | | | | | | Case 1:
% 158.19/24.76  | | | | | | | | | 
% 158.19/24.76  | | | | | | | | |   (64)  all_56_9 = e2 & op(e3, e0) = e2
% 158.19/24.76  | | | | | | | | | 
% 158.19/24.76  | | | | | | | | | REF_CLOSE: (4), (32), (62) are inconsistent by sub-proof #896.
% 158.19/24.76  | | | | | | | | | 
% 158.19/24.76  | | | | | | | | Case 2:
% 158.19/24.76  | | | | | | | | | 
% 158.19/24.76  | | | | | | | | |   (65)  all_56_10 = e2 & op(e2, e0) = e2
% 158.19/24.76  | | | | | | | | | 
% 158.19/24.76  | | | | | | | | | ALPHA: (65) implies:
% 158.19/24.76  | | | | | | | | |   (66)  op(e2, e0) = e2
% 158.19/24.76  | | | | | | | | | 
% 158.19/24.76  | | | | | | | | | REF_CLOSE: (6), (30), (38), (66) are inconsistent by sub-proof
% 158.19/24.77  | | | | | | | | |            #996.
% 158.19/24.77  | | | | | | | | | 
% 158.19/24.77  | | | | | | | | End of split
% 158.19/24.77  | | | | | | | | 
% 158.19/24.77  | | | | | | | Case 2:
% 158.19/24.77  | | | | | | | | 
% 158.19/24.77  | | | | | | | |   (67)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 &
% 158.19/24.77  | | | | | | | |           op(e0, e0) = e2)
% 158.19/24.77  | | | | | | | | 
% 158.19/24.77  | | | | | | | | REF_CLOSE: (2), (5), (6), (13), (15), (23), (24), (25), (26),
% 158.19/24.77  | | | | | | | |            (28), (32), (34), (35), (37), (42), (67) are
% 158.19/24.77  | | | | | | | |            inconsistent by sub-proof #124.
% 158.19/24.77  | | | | | | | | 
% 158.19/24.77  | | | | | | | End of split
% 158.19/24.77  | | | | | | | 
% 158.19/24.77  | | | | | | End of split
% 158.19/24.77  | | | | | | 
% 158.19/24.77  | | | | | Case 2:
% 158.19/24.77  | | | | | | 
% 158.19/24.77  | | | | | |   (68)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 &
% 158.19/24.77  | | | | | |           op(e0, e0) = e2)
% 158.19/24.77  | | | | | | 
% 158.19/24.77  | | | | | | BETA: splitting (68) gives:
% 158.19/24.77  | | | | | | 
% 158.19/24.77  | | | | | | Case 1:
% 158.19/24.77  | | | | | | | 
% 158.19/24.77  | | | | | | |   (69)  all_56_14 = e2 & op(e0, e1) = e2
% 158.19/24.77  | | | | | | | 
% 158.19/24.77  | | | | | | | ALPHA: (69) implies:
% 158.19/24.77  | | | | | | |   (70)  all_56_14 = e2
% 158.19/24.77  | | | | | | | 
% 158.19/24.77  | | | | | | | REF_CLOSE: (3), (5), (6), (8), (14), (24), (28), (31), (32), (34),
% 158.19/24.77  | | | | | | |            (35), (36), (37), (70) are inconsistent by sub-proof
% 158.19/24.77  | | | | | | |            #178.
% 158.19/24.77  | | | | | | | 
% 158.19/24.77  | | | | | | Case 2:
% 158.19/24.77  | | | | | | | 
% 158.19/24.77  | | | | | | |   (71)  all_56_15 = e2 & op(e0, e0) = e2
% 158.19/24.77  | | | | | | | 
% 158.19/24.77  | | | | | | | ALPHA: (71) implies:
% 158.19/24.77  | | | | | | |   (72)  op(e0, e0) = e2
% 158.19/24.77  | | | | | | | 
% 158.19/24.77  | | | | | | | REF_CLOSE: (2), (6), (32), (72) are inconsistent by sub-proof
% 158.19/24.77  | | | | | | |            #875.
% 158.19/24.77  | | | | | | | 
% 158.19/24.77  | | | | | | End of split
% 158.19/24.77  | | | | | | 
% 158.19/24.77  | | | | | End of split
% 158.19/24.77  | | | | | 
% 158.19/24.77  | | | | End of split
% 158.19/24.77  | | | | 
% 158.19/24.77  | | | End of split
% 158.19/24.77  | | | 
% 158.19/24.77  | | End of split
% 158.19/24.77  | | 
% 158.19/24.77  | Case 2:
% 158.19/24.77  | | 
% 158.19/24.77  | |   (73)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) =
% 158.19/24.77  | |           e3)
% 158.19/24.77  | | 
% 158.19/24.77  | | REF_CLOSE: (5), (6), (11), (17), (37), (73) are inconsistent by sub-proof
% 158.19/24.77  | |            #313.
% 158.19/24.77  | | 
% 158.19/24.77  | End of split
% 158.19/24.77  | 
% 158.19/24.77  End of proof
% 158.19/24.77  
% 158.19/24.77  Sub-proof #117 shows that the following formulas are inconsistent:
% 158.19/24.77  ----------------------------------------------------------------
% 158.19/24.77    (1)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.19/24.77    (2)   ~ (all_6_2 = e0)
% 158.19/24.77    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.19/24.77         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.19/24.77    (4)  all_54_5 = all_4_2
% 158.19/24.77    (5)   ~ (all_52_8 = all_6_2)
% 158.19/24.77    (6)   ~ (all_52_2 = all_6_2)
% 158.19/24.77    (7)  op(e0, e0) = e1
% 158.19/24.77    (8)  all_54_9 = all_52_6
% 158.19/24.77    (9)   ~ (all_52_6 = e1)
% 158.19/24.77    (10)   ~ (all_52_12 = e1)
% 158.19/24.77    (11)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.19/24.77          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.19/24.77    (12)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 158.19/24.77          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.19/24.77    (13)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.19/24.77          (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.19/24.77    (14)   ~ (all_24_2 = e1) | ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 &
% 158.19/24.77            $i(all_24_0)) | ( ~ (all_24_1 = e0) & op(e1, e1) = all_24_1 &
% 158.19/24.77            $i(all_24_1))
% 158.19/24.77    (15)   ~ (all_52_6 = e2)
% 158.19/24.77    (16)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.19/24.77          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 158.19/24.77    (17)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.19/24.77    (18)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 158.19/24.77              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.19/24.77            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.19/24.77                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 158.19/24.77              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.19/24.77          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 158.19/24.77              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.19/24.77            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.19/24.77                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 158.19/24.77              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.19/24.77          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 158.19/24.77              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.19/24.77            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.19/24.77                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 158.19/24.77              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.19/24.77          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 158.19/24.77              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.19/24.77            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 158.19/24.77                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 158.19/24.77                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.19/24.77                $i(all_57_13))))
% 158.19/24.77    (19)   ~ (all_52_4 = all_52_6)
% 158.19/24.77    (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.19/24.77          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.19/24.77    (21)  ( ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 & $i(all_10_0)) | ( ~
% 158.19/24.77            (all_10_1 = e0) & op(e2, e2) = all_10_1 & $i(all_10_1))
% 158.19/24.77    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.19/24.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.19/24.77    (23)  op(e0, e3) = all_52_3
% 158.19/24.77    (24)  op(e3, e1) = all_52_8
% 158.19/24.77    (25)   ~ (all_52_12 = all_6_2)
% 158.19/24.77    (26)   ~ (all_52_9 = all_4_2)
% 158.19/24.77    (27)  op(e1, e1) = e2
% 158.19/24.77    (28)   ~ (all_4_2 = e3)
% 158.19/24.77    (29)   ~ (all_52_6 = e0)
% 158.19/24.77    (30)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.19/24.77              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 158.19/24.77                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.19/24.77                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.19/24.77    (31)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.19/24.77          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.19/24.77    (32)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 158.19/24.77          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.19/24.77    (33)  op(e1, e3) = all_52_2
% 158.19/24.77    (34)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.19/24.77          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.19/24.77    (35)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.19/24.77          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.19/24.77    (36)   ~ (all_52_13 = all_4_2)
% 158.19/24.77    (37)  all_54_3 = all_52_12
% 158.19/24.77    (38)  op(e1, e0) = e0
% 158.19/24.77    (39)   ~ (all_52_2 = e2)
% 158.19/24.77    (40)  op(e1, e2) = all_52_6
% 158.19/24.77    (41)   ~ (all_52_12 = all_52_13)
% 158.19/24.77    (42)  op(e1, e0) = all_52_14
% 158.19/24.77    (43)  all_24_2 = all_4_2
% 158.19/24.77    (44)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.19/24.77          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.19/24.77    (45)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.19/24.77          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.19/24.77    (46)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.19/24.77          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.19/24.77    (47)  op(e2, e2) = all_4_2
% 158.19/24.77    (48)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 158.19/24.77    (49)   ~ (all_52_2 = all_52_6)
% 158.19/24.77    (50)  all_56_8 = e2
% 158.19/24.77    (51)  op(e0, e0) = all_14_2
% 158.19/24.77    (52)  op(e2, e3) = all_52_1
% 158.19/24.77    (53)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.19/24.77          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.19/24.77    (54)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.19/24.77          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.19/24.77    (55)  op(e3, e2) = all_52_4
% 158.19/24.77    (56)  all_54_0 = all_6_2
% 158.19/24.77    (57)  op(e2, e2) = e1
% 158.19/24.77    (58)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.19/24.77          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.19/24.77    (59)   ~ (e1 = e0)
% 158.19/24.77    (60)  op(e2, e1) = all_52_9
% 158.19/24.77    (61)   ~ (all_52_8 = all_52_9)
% 158.19/24.77    (62)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.19/24.77          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.19/24.77    (63)  op(e2, e0) = all_52_13
% 158.19/24.77    (64)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.19/24.77          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.19/24.77    (65)   ~ (e2 = e1)
% 158.19/24.77    (66)  op(e3, e3) = all_6_2
% 158.19/24.77    (67)  op(e3, e0) = all_52_12
% 158.19/24.77    (68)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.19/24.77          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.19/24.77            e3)
% 158.19/24.77    (69)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.19/24.77          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.19/24.77    (70)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.19/24.77          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.19/24.77    (71)   ~ (all_52_8 = e2)
% 158.19/24.77    (72)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.19/24.77          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.19/24.77    (73)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 158.32/24.78    (74)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.32/24.78            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.32/24.78            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.32/24.78            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.78              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.78          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.32/24.78            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.32/24.78              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.32/24.78            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.78              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.78          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.32/24.78            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.32/24.78              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.32/24.78            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.78              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.78          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.32/24.78            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.32/24.78            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.32/24.78              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.32/24.78            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.32/24.78            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.32/24.78            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.78            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.32/24.78              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.32/24.78            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.32/24.78          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.32/24.78            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.32/24.78              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.32/24.78            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.32/24.78            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.32/24.78          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.32/24.78            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.32/24.78              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.32/24.78            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.32/24.78            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.32/24.78          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.32/24.78            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.32/24.78              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.32/24.78            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.78              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.32/24.78          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.32/24.78            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.32/24.78            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.32/24.78            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.32/24.78            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.32/24.78            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.32/24.78            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.32/24.78            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.32/24.78              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.32/24.78            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.32/24.78            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.32/24.78            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.32/24.78            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.32/24.78              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.32/24.78            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.32/24.78          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.32/24.78            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.32/24.78              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.32/24.78              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.32/24.78            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.32/24.78            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.78            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.78            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.32/24.78              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.32/24.78            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.32/24.78          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.32/24.78            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.32/24.78              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.32/24.78            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.78              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.32/24.78          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.32/24.78            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.32/24.78              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.32/24.78              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.32/24.78            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.32/24.78          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.32/24.78            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.32/24.78            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.32/24.78                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.32/24.78                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.32/24.78                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.32/24.78                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.32/24.78                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.32/24.78                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.32/24.78                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.78                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.32/24.78                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.78                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.32/24.78                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.78                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.32/24.78                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.32/24.78                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.78                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.78                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.78                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.78                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.78                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.78                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.32/24.78                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.32/24.78                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.32/24.78                op(e0, e1) = e0)))
% 158.32/24.78    (75)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.32/24.78          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.32/24.78            e1)
% 158.32/24.78    (76)   ~ (all_52_2 = e0)
% 158.32/24.78    (77)   ~ (all_52_9 = e2)
% 158.32/24.78    (78)   ~ (all_6_2 = e2)
% 158.32/24.78    (79)   ~ (all_52_1 = all_4_2)
% 158.32/24.78    (80)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.32/24.78    (81)   ~ (e2 = e0)
% 158.32/24.78    (82)  all_54_8 = all_52_2
% 158.32/24.78  
% 158.32/24.78  Begin of proof
% 158.32/24.78  | 
% 158.32/24.78  | BETA: splitting (1) gives:
% 158.32/24.78  | 
% 158.32/24.78  | Case 1:
% 158.32/24.78  | | 
% 158.32/24.78  | |   (83)  all_54_9 = e3
% 158.32/24.78  | | 
% 158.32/24.78  | | COMBINE_EQS: (8), (83) imply:
% 158.32/24.78  | |   (84)  all_52_6 = e3
% 158.32/24.78  | | 
% 158.32/24.78  | | SIMP: (84) implies:
% 158.32/24.78  | |   (85)  all_52_6 = e3
% 158.32/24.78  | | 
% 158.32/24.78  | | REDUCE: (49), (85) imply:
% 158.32/24.78  | |   (86)   ~ (all_52_2 = e3)
% 158.32/24.78  | | 
% 158.32/24.78  | | REDUCE: (15), (85) imply:
% 158.32/24.78  | |   (87)   ~ (e3 = e2)
% 158.32/24.78  | | 
% 158.32/24.78  | | REDUCE: (9), (85) imply:
% 158.32/24.78  | |   (88)   ~ (e3 = e1)
% 158.32/24.78  | | 
% 158.32/24.78  | | REDUCE: (29), (85) imply:
% 158.32/24.78  | |   (89)   ~ (e3 = e0)
% 158.32/24.78  | | 
% 158.32/24.78  | | BETA: splitting (80) gives:
% 158.32/24.78  | | 
% 158.32/24.78  | | Case 1:
% 158.32/24.78  | | | 
% 158.32/24.78  | | |   (90)  all_54_8 = e3
% 158.32/24.78  | | | 
% 158.32/24.78  | | | REF_CLOSE: (82), (86), (90) are inconsistent by sub-proof #309.
% 158.32/24.78  | | | 
% 158.32/24.78  | | Case 2:
% 158.32/24.78  | | | 
% 158.32/24.78  | | |   (91)   ~ (all_54_8 = e3)
% 158.32/24.78  | | |   (92)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.32/24.78  | | | 
% 158.32/24.78  | | | BETA: splitting (92) gives:
% 158.32/24.78  | | | 
% 158.32/24.78  | | | Case 1:
% 158.32/24.78  | | | | 
% 158.32/24.78  | | | |   (93)  all_54_8 = e2
% 158.32/24.78  | | | | 
% 158.32/24.78  | | | | REF_CLOSE: (39), (82), (93) are inconsistent by sub-proof #608.
% 158.32/24.78  | | | | 
% 158.32/24.78  | | | Case 2:
% 158.32/24.78  | | | | 
% 158.32/24.78  | | | |   (94)   ~ (all_54_8 = e2)
% 158.32/24.78  | | | |   (95)  all_54_8 = e1 | all_54_8 = e0
% 158.32/24.78  | | | | 
% 158.32/24.78  | | | | BETA: splitting (18) gives:
% 158.32/24.78  | | | | 
% 158.32/24.78  | | | | Case 1:
% 158.32/24.78  | | | | | 
% 158.32/24.78  | | | | |   (96)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2,
% 158.32/24.78  | | | | |                 e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 158.32/24.78  | | | | |               all_57_0 & $i(all_57_0))) & ((all_57_14 = e3 & op(e1,
% 158.32/24.78  | | | | |                 e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 158.32/24.78  | | | | |               all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 158.32/24.78  | | | | |                 e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 158.32/24.78  | | | | |               all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 158.32/24.78  | | | | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 158.32/24.78  | | | | |               (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1)))
% 158.32/24.78  | | | | |           & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1)
% 158.32/24.78  | | | | |               & op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 =
% 158.32/24.78  | | | | |               e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2)
% 158.32/24.78  | | | | |               = all_57_7 & $i(all_57_7))))
% 158.32/24.78  | | | | | 
% 158.32/24.78  | | | | | BETA: splitting (96) gives:
% 158.32/24.78  | | | | | 
% 158.32/24.78  | | | | | Case 1:
% 158.32/24.78  | | | | | | 
% 158.32/24.78  | | | | | |   (97)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2,
% 158.32/24.78  | | | | | |               e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 158.32/24.78  | | | | | |             all_57_0 & $i(all_57_0))) & ((all_57_14 = e3 & op(e1,
% 158.32/24.78  | | | | | |               e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 158.32/24.78  | | | | | |             all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 158.32/24.78  | | | | | |               e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 158.32/24.78  | | | | | |             all_57_6 & $i(all_57_6)))
% 158.32/24.78  | | | | | | 
% 158.32/24.78  | | | | | | ALPHA: (97) implies:
% 158.32/24.78  | | | | | |   (98)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 158.32/24.78  | | | | | |           op(e2, e3) = all_57_0 & $i(all_57_0))
% 158.32/24.78  | | | | | | 
% 158.32/24.78  | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12), (13),
% 158.32/24.78  | | | | | |            (14), (16), (17), (18), (19), (20), (21), (22), (23),
% 158.32/24.78  | | | | | |            (24), (25), (26), (27), (28), (30), (31), (32), (33),
% 158.32/24.78  | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 158.32/24.78  | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 158.32/24.78  | | | | | |            (52), (53), (54), (55), (56), (57), (58), (60), (61),
% 158.32/24.78  | | | | | |            (62), (63), (64), (66), (67), (68), (69), (70), (71),
% 158.32/24.78  | | | | | |            (72), (73), (74), (75), (76), (77), (78), (79), (81),
% 158.32/24.78  | | | | | |            (82), (86), (87), (88), (89), (95), (98) are inconsistent
% 158.32/24.78  | | | | | |            by sub-proof #123.
% 158.32/24.78  | | | | | | 
% 158.32/24.78  | | | | | Case 2:
% 158.32/24.78  | | | | | | 
% 158.32/24.78  | | | | | |   (99)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3,
% 158.32/24.78  | | | | | |               e3) = e2) | ( ~ (all_57_1 = e3) & op(e3, e2) =
% 158.32/24.78  | | | | | |             all_57_1 & $i(all_57_1))) & ((all_57_14 = e2 & op(e1,
% 158.32/24.78  | | | | | |               e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 158.32/24.78  | | | | | |             all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 158.32/24.78  | | | | | |               e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 158.32/24.78  | | | | | |             all_57_7 & $i(all_57_7)))
% 158.32/24.78  | | | | | | 
% 158.32/24.78  | | | | | | ALPHA: (99) implies:
% 158.32/24.78  | | | | | |   (100)  op(e2, e2) = e2
% 158.32/24.78  | | | | | | 
% 158.32/24.78  | | | | | | REF_CLOSE: (22), (57), (65), (100) are inconsistent by sub-proof
% 158.32/24.78  | | | | | |            #993.
% 158.32/24.78  | | | | | | 
% 158.32/24.78  | | | | | End of split
% 158.32/24.78  | | | | | 
% 158.32/24.78  | | | | Case 2:
% 158.32/24.78  | | | | | 
% 158.32/24.78  | | | | |   (101)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 158.32/24.78  | | | | |                  e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) =
% 158.32/24.78  | | | | |                all_57_4 & $i(all_57_4))) & ((all_57_12 = e1 & op(e2,
% 158.32/24.78  | | | | |                  e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 158.32/24.78  | | | | |                all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 158.32/24.78  | | | | |                  e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 158.32/24.78  | | | | |                all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 158.32/24.78  | | | | |              e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 158.32/24.78  | | | | |                (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 158.32/24.78  | | | | |                $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) |
% 158.32/24.78  | | | | |              ( ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 158.32/24.78  | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0) |
% 158.32/24.78  | | | | |              ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.32/24.78  | | | | |                $i(all_57_13))))
% 158.32/24.78  | | | | | 
% 158.32/24.78  | | | | | REF_CLOSE: (7), (22), (27), (51), (59), (65), (101) are inconsistent
% 158.32/24.78  | | | | |            by sub-proof #748.
% 158.32/24.78  | | | | | 
% 158.32/24.78  | | | | End of split
% 158.32/24.78  | | | | 
% 158.32/24.78  | | | End of split
% 158.32/24.78  | | | 
% 158.32/24.78  | | End of split
% 158.32/24.78  | | 
% 158.32/24.78  | Case 2:
% 158.32/24.78  | | 
% 158.32/24.78  | |   (102)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.32/24.78  | | 
% 158.32/24.78  | | REF_CLOSE: (8), (9), (15), (29), (102) are inconsistent by sub-proof #673.
% 158.32/24.78  | | 
% 158.32/24.78  | End of split
% 158.32/24.78  | 
% 158.32/24.78  End of proof
% 158.32/24.78  
% 158.32/24.78  Sub-proof #118 shows that the following formulas are inconsistent:
% 158.32/24.78  ----------------------------------------------------------------
% 158.32/24.78    (1)  op(e0, e0) = e1
% 158.32/24.78    (2)  all_56_9 = e2
% 158.32/24.78    (3)   ~ (e3 = e2)
% 158.32/24.78    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.32/24.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.32/24.78    (5)  op(e1, e1) = e2
% 158.32/24.78    (6)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.32/24.78    (7)  op(e1, e0) = e0
% 158.32/24.78    (8)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 158.32/24.78         (all_56_11 = e0 & op(e1, e0) = e0)
% 158.32/24.78    (9)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.32/24.78         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.32/24.78    (10)   ~ (e1 = e0)
% 158.32/24.78    (11)   ~ (e2 = e1)
% 158.32/24.78    (12)   ~ (e3 = e1)
% 158.32/24.78    (13)   ~ (e2 = e0)
% 158.32/24.78    (14)   ~ (e3 = e0)
% 158.32/24.78  
% 158.32/24.78  Begin of proof
% 158.32/24.78  | 
% 158.32/24.78  | BETA: splitting (6) gives:
% 158.32/24.78  | 
% 158.32/24.78  | Case 1:
% 158.32/24.78  | | 
% 158.32/24.78  | |   (15)  all_56_8 = e1 & op(e1, e1) = e1
% 158.32/24.78  | | 
% 158.32/24.78  | | ALPHA: (15) implies:
% 158.32/24.78  | |   (16)  op(e1, e1) = e1
% 158.32/24.78  | | 
% 158.32/24.78  | | REF_CLOSE: (4), (5), (11), (16) are inconsistent by sub-proof #986.
% 158.32/24.78  | | 
% 158.32/24.78  | Case 2:
% 158.32/24.78  | | 
% 158.32/24.78  | |   (17)  all_56_11 = e1 & op(e1, e0) = e1
% 158.32/24.78  | | 
% 158.32/24.78  | | ALPHA: (17) implies:
% 158.32/24.78  | |   (18)  all_56_11 = e1
% 158.32/24.78  | | 
% 158.32/24.78  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (12), (13), (14), (18)
% 158.32/24.78  | |            are inconsistent by sub-proof #133.
% 158.32/24.78  | | 
% 158.32/24.78  | End of split
% 158.32/24.78  | 
% 158.32/24.78  End of proof
% 158.32/24.78  
% 158.32/24.78  Sub-proof #119 shows that the following formulas are inconsistent:
% 158.32/24.78  ----------------------------------------------------------------
% 158.32/24.78    (1)  op(e0, e0) = e1
% 158.32/24.78    (2)   ~ (e3 = e2)
% 158.32/24.78    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.32/24.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.32/24.78    (4)  op(e0, e3) = all_52_3
% 158.32/24.78    (5)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 158.32/24.78         (all_56_14 = e0 & op(e0, e1) = e0)
% 158.32/24.78    (6)  all_56_14 = e1
% 158.32/24.78    (7)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2) |
% 158.32/24.78         (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.32/24.78    (8)   ~ (e1 = e0)
% 158.32/24.78    (9)   ~ (e2 = e1)
% 158.32/24.78    (10)  all_56_13 = e3
% 158.32/24.78    (11)   ~ (e2 = e0)
% 158.32/24.78    (12)   ~ (e3 = e0)
% 158.32/24.78  
% 158.32/24.78  Begin of proof
% 158.32/24.78  | 
% 158.32/24.78  | BETA: splitting (5) gives:
% 158.32/24.78  | 
% 158.32/24.78  | Case 1:
% 158.32/24.78  | | 
% 158.32/24.78  | |   (13)  all_56_12 = e0 & op(e0, e3) = e0
% 158.32/24.78  | | 
% 158.32/24.78  | | ALPHA: (13) implies:
% 158.32/24.78  | |   (14)  op(e0, e3) = e0
% 158.32/24.78  | | 
% 158.32/24.78  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (14) are
% 158.32/24.78  | |            inconsistent by sub-proof #685.
% 158.32/24.78  | | 
% 158.32/24.78  | Case 2:
% 158.32/24.78  | | 
% 158.32/24.78  | |   (15)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 158.32/24.78  | |           e0)
% 158.32/24.78  | | 
% 158.32/24.78  | | BETA: splitting (15) gives:
% 158.32/24.78  | | 
% 158.32/24.78  | | Case 1:
% 158.32/24.78  | | | 
% 158.32/24.78  | | |   (16)  all_56_13 = e0 & op(e0, e2) = e0
% 158.32/24.78  | | | 
% 158.32/24.78  | | | REF_CLOSE: (10), (12), (16) are inconsistent by sub-proof #298.
% 158.32/24.78  | | | 
% 158.32/24.78  | | Case 2:
% 158.32/24.78  | | | 
% 158.32/24.78  | | |   (17)  all_56_14 = e0 & op(e0, e1) = e0
% 158.32/24.78  | | | 
% 158.32/24.78  | | | ALPHA: (17) implies:
% 158.32/24.78  | | |   (18)  all_56_14 = e0
% 158.32/24.78  | | | 
% 158.32/24.78  | | | REF_CLOSE: (6), (8), (18) are inconsistent by sub-proof #542.
% 158.32/24.78  | | | 
% 158.32/24.78  | | End of split
% 158.32/24.78  | | 
% 158.32/24.78  | End of split
% 158.32/24.78  | 
% 158.32/24.78  End of proof
% 158.32/24.78  
% 158.32/24.78  Sub-proof #120 shows that the following formulas are inconsistent:
% 158.32/24.78  ----------------------------------------------------------------
% 158.32/24.78    (1)   ~ (all_6_2 = e0)
% 158.32/24.78    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.32/24.78         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.32/24.78    (3)  all_54_5 = all_4_2
% 158.32/24.78    (4)   ~ (all_52_8 = all_6_2)
% 158.32/24.78    (5)   ~ (all_52_2 = all_6_2)
% 158.32/24.78    (6)  op(e0, e0) = e1
% 158.32/24.78    (7)   ~ (all_52_12 = e1)
% 158.32/24.78    (8)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.32/24.78         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.32/24.78    (9)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 158.32/24.78         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.32/24.78    (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.32/24.78          (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.32/24.78    (11)   ~ (all_24_2 = e1) | ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 &
% 158.32/24.78            $i(all_24_0)) | ( ~ (all_24_1 = e0) & op(e1, e1) = all_24_1 &
% 158.32/24.78            $i(all_24_1))
% 158.32/24.78    (12)   ~ (all_52_4 = e3)
% 158.32/24.78    (13)  op(e3, e2) = e1
% 158.32/24.78    (14)  all_54_13 = all_52_7
% 158.32/24.78    (15)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.32/24.78          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 158.32/24.78    (16)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.32/24.79    (17)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 158.32/24.79              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.32/24.79            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.32/24.79                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 158.32/24.79              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.32/24.79          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 158.32/24.79              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.32/24.79            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.32/24.79                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 158.32/24.79              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.32/24.79          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 158.32/24.79              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.32/24.79            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.32/24.79                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 158.32/24.79              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.32/24.79          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 158.32/24.79              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.32/24.79            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 158.32/24.79                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 158.32/24.79                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.32/24.79                $i(all_57_13))))
% 158.32/24.79    (18)   ~ (all_52_4 = all_52_6)
% 158.32/24.79    (19)  all_56_9 = e2
% 158.32/24.79    (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.32/24.79          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.32/24.79    (21)  op(e0, e1) = all_52_11
% 158.32/24.79    (22)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.32/24.79    (23)   ~ (e3 = e2)
% 158.32/24.79    (24)  ( ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 & $i(all_10_0)) | ( ~
% 158.32/24.79            (all_10_1 = e0) & op(e2, e2) = all_10_1 & $i(all_10_1))
% 158.32/24.79    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.32/24.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.32/24.79    (26)  op(e0, e3) = all_52_3
% 158.32/24.79    (27)  op(e3, e1) = all_52_8
% 158.32/24.79    (28)   ~ (all_52_12 = all_6_2)
% 158.32/24.79    (29)   ~ (all_52_12 = e3)
% 158.32/24.79    (30)   ~ (all_52_9 = all_4_2)
% 158.32/24.79    (31)  op(e1, e1) = e2
% 158.32/24.79    (32)   ~ (all_4_2 = e3)
% 158.32/24.79    (33)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.32/24.79              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 158.32/24.79                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.32/24.79                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.32/24.79    (34)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.32/24.79          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.32/24.79    (35)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 158.32/24.79          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.32/24.79    (36)  op(e1, e3) = all_52_2
% 158.32/24.79    (37)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.32/24.79          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.32/24.79    (38)  op(e0, e2) = all_52_7
% 158.32/24.79    (39)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.32/24.79          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.32/24.79    (40)   ~ (all_52_13 = all_4_2)
% 158.32/24.79    (41)  all_54_3 = all_52_12
% 158.32/24.79    (42)  op(e1, e0) = e0
% 158.32/24.79    (43)  all_56_5 = e1
% 158.32/24.79    (44)   ~ (all_52_2 = e2)
% 158.32/24.79    (45)  op(e1, e2) = all_52_6
% 158.32/24.79    (46)  all_56_10 = e3
% 158.32/24.79    (47)   ~ (all_52_12 = all_52_13)
% 158.32/24.79    (48)  op(e1, e0) = all_52_14
% 158.32/24.79    (49)  all_24_2 = all_4_2
% 158.32/24.79    (50)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.32/24.79          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.32/24.79    (51)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.32/24.79          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.32/24.79    (52)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.32/24.79          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.32/24.79    (53)  op(e2, e2) = all_4_2
% 158.32/24.79    (54)  all_56_1 = e1
% 158.32/24.79    (55)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 158.32/24.79    (56)   ~ (all_52_2 = all_52_6)
% 158.32/24.79    (57)  op(e3, e3) = e3
% 158.32/24.79    (58)   ~ (all_52_4 = all_52_7)
% 158.32/24.79    (59)   ~ (all_52_2 = e3)
% 158.32/24.79    (60)  all_56_8 = e2
% 158.32/24.79    (61)  op(e0, e0) = all_14_2
% 158.32/24.79    (62)  op(e2, e3) = all_52_1
% 158.32/24.79    (63)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.32/24.79          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.32/24.79    (64)  op(e1, e2) = e3
% 158.32/24.79    (65)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.32/24.79          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.32/24.79    (66)  op(e3, e2) = all_52_4
% 158.32/24.79    (67)   ~ (all_52_7 = all_4_2)
% 158.32/24.79    (68)  all_54_0 = all_6_2
% 158.32/24.79    (69)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.32/24.79          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.32/24.79    (70)   ~ (e1 = e0)
% 158.32/24.79    (71)  op(e2, e1) = all_52_9
% 158.32/24.79    (72)   ~ (all_52_8 = all_52_9)
% 158.32/24.79    (73)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.32/24.79          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.32/24.79    (74)  op(e2, e0) = all_52_13
% 158.32/24.79    (75)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.32/24.79          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.32/24.79    (76)   ~ (e2 = e1)
% 158.32/24.79    (77)  op(e3, e3) = all_6_2
% 158.32/24.79    (78)  op(e3, e0) = all_52_12
% 158.32/24.79    (79)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.32/24.79          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.32/24.79            e3)
% 158.32/24.79    (80)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.32/24.79          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.32/24.79    (81)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.32/24.79          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.32/24.79    (82)   ~ (all_52_8 = e2)
% 158.32/24.79    (83)  all_54_8 = e1 | all_54_8 = e0
% 158.32/24.79    (84)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.32/24.79          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.32/24.79    (85)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 158.32/24.79    (86)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.32/24.79            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.32/24.79            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.32/24.79            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.79              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.79          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.32/24.79            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.32/24.79              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.32/24.79            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.79              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.79          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.32/24.79            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.32/24.79              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.32/24.79            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.79              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.79          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.32/24.79            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.32/24.79            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.32/24.79              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.32/24.79            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.32/24.79            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.32/24.79            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.79            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.32/24.79              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.32/24.79            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.32/24.79          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.32/24.79            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.32/24.79              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.32/24.79            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.32/24.79            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.32/24.79          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.32/24.79            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.32/24.79              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.32/24.79            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.32/24.79            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.32/24.79          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.32/24.79            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.32/24.79              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.32/24.79            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.79              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.32/24.79          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.32/24.79            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.32/24.79            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.32/24.79            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.32/24.79            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.32/24.79            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.32/24.79            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.32/24.79            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.32/24.79              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.32/24.79            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.32/24.79            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.32/24.79            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.32/24.79            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.32/24.79              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.32/24.79            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.32/24.79          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.32/24.79            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.32/24.79              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.32/24.79              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.32/24.79            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.32/24.79            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.79            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.79            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.32/24.79              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.32/24.79            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.32/24.79          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.32/24.79            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.32/24.79              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.32/24.79            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.79              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.32/24.79          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.32/24.79            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.32/24.79              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.32/24.79              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.32/24.79            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.32/24.79          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.32/24.79            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.32/24.79            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.32/24.79                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.32/24.79                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.32/24.80                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.32/24.80                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.32/24.80                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.32/24.80                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.32/24.80                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.80                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.32/24.80                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.80                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.32/24.80                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.80                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.32/24.80                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.32/24.80                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.80                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.80                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.80                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.80                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.80                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.80                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.32/24.80                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.32/24.80                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.32/24.80                op(e0, e1) = e0)))
% 158.32/24.80    (87)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.32/24.80          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.32/24.80            e1)
% 158.32/24.80    (88)   ~ (all_52_2 = e0)
% 158.32/24.80    (89)   ~ (all_52_9 = e2)
% 158.32/24.80    (90)   ~ (all_6_2 = e2)
% 158.32/24.80    (91)   ~ (e3 = e1)
% 158.32/24.80    (92)   ~ (all_52_1 = all_4_2)
% 158.32/24.80    (93)   ~ (all_52_7 = all_52_11)
% 158.32/24.80    (94)   ~ (e2 = e0)
% 158.32/24.80    (95)   ~ (all_52_8 = e3)
% 158.32/24.80    (96)   ~ (e3 = e0)
% 158.32/24.80    (97)  all_54_8 = all_52_2
% 158.32/24.80    (98)   ~ (all_52_13 = e2)
% 158.32/24.80    (99)  all_56_4 = e0
% 158.32/24.80  
% 158.32/24.80  Begin of proof
% 158.32/24.80  | 
% 158.32/24.80  | BETA: splitting (35) gives:
% 158.32/24.80  | 
% 158.32/24.80  | Case 1:
% 158.32/24.80  | | 
% 158.32/24.80  | |   (100)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) =
% 158.32/24.80  | |            e3)
% 158.32/24.80  | | 
% 158.32/24.80  | | BETA: splitting (100) gives:
% 158.32/24.80  | | 
% 158.32/24.80  | | Case 1:
% 158.32/24.80  | | | 
% 158.32/24.80  | | |   (101)  all_56_4 = e3 & op(e3, e1) = e3
% 158.32/24.80  | | | 
% 158.32/24.80  | | | ALPHA: (101) implies:
% 158.32/24.80  | | |   (102)  op(e3, e1) = e3
% 158.32/24.80  | | | 
% 158.32/24.80  | | | REF_CLOSE: (25), (27), (95), (102) are inconsistent by sub-proof #982.
% 158.32/24.80  | | | 
% 158.32/24.80  | | Case 2:
% 158.32/24.80  | | | 
% 158.32/24.80  | | |   (103)  all_56_5 = e3 & op(e2, e1) = e3
% 158.32/24.80  | | | 
% 158.32/24.80  | | | ALPHA: (103) implies:
% 158.32/24.80  | | |   (104)  all_56_5 = e3
% 158.32/24.80  | | | 
% 158.32/24.80  | | | COMBINE_EQS: (43), (104) imply:
% 158.32/24.80  | | |   (105)  e3 = e1
% 158.32/24.80  | | | 
% 158.32/24.80  | | | SIMP: (105) implies:
% 158.32/24.80  | | |   (106)  e3 = e1
% 158.32/24.80  | | | 
% 158.32/24.80  | | | COMBINE_EQS: (46), (106) imply:
% 158.32/24.80  | | |   (107)  all_56_10 = e1
% 158.32/24.80  | | | 
% 158.32/24.80  | | | BETA: splitting (75) gives:
% 158.32/24.80  | | | 
% 158.32/24.80  | | | Case 1:
% 158.32/24.80  | | | | 
% 158.32/24.80  | | | |   (108)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1)
% 158.32/24.80  | | | |            = e1)
% 158.32/24.80  | | | | 
% 158.32/24.80  | | | | BETA: splitting (108) gives:
% 158.32/24.80  | | | | 
% 158.32/24.80  | | | | Case 1:
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | |   (109)  all_56_4 = e1 & op(e3, e1) = e1
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | | REF_CLOSE: (19), (25), (54), (57), (69), (70), (76), (91), (99), (109)
% 158.32/24.80  | | | | |            are inconsistent by sub-proof #127.
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | Case 2:
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | |   (110)  all_56_5 = e1 & op(e2, e1) = e1
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | | REF_CLOSE: (2), (23), (25), (32), (39), (43), (53), (57), (70), (73),
% 158.32/24.80  | | | | |            (76), (84), (91), (94), (96), (107) are inconsistent by
% 158.32/24.80  | | | | |            sub-proof #126.
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | End of split
% 158.32/24.80  | | | | 
% 158.32/24.80  | | | Case 2:
% 158.32/24.80  | | | | 
% 158.32/24.80  | | | |   (111)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0,
% 158.32/24.80  | | | |              e1) = e1)
% 158.32/24.80  | | | | 
% 158.32/24.80  | | | | BETA: splitting (111) gives:
% 158.32/24.80  | | | | 
% 158.32/24.80  | | | | Case 1:
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | |   (112)  all_56_8 = e1 & op(e1, e1) = e1
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | | ALPHA: (112) implies:
% 158.32/24.80  | | | | |   (113)  op(e1, e1) = e1
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | | REF_CLOSE: (25), (31), (76), (113) are inconsistent by sub-proof #986.
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | Case 2:
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | |   (114)  all_56_14 = e1 & op(e0, e1) = e1
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | | ALPHA: (114) implies:
% 158.32/24.80  | | | | |   (115)  all_56_14 = e1
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | | BETA: splitting (39) gives:
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | | Case 1:
% 158.32/24.80  | | | | | | 
% 158.32/24.80  | | | | | |   (116)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2,
% 158.32/24.80  | | | | | |              e2) = e3)
% 158.32/24.80  | | | | | | 
% 158.32/24.80  | | | | | | REF_CLOSE: (2), (23), (25), (32), (53), (57), (70), (73), (76),
% 158.32/24.80  | | | | | |            (84), (91), (94), (96), (116) are inconsistent by
% 158.32/24.80  | | | | | |            sub-proof #475.
% 158.32/24.80  | | | | | | 
% 158.32/24.80  | | | | | Case 2:
% 158.32/24.80  | | | | | | 
% 158.32/24.80  | | | | | |   (117)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 &
% 158.32/24.80  | | | | | |            op(e2, e0) = e3)
% 158.32/24.80  | | | | | | 
% 158.32/24.80  | | | | | | BETA: splitting (117) gives:
% 158.32/24.80  | | | | | | 
% 158.32/24.80  | | | | | | Case 1:
% 158.32/24.80  | | | | | | | 
% 158.32/24.80  | | | | | | | 
% 158.32/24.80  | | | | | | | BETA: splitting (50) gives:
% 158.32/24.80  | | | | | | | 
% 158.32/24.80  | | | | | | | Case 1:
% 158.32/24.80  | | | | | | | | 
% 158.32/24.80  | | | | | | | |   (118)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 &
% 158.32/24.80  | | | | | | | |            op(e2, e0) = e3)
% 158.32/24.80  | | | | | | | | 
% 158.32/24.80  | | | | | | | | BETA: splitting (118) gives:
% 158.32/24.80  | | | | | | | | 
% 158.32/24.80  | | | | | | | | Case 1:
% 158.32/24.80  | | | | | | | | | 
% 158.32/24.80  | | | | | | | | |   (119)  all_56_9 = e3 & op(e3, e0) = e3
% 158.32/24.80  | | | | | | | | | 
% 158.32/24.80  | | | | | | | | | ALPHA: (119) implies:
% 158.32/24.80  | | | | | | | | |   (120)  all_56_9 = e3
% 158.32/24.80  | | | | | | | | | 
% 158.32/24.80  | | | | | | | | | REF_CLOSE: (10), (20), (23), (25), (57), (69), (70), (76),
% 158.32/24.80  | | | | | | | | |            (91), (94), (96), (120) are inconsistent by
% 158.32/24.80  | | | | | | | | |            sub-proof #632.
% 158.32/24.80  | | | | | | | | | 
% 158.32/24.80  | | | | | | | | Case 2:
% 158.32/24.80  | | | | | | | | | 
% 158.32/24.80  | | | | | | | | |   (121)  all_56_10 = e3 & op(e2, e0) = e3
% 158.32/24.80  | | | | | | | | | 
% 158.32/24.80  | | | | | | | | | REF_CLOSE: (23), (25), (31), (35), (43), (91), (96), (99),
% 158.32/24.80  | | | | | | | | |            (115) are inconsistent by sub-proof #125.
% 158.32/24.80  | | | | | | | | | 
% 158.32/24.80  | | | | | | | | End of split
% 158.32/24.80  | | | | | | | | 
% 158.32/24.80  | | | | | | | Case 2:
% 158.32/24.80  | | | | | | | | 
% 158.32/24.80  | | | | | | | |   (122)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 &
% 158.32/24.80  | | | | | | | |            op(e0, e0) = e3)
% 158.32/24.80  | | | | | | | | 
% 158.32/24.80  | | | | | | | | REF_CLOSE: (6), (25), (42), (91), (96), (122) are inconsistent
% 158.32/24.80  | | | | | | | |            by sub-proof #294.
% 158.32/24.80  | | | | | | | | 
% 158.32/24.80  | | | | | | | End of split
% 158.32/24.80  | | | | | | | 
% 158.32/24.80  | | | | | | Case 2:
% 158.32/24.80  | | | | | | | 
% 158.32/24.80  | | | | | | |   (123)  all_56_10 = e3 & op(e2, e0) = e3
% 158.32/24.80  | | | | | | | 
% 158.32/24.80  | | | | | | | REF_CLOSE: (91), (107), (123) are inconsistent by sub-proof #295.
% 158.32/24.80  | | | | | | | 
% 158.32/24.80  | | | | | | End of split
% 158.32/24.80  | | | | | | 
% 158.32/24.80  | | | | | End of split
% 158.32/24.80  | | | | | 
% 158.32/24.80  | | | | End of split
% 158.32/24.80  | | | | 
% 158.32/24.80  | | | End of split
% 158.32/24.80  | | | 
% 158.32/24.80  | | End of split
% 158.32/24.80  | | 
% 158.32/24.80  | Case 2:
% 158.32/24.80  | | 
% 158.32/24.80  | |   (124)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 158.32/24.80  | |            e3)
% 158.32/24.80  | | 
% 158.32/24.80  | | BETA: splitting (124) gives:
% 158.32/24.80  | | 
% 158.32/24.80  | | Case 1:
% 158.32/24.80  | | | 
% 158.32/24.80  | | |   (125)  all_56_8 = e3 & op(e1, e1) = e3
% 158.32/24.80  | | | 
% 158.32/24.80  | | | ALPHA: (125) implies:
% 158.32/24.80  | | |   (126)  op(e1, e1) = e3
% 158.32/24.80  | | | 
% 158.32/24.80  | | | REF_CLOSE: (23), (25), (31), (126) are inconsistent by sub-proof #646.
% 158.32/24.80  | | | 
% 158.32/24.80  | | Case 2:
% 158.32/24.80  | | | 
% 158.32/24.80  | | |   (127)  all_56_14 = e3 & op(e0, e1) = e3
% 158.32/24.80  | | | 
% 158.32/24.80  | | | ALPHA: (127) implies:
% 158.32/24.80  | | |   (128)  all_56_14 = e3
% 158.32/24.80  | | |   (129)  op(e0, e1) = e3
% 158.32/24.80  | | | 
% 158.32/24.80  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.32/24.80  | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23),
% 158.32/24.80  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 158.32/24.80  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (44),
% 158.32/24.80  | | |            (45), (47), (48), (49), (50), (51), (52), (53), (55), (56),
% 158.32/24.80  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 158.32/24.80  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 158.32/24.80  | | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 158.32/24.80  | | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 158.32/24.80  | | |            (97), (98), (128), (129) are inconsistent by sub-proof #121.
% 158.32/24.80  | | | 
% 158.32/24.80  | | End of split
% 158.32/24.80  | | 
% 158.32/24.80  | End of split
% 158.32/24.80  | 
% 158.32/24.80  End of proof
% 158.32/24.80  
% 158.32/24.80  Sub-proof #121 shows that the following formulas are inconsistent:
% 158.32/24.80  ----------------------------------------------------------------
% 158.32/24.80    (1)   ~ (all_6_2 = e0)
% 158.32/24.80    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.32/24.80         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.32/24.80    (3)  all_54_5 = all_4_2
% 158.32/24.80    (4)   ~ (all_52_8 = all_6_2)
% 158.32/24.80    (5)   ~ (all_52_2 = all_6_2)
% 158.32/24.80    (6)  op(e0, e0) = e1
% 158.32/24.80    (7)   ~ (all_52_12 = e1)
% 158.32/24.80    (8)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.32/24.80         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.32/24.80    (9)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 158.32/24.80         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.32/24.80    (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.32/24.80          (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.32/24.80    (11)   ~ (all_24_2 = e1) | ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 &
% 158.32/24.80            $i(all_24_0)) | ( ~ (all_24_1 = e0) & op(e1, e1) = all_24_1 &
% 158.32/24.80            $i(all_24_1))
% 158.32/24.80    (12)   ~ (all_52_4 = e3)
% 158.32/24.80    (13)  op(e3, e2) = e1
% 158.32/24.80    (14)  all_54_13 = all_52_7
% 158.32/24.80    (15)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.32/24.80          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 158.32/24.80    (16)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.32/24.80    (17)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 158.32/24.80              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.32/24.80            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.32/24.80                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 158.32/24.80              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.32/24.80          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 158.32/24.80              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.32/24.80            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.32/24.80                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 158.32/24.80              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.32/24.80          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 158.32/24.80              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.32/24.80            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.32/24.80                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 158.32/24.80              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.32/24.80          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 158.32/24.80              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.32/24.80            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 158.32/24.80                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 158.32/24.80                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.32/24.80                $i(all_57_13))))
% 158.32/24.80    (18)   ~ (all_52_4 = all_52_6)
% 158.32/24.80    (19)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.32/24.80          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.32/24.80    (20)  op(e0, e1) = all_52_11
% 158.32/24.80    (21)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.32/24.80    (22)   ~ (e3 = e2)
% 158.32/24.80    (23)  ( ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 & $i(all_10_0)) | ( ~
% 158.32/24.80            (all_10_1 = e0) & op(e2, e2) = all_10_1 & $i(all_10_1))
% 158.32/24.80    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.32/24.80            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.32/24.80    (25)  op(e0, e3) = all_52_3
% 158.32/24.80    (26)  op(e3, e1) = all_52_8
% 158.32/24.80    (27)   ~ (all_52_12 = all_6_2)
% 158.32/24.80    (28)   ~ (all_52_12 = e3)
% 158.32/24.80    (29)  op(e0, e1) = e3
% 158.32/24.80    (30)   ~ (all_52_9 = all_4_2)
% 158.32/24.80    (31)  op(e1, e1) = e2
% 158.32/24.80    (32)   ~ (all_4_2 = e3)
% 158.32/24.80    (33)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.32/24.80              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 158.32/24.80                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.32/24.80                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.32/24.80    (34)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.32/24.80          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.32/24.80    (35)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 158.32/24.80          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.32/24.80    (36)  all_56_14 = e3
% 158.32/24.80    (37)  op(e1, e3) = all_52_2
% 158.32/24.80    (38)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.32/24.80          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.32/24.80    (39)  op(e0, e2) = all_52_7
% 158.32/24.80    (40)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.32/24.80          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.32/24.80    (41)   ~ (all_52_13 = all_4_2)
% 158.32/24.80    (42)  all_54_3 = all_52_12
% 158.32/24.80    (43)  op(e1, e0) = e0
% 158.32/24.80    (44)   ~ (all_52_2 = e2)
% 158.32/24.80    (45)  op(e1, e2) = all_52_6
% 158.32/24.80    (46)   ~ (all_52_12 = all_52_13)
% 158.32/24.80    (47)  op(e1, e0) = all_52_14
% 158.32/24.80    (48)  all_24_2 = all_4_2
% 158.32/24.80    (49)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.32/24.80          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.32/24.80    (50)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.32/24.80          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.32/24.80    (51)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.32/24.80          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.32/24.80    (52)  op(e2, e2) = all_4_2
% 158.32/24.80    (53)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 158.32/24.80    (54)   ~ (all_52_2 = all_52_6)
% 158.32/24.80    (55)  op(e3, e3) = e3
% 158.32/24.80    (56)   ~ (all_52_4 = all_52_7)
% 158.32/24.80    (57)   ~ (all_52_2 = e3)
% 158.32/24.80    (58)  all_56_8 = e2
% 158.32/24.80    (59)  op(e0, e0) = all_14_2
% 158.32/24.80    (60)  op(e2, e3) = all_52_1
% 158.32/24.80    (61)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.32/24.80          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.32/24.80    (62)  op(e1, e2) = e3
% 158.32/24.80    (63)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.32/24.80          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.32/24.80    (64)  op(e3, e2) = all_52_4
% 158.32/24.80    (65)   ~ (all_52_7 = all_4_2)
% 158.32/24.80    (66)  all_54_0 = all_6_2
% 158.32/24.81    (67)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.32/24.81          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.32/24.81    (68)   ~ (e1 = e0)
% 158.32/24.81    (69)  op(e2, e1) = all_52_9
% 158.32/24.81    (70)   ~ (all_52_8 = all_52_9)
% 158.32/24.81    (71)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.32/24.81          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.32/24.81    (72)  op(e2, e0) = all_52_13
% 158.32/24.81    (73)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.32/24.81          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.32/24.81    (74)   ~ (e2 = e1)
% 158.32/24.81    (75)  op(e3, e3) = all_6_2
% 158.32/24.81    (76)  op(e3, e0) = all_52_12
% 158.32/24.81    (77)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.32/24.81          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.32/24.81            e3)
% 158.32/24.81    (78)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.32/24.81          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.32/24.81    (79)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.32/24.81          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.32/24.81    (80)   ~ (all_52_8 = e2)
% 158.32/24.81    (81)  all_54_8 = e1 | all_54_8 = e0
% 158.32/24.81    (82)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.32/24.81          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.32/24.81    (83)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 158.32/24.81    (84)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.32/24.81            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.32/24.81            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.32/24.81            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.81              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.81          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.32/24.81            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.32/24.81              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.32/24.81            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.81              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.81          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.32/24.81            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.32/24.81              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.32/24.81            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.81              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.81          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.32/24.81            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.32/24.81            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.32/24.81              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.32/24.81            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.32/24.81            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.32/24.81            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.81            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.32/24.81              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.32/24.81            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.32/24.81          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.32/24.81            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.32/24.81              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.32/24.81            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.32/24.81            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.32/24.81          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.32/24.81            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.32/24.81              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.32/24.81            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.32/24.81            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.32/24.81          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.32/24.81            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.32/24.81              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.32/24.81            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.81              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.32/24.81          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.32/24.81            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.32/24.81            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.32/24.81            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.32/24.81            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.32/24.81            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.32/24.81            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.32/24.81            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.32/24.81              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.32/24.81            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.32/24.81            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.32/24.81            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.32/24.81            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.32/24.81              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.32/24.81            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.32/24.81          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.32/24.81            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.32/24.81              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.32/24.81              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.32/24.81            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.32/24.81            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.81            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.81            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.32/24.81              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.32/24.81            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.32/24.81          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.32/24.81            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.32/24.81              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.32/24.81            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.81              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.32/24.81          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.32/24.81            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.32/24.81              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.32/24.81              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.32/24.81            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.32/24.81          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.32/24.81            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.32/24.81            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.32/24.81                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.32/24.81                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.32/24.81                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.32/24.81                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.32/24.81                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.32/24.81                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.32/24.81                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.81                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.32/24.81                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.81                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.32/24.81                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.81                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.32/24.81                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.32/24.81                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.81                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.81                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.81                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.81                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.81                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.81                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.32/24.81                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.32/24.81                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.32/24.81                op(e0, e1) = e0)))
% 158.32/24.81    (85)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.32/24.81          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.32/24.81            e1)
% 158.32/24.81    (86)   ~ (all_52_2 = e0)
% 158.32/24.81    (87)   ~ (all_52_9 = e2)
% 158.32/24.81    (88)   ~ (all_6_2 = e2)
% 158.32/24.81    (89)   ~ (e3 = e1)
% 158.32/24.81    (90)   ~ (all_52_1 = all_4_2)
% 158.32/24.81    (91)   ~ (all_52_7 = all_52_11)
% 158.32/24.81    (92)   ~ (e2 = e0)
% 158.32/24.81    (93)   ~ (all_52_8 = e3)
% 158.32/24.81    (94)   ~ (e3 = e0)
% 158.32/24.81    (95)  all_54_8 = all_52_2
% 158.32/24.81    (96)   ~ (all_52_13 = e2)
% 158.32/24.81  
% 158.32/24.81  Begin of proof
% 158.32/24.81  | 
% 158.32/24.81  | BETA: splitting (17) gives:
% 158.32/24.81  | 
% 158.32/24.81  | Case 1:
% 158.32/24.81  | | 
% 158.32/24.81  | |   (97)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.32/24.81  | |               e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.32/24.81  | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.32/24.81  | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.32/24.81  | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.32/24.81  | |                 e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 158.32/24.81  | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 158.32/24.81  | |                 e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 158.32/24.81  | |               e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 158.32/24.81  | |               all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 158.32/24.81  | |               e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 158.32/24.81  | |               $i(all_57_7))))
% 158.32/24.81  | | 
% 158.32/24.81  | | BETA: splitting (97) gives:
% 158.32/24.81  | | 
% 158.32/24.81  | | Case 1:
% 158.32/24.81  | | | 
% 158.32/24.81  | | |   (98)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.32/24.81  | | |             e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.32/24.81  | | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.32/24.81  | | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.32/24.81  | | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.32/24.81  | | |               e3) = all_57_6 & $i(all_57_6)))
% 158.32/24.81  | | | 
% 158.32/24.81  | | | ALPHA: (98) implies:
% 158.32/24.81  | | |   (99)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.32/24.81  | | |             e3) = all_57_6 & $i(all_57_6))
% 158.32/24.81  | | |   (100)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1,
% 158.32/24.81  | | |              e3) = all_57_2 & $i(all_57_2))
% 158.32/24.81  | | |   (101)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2,
% 158.32/24.81  | | |              e3) = all_57_0 & $i(all_57_0))
% 158.32/24.81  | | | 
% 158.32/24.81  | | | BETA: splitting (99) gives:
% 158.32/24.81  | | | 
% 158.32/24.81  | | | Case 1:
% 158.32/24.81  | | | | 
% 158.32/24.81  | | | |   (102)  all_57_15 = e3 & op(e0, e0) = e3
% 158.32/24.81  | | | | 
% 158.32/24.81  | | | | ALPHA: (102) implies:
% 158.32/24.81  | | | |   (103)  op(e0, e0) = e3
% 158.32/24.81  | | | | 
% 158.32/24.81  | | | | REF_CLOSE: (2), (8), (9), (22), (24), (32), (33), (36), (40), (51),
% 158.32/24.81  | | | |            (52), (55), (58), (68), (71), (73), (74), (82), (89), (92),
% 158.32/24.81  | | | |            (94), (103) are inconsistent by sub-proof #136.
% 158.32/24.81  | | | | 
% 158.32/24.81  | | | Case 2:
% 158.32/24.81  | | | | 
% 158.32/24.81  | | | |   (104)   ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)
% 158.32/24.81  | | | | 
% 158.32/24.81  | | | | ALPHA: (104) implies:
% 158.32/24.81  | | | |   (105)   ~ (all_57_6 = e0)
% 158.32/24.81  | | | | 
% 158.32/24.81  | | | | BETA: splitting (84) gives:
% 158.32/24.81  | | | | 
% 158.32/24.81  | | | | Case 1:
% 158.32/24.81  | | | | | 
% 158.32/24.82  | | | | |   (106)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.32/24.82  | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.32/24.82  | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12)) |
% 158.32/24.82  | | | | |          (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 158.32/24.82  | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 158.32/24.82  | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.82  | | | | |          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.32/24.82  | | | | |            (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 158.32/24.82  | | | | |            & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.32/24.82  | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.32/24.82  | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 158.32/24.82  | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.82  | | | | |          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.82  | | | | |            (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 158.32/24.82  | | | | |            & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.32/24.82  | | | | |          (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 158.32/24.82  | | | | |            (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.32/24.82  | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.82  | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) =
% 158.32/24.82  | | | | |            e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 158.32/24.82  | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.32/24.82  | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.32/24.82  | | | | |            = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 158.32/24.82  | | | | |            all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 158.32/24.82  | | | | |            op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 158.32/24.82  | | | | |            & $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 &
% 158.32/24.82  | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.32/24.82  | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.32/24.82  | | | | |            = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 & 
% 158.32/24.82  | | | | |            ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.32/24.82  | | | | |          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.32/24.82  | | | | |            (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.32/24.82  | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 158.32/24.82  | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.32/24.82  | | | | |            (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.32/24.82  | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.32/24.82  | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.32/24.82  | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 158.32/24.82  | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.32/24.82  | | | | |          (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.32/24.82  | | | | |            (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.32/24.82  | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.32/24.82  | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.32/24.82  | | | | |            (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 158.32/24.82  | | | | |            & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 158.32/24.82  | | | | |          (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~
% 158.32/24.82  | | | | |            (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.32/24.82  | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.32/24.82  | | | | |          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) =
% 158.32/24.82  | | | | |            e1 & op(e1, e1) = e1)
% 158.32/24.82  | | | | | 
% 158.32/24.82  | | | | | BETA: splitting (106) gives:
% 158.32/24.82  | | | | | 
% 158.32/24.82  | | | | | Case 1:
% 158.32/24.82  | | | | | | 
% 158.32/24.82  | | | | | |   (107)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.32/24.82  | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.32/24.82  | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12))
% 158.32/24.82  | | | | | |          | (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 158.32/24.82  | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.32/24.82  | | | | | |            e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.32/24.82  | | | | | |          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.32/24.82  | | | | | |            (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.32/24.82  | | | | | |            all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.32/24.82  | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.32/24.82  | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.32/24.82  | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 158.32/24.82  | | | | | |              e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7 =
% 158.32/24.82  | | | | | |            e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 158.32/24.82  | | | | | |            e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.32/24.82  | | | | | |              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 =
% 158.32/24.82  | | | | | |            e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.32/24.82  | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.32/24.82  | | | | | |              e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_12
% 158.32/24.82  | | | | | |            = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2)
% 158.32/24.82  | | | | | |          | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.32/24.82  | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.32/24.82  | | | | | |            e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.32/24.82  | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 158.32/24.82  | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.32/24.82  | | | | | |            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.32/24.82  | | | | | | 
% 158.32/24.82  | | | | | | BETA: splitting (107) gives:
% 158.32/24.82  | | | | | | 
% 158.32/24.82  | | | | | | Case 1:
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | |   (108)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.32/24.82  | | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.32/24.82  | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.32/24.82  | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.32/24.82  | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.32/24.82  | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 158.32/24.82  | | | | | | |              e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_3
% 158.32/24.82  | | | | | | |            = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 158.32/24.82  | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 &
% 158.32/24.82  | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.32/24.82  | | | | | | |            all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) &
% 158.32/24.82  | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) =
% 158.32/24.82  | | | | | | |            e2 & op(e2, e2) = e3 & $i(all_57_10))
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | | BETA: splitting (108) gives:
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | | Case 1:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | |   (109)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.32/24.82  | | | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.32/24.82  | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.32/24.82  | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.32/24.82  | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.32/24.82  | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.32/24.82  | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10))
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | | REF_CLOSE: (22), (24), (32), (52), (55), (109) are inconsistent
% 158.32/24.82  | | | | | | | |            by sub-proof #710.
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | Case 2:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | |   (110)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.32/24.82  | | | | | | | |            (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.32/24.82  | | | | | | | |            all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.32/24.82  | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.32/24.82  | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.32/24.82  | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 &
% 158.32/24.82  | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10))
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | | BETA: splitting (110) gives:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | | Case 1:
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | |   (111)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.32/24.82  | | | | | | | | |          (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.32/24.82  | | | | | | | | |          all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.32/24.82  | | | | | | | | |          $i(all_57_12)
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | ALPHA: (111) implies:
% 158.32/24.82  | | | | | | | | |   (112)  op(e1, e2) = e1
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | REF_CLOSE: (24), (62), (89), (112) are inconsistent by
% 158.32/24.82  | | | | | | | | |            sub-proof #939.
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | Case 2:
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | |   (113)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.32/24.82  | | | | | | | | |          (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.82  | | | | | | | | |            e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.32/24.82  | | | | | | | | |          $i(all_57_10)
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | ALPHA: (113) implies:
% 158.32/24.82  | | | | | | | | |   (114)  op(e2, e3) = e2
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | REF_CLOSE: (24), (32), (52), (101), (114) are inconsistent by
% 158.32/24.82  | | | | | | | | |            sub-proof #694.
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | End of split
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | End of split
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | Case 2:
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | |   (115)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.82  | | | | | | |            (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.32/24.82  | | | | | | |            all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.32/24.82  | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.32/24.82  | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.32/24.82  | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.32/24.82  | | | | | | |              e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.32/24.82  | | | | | | |            all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.32/24.82  | | | | | | |            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 158.32/24.82  | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.32/24.82  | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 158.32/24.82  | | | | | | |              e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 158.32/24.82  | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3,
% 158.32/24.82  | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.32/24.82  | | | | | | |            op(e2, e1) = e2 & $i(all_57_12))
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | | BETA: splitting (115) gives:
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | | Case 1:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | |   (116)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.82  | | | | | | | |            (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.32/24.82  | | | | | | | |            all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.32/24.82  | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.32/24.82  | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.32/24.82  | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 158.32/24.82  | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10))
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | | BETA: splitting (116) gives:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | | Case 1:
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | |   (117)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.82  | | | | | | | | |          (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.32/24.82  | | | | | | | | |          all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.32/24.82  | | | | | | | | |          $i(all_57_12)
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | ALPHA: (117) implies:
% 158.32/24.82  | | | | | | | | |   (118)  op(e0, e0) = e2
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | REF_CLOSE: (6), (24), (74), (118) are inconsistent by
% 158.32/24.82  | | | | | | | | |            sub-proof #875.
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | Case 2:
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | |   (119)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 158.32/24.82  | | | | | | | | |          (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.82  | | | | | | | | |            e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.32/24.82  | | | | | | | | |          $i(all_57_10)
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | ALPHA: (119) implies:
% 158.32/24.82  | | | | | | | | |   (120)  op(e2, e3) = e2
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | REF_CLOSE: (24), (32), (52), (101), (120) are inconsistent by
% 158.32/24.82  | | | | | | | | |            sub-proof #694.
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | End of split
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | Case 2:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | |   (121)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2,
% 158.32/24.82  | | | | | | | |              e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 &
% 158.32/24.82  | | | | | | | |            all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 158.32/24.82  | | | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.32/24.82  | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.32/24.82  | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 158.32/24.82  | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.32/24.82  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.32/24.82  | | | | | | | |            $i(all_57_12))
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | | BETA: splitting (121) gives:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | | Case 1:
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | |   (122)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.32/24.82  | | | | | | | | |          op(e2, e3) = e2 & op(e2, e2) = e2
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | ALPHA: (122) implies:
% 158.32/24.82  | | | | | | | | |   (123)  op(e2, e3) = e2
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | REF_CLOSE: (24), (32), (52), (101), (123) are inconsistent by
% 158.32/24.82  | | | | | | | | |            sub-proof #694.
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | Case 2:
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | |   (124)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.32/24.82  | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.82  | | | | | | | | |              e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.32/24.82  | | | | | | | | |            $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 158.32/24.82  | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) =
% 158.32/24.82  | | | | | | | | |            e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.32/24.82  | | | | | | | | |            op(e2, e1) = e2 & $i(all_57_12))
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | REF_CLOSE: (22), (24), (31), (69), (87), (124) are
% 158.32/24.82  | | | | | | | | |            inconsistent by sub-proof #140.
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | End of split
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | End of split
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | End of split
% 158.32/24.82  | | | | | | 
% 158.32/24.82  | | | | | Case 2:
% 158.32/24.82  | | | | | | 
% 158.32/24.82  | | | | | |   (125)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.82  | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.32/24.82  | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.32/24.82  | | | | | |          (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3)
% 158.32/24.82  | | | | | |            = e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2
% 158.32/24.82  | | | | | |            & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2
% 158.32/24.82  | | | | | |            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) =
% 158.32/24.82  | | | | | |            e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.32/24.82  | | | | | |            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 158.32/24.82  | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.32/24.82  | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_4 =
% 158.32/24.82  | | | | | |            e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.32/24.82  | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.32/24.82  | | | | | |              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 =
% 158.32/24.82  | | | | | |            e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) =
% 158.32/24.82  | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 158.32/24.82  | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_8 =
% 158.32/24.82  | | | | | |            e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 158.32/24.82  | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.32/24.82  | | | | | |              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 =
% 158.32/24.82  | | | | | |            e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.32/24.82  | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 158.32/24.82  | | | | | |              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 158.32/24.82  | | | | | |            = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.32/24.82  | | | | | | 
% 158.32/24.82  | | | | | | BETA: splitting (125) gives:
% 158.32/24.82  | | | | | | 
% 158.32/24.82  | | | | | | Case 1:
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | |   (126)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.82  | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2)
% 158.32/24.82  | | | | | | |            = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.32/24.82  | | | | | | |            $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~
% 158.32/24.82  | | | | | | |            (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.32/24.82  | | | | | | |          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.32/24.82  | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.32/24.82  | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.32/24.82  | | | | | | |            $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.32/24.82  | | | | | | |            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1
% 158.32/24.82  | | | | | | |            & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.32/24.82  | | | | | | |            all_57_14 & $i(all_57_14))
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | | BETA: splitting (126) gives:
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | | Case 1:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | |   (127)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.82  | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.82  | | | | | | | |              e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.32/24.82  | | | | | | | |            $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~
% 158.32/24.82  | | | | | | | |            (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | | BETA: splitting (127) gives:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | | Case 1:
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | |   (128)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.82  | | | | | | | | |          (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.82  | | | | | | | | |            e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.32/24.82  | | | | | | | | |          $i(all_57_10)
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | ALPHA: (128) implies:
% 158.32/24.82  | | | | | | | | |   (129)  op(e0, e0) = e3
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | REF_CLOSE: (2), (8), (9), (22), (24), (32), (33), (36), (40),
% 158.32/24.82  | | | | | | | | |            (51), (52), (55), (58), (68), (71), (73), (74),
% 158.32/24.82  | | | | | | | | |            (82), (89), (92), (94), (129) are inconsistent by
% 158.32/24.82  | | | | | | | | |            sub-proof #136.
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | Case 2:
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | |   (130)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 158.32/24.82  | | | | | | | | |          op(e3, e3) = e3 & op(e3, e2) = e3
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | ALPHA: (130) implies:
% 158.32/24.82  | | | | | | | | |   (131)  op(e3, e2) = e3
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | | REF_CLOSE: (12), (24), (64), (131) are inconsistent by
% 158.32/24.82  | | | | | | | | |            sub-proof #998.
% 158.32/24.82  | | | | | | | | | 
% 158.32/24.82  | | | | | | | | End of split
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | Case 2:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | |   (132)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.32/24.82  | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.32/24.82  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.32/24.82  | | | | | | | |            $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.32/24.82  | | | | | | | |            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) =
% 158.32/24.82  | | | | | | | |            e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.32/24.82  | | | | | | | |            all_57_14 & $i(all_57_14))
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | | REF_CLOSE: (24), (55), (72), (89), (96), (132) are inconsistent
% 158.32/24.82  | | | | | | | |            by sub-proof #994.
% 158.32/24.82  | | | | | | | | 
% 158.32/24.82  | | | | | | | End of split
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | Case 2:
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | |   (133)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.32/24.82  | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 158.32/24.82  | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.32/24.82  | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.32/24.82  | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1
% 158.32/24.82  | | | | | | |            & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 158.32/24.82  | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_8
% 158.32/24.82  | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1,
% 158.32/24.82  | | | | | | |              e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.32/24.82  | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.32/24.82  | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) &
% 158.32/24.82  | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) =
% 158.32/24.82  | | | | | | |            e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 158.32/24.82  | | | | | | |            & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.32/24.82  | | | | | | |            op(e1, e1) = e1)
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | | BETA: splitting (133) gives:
% 158.32/24.82  | | | | | | | 
% 158.32/24.82  | | | | | | | Case 1:
% 158.32/24.82  | | | | | | | | 
% 158.32/24.83  | | | | | | | |   (134)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.32/24.83  | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.83  | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.32/24.83  | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.32/24.83  | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) =
% 158.32/24.83  | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 158.32/24.83  | | | | | | | |            all_57_14 & $i(all_57_14))
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | | BETA: splitting (134) gives:
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | | Case 1:
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | |   (135)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.32/24.83  | | | | | | | | |          (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.83  | | | | | | | | |            e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.32/24.83  | | | | | | | | |          $i(all_57_10)
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | ALPHA: (135) implies:
% 158.32/24.83  | | | | | | | | |   (136)  op(e1, e1) = e3
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | REF_CLOSE: (22), (24), (31), (136) are inconsistent by
% 158.32/24.83  | | | | | | | | |            sub-proof #646.
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | Case 2:
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | |   (137)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.32/24.83  | | | | | | | | |          (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2
% 158.32/24.83  | | | | | | | | |          & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.32/24.83  | | | | | | | | |          $i(all_57_14)
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | ALPHA: (137) implies:
% 158.32/24.83  | | | | | | | | |   (138)  op(e2, e2) = e1
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.32/24.83  | | | | | | | | |            (11), (15), (16), (17), (18), (19), (22), (23),
% 158.32/24.83  | | | | | | | | |            (24), (25), (26), (27), (30), (31), (32), (33),
% 158.32/24.83  | | | | | | | | |            (34), (35), (37), (38), (40), (41), (42), (43),
% 158.32/24.83  | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 158.32/24.83  | | | | | | | | |            (52), (53), (54), (57), (58), (59), (60), (61),
% 158.32/24.83  | | | | | | | | |            (63), (64), (66), (67), (69), (70), (71), (72),
% 158.32/24.83  | | | | | | | | |            (73), (75), (76), (77), (78), (79), (80), (81),
% 158.32/24.83  | | | | | | | | |            (82), (83), (84), (85), (86), (87), (88), (89),
% 158.32/24.83  | | | | | | | | |            (90), (92), (94), (95), (101), (138) are
% 158.32/24.83  | | | | | | | | |            inconsistent by sub-proof #123.
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | End of split
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | Case 2:
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | |   (139)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.32/24.83  | | | | | | | |            (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 158.32/24.83  | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.32/24.83  | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.32/24.83  | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.32/24.83  | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 158.32/24.83  | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 158.32/24.83  | | | | | | | |            all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.32/24.83  | | | | | | | |            op(e1, e1) = e1)
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | | BETA: splitting (139) gives:
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | | Case 1:
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | |   (140)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.32/24.83  | | | | | | | | |          (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 158.32/24.83  | | | | | | | | |          all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.32/24.83  | | | | | | | | |          $i(all_57_14)
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | ALPHA: (140) implies:
% 158.32/24.83  | | | | | | | | |   (141)  all_57_2 = e1
% 158.32/24.83  | | | | | | | | |   (142)   ~ (all_57_14 = e3)
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | REF_CLOSE: (100), (141), (142) are inconsistent by sub-proof
% 158.32/24.83  | | | | | | | | |            #749.
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | Case 2:
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | |   (143)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~
% 158.32/24.83  | | | | | | | | |            (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.83  | | | | | | | | |              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.32/24.83  | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 & 
% 158.32/24.83  | | | | | | | | |            ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | REF_CLOSE: (22), (24), (31), (74), (143) are inconsistent by
% 158.32/24.83  | | | | | | | | |            sub-proof #139.
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | End of split
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | End of split
% 158.32/24.83  | | | | | | | 
% 158.32/24.83  | | | | | | End of split
% 158.32/24.83  | | | | | | 
% 158.32/24.83  | | | | | End of split
% 158.32/24.83  | | | | | 
% 158.32/24.83  | | | | Case 2:
% 158.32/24.83  | | | | | 
% 158.32/24.83  | | | | |   (144)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.32/24.83  | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.32/24.83  | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.32/24.83  | | | | |          (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.32/24.83  | | | | |            (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.32/24.83  | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.32/24.83  | | | | |          (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.32/24.83  | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 158.32/24.83  | | | | |            & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.32/24.83  | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.32/24.83  | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 158.32/24.83  | | | | |            & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 158.32/24.83  | | | | |          (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.32/24.83  | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 158.32/24.83  | | | | |            & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.32/24.83  | | | | |          (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) =
% 158.32/24.83  | | | | |            e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.32/24.83  | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.32/24.83  | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.32/24.83  | | | | |            = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 & 
% 158.32/24.83  | | | | |            ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) |
% 158.32/24.83  | | | | |          (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.32/24.83  | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.32/24.83  | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 158.32/24.83  | | | | |          (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.83  | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 158.32/24.83  | | | | |            & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.32/24.83  | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) =
% 158.32/24.83  | | | | |            e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.32/24.83  | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 &
% 158.32/24.83  | | | | |            op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 158.32/24.83  | | | | |            & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.32/24.83  | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.32/24.83  | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.32/24.83  | | | | |            = e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.32/24.83  | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 158.32/24.83  | | | | |            all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 158.32/24.83  | | | | |            = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 & 
% 158.32/24.83  | | | | |            ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) |
% 158.32/24.83  | | | | |          (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2)
% 158.32/24.83  | | | | |            = e2 & op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1
% 158.32/24.83  | | | | |            &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 158.32/24.83  | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.32/24.83  | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.32/24.83  | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.32/24.83  | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.32/24.83  | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.32/24.83  | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 158.32/24.83  | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 158.32/24.83  | | | | |                & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.32/24.83  | | | | |                all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.32/24.83  | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.32/24.83  | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.32/24.83  | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.32/24.83  | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 158.32/24.83  | | | | |                & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.32/24.83  | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.83  | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.32/24.83  | | | | |              (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 158.32/24.83  | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 158.32/24.83  | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 158.32/24.83  | | | | |                & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.32/24.83  | | | | |                all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.83  | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.32/24.83  | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.32/24.83  | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.32/24.83  | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.32/24.83  | | | | |                all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.32/24.83  | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.32/24.83  | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~
% 158.32/24.83  | | | | |                (e1 = e0) & op(e0, e1) = e0)))
% 158.32/24.83  | | | | | 
% 158.32/24.83  | | | | | BETA: splitting (144) gives:
% 158.32/24.83  | | | | | 
% 158.32/24.83  | | | | | Case 1:
% 158.32/24.83  | | | | | | 
% 158.32/24.83  | | | | | |   (145)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.32/24.83  | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.32/24.83  | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.32/24.83  | | | | | |          | (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.32/24.83  | | | | | |            (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.32/24.83  | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.32/24.83  | | | | | |          | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.32/24.83  | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 158.32/24.83  | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.32/24.83  | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.32/24.83  | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.32/24.83  | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.32/24.83  | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 158.32/24.83  | | | | | |            all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 158.32/24.83  | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1,
% 158.32/24.83  | | | | | |              e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.32/24.83  | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1)
% 158.32/24.83  | | | | | |          | (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.83  | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 158.32/24.83  | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.32/24.83  | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 158.32/24.83  | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 158.32/24.83  | | | | | |            & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1
% 158.32/24.83  | | | | | |            & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.32/24.83  | | | | | |            e1 & $i(all_57_14))
% 158.32/24.83  | | | | | | 
% 158.32/24.83  | | | | | | BETA: splitting (145) gives:
% 158.32/24.83  | | | | | | 
% 158.32/24.83  | | | | | | Case 1:
% 158.32/24.83  | | | | | | | 
% 158.32/24.83  | | | | | | |   (146)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.32/24.83  | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.32/24.83  | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.32/24.83  | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.32/24.83  | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.32/24.83  | | | | | | |            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.32/24.83  | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5
% 158.32/24.83  | | | | | | |            = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 158.32/24.83  | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 &
% 158.32/24.83  | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.32/24.83  | | | | | | |            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.32/24.83  | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) =
% 158.32/24.83  | | | | | | |            e0 & op(e0, e0) = e1 & $i(all_57_14))
% 158.32/24.83  | | | | | | | 
% 158.32/24.83  | | | | | | | BETA: splitting (146) gives:
% 158.32/24.83  | | | | | | | 
% 158.32/24.83  | | | | | | | Case 1:
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | |   (147)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.32/24.83  | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3
% 158.32/24.83  | | | | | | | |            & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.32/24.83  | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.32/24.83  | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 158.32/24.83  | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.32/24.83  | | | | | | | |            all_57_14 & $i(all_57_14))
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | | BETA: splitting (147) gives:
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | | Case 1:
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | |   (148)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.32/24.83  | | | | | | | | |          (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3
% 158.32/24.83  | | | | | | | | |          & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.32/24.83  | | | | | | | | |          $i(all_57_14)
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | ALPHA: (148) implies:
% 158.32/24.83  | | | | | | | | |   (149)  op(e3, e3) = e1
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | REF_CLOSE: (24), (55), (89), (149) are inconsistent by
% 158.32/24.83  | | | | | | | | |            sub-proof #995.
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | Case 2:
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | |   (150)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.32/24.83  | | | | | | | | |          (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2
% 158.32/24.83  | | | | | | | | |          & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.32/24.83  | | | | | | | | |          $i(all_57_14)
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | ALPHA: (150) implies:
% 158.32/24.83  | | | | | | | | |   (151)  op(e2, e2) = e1
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.32/24.83  | | | | | | | | |            (11), (15), (16), (17), (18), (19), (22), (23),
% 158.32/24.83  | | | | | | | | |            (24), (25), (26), (27), (30), (31), (32), (33),
% 158.32/24.83  | | | | | | | | |            (34), (35), (37), (38), (40), (41), (42), (43),
% 158.32/24.83  | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 158.32/24.83  | | | | | | | | |            (52), (53), (54), (57), (58), (59), (60), (61),
% 158.32/24.83  | | | | | | | | |            (63), (64), (66), (67), (69), (70), (71), (72),
% 158.32/24.83  | | | | | | | | |            (73), (75), (76), (77), (78), (79), (80), (81),
% 158.32/24.83  | | | | | | | | |            (82), (83), (84), (85), (86), (87), (88), (89),
% 158.32/24.83  | | | | | | | | |            (90), (92), (94), (95), (101), (151) are
% 158.32/24.83  | | | | | | | | |            inconsistent by sub-proof #123.
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | End of split
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | Case 2:
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | |   (152)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.32/24.83  | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.32/24.83  | | | | | | | |              e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.32/24.83  | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 &
% 158.32/24.83  | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) =
% 158.32/24.83  | | | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.32/24.83  | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14))
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | | BETA: splitting (152) gives:
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | | Case 1:
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | |   (153)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.32/24.83  | | | | | | | | |          (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.32/24.83  | | | | | | | | |            e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.32/24.83  | | | | | | | | |          $i(all_57_12)
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | ALPHA: (153) implies:
% 158.32/24.83  | | | | | | | | |   (154)  op(e2, e1) = e2
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | REF_CLOSE: (24), (69), (87), (154) are inconsistent by
% 158.32/24.83  | | | | | | | | |            sub-proof #1002.
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | Case 2:
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | |   (155)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.32/24.83  | | | | | | | | |          (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.32/24.83  | | | | | | | | |          all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.32/24.83  | | | | | | | | |          $i(all_57_14)
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | ALPHA: (155) implies:
% 158.32/24.83  | | | | | | | | |   (156)  op(e1, e2) = e1
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | | REF_CLOSE: (24), (62), (89), (156) are inconsistent by
% 158.32/24.83  | | | | | | | | |            sub-proof #939.
% 158.32/24.83  | | | | | | | | | 
% 158.32/24.83  | | | | | | | | End of split
% 158.32/24.83  | | | | | | | | 
% 158.32/24.83  | | | | | | | End of split
% 158.32/24.83  | | | | | | | 
% 158.32/24.83  | | | | | | Case 2:
% 158.32/24.83  | | | | | | | 
% 158.32/24.83  | | | | | | |   (157)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.32/24.83  | | | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.32/24.83  | | | | | | |            = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.32/24.83  | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~
% 158.32/24.83  | | | | | | |            (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.32/24.83  | | | | | | |          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.83  | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 158.32/24.83  | | | | | | |            = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.32/24.83  | | | | | | |            $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~
% 158.32/24.83  | | | | | | |            (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) |
% 158.32/24.83  | | | | | | |          (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.32/24.83  | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.32/24.83  | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.83  | | | | | | |            $i(all_57_14))
% 158.32/24.83  | | | | | | | 
% 158.32/24.83  | | | | | | | BETA: splitting (157) gives:
% 158.32/24.83  | | | | | | | 
% 158.32/24.83  | | | | | | | Case 1:
% 158.32/24.83  | | | | | | | | 
% 158.32/24.84  | | | | | | | |   (158)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.32/24.84  | | | | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 158.32/24.84  | | | | | | | |              e0) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.32/24.84  | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~
% 158.32/24.84  | | | | | | | |            (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1)
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | | REF_CLOSE: (24), (31), (72), (96), (158) are inconsistent by
% 158.32/24.84  | | | | | | | |            sub-proof #198.
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | Case 2:
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | |   (159)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.84  | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.84  | | | | | | | |              e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.32/24.84  | | | | | | | |            $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~
% 158.32/24.84  | | | | | | | |            (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) |
% 158.32/24.84  | | | | | | | |          (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.32/24.84  | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3
% 158.32/24.84  | | | | | | | |            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.84  | | | | | | | |            $i(all_57_14))
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | | BETA: splitting (159) gives:
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | | Case 1:
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | |   (160)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.32/24.84  | | | | | | | | |          (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.84  | | | | | | | | |            e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.32/24.84  | | | | | | | | |          $i(all_57_10)
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | | ALPHA: (160) implies:
% 158.32/24.84  | | | | | | | | |   (161)  op(e0, e0) = e3
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | | REF_CLOSE: (2), (8), (9), (22), (24), (32), (33), (36), (40),
% 158.32/24.84  | | | | | | | | |            (51), (52), (55), (58), (68), (71), (73), (74),
% 158.32/24.84  | | | | | | | | |            (82), (89), (92), (94), (161) are inconsistent by
% 158.32/24.84  | | | | | | | | |            sub-proof #136.
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | Case 2:
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | |   (162)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 158.32/24.84  | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3
% 158.32/24.84  | | | | | | | | |            & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 158.32/24.84  | | | | | | | | |              e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 158.32/24.84  | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.84  | | | | | | | | |            $i(all_57_14))
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | | REF_CLOSE: (24), (26), (55), (89), (93), (162) are
% 158.32/24.84  | | | | | | | | |            inconsistent by sub-proof #981.
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | End of split
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | End of split
% 158.32/24.84  | | | | | | | 
% 158.32/24.84  | | | | | | End of split
% 158.32/24.84  | | | | | | 
% 158.32/24.84  | | | | | Case 2:
% 158.32/24.84  | | | | | | 
% 158.32/24.84  | | | | | |   (163)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.84  | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 158.32/24.84  | | | | | |            e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.32/24.84  | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2)
% 158.32/24.84  | | | | | |            = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 158.32/24.84  | | | | | |            & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1
% 158.32/24.84  | | | | | |            & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.32/24.84  | | | | | |            e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.32/24.84  | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.32/24.84  | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 158.32/24.84  | | | | | |              e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 158.32/24.84  | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2, e2)
% 158.32/24.84  | | | | | |            = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.32/24.84  | | | | | |              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.32/24.84  | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3)
% 158.32/24.84  | | | | | |          | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 158.32/24.84  | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 158.32/24.84  | | | | | |            all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1,
% 158.32/24.84  | | | | | |              e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.32/24.84  | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.32/24.84  | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3
% 158.32/24.84  | | | | | |                & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2
% 158.32/24.84  | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 158.32/24.84  | | | | | |                e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.32/24.84  | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.32/24.84  | | | | | |                  = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.32/24.84  | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.32/24.84  | | | | | |                (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.32/24.84  | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 158.32/24.84  | | | | | |                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.32/24.84  | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 158.32/24.84  | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 158.32/24.84  | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.32/24.84  | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 158.32/24.84  | | | | | |                & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.32/24.84  | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 158.32/24.84  | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 158.32/24.84  | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) =
% 158.32/24.84  | | | | | |                e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.84  | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.32/24.84  | | | | | |                  = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.32/24.84  | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.32/24.84  | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 158.32/24.84  | | | | | |                e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.84  | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.32/24.84  | | | | | |                  = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.84  | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.32/24.84  | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.32/24.84  | | | | | | 
% 158.32/24.84  | | | | | | BETA: splitting (163) gives:
% 158.32/24.84  | | | | | | 
% 158.32/24.84  | | | | | | Case 1:
% 158.32/24.84  | | | | | | | 
% 158.32/24.84  | | | | | | |   (164)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.84  | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1)
% 158.32/24.84  | | | | | | |            = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.32/24.84  | | | | | | |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~
% 158.32/24.84  | | | | | | |            (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.32/24.84  | | | | | | |          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 158.32/24.84  | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.32/24.84  | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.84  | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.32/24.84  | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.32/24.84  | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 158.32/24.84  | | | | | | |              e0) = e3 & $i(all_57_10))
% 158.32/24.84  | | | | | | | 
% 158.32/24.84  | | | | | | | BETA: splitting (164) gives:
% 158.32/24.84  | | | | | | | 
% 158.32/24.84  | | | | | | | Case 1:
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | |   (165)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.32/24.84  | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.32/24.84  | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.32/24.84  | | | | | | | |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~
% 158.32/24.84  | | | | | | | |            (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | | REF_CLOSE: (6), (24), (69), (74), (87), (165) are inconsistent
% 158.32/24.84  | | | | | | | |            by sub-proof #374.
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | Case 2:
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | |   (166)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 158.32/24.84  | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2
% 158.32/24.84  | | | | | | | |            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.84  | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.32/24.84  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.32/24.84  | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 158.32/24.84  | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10))
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | | BETA: splitting (166) gives:
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | | Case 1:
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | |   (167)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 158.32/24.84  | | | | | | | | |          (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2
% 158.32/24.84  | | | | | | | | |          & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.84  | | | | | | | | |          $i(all_57_14)
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | | ALPHA: (167) implies:
% 158.32/24.84  | | | | | | | | |   (168)  op(e2, e2) = e1
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.32/24.84  | | | | | | | | |            (11), (15), (16), (17), (18), (19), (22), (23),
% 158.32/24.84  | | | | | | | | |            (24), (25), (26), (27), (30), (31), (32), (33),
% 158.32/24.84  | | | | | | | | |            (34), (35), (37), (38), (40), (41), (42), (43),
% 158.32/24.84  | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 158.32/24.84  | | | | | | | | |            (52), (53), (54), (57), (58), (59), (60), (61),
% 158.32/24.84  | | | | | | | | |            (63), (64), (66), (67), (69), (70), (71), (72),
% 158.32/24.84  | | | | | | | | |            (73), (75), (76), (77), (78), (79), (80), (81),
% 158.32/24.84  | | | | | | | | |            (82), (83), (84), (85), (86), (87), (88), (89),
% 158.32/24.84  | | | | | | | | |            (90), (92), (94), (95), (101), (168) are
% 158.32/24.84  | | | | | | | | |            inconsistent by sub-proof #123.
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | Case 2:
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | |   (169)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~
% 158.32/24.84  | | | | | | | | |          (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.32/24.84  | | | | | | | | |            e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.32/24.84  | | | | | | | | |          $i(all_57_10)
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | | ALPHA: (169) implies:
% 158.32/24.84  | | | | | | | | |   (170)  op(e0, e0) = e3
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | | REF_CLOSE: (2), (8), (9), (22), (24), (32), (33), (36), (40),
% 158.32/24.84  | | | | | | | | |            (51), (52), (55), (58), (68), (71), (73), (74),
% 158.32/24.84  | | | | | | | | |            (82), (89), (92), (94), (170) are inconsistent by
% 158.32/24.84  | | | | | | | | |            sub-proof #136.
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | End of split
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | End of split
% 158.32/24.84  | | | | | | | 
% 158.32/24.84  | | | | | | Case 2:
% 158.32/24.84  | | | | | | | 
% 158.32/24.84  | | | | | | |   (171)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 158.32/24.84  | | | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.32/24.84  | | | | | | |            = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.32/24.84  | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~
% 158.32/24.84  | | | | | | |            (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) |
% 158.32/24.84  | | | | | | |          (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 158.32/24.84  | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 158.32/24.84  | | | | | | |            all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.32/24.84  | | | | | | |            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 158.32/24.84  | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 158.32/24.84  | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) =
% 158.32/24.84  | | | | | | |                e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.32/24.84  | | | | | | |                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.32/24.84  | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) =
% 158.32/24.84  | | | | | | |                e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13
% 158.32/24.84  | | | | | | |                = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.32/24.84  | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.32/24.84  | | | | | | |                e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.32/24.84  | | | | | | |                  e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.32/24.84  | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.32/24.84  | | | | | | |                  e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.32/24.84  | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.32/24.84  | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) =
% 158.32/24.84  | | | | | | |                e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7
% 158.32/24.84  | | | | | | |                = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.32/24.84  | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) =
% 158.32/24.84  | | | | | | |                e1 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15
% 158.32/24.84  | | | | | | |                = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.32/24.84  | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.32/24.84  | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) =
% 158.32/24.84  | | | | | | |                e3 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.32/24.84  | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.84  | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) =
% 158.32/24.84  | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.32/24.84  | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.32/24.84  | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.32/24.84  | | | | | | |                all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.32/24.84  | | | | | | |                  e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.32/24.84  | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.32/24.84  | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.32/24.84  | | | | | | | 
% 158.32/24.84  | | | | | | | BETA: splitting (171) gives:
% 158.32/24.84  | | | | | | | 
% 158.32/24.84  | | | | | | | Case 1:
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | |   (172)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 158.32/24.84  | | | | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 158.32/24.84  | | | | | | | |              e0) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.32/24.84  | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~
% 158.32/24.84  | | | | | | | |            (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3)
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | | REF_CLOSE: (6), (24), (28), (74), (76), (172) are inconsistent
% 158.32/24.84  | | | | | | | |            by sub-proof #373.
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | Case 2:
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | |   (173)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.32/24.84  | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 158.32/24.84  | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.32/24.84  | | | | | | | |            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 158.32/24.84  | | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 158.32/24.84  | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3)
% 158.32/24.84  | | | | | | | |                = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.32/24.84  | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 158.32/24.84  | | | | | | | |                ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 158.32/24.84  | | | | | | | |                = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.32/24.84  | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.32/24.84  | | | | | | | |                  e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.32/24.84  | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 158.32/24.84  | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.32/24.84  | | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.32/24.84  | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 158.32/24.84  | | | | | | | |                e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.32/24.84  | | | | | | | |                all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.32/24.84  | | | | | | | |                  e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.32/24.84  | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.32/24.84  | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.84  | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.32/24.84  | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 =
% 158.32/24.84  | | | | | | | |                  e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.32/24.84  | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.32/24.84  | | | | | | | |                  e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.32/24.84  | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 158.32/24.84  | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.84  | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) =
% 158.32/24.84  | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14
% 158.32/24.84  | | | | | | | |                = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.32/24.84  | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.32/24.84  | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 158.32/24.84  | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.32/24.84  | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.32/24.84  | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 158.32/24.84  | | | | | | | |                &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | | BETA: splitting (173) gives:
% 158.32/24.84  | | | | | | | | 
% 158.32/24.84  | | | | | | | | Case 1:
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | |   (174)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.32/24.84  | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | | ALPHA: (174) implies:
% 158.32/24.84  | | | | | | | | |   (175)  op(e2, e0) = e2
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | | REF_CLOSE: (24), (72), (96), (175) are inconsistent by
% 158.32/24.84  | | | | | | | | |            sub-proof #996.
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.84  | | | | | | | | Case 2:
% 158.32/24.84  | | | | | | | | | 
% 158.32/24.85  | | | | | | | | |   (176)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.32/24.85  | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.32/24.85  | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.32/24.85  | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.32/24.85  | | | | | | | | |                  = e3) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.32/24.85  | | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 158.32/24.85  | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.32/24.85  | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3)
% 158.32/24.85  | | | | | | | | |                = e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 158.32/24.85  | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 158.32/24.85  | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.32/24.85  | | | | | | | | |              | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 158.32/24.85  | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9
% 158.32/24.85  | | | | | | | | |                = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.85  | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2)
% 158.32/24.85  | | | | | | | | |                = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.32/24.85  | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.32/24.85  | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.32/24.85  | | | | | | | | |              | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 158.32/24.85  | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 158.32/24.85  | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7
% 158.32/24.85  | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 158.32/24.85  | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 158.32/24.85  | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3,
% 158.32/24.85  | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.32/24.85  | | | | | | | | |              | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.32/24.85  | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.32/24.85  | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8
% 158.32/24.85  | | | | | | | | |                = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.32/24.85  | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 158.32/24.85  | | | | | | | | |                = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.32/24.85  | | | | | | | | |                all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.32/24.85  | | | | | | | | |                  = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.32/24.85  | | | | | | | | |                e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.32/24.85  | | | | | | | | |              (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.32/24.85  | | | | | | | | |                op(e0, e1) = e0)))
% 158.32/24.85  | | | | | | | | | 
% 158.32/24.85  | | | | | | | | | BETA: splitting (176) gives:
% 158.32/24.85  | | | | | | | | | 
% 158.32/24.85  | | | | | | | | | Case 1:
% 158.32/24.85  | | | | | | | | | | 
% 158.32/24.85  | | | | | | | | | |   (177)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.32/24.85  | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 158.32/24.85  | | | | | | | | | | 
% 158.32/24.85  | | | | | | | | | | ALPHA: (177) implies:
% 158.32/24.85  | | | | | | | | | |   (178)  op(e1, e1) = e1
% 158.32/24.85  | | | | | | | | | | 
% 158.32/24.85  | | | | | | | | | | REF_CLOSE: (24), (31), (74), (178) are inconsistent by
% 158.32/24.85  | | | | | | | | | |            sub-proof #986.
% 158.32/24.85  | | | | | | | | | | 
% 158.32/24.85  | | | | | | | | | Case 2:
% 158.32/24.85  | | | | | | | | | | 
% 158.32/24.85  | | | | | | | | | |   (179)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6
% 158.32/24.85  | | | | | | | | | |              = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.32/24.85  | | | | | | | | | |              (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 158.32/24.85  | | | | | | | | | |              = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.32/24.85  | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.32/24.85  | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.32/24.85  | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.32/24.85  | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.32/24.85  | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3)
% 158.32/24.85  | | | | | | | | | |              = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.32/24.85  | | | | | | | | | |              (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.32/24.85  | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.32/24.85  | | | | | | | | | |                = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.32/24.85  | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.32/24.85  | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.32/24.85  | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2)
% 158.32/24.85  | | | | | | | | | |              = e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.32/24.85  | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.32/24.85  | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 158.32/24.85  | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 158.32/24.85  | | | | | | | | | |              & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9
% 158.32/24.85  | | | | | | | | | |              = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.32/24.85  | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1)
% 158.32/24.85  | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.32/24.85  | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 158.32/24.85  | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 158.32/24.85  | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.32/24.85  | | | | | | | | | |              e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.32/24.85  | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8
% 158.32/24.85  | | | | | | | | | |              = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 158.32/24.85  | | | | | | | | | |              (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.32/24.85  | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.32/24.85  | | | | | | | | | |              $i(all_57_14)) | (all_57_8 = e0 & all_57_15 =
% 158.32/24.85  | | | | | | | | | |              e0 &  ~ (e1 = e0) & op(e0, e1) = e0))
% 158.32/24.85  | | | | | | | | | | 
% 158.32/24.85  | | | | | | | | | | ALPHA: (179) implies:
% 158.32/24.85  | | | | | | | | | |   (180)  op(e0, e0) = all_57_15
% 158.39/24.85  | | | | | | | | | |   (181)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.39/24.85  | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 158.39/24.85  | | | | | | | | | |            = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.39/24.85  | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.39/24.85  | | | | | | | | | |              e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.39/24.85  | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.39/24.85  | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.39/24.85  | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.39/24.85  | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.39/24.85  | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.39/24.85  | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.39/24.85  | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.39/24.85  | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.39/24.85  | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.39/24.85  | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.39/24.85  | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14
% 158.39/24.85  | | | | | | | | | |            = e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 158.39/24.85  | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.39/24.85  | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.39/24.85  | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10
% 158.39/24.85  | | | | | | | | | |            = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.39/24.85  | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.39/24.85  | | | | | | | | | |            e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.39/24.85  | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 158.39/24.85  | | | | | | | | | |            e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.39/24.85  | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.39/24.85  | | | | | | | | | |              e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.39/24.85  | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.39/24.85  | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.39/24.85  | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.39/24.85  | | | | | | | | | |              e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.39/24.85  | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.39/24.85  | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | BETA: splitting (181) gives:
% 158.39/24.85  | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | Case 1:
% 158.39/24.85  | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | |   (182)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.39/24.85  | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.39/24.85  | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.39/24.85  | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.39/24.85  | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.39/24.85  | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.39/24.85  | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.39/24.85  | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.39/24.85  | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.39/24.85  | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.39/24.85  | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.39/24.85  | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.39/24.85  | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.39/24.85  | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.39/24.85  | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.39/24.85  | | | | | | | | | | |            e0)
% 158.39/24.85  | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | REF_CLOSE: (24), (31), (55), (72), (92), (94), (96), (99),
% 158.39/24.85  | | | | | | | | | | |            (105), (182) are inconsistent by sub-proof #122.
% 158.39/24.85  | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | Case 2:
% 158.39/24.85  | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | |   (183)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.39/24.85  | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.39/24.85  | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.39/24.85  | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.39/24.85  | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.39/24.85  | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.39/24.85  | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.39/24.85  | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.39/24.85  | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.39/24.85  | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.39/24.85  | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.39/24.85  | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.39/24.85  | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.39/24.85  | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.39/24.85  | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 158.39/24.85  | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.39/24.85  | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.39/24.85  | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | BETA: splitting (183) gives:
% 158.39/24.85  | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | Case 1:
% 158.39/24.85  | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | |   (184)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.39/24.85  | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.39/24.85  | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.39/24.85  | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.39/24.85  | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.39/24.85  | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.39/24.85  | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 158.39/24.85  | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | BETA: splitting (184) gives:
% 158.39/24.85  | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | Case 1:
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | |   (185)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 158.39/24.85  | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 158.39/24.85  | | | | | | | | | | | | |          = e1 & op(e0, e2) = e0
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | | ALPHA: (185) implies:
% 158.39/24.85  | | | | | | | | | | | | |   (186)  op(e1, e1) = e0
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | | REF_CLOSE: (24), (31), (92), (186) are inconsistent by
% 158.39/24.85  | | | | | | | | | | | | |            sub-proof #914.
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | Case 2:
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | |   (187)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.39/24.85  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.39/24.85  | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.39/24.85  | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.39/24.85  | | | | | | | | | | | | |            e0)
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | | REF_CLOSE: (6), (24), (55), (59), (68), (94), (180), (187)
% 158.39/24.85  | | | | | | | | | | | | |            are inconsistent by sub-proof #306.
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | End of split
% 158.39/24.85  | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | Case 2:
% 158.39/24.85  | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | |   (188)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.39/24.85  | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.39/24.85  | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.39/24.85  | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.39/24.85  | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.39/24.85  | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.39/24.85  | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.39/24.85  | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.39/24.85  | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 158.39/24.85  | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 158.39/24.85  | | | | | | | | | | | |            = e0)
% 158.39/24.85  | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | BETA: splitting (188) gives:
% 158.39/24.85  | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | Case 1:
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | |   (189)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.39/24.85  | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.39/24.85  | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.39/24.85  | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.39/24.85  | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.39/24.85  | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | | REF_CLOSE: (24), (31), (72), (92), (96), (189) are
% 158.39/24.85  | | | | | | | | | | | | |            inconsistent by sub-proof #164.
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | Case 2:
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | |   (190)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 158.39/24.85  | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.39/24.85  | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.39/24.85  | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 158.39/24.85  | | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | | REF_CLOSE: (6), (24), (43), (59), (68), (180), (190) are
% 158.39/24.85  | | | | | | | | | | | | |            inconsistent by sub-proof #289.
% 158.39/24.85  | | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | | End of split
% 158.39/24.85  | | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | | End of split
% 158.39/24.85  | | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | | End of split
% 158.39/24.85  | | | | | | | | | | 
% 158.39/24.85  | | | | | | | | | End of split
% 158.39/24.85  | | | | | | | | | 
% 158.39/24.85  | | | | | | | | End of split
% 158.39/24.85  | | | | | | | | 
% 158.39/24.85  | | | | | | | End of split
% 158.39/24.86  | | | | | | | 
% 158.39/24.86  | | | | | | End of split
% 158.39/24.86  | | | | | | 
% 158.39/24.86  | | | | | End of split
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | End of split
% 158.39/24.86  | | | | 
% 158.39/24.86  | | | End of split
% 158.39/24.86  | | | 
% 158.39/24.86  | | Case 2:
% 158.39/24.86  | | | 
% 158.39/24.86  | | |   (191)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3)
% 158.39/24.86  | | |              = e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.39/24.86  | | |              $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 158.39/24.86  | | |              (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 158.39/24.86  | | |          ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) &
% 158.39/24.86  | | |              op(e0, e2) = all_57_7 & $i(all_57_7)))
% 158.39/24.86  | | | 
% 158.39/24.86  | | | ALPHA: (191) implies:
% 158.39/24.86  | | |   (192)  op(e2, e2) = e2
% 158.39/24.86  | | |   (193)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 158.39/24.86  | | |              e2) = all_57_7 & $i(all_57_7))
% 158.39/24.86  | | |   (194)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) & op(e3,
% 158.39/24.86  | | |              e2) = all_57_1 & $i(all_57_1))
% 158.39/24.86  | | | 
% 158.39/24.86  | | | BETA: splitting (193) gives:
% 158.39/24.86  | | | 
% 158.39/24.86  | | | Case 1:
% 158.39/24.86  | | | | 
% 158.39/24.86  | | | |   (195)  all_57_15 = e2 & op(e0, e0) = e2
% 158.39/24.86  | | | | 
% 158.39/24.86  | | | | ALPHA: (195) implies:
% 158.39/24.86  | | | |   (196)  op(e0, e0) = e2
% 158.39/24.86  | | | | 
% 158.39/24.86  | | | | REF_CLOSE: (6), (24), (74), (196) are inconsistent by sub-proof #875.
% 158.39/24.86  | | | | 
% 158.39/24.86  | | | Case 2:
% 158.39/24.86  | | | | 
% 158.39/24.86  | | | |   (197)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)
% 158.39/24.86  | | | | 
% 158.39/24.86  | | | | ALPHA: (197) implies:
% 158.39/24.86  | | | |   (198)   ~ (all_57_7 = e0)
% 158.39/24.86  | | | |   (199)  op(e0, e2) = all_57_7
% 158.39/24.86  | | | | 
% 158.39/24.86  | | | | BETA: splitting (194) gives:
% 158.39/24.86  | | | | 
% 158.39/24.86  | | | | Case 1:
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | |   (200)  all_57_10 = e2 & op(e3, e3) = e2
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | ALPHA: (200) implies:
% 158.39/24.86  | | | | |   (201)  op(e3, e3) = e2
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | REF_CLOSE: (22), (24), (55), (201) are inconsistent by sub-proof #958.
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | Case 2:
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | |   (202)   ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1)
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | ALPHA: (202) implies:
% 158.39/24.86  | | | | |   (203)  op(e3, e2) = all_57_1
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | GROUND_INST: instantiating (24) with all_52_11, e3, e1, e0,
% 158.39/24.86  | | | | |              simplifying with (20), (29) gives:
% 158.39/24.86  | | | | |   (204)  all_52_11 = e3
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | GROUND_INST: instantiating (24) with all_52_7, all_57_7, e2, e0,
% 158.39/24.86  | | | | |              simplifying with (39), (199) gives:
% 158.39/24.86  | | | | |   (205)  all_57_7 = all_52_7
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | GROUND_INST: instantiating (24) with all_4_2, e2, e2, e2, simplifying
% 158.39/24.86  | | | | |              with (52), (192) gives:
% 158.39/24.86  | | | | |   (206)  all_4_2 = e2
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | GROUND_INST: instantiating (24) with all_52_4, all_57_1, e2, e3,
% 158.39/24.86  | | | | |              simplifying with (64), (203) gives:
% 158.39/24.86  | | | | |   (207)  all_57_1 = all_52_4
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | GROUND_INST: instantiating (24) with e1, all_57_1, e2, e3, simplifying
% 158.39/24.86  | | | | |              with (13), (203) gives:
% 158.39/24.86  | | | | |   (208)  all_57_1 = e1
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | COMBINE_EQS: (207), (208) imply:
% 158.39/24.86  | | | | |   (209)  all_52_4 = e1
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | SIMP: (209) implies:
% 158.39/24.86  | | | | |   (210)  all_52_4 = e1
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | REDUCE: (198), (205) imply:
% 158.39/24.86  | | | | |   (211)   ~ (all_52_7 = e0)
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | REDUCE: (56), (210) imply:
% 158.39/24.86  | | | | |   (212)   ~ (all_52_7 = e1)
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | SIMP: (212) implies:
% 158.39/24.86  | | | | |   (213)   ~ (all_52_7 = e1)
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | REDUCE: (91), (204) imply:
% 158.39/24.86  | | | | |   (214)   ~ (all_52_7 = e3)
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | REDUCE: (65), (206) imply:
% 158.39/24.86  | | | | |   (215)   ~ (all_52_7 = e2)
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | | REF_CLOSE: (14), (21), (211), (213), (214), (215) are inconsistent by
% 158.39/24.86  | | | | |            sub-proof #207.
% 158.39/24.86  | | | | | 
% 158.39/24.86  | | | | End of split
% 158.39/24.86  | | | | 
% 158.39/24.86  | | | End of split
% 158.39/24.86  | | | 
% 158.39/24.86  | | End of split
% 158.39/24.86  | | 
% 158.39/24.86  | Case 2:
% 158.39/24.86  | | 
% 158.39/24.86  | |   (216)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 158.39/24.86  | |                e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 158.39/24.86  | |                $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 158.39/24.86  | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 158.39/24.86  | |            ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.39/24.86  | |                op(e0, e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 &
% 158.39/24.86  | |            op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 158.39/24.86  | |                (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.39/24.86  | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 158.39/24.86  | |                op(e2, e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 &
% 158.39/24.86  | |                op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) =
% 158.39/24.86  | |                all_57_13 & $i(all_57_13))))
% 158.39/24.86  | | 
% 158.39/24.86  | | REF_CLOSE: (6), (24), (31), (59), (68), (74), (216) are inconsistent by
% 158.39/24.86  | |            sub-proof #748.
% 158.39/24.86  | | 
% 158.39/24.86  | End of split
% 158.39/24.86  | 
% 158.39/24.86  End of proof
% 158.39/24.86  
% 158.39/24.86  Sub-proof #122 shows that the following formulas are inconsistent:
% 158.39/24.86  ----------------------------------------------------------------
% 158.39/24.86    (1)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.39/24.86           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.39/24.86           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 158.39/24.86           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 158.39/24.86           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 158.39/24.86           e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 158.39/24.86           & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.39/24.86           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.39/24.86           e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.39/24.86             = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.39/24.86    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.39/24.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.39/24.86    (3)  op(e1, e1) = e2
% 158.39/24.86    (4)   ~ (all_57_6 = e0)
% 158.39/24.86    (5)  op(e3, e3) = e3
% 158.39/24.86    (6)  op(e2, e0) = all_52_13
% 158.39/24.86    (7)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 158.39/24.86           all_57_6 & $i(all_57_6))
% 158.39/24.86    (8)   ~ (e2 = e0)
% 158.39/24.86    (9)   ~ (e3 = e0)
% 158.39/24.86    (10)   ~ (all_52_13 = e2)
% 158.39/24.86  
% 158.39/24.86  Begin of proof
% 158.39/24.86  | 
% 158.39/24.86  | BETA: splitting (1) gives:
% 158.39/24.86  | 
% 158.39/24.86  | Case 1:
% 158.39/24.86  | | 
% 158.39/24.86  | |   (11)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.39/24.86  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.39/24.86  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.39/24.86  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.39/24.86  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.39/24.86  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.39/24.86  | | 
% 158.39/24.86  | | BETA: splitting (11) gives:
% 158.39/24.86  | | 
% 158.39/24.86  | | Case 1:
% 158.39/24.86  | | | 
% 158.39/24.86  | | |   (12)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.39/24.86  | | |           e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 158.39/24.86  | | | 
% 158.39/24.86  | | | ALPHA: (12) implies:
% 158.39/24.86  | | |   (13)  all_57_6 = e0
% 158.39/24.86  | | |   (14)   ~ (all_57_15 = e3)
% 158.39/24.86  | | | 
% 158.39/24.86  | | | REF_CLOSE: (7), (13), (14) are inconsistent by sub-proof #684.
% 158.39/24.86  | | | 
% 158.39/24.86  | | Case 2:
% 158.39/24.86  | | | 
% 158.39/24.86  | | |   (15)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.39/24.86  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.39/24.86  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.39/24.86  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.39/24.86  | | | 
% 158.39/24.86  | | | REF_CLOSE: (2), (3), (6), (8), (10), (15) are inconsistent by sub-proof
% 158.39/24.86  | | |            #169.
% 158.39/24.86  | | | 
% 158.39/24.86  | | End of split
% 158.39/24.86  | | 
% 158.39/24.86  | Case 2:
% 158.39/24.86  | | 
% 158.39/24.86  | |   (16)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.39/24.86  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.39/24.86  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.39/24.86  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.39/24.86  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.39/24.86  | | 
% 158.39/24.86  | | REF_CLOSE: (2), (4), (5), (6), (9), (10), (16) are inconsistent by sub-proof
% 158.39/24.86  | |            #683.
% 158.39/24.86  | | 
% 158.39/24.86  | End of split
% 158.39/24.86  | 
% 158.39/24.86  End of proof
% 158.39/24.86  
% 158.39/24.86  Sub-proof #123 shows that the following formulas are inconsistent:
% 158.39/24.86  ----------------------------------------------------------------
% 158.39/24.86    (1)   ~ (all_6_2 = e0)
% 158.39/24.86    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.39/24.86         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.39/24.86    (3)  all_54_5 = all_4_2
% 158.39/24.86    (4)   ~ (all_52_8 = all_6_2)
% 158.39/24.86    (5)   ~ (all_52_2 = all_6_2)
% 158.39/24.86    (6)  op(e0, e0) = e1
% 158.39/24.86    (7)   ~ (all_52_12 = e1)
% 158.39/24.86    (8)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.39/24.86         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.39/24.86    (9)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 158.39/24.86         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.39/24.86    (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.39/24.86          (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.39/24.86    (11)   ~ (all_24_2 = e1) | ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 &
% 158.39/24.86            $i(all_24_0)) | ( ~ (all_24_1 = e0) & op(e1, e1) = all_24_1 &
% 158.39/24.86            $i(all_24_1))
% 158.39/24.86    (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.39/24.86          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 158.39/24.86    (13)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.39/24.86    (14)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 158.39/24.86              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.39/24.86            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.39/24.86                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 158.39/24.86              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.39/24.86          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 158.39/24.86              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.39/24.86            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.39/24.86                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 158.39/24.86              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.39/24.86          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 158.39/24.86              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.39/24.86            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.39/24.86                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 158.39/24.86              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.39/24.86          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 158.39/24.86              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.39/24.86            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 158.39/24.86                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 158.39/24.86                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.39/24.86                $i(all_57_13))))
% 158.39/24.86    (15)   ~ (all_52_4 = all_52_6)
% 158.39/24.86    (16)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.39/24.86          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.39/24.86    (17)   ~ (e3 = e2)
% 158.39/24.86    (18)  ( ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 & $i(all_10_0)) | ( ~
% 158.39/24.86            (all_10_1 = e0) & op(e2, e2) = all_10_1 & $i(all_10_1))
% 158.39/24.86    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.39/24.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.39/24.86    (20)  op(e0, e3) = all_52_3
% 158.39/24.86    (21)  op(e3, e1) = all_52_8
% 158.39/24.86    (22)   ~ (all_52_12 = all_6_2)
% 158.39/24.86    (23)   ~ (all_52_9 = all_4_2)
% 158.39/24.86    (24)  op(e1, e1) = e2
% 158.39/24.86    (25)   ~ (all_4_2 = e3)
% 158.39/24.86    (26)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.39/24.86              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 158.39/24.86                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.39/24.86                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.39/24.86    (27)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.39/24.86          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.39/24.86    (28)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 158.39/24.86          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.39/24.86    (29)  op(e1, e3) = all_52_2
% 158.39/24.86    (30)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.39/24.86          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.39/24.86    (31)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.39/24.86          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.39/24.86    (32)   ~ (all_52_13 = all_4_2)
% 158.39/24.86    (33)  all_54_3 = all_52_12
% 158.39/24.86    (34)  op(e1, e0) = e0
% 158.39/24.86    (35)   ~ (all_52_2 = e2)
% 158.39/24.86    (36)  op(e1, e2) = all_52_6
% 158.39/24.86    (37)   ~ (all_52_12 = all_52_13)
% 158.39/24.86    (38)  op(e1, e0) = all_52_14
% 158.39/24.86    (39)  all_24_2 = all_4_2
% 158.39/24.86    (40)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.39/24.86          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.39/24.86    (41)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.39/24.86          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.39/24.86    (42)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.39/24.86          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.39/24.86    (43)  op(e2, e2) = all_4_2
% 158.39/24.86    (44)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 158.39/24.86    (45)   ~ (all_52_2 = all_52_6)
% 158.39/24.86    (46)   ~ (all_52_2 = e3)
% 158.39/24.86    (47)  all_56_8 = e2
% 158.39/24.86    (48)  op(e0, e0) = all_14_2
% 158.39/24.86    (49)  op(e2, e3) = all_52_1
% 158.39/24.86    (50)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.39/24.87          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.39/24.87    (51)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.39/24.87          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.39/24.87    (52)  op(e3, e2) = all_52_4
% 158.39/24.87    (53)  all_54_0 = all_6_2
% 158.39/24.87    (54)  op(e2, e2) = e1
% 158.39/24.87    (55)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.39/24.87          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.39/24.87    (56)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 158.39/24.87            all_57_0 & $i(all_57_0))
% 158.39/24.87    (57)  op(e2, e1) = all_52_9
% 158.39/24.87    (58)   ~ (all_52_8 = all_52_9)
% 158.39/24.87    (59)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.39/24.87          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.39/24.87    (60)  op(e2, e0) = all_52_13
% 158.39/24.87    (61)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.39/24.87          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.39/24.87    (62)  op(e3, e3) = all_6_2
% 158.39/24.87    (63)  op(e3, e0) = all_52_12
% 158.39/24.87    (64)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.39/24.87          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.39/24.87            e3)
% 158.39/24.87    (65)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.39/24.87          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.39/24.87    (66)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.39/24.87          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.39/24.87    (67)   ~ (all_52_8 = e2)
% 158.39/24.87    (68)  all_54_8 = e1 | all_54_8 = e0
% 158.39/24.87    (69)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.39/24.87          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.39/24.87    (70)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 158.39/24.87    (71)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.39/24.87            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.39/24.87            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.39/24.87            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.39/24.87              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.39/24.87          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.39/24.87            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.39/24.87              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.39/24.87            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.39/24.87              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.39/24.87          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.39/24.87            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.39/24.87              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.39/24.87            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.39/24.87              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.39/24.87          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.39/24.87            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.39/24.87            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.39/24.87              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.39/24.87            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.39/24.87            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.39/24.87            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.39/24.87            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.39/24.87              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.39/24.87            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.39/24.87          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.39/24.87            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.39/24.87              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.39/24.87            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.39/24.87            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.39/24.87          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.39/24.87            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.39/24.87              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.39/24.87            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.39/24.87            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.39/24.87          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.39/24.87            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.39/24.87              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.39/24.87            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.39/24.87              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.39/24.87          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.39/24.87            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.39/24.87            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.39/24.87            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.39/24.87            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.39/24.87            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.39/24.87            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.39/24.87            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.39/24.87              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.39/24.87            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.39/24.87            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.39/24.87            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.39/24.87            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.39/24.87              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.39/24.87            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.39/24.87          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.39/24.87            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.39/24.87              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.39/24.87              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.39/24.87            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.39/24.87            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.39/24.87            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.39/24.87            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.39/24.87              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.39/24.87            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.39/24.87          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.39/24.87            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.39/24.87              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.39/24.87            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.39/24.87              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.39/24.87          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.39/24.87            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.39/24.87              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.39/24.87              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.39/24.87            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.39/24.87          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.39/24.87            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.39/24.87            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.39/24.87                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.39/24.87                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.39/24.87                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.39/24.87                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.39/24.87                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.39/24.87                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.39/24.87                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.39/24.87                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.39/24.87                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.39/24.87                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.39/24.87                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.39/24.87                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.39/24.87                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.39/24.87                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.39/24.87                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.39/24.87                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.39/24.87                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.39/24.87                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.39/24.87                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.39/24.87                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.39/24.87                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.39/24.87                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.39/24.87                op(e0, e1) = e0)))
% 158.39/24.87    (72)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.39/24.87          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.39/24.87            e1)
% 158.39/24.87    (73)   ~ (all_52_2 = e0)
% 158.39/24.87    (74)   ~ (all_52_9 = e2)
% 158.39/24.87    (75)   ~ (all_6_2 = e2)
% 158.39/24.87    (76)   ~ (e3 = e1)
% 158.39/24.87    (77)   ~ (all_52_1 = all_4_2)
% 158.39/24.87    (78)   ~ (e2 = e0)
% 158.39/24.87    (79)   ~ (e3 = e0)
% 158.39/24.87    (80)  all_54_8 = all_52_2
% 158.39/24.87  
% 158.39/24.87  Begin of proof
% 158.39/24.87  | 
% 158.39/24.87  | BETA: splitting (51) gives:
% 158.39/24.87  | 
% 158.39/24.87  | Case 1:
% 158.39/24.87  | | 
% 158.39/24.87  | |   (81)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) =
% 158.39/24.87  | |           e3)
% 158.39/24.87  | | 
% 158.39/24.87  | | BETA: splitting (81) gives:
% 158.39/24.87  | | 
% 158.39/24.87  | | Case 1:
% 158.39/24.87  | | | 
% 158.39/24.87  | | |   (82)  all_56_6 = e3 & op(e1, e3) = e3
% 158.39/24.87  | | | 
% 158.39/24.87  | | | REF_CLOSE: (19), (29), (46), (82) are inconsistent by sub-proof #681.
% 158.39/24.87  | | | 
% 158.39/24.87  | | Case 2:
% 158.39/24.87  | | | 
% 158.42/24.87  | | |   (83)  all_56_7 = e3 & op(e1, e2) = e3
% 158.42/24.87  | | | 
% 158.42/24.87  | | | ALPHA: (83) implies:
% 158.42/24.87  | | |   (84)  all_56_7 = e3
% 158.42/24.87  | | |   (85)  op(e1, e2) = e3
% 158.42/24.87  | | | 
% 158.42/24.87  | | | BETA: splitting (56) gives:
% 158.42/24.87  | | | 
% 158.42/24.87  | | | Case 1:
% 158.42/24.87  | | | | 
% 158.42/24.87  | | | |   (86)  all_57_12 = e3 & op(e2, e2) = e3
% 158.42/24.87  | | | | 
% 158.42/24.87  | | | | ALPHA: (86) implies:
% 158.42/24.87  | | | |   (87)  op(e2, e2) = e3
% 158.42/24.87  | | | | 
% 158.42/24.87  | | | | REF_CLOSE: (19), (54), (76), (87) are inconsistent by sub-proof #847.
% 158.42/24.87  | | | | 
% 158.42/24.87  | | | Case 2:
% 158.42/24.87  | | | | 
% 158.42/24.87  | | | |   (88)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0)
% 158.42/24.87  | | | | 
% 158.42/24.87  | | | | ALPHA: (88) implies:
% 158.42/24.87  | | | |   (89)   ~ (all_57_0 = e2)
% 158.42/24.87  | | | |   (90)  op(e2, e3) = all_57_0
% 158.42/24.87  | | | | 
% 158.42/24.87  | | | | BETA: splitting (68) gives:
% 158.42/24.87  | | | | 
% 158.42/24.87  | | | | Case 1:
% 158.42/24.87  | | | | | 
% 158.42/24.87  | | | | |   (91)  all_54_8 = e1
% 158.42/24.87  | | | | | 
% 158.42/24.87  | | | | | COMBINE_EQS: (80), (91) imply:
% 158.42/24.87  | | | | |   (92)  all_52_2 = e1
% 158.42/24.87  | | | | | 
% 158.42/24.87  | | | | | SIMP: (92) implies:
% 158.42/24.87  | | | | |   (93)  all_52_2 = e1
% 158.42/24.87  | | | | | 
% 158.42/24.87  | | | | | REDUCE: (5), (93) imply:
% 158.42/24.87  | | | | |   (94)   ~ (all_6_2 = e1)
% 158.42/24.87  | | | | | 
% 158.42/24.87  | | | | | SIMP: (94) implies:
% 158.42/24.87  | | | | |   (95)   ~ (all_6_2 = e1)
% 158.42/24.87  | | | | | 
% 158.42/24.87  | | | | | REDUCE: (35), (93) imply:
% 158.42/24.87  | | | | |   (96)   ~ (e2 = e1)
% 158.42/24.87  | | | | | 
% 158.42/24.87  | | | | | SIMP: (96) implies:
% 158.42/24.87  | | | | |   (97)   ~ (e2 = e1)
% 158.42/24.87  | | | | | 
% 158.42/24.87  | | | | | REDUCE: (73), (93) imply:
% 158.42/24.87  | | | | |   (98)   ~ (e1 = e0)
% 158.42/24.87  | | | | | 
% 158.42/24.87  | | | | | BETA: splitting (44) gives:
% 158.42/24.87  | | | | | 
% 158.42/24.87  | | | | | Case 1:
% 158.42/24.87  | | | | | | 
% 158.42/24.87  | | | | | |   (99)  all_54_0 = e3
% 158.42/24.87  | | | | | | 
% 158.42/24.87  | | | | | | COMBINE_EQS: (53), (99) imply:
% 158.42/24.87  | | | | | |   (100)  all_6_2 = e3
% 158.42/24.87  | | | | | | 
% 158.42/24.87  | | | | | | SIMP: (100) implies:
% 158.42/24.87  | | | | | |   (101)  all_6_2 = e3
% 158.42/24.87  | | | | | | 
% 158.42/24.87  | | | | | | REDUCE: (4), (101) imply:
% 158.42/24.87  | | | | | |   (102)   ~ (all_52_8 = e3)
% 158.42/24.87  | | | | | | 
% 158.42/24.87  | | | | | | REDUCE: (22), (101) imply:
% 158.42/24.87  | | | | | |   (103)   ~ (all_52_12 = e3)
% 158.42/24.87  | | | | | | 
% 158.42/24.87  | | | | | | REDUCE: (62), (101) imply:
% 158.42/24.87  | | | | | |   (104)  op(e3, e3) = e3
% 158.42/24.87  | | | | | | 
% 158.42/24.87  | | | | | | BETA: splitting (70) gives:
% 158.42/24.87  | | | | | | 
% 158.42/24.87  | | | | | | Case 1:
% 158.42/24.87  | | | | | | | 
% 158.42/24.87  | | | | | | |   (105)  all_54_3 = e3
% 158.42/24.87  | | | | | | | 
% 158.42/24.87  | | | | | | | REF_CLOSE: (33), (103), (105) are inconsistent by sub-proof #310.
% 158.42/24.87  | | | | | | | 
% 158.42/24.87  | | | | | | Case 2:
% 158.42/24.87  | | | | | | | 
% 158.42/24.87  | | | | | | |   (106)   ~ (all_54_3 = e3)
% 158.42/24.87  | | | | | | |   (107)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 158.42/24.87  | | | | | | | 
% 158.42/24.87  | | | | | | | BETA: splitting (107) gives:
% 158.42/24.87  | | | | | | | 
% 158.42/24.87  | | | | | | | Case 1:
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | |   (108)  all_54_3 = e2
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | | COMBINE_EQS: (33), (108) imply:
% 158.42/24.87  | | | | | | | |   (109)  all_52_12 = e2
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | | SIMP: (109) implies:
% 158.42/24.87  | | | | | | | |   (110)  all_52_12 = e2
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | | REDUCE: (37), (110) imply:
% 158.42/24.87  | | | | | | | |   (111)   ~ (all_52_13 = e2)
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | | SIMP: (111) implies:
% 158.42/24.87  | | | | | | | |   (112)   ~ (all_52_13 = e2)
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | | BETA: splitting (66) gives:
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | | Case 1:
% 158.42/24.87  | | | | | | | | | 
% 158.42/24.87  | | | | | | | | |   (113)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 &
% 158.42/24.87  | | | | | | | | |            op(e2, e2) = e2)
% 158.42/24.87  | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | BETA: splitting (113) gives:
% 158.42/24.87  | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | Case 1:
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | |   (114)  all_56_2 = e2 & op(e2, e3) = e2
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | | ALPHA: (114) implies:
% 158.42/24.87  | | | | | | | | | |   (115)  op(e2, e3) = e2
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | | REF_CLOSE: (19), (89), (90), (115) are inconsistent by
% 158.42/24.87  | | | | | | | | | |            sub-proof #783.
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | Case 2:
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | |   (116)  all_56_3 = e2 & op(e2, e2) = e2
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | | ALPHA: (116) implies:
% 158.42/24.87  | | | | | | | | | |   (117)  op(e2, e2) = e2
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | | REF_CLOSE: (19), (54), (97), (117) are inconsistent by
% 158.42/24.87  | | | | | | | | | |            sub-proof #993.
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | End of split
% 158.42/24.87  | | | | | | | | | 
% 158.42/24.87  | | | | | | | | Case 2:
% 158.42/24.87  | | | | | | | | | 
% 158.42/24.87  | | | | | | | | |   (118)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 &
% 158.42/24.87  | | | | | | | | |            op(e2, e0) = e2)
% 158.42/24.87  | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | REF_CLOSE: (19), (57), (60), (74), (112), (118) are
% 158.42/24.87  | | | | | | | | |            inconsistent by sub-proof #160.
% 158.42/24.87  | | | | | | | | | 
% 158.42/24.87  | | | | | | | | End of split
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | Case 2:
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | |   (119)   ~ (all_54_3 = e2)
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | | REDUCE: (33), (119) imply:
% 158.42/24.87  | | | | | | | |   (120)   ~ (all_52_12 = e2)
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | | BETA: splitting (42) gives:
% 158.42/24.87  | | | | | | | | 
% 158.42/24.87  | | | | | | | | Case 1:
% 158.42/24.87  | | | | | | | | | 
% 158.42/24.87  | | | | | | | | |   (121)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 &
% 158.42/24.87  | | | | | | | | |            op(e2, e0) = e2)
% 158.42/24.87  | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | BETA: splitting (121) gives:
% 158.42/24.87  | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | Case 1:
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | |   (122)  all_56_9 = e2 & op(e3, e0) = e2
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | | REF_CLOSE: (19), (63), (120), (122) are inconsistent by
% 158.42/24.87  | | | | | | | | | |            sub-proof #880.
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.87  | | | | | | | | | Case 2:
% 158.42/24.87  | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | |   (123)  all_56_10 = e2 & op(e2, e0) = e2
% 158.42/24.88  | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | ALPHA: (123) implies:
% 158.42/24.88  | | | | | | | | | |   (124)  all_56_10 = e2
% 158.42/24.88  | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | BETA: splitting (40) gives:
% 158.42/24.88  | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | Case 1:
% 158.42/24.88  | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | |   (125)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 158.42/24.88  | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 158.42/24.88  | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | BETA: splitting (125) gives:
% 158.42/24.88  | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | Case 1:
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | |   (126)  all_56_9 = e3 & op(e3, e0) = e3
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | ALPHA: (126) implies:
% 158.42/24.88  | | | | | | | | | | | |   (127)  all_56_9 = e3
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | REF_CLOSE: (10), (16), (17), (19), (55), (76), (78), (79),
% 158.42/24.88  | | | | | | | | | | | |            (97), (98), (104), (127) are inconsistent by
% 158.42/24.88  | | | | | | | | | | | |            sub-proof #632.
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | Case 2:
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | |   (128)  all_56_10 = e3 & op(e2, e0) = e3
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | REF_CLOSE: (17), (124), (128) are inconsistent by sub-proof
% 158.42/24.88  | | | | | | | | | | | |            #894.
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | End of split
% 158.42/24.88  | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | Case 2:
% 158.42/24.88  | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | |   (129)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 158.42/24.88  | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 158.42/24.88  | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | BETA: splitting (129) gives:
% 158.42/24.88  | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | Case 1:
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | |   (130)  all_56_11 = e3 & op(e1, e0) = e3
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | ALPHA: (130) implies:
% 158.42/24.88  | | | | | | | | | | | |   (131)  op(e1, e0) = e3
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | REF_CLOSE: (19), (34), (79), (131) are inconsistent by
% 158.42/24.88  | | | | | | | | | | | |            sub-proof #314.
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | Case 2:
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | |   (132)  all_56_15 = e3 & op(e0, e0) = e3
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | ALPHA: (132) implies:
% 158.42/24.88  | | | | | | | | | | | |   (133)  all_56_15 = e3
% 158.42/24.88  | | | | | | | | | | | |   (134)  op(e0, e0) = e3
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | BETA: splitting (28) gives:
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | Case 1:
% 158.42/24.88  | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | |   (135)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 158.42/24.88  | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 158.42/24.88  | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | BETA: splitting (135) gives:
% 158.42/24.88  | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | Case 1:
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | |   (136)  all_56_4 = e3 & op(e3, e1) = e3
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | | ALPHA: (136) implies:
% 158.42/24.88  | | | | | | | | | | | | | |   (137)  op(e3, e1) = e3
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (102), (137) are inconsistent by
% 158.42/24.88  | | | | | | | | | | | | | |            sub-proof #982.
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | Case 2:
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | |   (138)  all_56_5 = e3 & op(e2, e1) = e3
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | | ALPHA: (138) implies:
% 158.42/24.88  | | | | | | | | | | | | | |   (139)  op(e2, e1) = e3
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (8), (10), (11), (12), (13), (14), (15),
% 158.42/24.88  | | | | | | | | | | | | | |            (16), (18), (19), (20), (21), (23), (24), (26),
% 158.42/24.88  | | | | | | | | | | | | | |            (27), (29), (30), (31), (32), (35), (36), (37),
% 158.42/24.88  | | | | | | | | | | | | | |            (38), (39), (41), (42), (43), (45), (47), (48),
% 158.42/24.88  | | | | | | | | | | | | | |            (49), (50), (51), (52), (55), (57), (58), (59),
% 158.42/24.88  | | | | | | | | | | | | | |            (60), (63), (64), (65), (66), (67), (69), (71),
% 158.42/24.88  | | | | | | | | | | | | | |            (72), (74), (76), (77), (78), (79), (84), (85),
% 158.42/24.88  | | | | | | | | | | | | | |            (97), (98), (103), (104), (133), (134), (139) are
% 158.42/24.88  | | | | | | | | | | | | | |            inconsistent by sub-proof #137.
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | End of split
% 158.42/24.88  | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | Case 2:
% 158.42/24.88  | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | |   (140)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 158.42/24.88  | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 158.42/24.88  | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | BETA: splitting (140) gives:
% 158.42/24.88  | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | Case 1:
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | |   (141)  all_56_8 = e3 & op(e1, e1) = e3
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | | REF_CLOSE: (17), (47), (141) are inconsistent by sub-proof
% 158.42/24.88  | | | | | | | | | | | | | |            #193.
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | Case 2:
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | |   (142)  all_56_14 = e3 & op(e0, e1) = e3
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | | ALPHA: (142) implies:
% 158.42/24.88  | | | | | | | | | | | | | |   (143)  all_56_14 = e3
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (9), (17), (19), (25), (26), (31), (42),
% 158.42/24.88  | | | | | | | | | | | | | |            (43), (47), (59), (61), (69), (76), (78), (79),
% 158.42/24.88  | | | | | | | | | | | | | |            (97), (98), (104), (134), (143) are inconsistent
% 158.42/24.88  | | | | | | | | | | | | | |            by sub-proof #136.
% 158.42/24.88  | | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | | End of split
% 158.42/24.88  | | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | | End of split
% 158.42/24.88  | | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | | End of split
% 158.42/24.88  | | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | | End of split
% 158.42/24.88  | | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | End of split
% 158.42/24.88  | | | | | | | | | 
% 158.42/24.88  | | | | | | | | Case 2:
% 158.42/24.88  | | | | | | | | | 
% 158.42/24.88  | | | | | | | | |   (144)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2
% 158.42/24.88  | | | | | | | | |            & op(e0, e0) = e2)
% 158.42/24.88  | | | | | | | | | 
% 158.42/24.88  | | | | | | | | | REF_CLOSE: (6), (17), (19), (27), (29), (46), (47), (50),
% 158.42/24.88  | | | | | | | | |            (51), (76), (78), (79), (84), (97), (98), (144) are
% 158.42/24.88  | | | | | | | | |            inconsistent by sub-proof #124.
% 158.42/24.88  | | | | | | | | | 
% 158.42/24.88  | | | | | | | | End of split
% 158.42/24.88  | | | | | | | | 
% 158.42/24.88  | | | | | | | End of split
% 158.42/24.88  | | | | | | | 
% 158.42/24.88  | | | | | | End of split
% 158.42/24.88  | | | | | | 
% 158.42/24.88  | | | | | Case 2:
% 158.42/24.88  | | | | | | 
% 158.42/24.88  | | | | | |   (145)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 158.42/24.88  | | | | | | 
% 158.42/24.88  | | | | | | REF_CLOSE: (1), (53), (75), (95), (145) are inconsistent by
% 158.42/24.88  | | | | | |            sub-proof #853.
% 158.42/24.88  | | | | | | 
% 158.42/24.88  | | | | | End of split
% 158.42/24.88  | | | | | 
% 158.42/24.88  | | | | Case 2:
% 158.42/24.88  | | | | | 
% 158.42/24.88  | | | | |   (146)  all_54_8 = e0
% 158.42/24.88  | | | | | 
% 158.42/24.88  | | | | | REF_CLOSE: (73), (80), (146) are inconsistent by sub-proof #613.
% 158.42/24.88  | | | | | 
% 158.42/24.88  | | | | End of split
% 158.42/24.88  | | | | 
% 158.42/24.88  | | | End of split
% 158.42/24.88  | | | 
% 158.42/24.88  | | End of split
% 158.42/24.88  | | 
% 158.42/24.88  | Case 2:
% 158.42/24.88  | | 
% 158.42/24.88  | |   (147)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) =
% 158.42/24.88  | |            e3)
% 158.42/24.88  | | 
% 158.42/24.88  | | REF_CLOSE: (17), (19), (24), (34), (79), (147) are inconsistent by sub-proof
% 158.42/24.88  | |            #313.
% 158.42/24.88  | | 
% 158.42/24.88  | End of split
% 158.42/24.88  | 
% 158.42/24.88  End of proof
% 158.42/24.88  
% 158.42/24.88  Sub-proof #124 shows that the following formulas are inconsistent:
% 158.42/24.88  ----------------------------------------------------------------
% 158.42/24.88    (1)  op(e0, e0) = e1
% 158.42/24.88    (2)   ~ (e3 = e2)
% 158.42/24.88    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.88    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.42/24.88         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.42/24.88    (5)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.42/24.88    (6)  op(e1, e3) = all_52_2
% 158.42/24.88    (7)   ~ (all_52_2 = e3)
% 158.42/24.88    (8)  all_56_8 = e2
% 158.42/24.88    (9)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.42/24.88         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.42/24.88    (10)  all_56_7 = e3
% 158.42/24.88    (11)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.42/24.88          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.42/24.88    (12)   ~ (e1 = e0)
% 158.42/24.88    (13)   ~ (e2 = e1)
% 158.42/24.88    (14)   ~ (e3 = e1)
% 158.42/24.88    (15)   ~ (e2 = e0)
% 158.42/24.88    (16)   ~ (e3 = e0)
% 158.42/24.88  
% 158.42/24.88  Begin of proof
% 158.42/24.88  | 
% 158.42/24.88  | BETA: splitting (5) gives:
% 158.42/24.88  | 
% 158.42/24.88  | Case 1:
% 158.42/24.88  | | 
% 158.42/24.88  | |   (17)  all_56_11 = e2 & op(e1, e0) = e2
% 158.42/24.88  | | 
% 158.42/24.88  | | ALPHA: (17) implies:
% 158.42/24.88  | |   (18)  all_56_11 = e2
% 158.42/24.88  | | 
% 158.42/24.88  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 158.42/24.88  | |            (15), (16), (18) are inconsistent by sub-proof #183.
% 158.42/24.88  | | 
% 158.42/24.88  | Case 2:
% 158.42/24.88  | | 
% 158.42/24.88  | |   (19)  all_56_15 = e2 & op(e0, e0) = e2
% 158.42/24.88  | | 
% 158.42/24.88  | | ALPHA: (19) implies:
% 158.42/24.88  | |   (20)  op(e0, e0) = e2
% 158.42/24.88  | | 
% 158.42/24.88  | | REF_CLOSE: (1), (3), (13), (20) are inconsistent by sub-proof #875.
% 158.42/24.88  | | 
% 158.42/24.88  | End of split
% 158.42/24.88  | 
% 158.42/24.88  End of proof
% 158.42/24.88  
% 158.42/24.88  Sub-proof #125 shows that the following formulas are inconsistent:
% 158.42/24.88  ----------------------------------------------------------------
% 158.42/24.88    (1)   ~ (e3 = e2)
% 158.42/24.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.88    (3)  op(e1, e1) = e2
% 158.42/24.88    (4)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 158.42/24.88         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.42/24.88    (5)  all_56_5 = e1
% 158.42/24.88    (6)  all_56_14 = e1
% 158.42/24.88    (7)   ~ (e3 = e1)
% 158.42/24.88    (8)   ~ (e3 = e0)
% 158.42/24.88    (9)  all_56_4 = e0
% 158.42/24.88  
% 158.42/24.88  Begin of proof
% 158.42/24.88  | 
% 158.42/24.88  | BETA: splitting (4) gives:
% 158.42/24.88  | 
% 158.42/24.88  | Case 1:
% 158.42/24.88  | | 
% 158.42/24.88  | |   (10)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) =
% 158.42/24.88  | |           e3)
% 158.42/24.88  | | 
% 158.42/24.88  | | BETA: splitting (10) gives:
% 158.42/24.88  | | 
% 158.42/24.88  | | Case 1:
% 158.42/24.88  | | | 
% 158.42/24.88  | | |   (11)  all_56_4 = e3 & op(e3, e1) = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | ALPHA: (11) implies:
% 158.42/24.88  | | |   (12)  all_56_4 = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | REF_CLOSE: (8), (9), (12) are inconsistent by sub-proof #150.
% 158.42/24.88  | | | 
% 158.42/24.88  | | Case 2:
% 158.42/24.88  | | | 
% 158.42/24.88  | | |   (13)  all_56_5 = e3 & op(e2, e1) = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | ALPHA: (13) implies:
% 158.42/24.88  | | |   (14)  all_56_5 = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | COMBINE_EQS: (5), (14) imply:
% 158.42/24.88  | | |   (15)  e3 = e1
% 158.42/24.88  | | | 
% 158.42/24.88  | | | REDUCE: (7), (15) imply:
% 158.42/24.88  | | |   (16)  $false
% 158.42/24.88  | | | 
% 158.42/24.88  | | | CLOSE: (16) is inconsistent.
% 158.42/24.88  | | | 
% 158.42/24.88  | | End of split
% 158.42/24.88  | | 
% 158.42/24.88  | Case 2:
% 158.42/24.88  | | 
% 158.42/24.88  | |   (17)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 158.42/24.88  | |           e3)
% 158.42/24.88  | | 
% 158.42/24.88  | | BETA: splitting (17) gives:
% 158.42/24.88  | | 
% 158.42/24.88  | | Case 1:
% 158.42/24.88  | | | 
% 158.42/24.88  | | |   (18)  all_56_8 = e3 & op(e1, e1) = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | ALPHA: (18) implies:
% 158.42/24.88  | | |   (19)  op(e1, e1) = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | REF_CLOSE: (1), (2), (3), (19) are inconsistent by sub-proof #646.
% 158.42/24.88  | | | 
% 158.42/24.88  | | Case 2:
% 158.42/24.88  | | | 
% 158.42/24.88  | | |   (20)  all_56_14 = e3 & op(e0, e1) = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | ALPHA: (20) implies:
% 158.42/24.88  | | |   (21)  all_56_14 = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | COMBINE_EQS: (6), (21) imply:
% 158.42/24.88  | | |   (22)  e3 = e1
% 158.42/24.88  | | | 
% 158.42/24.88  | | | REDUCE: (7), (22) imply:
% 158.42/24.88  | | |   (23)  $false
% 158.42/24.88  | | | 
% 158.42/24.88  | | | CLOSE: (23) is inconsistent.
% 158.42/24.88  | | | 
% 158.42/24.88  | | End of split
% 158.42/24.88  | | 
% 158.42/24.88  | End of split
% 158.42/24.88  | 
% 158.42/24.88  End of proof
% 158.42/24.88  
% 158.42/24.88  Sub-proof #126 shows that the following formulas are inconsistent:
% 158.42/24.88  ----------------------------------------------------------------
% 158.42/24.88    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.42/24.88         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.42/24.88    (2)   ~ (e3 = e2)
% 158.42/24.88    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.88    (4)   ~ (all_4_2 = e3)
% 158.42/24.88    (5)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.42/24.88         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.42/24.88    (6)  all_56_5 = e1
% 158.42/24.88    (7)  op(e2, e2) = all_4_2
% 158.42/24.88    (8)  op(e3, e3) = e3
% 158.42/24.88    (9)  all_56_10 = e1
% 158.42/24.88    (10)   ~ (e1 = e0)
% 158.42/24.88    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.42/24.88          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.42/24.88    (12)   ~ (e2 = e1)
% 158.42/24.88    (13)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.42/24.88          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.42/24.88    (14)   ~ (e3 = e1)
% 158.42/24.88    (15)   ~ (e2 = e0)
% 158.42/24.88    (16)   ~ (e3 = e0)
% 158.42/24.88  
% 158.42/24.88  Begin of proof
% 158.42/24.88  | 
% 158.42/24.88  | BETA: splitting (5) gives:
% 158.42/24.88  | 
% 158.42/24.88  | Case 1:
% 158.42/24.88  | | 
% 158.42/24.88  | |   (17)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 158.42/24.88  | |           e3)
% 158.42/24.88  | | 
% 158.42/24.88  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (11), (12), (13), (14), (15),
% 158.42/24.88  | |            (16), (17) are inconsistent by sub-proof #475.
% 158.42/24.88  | | 
% 158.42/24.88  | Case 2:
% 158.42/24.88  | | 
% 158.42/24.88  | |   (18)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 158.42/24.88  | |           e3)
% 158.42/24.88  | | 
% 158.42/24.88  | | BETA: splitting (18) gives:
% 158.42/24.88  | | 
% 158.42/24.88  | | Case 1:
% 158.42/24.88  | | | 
% 158.42/24.88  | | |   (19)  all_56_5 = e3 & op(e2, e1) = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | ALPHA: (19) implies:
% 158.42/24.88  | | |   (20)  all_56_5 = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | REF_CLOSE: (6), (14), (20) are inconsistent by sub-proof #531.
% 158.42/24.88  | | | 
% 158.42/24.88  | | Case 2:
% 158.42/24.88  | | | 
% 158.42/24.88  | | |   (21)  all_56_10 = e3 & op(e2, e0) = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | ALPHA: (21) implies:
% 158.42/24.88  | | |   (22)  all_56_10 = e3
% 158.42/24.88  | | | 
% 158.42/24.88  | | | REF_CLOSE: (9), (14), (22) are inconsistent by sub-proof #887.
% 158.42/24.88  | | | 
% 158.42/24.88  | | End of split
% 158.42/24.88  | | 
% 158.42/24.88  | End of split
% 158.42/24.88  | 
% 158.42/24.88  End of proof
% 158.42/24.88  
% 158.42/24.88  Sub-proof #127 shows that the following formulas are inconsistent:
% 158.42/24.88  ----------------------------------------------------------------
% 158.42/24.88    (1)  all_56_9 = e2
% 158.42/24.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.88    (3)  all_56_1 = e1
% 158.42/24.88    (4)  op(e3, e3) = e3
% 158.42/24.88    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.42/24.88         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.42/24.88    (6)   ~ (e1 = e0)
% 158.42/24.88    (7)   ~ (e2 = e1)
% 158.42/24.88    (8)   ~ (e3 = e1)
% 158.42/24.88    (9)  all_56_4 = e1 & op(e3, e1) = e1
% 158.42/24.88    (10)  all_56_4 = e0
% 158.42/24.88  
% 158.42/24.88  Begin of proof
% 158.42/24.88  | 
% 158.42/24.88  | ALPHA: (9) implies:
% 158.42/24.88  |   (11)  all_56_4 = e1
% 158.42/24.88  | 
% 158.42/24.88  | COMBINE_EQS: (10), (11) imply:
% 158.42/24.88  |   (12)  e1 = e0
% 158.42/24.88  | 
% 158.42/24.88  | COMBINE_EQS: (3), (12) imply:
% 158.42/24.88  |   (13)  all_56_1 = e0
% 158.42/24.88  | 
% 158.42/24.88  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13) are inconsistent by
% 158.42/24.88  |            sub-proof #515.
% 158.42/24.88  | 
% 158.42/24.88  End of proof
% 158.42/24.88  
% 158.42/24.88  Sub-proof #128 shows that the following formulas are inconsistent:
% 158.42/24.88  ----------------------------------------------------------------
% 158.42/24.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.88    (2)  all_56_11 = e0
% 158.42/24.88    (3)  op(e1, e1) = e2
% 158.42/24.88    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.42/24.88         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.42/24.88    (5)  all_56_1 = e1
% 158.42/24.88    (6)  op(e3, e3) = e3
% 158.42/24.88    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 158.42/24.88    (8)  op(e1, e2) = e3
% 158.42/24.88    (9)   ~ (e1 = e0)
% 158.42/24.88    (10)   ~ (e2 = e1)
% 158.42/24.88    (11)  all_56_6 = e1
% 158.42/24.88    (12)   ~ (e3 = e1)
% 158.42/24.88    (13)   ~ (e3 = e0)
% 158.42/24.88  
% 158.42/24.88  Begin of proof
% 158.42/24.88  | 
% 158.42/24.88  | BETA: splitting (7) gives:
% 158.42/24.88  | 
% 158.42/24.88  | Case 1:
% 158.42/24.88  | | 
% 158.42/24.88  | |   (14)  all_56_0 = e0 & op(e3, e3) = e0
% 158.42/24.88  | | 
% 158.42/24.88  | | ALPHA: (14) implies:
% 158.42/24.88  | |   (15)  op(e3, e3) = e0
% 158.42/24.88  | | 
% 158.42/24.88  | | REF_CLOSE: (1), (6), (13), (15) are inconsistent by sub-proof #971.
% 158.42/24.88  | | 
% 158.42/24.88  | Case 2:
% 158.42/24.88  | | 
% 158.42/24.88  | |   (16)  all_56_1 = e0 & op(e3, e2) = e0
% 158.42/24.88  | | 
% 158.42/24.88  | | ALPHA: (16) implies:
% 158.42/24.89  | |   (17)  all_56_1 = e0
% 158.42/24.89  | | 
% 158.42/24.89  | | COMBINE_EQS: (5), (17) imply:
% 158.42/24.89  | |   (18)  e1 = e0
% 158.42/24.89  | | 
% 158.42/24.89  | | COMBINE_EQS: (11), (18) imply:
% 158.42/24.89  | |   (19)  all_56_6 = e0
% 158.42/24.89  | | 
% 158.42/24.89  | | BETA: splitting (4) gives:
% 158.42/24.89  | | 
% 158.42/24.89  | | Case 1:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (20)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 158.42/24.89  | | |           e1)
% 158.42/24.89  | | | 
% 158.42/24.89  | | | REF_CLOSE: (1), (8), (9), (12), (19), (20) are inconsistent by sub-proof
% 158.42/24.89  | | |            #134.
% 158.42/24.89  | | | 
% 158.42/24.89  | | Case 2:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (21)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 158.42/24.89  | | |           e1)
% 158.42/24.89  | | | 
% 158.42/24.89  | | | REF_CLOSE: (1), (2), (3), (9), (10), (21) are inconsistent by sub-proof
% 158.42/24.89  | | |            #132.
% 158.42/24.89  | | | 
% 158.42/24.89  | | End of split
% 158.42/24.89  | | 
% 158.42/24.89  | End of split
% 158.42/24.89  | 
% 158.42/24.89  End of proof
% 158.42/24.89  
% 158.42/24.89  Sub-proof #129 shows that the following formulas are inconsistent:
% 158.42/24.89  ----------------------------------------------------------------
% 158.42/24.89    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.42/24.89         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.42/24.89    (2)  op(e0, e0) = e1
% 158.42/24.89    (3)  op(e0, e3) = e2
% 158.42/24.89    (4)   ~ (e3 = e2)
% 158.42/24.89    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.89    (6)  op(e0, e3) = all_52_3
% 158.42/24.89    (7)  all_56_13 = e1
% 158.42/24.89    (8)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 158.42/24.89         (all_56_14 = e0 & op(e0, e1) = e0)
% 158.42/24.89    (9)  op(e3, e3) = e3
% 158.42/24.89    (10)   ~ (e1 = e0)
% 158.42/24.89    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.42/24.89          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.42/24.89    (12)   ~ (e2 = e1)
% 158.42/24.89    (13)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.42/24.89          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.42/24.89            e3)
% 158.42/24.89    (14)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.42/24.89          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.42/24.89    (15)   ~ (e3 = e1)
% 158.42/24.89    (16)   ~ (e2 = e0)
% 158.42/24.89    (17)   ~ (e3 = e0)
% 158.42/24.89  
% 158.42/24.89  Begin of proof
% 158.42/24.89  | 
% 158.42/24.89  | BETA: splitting (13) gives:
% 158.42/24.89  | 
% 158.42/24.89  | Case 1:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (18)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 158.42/24.89  | |           e3)
% 158.42/24.89  | | 
% 158.42/24.89  | | BETA: splitting (18) gives:
% 158.42/24.89  | | 
% 158.42/24.89  | | Case 1:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (19)  all_56_12 = e3 & op(e0, e3) = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | ALPHA: (19) implies:
% 158.42/24.89  | | |   (20)  all_56_12 = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | REF_CLOSE: (1), (4), (5), (9), (10), (11), (12), (14), (15), (16), (17),
% 158.42/24.89  | | |            (20) are inconsistent by sub-proof #729.
% 158.42/24.89  | | | 
% 158.42/24.89  | | Case 2:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (21)  all_56_13 = e3 & op(e0, e2) = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | REF_CLOSE: (7), (15), (21) are inconsistent by sub-proof #161.
% 158.42/24.89  | | | 
% 158.42/24.89  | | End of split
% 158.42/24.89  | | 
% 158.42/24.89  | Case 2:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (22)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.42/24.89  | |           e3)
% 158.42/24.89  | | 
% 158.42/24.89  | | BETA: splitting (22) gives:
% 158.42/24.89  | | 
% 158.42/24.89  | | Case 1:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (23)  all_56_14 = e3 & op(e0, e1) = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | ALPHA: (23) implies:
% 158.42/24.89  | | |   (24)  all_56_14 = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | REF_CLOSE: (3), (5), (6), (7), (8), (10), (16), (17), (24) are
% 158.42/24.89  | | |            inconsistent by sub-proof #130.
% 158.42/24.89  | | | 
% 158.42/24.89  | | Case 2:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (25)  all_56_15 = e3 & op(e0, e0) = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | ALPHA: (25) implies:
% 158.42/24.89  | | |   (26)  op(e0, e0) = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | REF_CLOSE: (2), (5), (15), (26) are inconsistent by sub-proof #473.
% 158.42/24.89  | | | 
% 158.42/24.89  | | End of split
% 158.42/24.89  | | 
% 158.42/24.89  | End of split
% 158.42/24.89  | 
% 158.42/24.89  End of proof
% 158.42/24.89  
% 158.42/24.89  Sub-proof #130 shows that the following formulas are inconsistent:
% 158.42/24.89  ----------------------------------------------------------------
% 158.42/24.89    (1)  op(e0, e3) = e2
% 158.42/24.89    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.89    (3)  op(e0, e3) = all_52_3
% 158.42/24.89    (4)  all_56_13 = e1
% 158.42/24.89    (5)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 158.42/24.89         (all_56_14 = e0 & op(e0, e1) = e0)
% 158.42/24.89    (6)  all_56_14 = e3
% 158.42/24.89    (7)   ~ (e1 = e0)
% 158.42/24.89    (8)   ~ (e2 = e0)
% 158.42/24.89    (9)   ~ (e3 = e0)
% 158.42/24.89  
% 158.42/24.89  Begin of proof
% 158.42/24.89  | 
% 158.42/24.89  | BETA: splitting (5) gives:
% 158.42/24.89  | 
% 158.42/24.89  | Case 1:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (10)  all_56_12 = e0 & op(e0, e3) = e0
% 158.42/24.89  | | 
% 158.42/24.89  | | ALPHA: (10) implies:
% 158.42/24.89  | |   (11)  op(e0, e3) = e0
% 158.42/24.89  | | 
% 158.42/24.89  | | REF_CLOSE: (1), (2), (3), (8), (11) are inconsistent by sub-proof #689.
% 158.42/24.89  | | 
% 158.42/24.89  | Case 2:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (12)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 158.42/24.89  | |           e0)
% 158.42/24.89  | | 
% 158.42/24.89  | | BETA: splitting (12) gives:
% 158.42/24.89  | | 
% 158.42/24.89  | | Case 1:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (13)  all_56_13 = e0 & op(e0, e2) = e0
% 158.42/24.89  | | | 
% 158.42/24.89  | | | ALPHA: (13) implies:
% 158.42/24.89  | | |   (14)  all_56_13 = e0
% 158.42/24.89  | | | 
% 158.42/24.89  | | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #131.
% 158.42/24.89  | | | 
% 158.42/24.89  | | Case 2:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (15)  all_56_14 = e0 & op(e0, e1) = e0
% 158.42/24.89  | | | 
% 158.42/24.89  | | | REF_CLOSE: (6), (9), (15) are inconsistent by sub-proof #175.
% 158.42/24.89  | | | 
% 158.42/24.89  | | End of split
% 158.42/24.89  | | 
% 158.42/24.89  | End of split
% 158.42/24.89  | 
% 158.42/24.89  End of proof
% 158.42/24.89  
% 158.42/24.89  Sub-proof #131 shows that the following formulas are inconsistent:
% 158.42/24.89  ----------------------------------------------------------------
% 158.42/24.89    (1)  all_56_13 = e1
% 158.42/24.89    (2)  all_56_13 = e0
% 158.42/24.89    (3)   ~ (e1 = e0)
% 158.42/24.89  
% 158.42/24.89  Begin of proof
% 158.42/24.89  | 
% 158.42/24.89  | COMBINE_EQS: (1), (2) imply:
% 158.42/24.89  |   (4)  e1 = e0
% 158.42/24.89  | 
% 158.42/24.89  | SIMP: (4) implies:
% 158.42/24.89  |   (5)  e1 = e0
% 158.42/24.89  | 
% 158.42/24.89  | REDUCE: (3), (5) imply:
% 158.42/24.89  |   (6)  $false
% 158.42/24.89  | 
% 158.42/24.89  | CLOSE: (6) is inconsistent.
% 158.42/24.89  | 
% 158.42/24.89  End of proof
% 158.42/24.89  
% 158.42/24.89  Sub-proof #132 shows that the following formulas are inconsistent:
% 158.42/24.89  ----------------------------------------------------------------
% 158.42/24.89    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.89    (2)  all_56_11 = e0
% 158.42/24.89    (3)  op(e1, e1) = e2
% 158.42/24.89    (4)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.42/24.89    (5)   ~ (e1 = e0)
% 158.42/24.89    (6)   ~ (e2 = e1)
% 158.42/24.89  
% 158.42/24.89  Begin of proof
% 158.42/24.89  | 
% 158.42/24.89  | BETA: splitting (4) gives:
% 158.42/24.89  | 
% 158.42/24.89  | Case 1:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (7)  all_56_8 = e1 & op(e1, e1) = e1
% 158.42/24.89  | | 
% 158.42/24.89  | | ALPHA: (7) implies:
% 158.42/24.89  | |   (8)  op(e1, e1) = e1
% 158.42/24.89  | | 
% 158.42/24.89  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #986.
% 158.42/24.89  | | 
% 158.42/24.89  | Case 2:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (9)  all_56_11 = e1 & op(e1, e0) = e1
% 158.42/24.89  | | 
% 158.42/24.89  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #885.
% 158.42/24.89  | | 
% 158.42/24.89  | End of split
% 158.42/24.89  | 
% 158.42/24.89  End of proof
% 158.42/24.89  
% 158.42/24.89  Sub-proof #133 shows that the following formulas are inconsistent:
% 158.42/24.89  ----------------------------------------------------------------
% 158.42/24.89    (1)  op(e0, e0) = e1
% 158.42/24.89    (2)  all_56_9 = e2
% 158.42/24.89    (3)   ~ (e3 = e2)
% 158.42/24.89    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.89    (5)  op(e1, e0) = e0
% 158.42/24.89    (6)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 158.42/24.89         (all_56_11 = e0 & op(e1, e0) = e0)
% 158.42/24.89    (7)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.42/24.89         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.42/24.89    (8)  all_56_11 = e1
% 158.42/24.89    (9)   ~ (e1 = e0)
% 158.42/24.89    (10)   ~ (e3 = e1)
% 158.42/24.89    (11)   ~ (e2 = e0)
% 158.42/24.89    (12)   ~ (e3 = e0)
% 158.42/24.89  
% 158.42/24.89  Begin of proof
% 158.42/24.89  | 
% 158.42/24.89  | BETA: splitting (7) gives:
% 158.42/24.89  | 
% 158.42/24.89  | Case 1:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (13)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 158.42/24.89  | |           e3)
% 158.42/24.89  | | 
% 158.42/24.89  | | BETA: splitting (13) gives:
% 158.42/24.89  | | 
% 158.42/24.89  | | Case 1:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (14)  all_56_9 = e3 & op(e3, e0) = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | ALPHA: (14) implies:
% 158.42/24.89  | | |   (15)  all_56_9 = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | REF_CLOSE: (2), (3), (15) are inconsistent by sub-proof #888.
% 158.42/24.89  | | | 
% 158.42/24.89  | | Case 2:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (16)  all_56_10 = e3 & op(e2, e0) = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | ALPHA: (16) implies:
% 158.42/24.89  | | |   (17)  all_56_10 = e3
% 158.42/24.89  | | | 
% 158.42/24.89  | | | REF_CLOSE: (2), (6), (8), (9), (11), (12), (17) are inconsistent by
% 158.42/24.89  | | |            sub-proof #474.
% 158.42/24.89  | | | 
% 158.42/24.89  | | End of split
% 158.42/24.89  | | 
% 158.42/24.89  | Case 2:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (18)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.42/24.89  | |           e3)
% 158.42/24.89  | | 
% 158.42/24.89  | | REF_CLOSE: (1), (4), (5), (10), (12), (18) are inconsistent by sub-proof
% 158.42/24.89  | |            #294.
% 158.42/24.89  | | 
% 158.42/24.89  | End of split
% 158.42/24.89  | 
% 158.42/24.89  End of proof
% 158.42/24.89  
% 158.42/24.89  Sub-proof #134 shows that the following formulas are inconsistent:
% 158.42/24.89  ----------------------------------------------------------------
% 158.42/24.89    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.89    (2)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1)
% 158.42/24.89    (3)  all_56_6 = e0
% 158.42/24.89    (4)  op(e1, e2) = e3
% 158.42/24.89    (5)   ~ (e1 = e0)
% 158.42/24.89    (6)   ~ (e3 = e1)
% 158.42/24.89  
% 158.42/24.89  Begin of proof
% 158.42/24.89  | 
% 158.42/24.89  | BETA: splitting (2) gives:
% 158.42/24.89  | 
% 158.42/24.89  | Case 1:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (7)  all_56_6 = e1 & op(e1, e3) = e1
% 158.42/24.89  | | 
% 158.42/24.89  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #917.
% 158.42/24.89  | | 
% 158.42/24.89  | Case 2:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (8)  all_56_7 = e1 & op(e1, e2) = e1
% 158.42/24.89  | | 
% 158.42/24.89  | | ALPHA: (8) implies:
% 158.42/24.89  | |   (9)  op(e1, e2) = e1
% 158.42/24.89  | | 
% 158.42/24.89  | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #939.
% 158.42/24.89  | | 
% 158.42/24.89  | End of split
% 158.42/24.89  | 
% 158.42/24.89  End of proof
% 158.42/24.89  
% 158.42/24.89  Sub-proof #135 shows that the following formulas are inconsistent:
% 158.42/24.89  ----------------------------------------------------------------
% 158.42/24.89    (1)  op(e0, e0) = e1
% 158.42/24.89    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.89    (3)  op(e1, e1) = e2
% 158.42/24.89    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.42/24.89         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.42/24.89    (5)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.42/24.89    (6)  all_56_8 = e2
% 158.42/24.89    (7)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.42/24.89         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.42/24.89    (8)  op(e1, e2) = e3
% 158.42/24.89    (9)  all_56_7 = e3
% 158.42/24.89    (10)   ~ (e1 = e0)
% 158.42/24.89    (11)   ~ (e2 = e1)
% 158.42/24.89    (12)   ~ (e3 = e1)
% 158.42/24.89    (13)   ~ (e2 = e0)
% 158.42/24.89    (14)   ~ (e3 = e0)
% 158.42/24.89  
% 158.42/24.89  Begin of proof
% 158.42/24.89  | 
% 158.42/24.89  | BETA: splitting (5) gives:
% 158.42/24.89  | 
% 158.42/24.89  | Case 1:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (15)  all_56_11 = e2 & op(e1, e0) = e2
% 158.42/24.89  | | 
% 158.42/24.89  | | ALPHA: (15) implies:
% 158.42/24.89  | |   (16)  all_56_11 = e2
% 158.42/24.89  | | 
% 158.42/24.89  | | BETA: splitting (4) gives:
% 158.42/24.89  | | 
% 158.42/24.89  | | Case 1:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (17)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 158.42/24.89  | | |           e1)
% 158.42/24.89  | | | 
% 158.42/24.89  | | | BETA: splitting (17) gives:
% 158.42/24.89  | | | 
% 158.42/24.89  | | | Case 1:
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | |   (18)  all_56_6 = e1 & op(e1, e3) = e1
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | | ALPHA: (18) implies:
% 158.42/24.89  | | | |   (19)  all_56_6 = e1
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | | REF_CLOSE: (6), (7), (9), (10), (13), (14), (16), (19) are inconsistent
% 158.42/24.89  | | | |            by sub-proof #190.
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | Case 2:
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | |   (20)  all_56_7 = e1 & op(e1, e2) = e1
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | | ALPHA: (20) implies:
% 158.42/24.89  | | | |   (21)  op(e1, e2) = e1
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | | REF_CLOSE: (2), (8), (12), (21) are inconsistent by sub-proof #939.
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | End of split
% 158.42/24.89  | | | 
% 158.42/24.89  | | Case 2:
% 158.42/24.89  | | | 
% 158.42/24.89  | | |   (22)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 158.42/24.89  | | |           e1)
% 158.42/24.89  | | | 
% 158.42/24.89  | | | BETA: splitting (22) gives:
% 158.42/24.89  | | | 
% 158.42/24.89  | | | Case 1:
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | |   (23)  all_56_8 = e1 & op(e1, e1) = e1
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | | ALPHA: (23) implies:
% 158.42/24.89  | | | |   (24)  op(e1, e1) = e1
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | | REF_CLOSE: (2), (3), (11), (24) are inconsistent by sub-proof #986.
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | Case 2:
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | |   (25)  all_56_11 = e1 & op(e1, e0) = e1
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | | ALPHA: (25) implies:
% 158.42/24.89  | | | |   (26)  all_56_11 = e1
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | | REF_CLOSE: (11), (16), (26) are inconsistent by sub-proof #621.
% 158.42/24.89  | | | | 
% 158.42/24.89  | | | End of split
% 158.42/24.89  | | | 
% 158.42/24.89  | | End of split
% 158.42/24.89  | | 
% 158.42/24.89  | Case 2:
% 158.42/24.89  | | 
% 158.42/24.89  | |   (27)  all_56_15 = e2 & op(e0, e0) = e2
% 158.42/24.89  | | 
% 158.42/24.89  | | ALPHA: (27) implies:
% 158.42/24.89  | |   (28)  op(e0, e0) = e2
% 158.42/24.89  | | 
% 158.42/24.89  | | REF_CLOSE: (1), (2), (11), (28) are inconsistent by sub-proof #875.
% 158.42/24.89  | | 
% 158.42/24.89  | End of split
% 158.42/24.89  | 
% 158.42/24.89  End of proof
% 158.42/24.89  
% 158.42/24.89  Sub-proof #136 shows that the following formulas are inconsistent:
% 158.42/24.89  ----------------------------------------------------------------
% 158.42/24.89    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.42/24.89         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.42/24.89    (2)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.42/24.89         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.42/24.89    (3)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 158.42/24.89         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.42/24.89    (4)   ~ (e3 = e2)
% 158.42/24.89    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.89    (6)   ~ (all_4_2 = e3)
% 158.42/24.89    (7)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.42/24.89             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 158.42/24.89               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.42/24.89               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.42/24.89    (8)  all_56_14 = e3
% 158.42/24.89    (9)  op(e0, e0) = e3
% 158.42/24.89    (10)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.42/24.89          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.42/24.89    (11)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.42/24.89          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.42/24.89    (12)  op(e2, e2) = all_4_2
% 158.42/24.89    (13)  op(e3, e3) = e3
% 158.42/24.89    (14)  all_56_8 = e2
% 158.42/24.89    (15)   ~ (e1 = e0)
% 158.42/24.90    (16)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.42/24.90          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.42/24.90    (17)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.42/24.90          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.42/24.90    (18)   ~ (e2 = e1)
% 158.42/24.90    (19)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.42/24.90          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.42/24.90    (20)   ~ (e3 = e1)
% 158.42/24.90    (21)   ~ (e2 = e0)
% 158.42/24.90    (22)   ~ (e3 = e0)
% 158.42/24.90  
% 158.42/24.90  Begin of proof
% 158.42/24.90  | 
% 158.42/24.90  | BETA: splitting (10) gives:
% 158.42/24.90  | 
% 158.42/24.90  | Case 1:
% 158.42/24.90  | | 
% 158.42/24.90  | |   (23)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 158.42/24.90  | |           e3)
% 158.42/24.90  | | 
% 158.42/24.90  | | REF_CLOSE: (1), (4), (5), (6), (12), (13), (15), (16), (18), (19), (20),
% 158.42/24.90  | |            (21), (22), (23) are inconsistent by sub-proof #475.
% 158.42/24.90  | | 
% 158.42/24.90  | Case 2:
% 158.42/24.90  | | 
% 158.42/24.90  | |   (24)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 158.42/24.90  | |           e3)
% 158.42/24.90  | | 
% 158.42/24.90  | | BETA: splitting (24) gives:
% 158.42/24.90  | | 
% 158.42/24.90  | | Case 1:
% 158.42/24.90  | | | 
% 158.42/24.90  | | |   (25)  all_56_5 = e3 & op(e2, e1) = e3
% 158.42/24.90  | | | 
% 158.42/24.90  | | | REF_CLOSE: (3), (8), (14), (15), (17), (18), (20), (21), (22), (25) are
% 158.42/24.90  | | |            inconsistent by sub-proof #174.
% 158.42/24.90  | | | 
% 158.42/24.90  | | Case 2:
% 158.42/24.90  | | | 
% 158.42/24.90  | | |   (26)  all_56_10 = e3 & op(e2, e0) = e3
% 158.42/24.90  | | | 
% 158.42/24.90  | | | ALPHA: (26) implies:
% 158.42/24.90  | | |   (27)  all_56_10 = e3
% 158.42/24.90  | | | 
% 158.42/24.90  | | | REF_CLOSE: (2), (4), (5), (7), (9), (11), (15), (18), (20), (21), (22),
% 158.42/24.90  | | |            (27) are inconsistent by sub-proof #466.
% 158.42/24.90  | | | 
% 158.42/24.90  | | End of split
% 158.42/24.90  | | 
% 158.42/24.90  | End of split
% 158.42/24.90  | 
% 158.42/24.90  End of proof
% 158.42/24.90  
% 158.42/24.90  Sub-proof #137 shows that the following formulas are inconsistent:
% 158.42/24.90  ----------------------------------------------------------------
% 158.42/24.90    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.42/24.90         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.42/24.90    (2)  all_54_5 = all_4_2
% 158.42/24.90    (3)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.42/24.90         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.42/24.90    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.42/24.90         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.42/24.90    (5)   ~ (all_24_2 = e1) | ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 &
% 158.42/24.90           $i(all_24_0)) | ( ~ (all_24_1 = e0) & op(e1, e1) = all_24_1 &
% 158.42/24.90           $i(all_24_1))
% 158.42/24.90    (6)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.42/24.90         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 158.42/24.90    (7)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.42/24.90    (8)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.42/24.90             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.42/24.90           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.42/24.90               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.42/24.90             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.42/24.90         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.42/24.90             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.42/24.90           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.42/24.90               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.42/24.90             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.42/24.90         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.42/24.90             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.42/24.90           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.42/24.90               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.42/24.90             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.42/24.90         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.42/24.90             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.42/24.90           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.42/24.90               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.42/24.90             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.42/24.90    (9)   ~ (all_52_4 = all_52_6)
% 158.42/24.90    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.42/24.90          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.42/24.90    (11)  ( ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 & $i(all_10_0)) | ( ~
% 158.42/24.90            (all_10_1 = e0) & op(e2, e2) = all_10_1 & $i(all_10_1))
% 158.42/24.90    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.42/24.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.42/24.90    (13)  op(e0, e3) = all_52_3
% 158.42/24.90    (14)  op(e3, e1) = all_52_8
% 158.42/24.90    (15)   ~ (all_52_12 = e3)
% 158.42/24.90    (16)   ~ (all_52_9 = all_4_2)
% 158.42/24.90    (17)  op(e1, e1) = e2
% 158.42/24.90    (18)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.42/24.90              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 158.42/24.90                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.42/24.90                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.42/24.90    (19)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.42/24.90          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.42/24.90    (20)  op(e1, e3) = all_52_2
% 158.42/24.90    (21)  op(e0, e0) = e3
% 158.42/24.90    (22)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.42/24.90          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.42/24.90    (23)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.42/24.90          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.42/24.90    (24)   ~ (all_52_13 = all_4_2)
% 158.42/24.90    (25)   ~ (all_52_2 = e2)
% 158.42/24.90    (26)  op(e1, e2) = all_52_6
% 158.42/24.90    (27)   ~ (all_52_12 = all_52_13)
% 158.42/24.90    (28)  op(e1, e0) = all_52_14
% 158.42/24.90    (29)  all_24_2 = all_4_2
% 158.42/24.90    (30)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.42/24.90          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.42/24.90    (31)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.42/24.90          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.42/24.90    (32)  op(e2, e2) = all_4_2
% 158.42/24.90    (33)  all_56_15 = e3
% 158.42/24.90    (34)   ~ (all_52_2 = all_52_6)
% 158.42/24.90    (35)  op(e3, e3) = e3
% 158.42/24.90    (36)  all_56_8 = e2
% 158.42/24.90    (37)  op(e0, e0) = all_14_2
% 158.42/24.90    (38)  op(e2, e3) = all_52_1
% 158.42/24.90    (39)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.42/24.90          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.42/24.90    (40)  op(e1, e2) = e3
% 158.42/24.90    (41)  all_56_7 = e3
% 158.42/24.90    (42)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.42/24.90          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.42/24.90    (43)  op(e3, e2) = all_52_4
% 158.42/24.90    (44)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.42/24.90          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.42/24.90    (45)   ~ (e1 = e0)
% 158.42/24.90    (46)  op(e2, e1) = all_52_9
% 158.42/24.90    (47)   ~ (all_52_8 = all_52_9)
% 158.42/24.90    (48)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.42/24.90          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.42/24.90    (49)  op(e2, e0) = all_52_13
% 158.42/24.90    (50)  op(e2, e1) = e3
% 158.42/24.90    (51)   ~ (e2 = e1)
% 158.42/24.90    (52)  op(e3, e0) = all_52_12
% 158.42/24.90    (53)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.42/24.90          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.42/24.90            e3)
% 158.42/24.90    (54)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.42/24.90          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.42/24.90    (55)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.42/24.90          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.42/24.90    (56)   ~ (all_52_8 = e2)
% 158.42/24.90    (57)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.42/24.90          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.42/24.91    (58)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.42/24.91            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.42/24.91            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.42/24.91            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.42/24.91              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.42/24.91          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.42/24.91            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.42/24.91              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.42/24.91            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.42/24.91              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.42/24.91          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.42/24.91            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.42/24.91              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.42/24.91            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.42/24.91              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.42/24.91          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.42/24.91            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.42/24.91            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.42/24.91              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.42/24.91            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.42/24.91            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.42/24.91            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.42/24.91            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.42/24.91              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.42/24.91            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.42/24.91          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.42/24.91            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.42/24.91              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.42/24.91            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.42/24.91            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.42/24.91          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.42/24.91            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.42/24.91              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.42/24.91            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.42/24.91            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.42/24.91          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.42/24.91            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.42/24.91              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.42/24.91            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.42/24.91              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.42/24.91          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.42/24.91            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.42/24.91            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.42/24.91            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.42/24.91            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.42/24.91            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.42/24.91            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.42/24.91            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.42/24.91              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.42/24.91            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.42/24.91            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.42/24.91            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.42/24.91            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.42/24.91              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.42/24.91            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.42/24.91          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.42/24.91            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.42/24.91              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.42/24.91              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.42/24.91            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.42/24.91            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.42/24.91            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.42/24.91            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.42/24.91              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.42/24.91            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.42/24.91          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.42/24.91            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.42/24.91              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.42/24.91            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.42/24.91              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.42/24.91          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.42/24.91            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.42/24.91              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.42/24.91              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.42/24.91            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.42/24.91          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.42/24.91            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.42/24.91            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.42/24.91                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.42/24.91                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.42/24.91                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.42/24.91                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.42/24.91                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.42/24.91                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.42/24.91                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.42/24.91                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.42/24.91                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.42/24.91                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.42/24.91                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.42/24.91                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.42/24.91                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.42/24.91                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.42/24.91                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.42/24.91                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.42/24.91                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.42/24.91                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.42/24.91                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.42/24.91                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.42/24.91                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.42/24.91                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.42/24.91                op(e0, e1) = e0)))
% 158.42/24.91    (59)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.42/24.91          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.42/24.91            e1)
% 158.42/24.91    (60)   ~ (all_52_9 = e2)
% 158.42/24.91    (61)   ~ (e3 = e1)
% 158.42/24.91    (62)   ~ (all_52_1 = all_4_2)
% 158.42/24.91    (63)   ~ (e2 = e0)
% 158.42/24.91    (64)   ~ (e3 = e0)
% 158.42/24.91  
% 158.42/24.91  Begin of proof
% 158.42/24.91  | 
% 158.42/24.91  | GROUND_INST: instantiating (12) with all_52_6, e3, e2, e1, simplifying with
% 158.42/24.91  |              (26), (40) gives:
% 158.42/24.91  |   (65)  all_52_6 = e3
% 158.42/24.91  | 
% 158.42/24.91  | GROUND_INST: instantiating (12) with all_52_9, e3, e1, e2, simplifying with
% 158.42/24.91  |              (46), (50) gives:
% 158.42/24.91  |   (66)  all_52_9 = e3
% 158.42/24.91  | 
% 158.42/24.91  | REDUCE: (34), (65) imply:
% 158.42/24.91  |   (67)   ~ (all_52_2 = e3)
% 158.42/24.91  | 
% 158.42/24.91  | REDUCE: (9), (65) imply:
% 158.42/24.91  |   (68)   ~ (all_52_4 = e3)
% 158.42/24.91  | 
% 158.42/24.91  | REDUCE: (47), (66) imply:
% 158.42/24.91  |   (69)   ~ (all_52_8 = e3)
% 158.42/24.91  | 
% 158.42/24.91  | REDUCE: (16), (66) imply:
% 158.42/24.91  |   (70)   ~ (all_4_2 = e3)
% 158.42/24.91  | 
% 158.42/24.91  | SIMP: (70) implies:
% 158.42/24.91  |   (71)   ~ (all_4_2 = e3)
% 158.42/24.91  | 
% 158.42/24.91  | REDUCE: (60), (66) imply:
% 158.42/24.91  |   (72)   ~ (e3 = e2)
% 158.42/24.91  | 
% 158.42/24.91  | BETA: splitting (11) gives:
% 158.42/24.91  | 
% 158.42/24.91  | Case 1:
% 158.42/24.91  | | 
% 158.42/24.91  | |   (73)   ~ (all_10_0 = e3) & op(e2, e1) = all_10_0 & $i(all_10_0)
% 158.42/24.91  | | 
% 158.42/24.91  | | ALPHA: (73) implies:
% 158.42/24.91  | |   (74)   ~ (all_10_0 = e3)
% 158.42/24.91  | |   (75)  op(e2, e1) = all_10_0
% 158.42/24.91  | | 
% 158.42/24.91  | | GROUND_INST: instantiating (12) with e3, all_10_0, e1, e2, simplifying with
% 158.42/24.91  | |              (50), (75) gives:
% 158.42/24.91  | |   (76)  all_10_0 = e3
% 158.42/24.91  | | 
% 158.42/24.91  | | REDUCE: (74), (76) imply:
% 158.42/24.91  | |   (77)  $false
% 158.42/24.91  | | 
% 158.42/24.91  | | CLOSE: (77) is inconsistent.
% 158.42/24.91  | | 
% 158.42/24.91  | Case 2:
% 158.42/24.91  | | 
% 158.42/24.91  | |   (78)   ~ (all_10_1 = e0) & op(e2, e2) = all_10_1 & $i(all_10_1)
% 158.42/24.91  | | 
% 158.42/24.91  | | ALPHA: (78) implies:
% 158.42/24.91  | |   (79)   ~ (all_10_1 = e0)
% 158.42/24.91  | |   (80)  op(e2, e2) = all_10_1
% 158.42/24.91  | | 
% 158.42/24.91  | | GROUND_INST: instantiating (12) with all_4_2, all_10_1, e2, e2, simplifying
% 158.42/24.91  | |              with (32), (80) gives:
% 158.42/24.91  | |   (81)  all_10_1 = all_4_2
% 158.42/24.91  | | 
% 158.42/24.91  | | REDUCE: (79), (81) imply:
% 158.42/24.91  | |   (82)   ~ (all_4_2 = e0)
% 158.42/24.91  | | 
% 158.42/24.91  | | BETA: splitting (5) gives:
% 158.42/24.91  | | 
% 158.42/24.91  | | Case 1:
% 158.42/24.91  | | | 
% 158.42/24.91  | | |   (83)   ~ (all_24_2 = e1)
% 158.42/24.91  | | | 
% 158.42/24.91  | | | REDUCE: (29), (83) imply:
% 158.42/24.91  | | |   (84)   ~ (all_4_2 = e1)
% 158.42/24.91  | | | 
% 158.42/24.91  | | | BETA: splitting (7) gives:
% 158.42/24.91  | | | 
% 158.42/24.91  | | | Case 1:
% 158.42/24.91  | | | | 
% 158.42/24.91  | | | |   (85)  all_54_5 = e3
% 158.42/24.91  | | | | 
% 158.42/24.91  | | | | REF_CLOSE: (2), (71), (85) are inconsistent by sub-proof #930.
% 158.42/24.91  | | | | 
% 158.42/24.91  | | | Case 2:
% 158.42/24.91  | | | | 
% 158.42/24.91  | | | |   (86)   ~ (all_54_5 = e3)
% 158.42/24.91  | | | |   (87)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.42/24.91  | | | | 
% 158.42/24.91  | | | | BETA: splitting (87) gives:
% 158.42/24.91  | | | | 
% 158.42/24.91  | | | | Case 1:
% 158.42/24.91  | | | | | 
% 158.42/24.91  | | | | |   (88)  all_54_5 = e2
% 158.42/24.91  | | | | | 
% 158.42/24.91  | | | | | COMBINE_EQS: (2), (88) imply:
% 158.42/24.91  | | | | |   (89)  all_4_2 = e2
% 158.42/24.91  | | | | | 
% 158.42/24.91  | | | | | SIMP: (89) implies:
% 158.42/24.91  | | | | |   (90)  all_4_2 = e2
% 158.42/24.91  | | | | | 
% 158.42/24.91  | | | | | REDUCE: (62), (90) imply:
% 158.42/24.91  | | | | |   (91)   ~ (all_52_1 = e2)
% 158.42/24.91  | | | | | 
% 158.42/24.91  | | | | | REDUCE: (24), (90) imply:
% 158.42/24.91  | | | | |   (92)   ~ (all_52_13 = e2)
% 158.42/24.91  | | | | | 
% 158.42/24.91  | | | | | REDUCE: (71), (90) imply:
% 158.42/24.91  | | | | |   (93)   ~ (e3 = e2)
% 158.42/24.91  | | | | | 
% 158.42/24.91  | | | | | REDUCE: (32), (90) imply:
% 158.42/24.91  | | | | |   (94)  op(e2, e2) = e2
% 158.42/24.91  | | | | | 
% 158.42/24.91  | | | | | BETA: splitting (31) gives:
% 158.42/24.91  | | | | | 
% 158.42/24.91  | | | | | Case 1:
% 158.42/24.91  | | | | | | 
% 158.42/24.91  | | | | | |   (95)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2,
% 158.42/24.91  | | | | | |             e0) = e2)
% 158.42/24.91  | | | | | | 
% 158.42/24.91  | | | | | | BETA: splitting (95) gives:
% 158.42/24.91  | | | | | | 
% 158.42/24.91  | | | | | | Case 1:
% 158.42/24.91  | | | | | | | 
% 158.42/24.91  | | | | | | |   (96)  all_56_9 = e2 & op(e3, e0) = e2
% 158.42/24.91  | | | | | | | 
% 158.42/24.91  | | | | | | | ALPHA: (96) implies:
% 158.42/24.91  | | | | | | |   (97)  all_56_9 = e2
% 158.42/24.91  | | | | | | |   (98)  op(e3, e0) = e2
% 158.42/24.91  | | | | | | | 
% 158.42/24.91  | | | | | | | BETA: splitting (1) gives:
% 158.42/24.91  | | | | | | | 
% 158.42/24.91  | | | | | | | Case 1:
% 158.42/24.91  | | | | | | | | 
% 158.42/24.91  | | | | | | | |   (99)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 158.42/24.91  | | | | | | | |           op(e2, e3) = e2)
% 158.42/24.91  | | | | | | | | 
% 158.42/24.91  | | | | | | | | REF_CLOSE: (12), (35), (38), (72), (91), (99) are inconsistent
% 158.42/24.91  | | | | | | | |            by sub-proof #868.
% 158.42/24.91  | | | | | | | | 
% 158.42/24.91  | | | | | | | Case 2:
% 158.42/24.91  | | | | | | | | 
% 158.42/24.91  | | | | | | | |   (100)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 158.42/24.91  | | | | | | | |            op(e0, e3) = e2)
% 158.42/24.91  | | | | | | | | 
% 158.42/24.91  | | | | | | | | BETA: splitting (100) gives:
% 158.42/24.91  | | | | | | | | 
% 158.42/24.91  | | | | | | | | Case 1:
% 158.42/24.91  | | | | | | | | | 
% 158.42/24.91  | | | | | | | | |   (101)  all_56_6 = e2 & op(e1, e3) = e2
% 158.42/24.91  | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | REF_CLOSE: (12), (20), (25), (101) are inconsistent by
% 158.42/24.91  | | | | | | | | |            sub-proof #761.
% 158.42/24.91  | | | | | | | | | 
% 158.42/24.91  | | | | | | | | Case 2:
% 158.42/24.91  | | | | | | | | | 
% 158.42/24.91  | | | | | | | | |   (102)  all_56_12 = e2 & op(e0, e3) = e2
% 158.42/24.91  | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | ALPHA: (102) implies:
% 158.42/24.91  | | | | | | | | |   (103)  all_56_12 = e2
% 158.42/24.91  | | | | | | | | |   (104)  op(e0, e3) = e2
% 158.42/24.91  | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | BETA: splitting (58) gives:
% 158.42/24.91  | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | Case 1:
% 158.42/24.91  | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | |   (105)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 158.42/24.91  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 158.42/24.91  | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.42/24.91  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.42/24.91  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 158.42/24.91  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.42/24.91  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 158.42/24.91  | | | | | | | | | |            & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12
% 158.42/24.91  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.42/24.91  | | | | | | | | | |            all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.42/24.91  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.42/24.91  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.42/24.91  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 &
% 158.42/24.91  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 158.42/24.91  | | | | | | | | | |            & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12
% 158.42/24.91  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.42/24.91  | | | | | | | | | |            all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.42/24.91  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.42/24.91  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.42/24.91  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 158.42/24.91  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 158.42/24.91  | | | | | | | | | |            & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 158.42/24.91  | | | | | | | | | |            & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 158.42/24.91  | | | | | | | | | |            e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.42/24.91  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.42/24.91  | | | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.42/24.91  | | | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 158.42/24.91  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 158.42/24.91  | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.42/24.91  | | | | | | | | | |            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 &
% 158.42/24.91  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 158.42/24.91  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 158.42/24.91  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 158.42/24.91  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3
% 158.42/24.91  | | | | | | | | | |            & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 =
% 158.42/24.91  | | | | | | | | | |            e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.42/24.91  | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.42/24.91  | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 158.42/24.91  | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.42/24.91  | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 158.42/24.91  | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.42/24.91  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.42/24.91  | | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.42/24.91  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 158.42/24.91  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 158.42/24.91  | | | | | | | | | |            & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14
% 158.42/24.91  | | | | | | | | | |              = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.42/24.91  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.42/24.91  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 158.42/24.91  | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3)
% 158.42/24.91  | | | | | | | | | |            = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.42/24.91  | | | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1
% 158.42/24.91  | | | | | | | | | |            & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10
% 158.42/24.91  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 158.42/24.91  | | | | | | | | | |            e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.42/24.91  | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.42/24.91  | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.42/24.91  | | | | | | | | | |            e1)
% 158.42/24.91  | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | BETA: splitting (105) gives:
% 158.42/24.91  | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | Case 1:
% 158.42/24.91  | | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | |   (106)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 158.42/24.91  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 158.42/24.91  | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.42/24.91  | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.42/24.91  | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.42/24.91  | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 158.42/24.91  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.42/24.91  | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 158.42/24.91  | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 158.42/24.91  | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 158.42/24.91  | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.42/24.91  | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 158.42/24.91  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.42/24.91  | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.42/24.91  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 158.42/24.91  | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.42/24.91  | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.42/24.91  | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.42/24.91  | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 158.42/24.91  | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 158.42/24.91  | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 158.42/24.91  | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.42/24.91  | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.42/24.91  | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 158.42/24.91  | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.42/24.91  | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.42/24.91  | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.42/24.91  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 158.42/24.91  | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.42/24.91  | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.42/24.91  | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.42/24.91  | | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | | BETA: splitting (106) gives:
% 158.42/24.91  | | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | | Case 1:
% 158.42/24.91  | | | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | | |   (107)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 158.42/24.91  | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 158.42/24.91  | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.42/24.91  | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.42/24.91  | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.42/24.91  | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 158.42/24.91  | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.42/24.91  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 158.42/24.91  | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 158.42/24.91  | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 158.42/24.91  | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.42/24.91  | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 158.42/24.91  | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.42/24.91  | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.42/24.91  | | | | | | | | | | | |            e3 & $i(all_57_10))
% 158.42/24.91  | | | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | | | REF_CLOSE: (12), (38), (91), (107) are inconsistent by
% 158.42/24.91  | | | | | | | | | | | |            sub-proof #1005.
% 158.42/24.91  | | | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | | Case 2:
% 158.42/24.91  | | | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | | |   (108)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.42/24.91  | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 158.42/24.91  | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 158.42/24.91  | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.42/24.91  | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.42/24.91  | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.42/24.91  | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.42/24.91  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 158.42/24.91  | | | | | | | | | | | |            &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 158.42/24.91  | | | | | | | | | | | |            e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 158.42/24.91  | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.42/24.91  | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 158.42/24.91  | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 158.42/24.91  | | | | | | | | | | | |            e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 158.42/24.91  | | | | | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 158.42/24.91  | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 158.42/24.91  | | | | | | | | | | | |            & $i(all_57_12))
% 158.42/24.91  | | | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | | | REF_CLOSE: (12), (38), (43), (46), (60), (68), (91), (108)
% 158.42/24.91  | | | | | | | | | | | |            are inconsistent by sub-proof #566.
% 158.42/24.91  | | | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | | End of split
% 158.42/24.91  | | | | | | | | | | | 
% 158.42/24.91  | | | | | | | | | | Case 2:
% 158.42/24.91  | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | |   (109)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.42/24.92  | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.42/24.92  | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.42/24.92  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.42/24.92  | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 158.42/24.92  | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 158.42/24.92  | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 158.42/24.92  | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.42/24.92  | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 158.42/24.92  | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.42/24.92  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 158.42/24.92  | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.42/24.92  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.42/24.92  | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.42/24.92  | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 158.42/24.92  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.42/24.92  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 158.42/24.92  | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 158.42/24.92  | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 158.42/24.92  | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.42/24.92  | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.42/24.92  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 158.42/24.92  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.42/24.92  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.42/24.92  | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.42/24.92  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.42/24.92  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.42/24.92  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.42/24.92  | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.42/24.92  | | | | | | | | | | |            e1)
% 158.42/24.92  | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | BETA: splitting (109) gives:
% 158.42/24.92  | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | Case 1:
% 158.42/24.92  | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | |   (110)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.42/24.92  | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.42/24.92  | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.42/24.92  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.42/24.92  | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 158.42/24.92  | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 158.42/24.92  | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 158.42/24.92  | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.42/24.92  | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 158.42/24.92  | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.42/24.92  | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 158.42/24.92  | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.42/24.92  | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 158.42/24.92  | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | BETA: splitting (110) gives:
% 158.42/24.92  | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | Case 1:
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | |   (111)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.42/24.92  | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.42/24.92  | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.42/24.92  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.42/24.92  | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 158.42/24.92  | | | | | | | | | | | | |              e2) = e3)
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | BETA: splitting (111) gives:
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | Case 1:
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | |   (112)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.42/24.92  | | | | | | | | | | | | | |          ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.42/24.92  | | | | | | | | | | | | | |          op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.42/24.92  | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | | ALPHA: (112) implies:
% 158.42/24.92  | | | | | | | | | | | | | |   (113)  op(e0, e3) = e0
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (63), (104), (113) are inconsistent by
% 158.42/24.92  | | | | | | | | | | | | | |            sub-proof #689.
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | Case 2:
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | |   (114)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 158.42/24.92  | | | | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e2) = e3
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | | ALPHA: (114) implies:
% 158.42/24.92  | | | | | | | | | | | | | |   (115)  op(e3, e2) = e3
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | | REF_CLOSE: (12), (43), (68), (115) are inconsistent by
% 158.42/24.92  | | | | | | | | | | | | | |            sub-proof #998.
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | End of split
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | Case 2:
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | |   (116)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 158.42/24.92  | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 158.42/24.92  | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.42/24.92  | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 158.42/24.92  | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 158.42/24.92  | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.42/24.92  | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.42/24.92  | | | | | | | | | | | | |            $i(all_57_14))
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | REF_CLOSE: (12), (35), (49), (61), (92), (116) are
% 158.42/24.92  | | | | | | | | | | | | |            inconsistent by sub-proof #994.
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | End of split
% 158.42/24.92  | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | Case 2:
% 158.42/24.92  | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | |   (117)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 158.42/24.92  | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.42/24.92  | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.42/24.92  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 158.42/24.92  | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.42/24.92  | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 158.42/24.92  | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.42/24.92  | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.42/24.92  | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 158.42/24.92  | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.42/24.92  | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.42/24.92  | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.42/24.92  | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.42/24.92  | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.42/24.92  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.42/24.92  | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.42/24.92  | | | | | | | | | | | |            e1)
% 158.42/24.92  | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | BETA: splitting (117) gives:
% 158.42/24.92  | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | Case 1:
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | |   (118)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 158.42/24.92  | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.42/24.92  | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.42/24.92  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 158.42/24.92  | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.42/24.92  | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 158.42/24.92  | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | REF_CLOSE: (2), (12), (14), (32), (69), (84), (87), (118) are
% 158.42/24.92  | | | | | | | | | | | | |            inconsistent by sub-proof #222.
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | Case 2:
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | |   (119)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.42/24.92  | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 158.42/24.92  | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.42/24.92  | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.42/24.92  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.42/24.92  | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.42/24.92  | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.42/24.92  | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.42/24.92  | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.42/24.92  | | | | | | | | | | | | |            e1)
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | BETA: splitting (119) gives:
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | Case 1:
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | |   (120)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.42/24.92  | | | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 158.42/24.92  | | | | | | | | | | | | | |          = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.42/24.92  | | | | | | | | | | | | | |          $i(all_57_14)
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | | ALPHA: (120) implies:
% 158.42/24.92  | | | | | | | | | | | | | |   (121)  op(e0, e0) = e1
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | | REF_CLOSE: (12), (21), (61), (121) are inconsistent by
% 158.42/24.92  | | | | | | | | | | | | | |            sub-proof #473.
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | Case 2:
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | |   (122)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 158.42/24.92  | | | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.42/24.92  | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.42/24.92  | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 158.42/24.92  | | | | | | | | | | | | | |            = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 158.42/24.92  | | | | | | | | | | | | | |              e1) = e1)
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (17), (51), (52), (122) are
% 158.42/24.92  | | | | | | | | | | | | | |            inconsistent by sub-proof #747.
% 158.42/24.92  | | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | | End of split
% 158.42/24.92  | | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | | End of split
% 158.42/24.92  | | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | | End of split
% 158.42/24.92  | | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | | End of split
% 158.42/24.92  | | | | | | | | | | 
% 158.42/24.92  | | | | | | | | | Case 2:
% 158.42/24.92  | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | |   (123)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.51/24.92  | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 158.51/24.92  | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.51/24.92  | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.51/24.92  | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 158.51/24.92  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 158.51/24.92  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 158.51/24.92  | | | | | | | | | |            e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.51/24.92  | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.51/24.92  | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.51/24.92  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 =
% 158.51/24.92  | | | | | | | | | |            e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.51/24.92  | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 158.51/24.92  | | | | | | | | | |              e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 158.51/24.92  | | | | | | | | | |          (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 158.51/24.92  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.51/24.92  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.51/24.92  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.51/24.92  | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.51/24.92  | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.51/24.92  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.51/24.92  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.51/24.92  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3
% 158.51/24.92  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3
% 158.51/24.92  | | | | | | | | | |            & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 =
% 158.51/24.92  | | | | | | | | | |            e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.51/24.92  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.51/24.92  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 158.51/24.92  | | | | | | | | | |          (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.51/24.92  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.51/24.92  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.51/24.92  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.51/24.92  | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.51/24.92  | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.51/24.92  | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2)
% 158.51/24.92  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 &
% 158.51/24.92  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0
% 158.51/24.92  | | | | | | | | | |            & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10
% 158.51/24.92  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 158.51/24.92  | | | | | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.51/24.92  | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 158.51/24.92  | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 158.51/24.92  | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 158.51/24.92  | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.51/24.92  | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 158.51/24.92  | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 158.51/24.92  | | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 158.51/24.92  | | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 158.51/24.92  | | | | | | | | | |            all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.51/24.92  | | | | | | | | | |            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 158.51/24.92  | | | | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 158.51/24.92  | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3,
% 158.51/24.92  | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 158.51/24.92  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_11 = e2 &
% 158.51/24.92  | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2,
% 158.51/24.92  | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 158.51/24.92  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 158.51/24.92  | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 158.51/24.92  | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.51/24.92  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.51/24.92  | | | | | | | | | |                (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0
% 158.51/24.92  | | | | | | | | | |                & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.51/24.92  | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.51/24.92  | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.51/24.92  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.51/24.92  | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 158.51/24.92  | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.51/24.92  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.51/24.92  | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.51/24.92  | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.51/24.92  | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 158.51/24.92  | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 158.51/24.92  | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.51/24.92  | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.51/24.92  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 = e2
% 158.51/24.92  | | | | | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.51/24.92  | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.51/24.92  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 158.51/24.92  | | | | | | | | | |                & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.51/24.92  | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.51/24.92  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 158.51/24.92  | | | | | | | | | |                & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.51/24.92  | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.51/24.92  | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 158.51/24.92  | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0,
% 158.51/24.92  | | | | | | | | | |                  e1) = e0)))
% 158.51/24.92  | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | BETA: splitting (123) gives:
% 158.51/24.92  | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | Case 1:
% 158.51/24.92  | | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | |   (124)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.51/24.92  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 158.51/24.92  | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.51/24.92  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.51/24.92  | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 158.51/24.92  | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.51/24.92  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.51/24.92  | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 158.51/24.92  | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 158.51/24.92  | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 158.51/24.92  | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.51/24.92  | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.51/24.92  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 158.51/24.92  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.51/24.92  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.51/24.92  | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 158.51/24.92  | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 158.51/24.92  | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.51/24.92  | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 158.51/24.92  | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 158.51/24.92  | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 158.51/24.92  | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.51/24.92  | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.51/24.92  | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 158.51/24.92  | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 158.51/24.92  | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.51/24.92  | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 158.51/24.92  | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.51/24.92  | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.51/24.92  | | | | | | | | | | |            $i(all_57_14))
% 158.51/24.92  | | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | | BETA: splitting (124) gives:
% 158.51/24.92  | | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | | Case 1:
% 158.51/24.92  | | | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | | |   (125)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.51/24.92  | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 158.51/24.92  | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.51/24.92  | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.51/24.92  | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 158.51/24.92  | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.51/24.92  | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.51/24.92  | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 158.51/24.92  | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 158.51/24.92  | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 158.51/24.92  | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.51/24.92  | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.51/24.92  | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 158.51/24.92  | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.51/24.92  | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 158.51/24.92  | | | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | | | BETA: splitting (125) gives:
% 158.51/24.92  | | | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | | | Case 1:
% 158.51/24.92  | | | | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | | | |   (126)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.51/24.92  | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 158.51/24.92  | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.51/24.92  | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.51/24.92  | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 158.51/24.92  | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.51/24.92  | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.51/24.92  | | | | | | | | | | | | |            $i(all_57_14))
% 158.51/24.92  | | | | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | | | | BETA: splitting (126) gives:
% 158.51/24.92  | | | | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | | | | Case 1:
% 158.51/24.92  | | | | | | | | | | | | | | 
% 158.51/24.92  | | | | | | | | | | | | | |   (127)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.51/24.92  | | | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 158.51/24.92  | | | | | | | | | | | | | |          = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.51/24.93  | | | | | | | | | | | | | |          $i(all_57_14)
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | | ALPHA: (127) implies:
% 158.51/24.93  | | | | | | | | | | | | | |   (128)  op(e3, e3) = e1
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | | REF_CLOSE: (12), (35), (61), (128) are inconsistent by
% 158.51/24.93  | | | | | | | | | | | | | |            sub-proof #995.
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | Case 2:
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | |   (129)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 158.51/24.93  | | | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 158.51/24.93  | | | | | | | | | | | | | |          = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.51/24.93  | | | | | | | | | | | | | |          $i(all_57_14)
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | | ALPHA: (129) implies:
% 158.51/24.93  | | | | | | | | | | | | | |   (130)  op(e2, e2) = e1
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | | REF_CLOSE: (2), (12), (32), (84), (87), (130) are
% 158.51/24.93  | | | | | | | | | | | | | |            inconsistent by sub-proof #691.
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | End of split
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | Case 2:
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | |   (131)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 158.51/24.93  | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.51/24.93  | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.51/24.93  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 158.51/24.93  | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.51/24.93  | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.51/24.93  | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.51/24.93  | | | | | | | | | | | | |            $i(all_57_14))
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | REF_CLOSE: (12), (21), (46), (60), (61), (131) are
% 158.51/24.93  | | | | | | | | | | | | |            inconsistent by sub-proof #144.
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | End of split
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | Case 2:
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | |   (132)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 158.51/24.93  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.51/24.93  | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.51/24.93  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.51/24.93  | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.51/24.93  | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.51/24.93  | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 158.51/24.93  | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 158.51/24.93  | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.51/24.93  | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 158.51/24.93  | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 158.51/24.93  | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.51/24.93  | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 158.51/24.93  | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 158.51/24.93  | | | | | | | | | | | |            & $i(all_57_14))
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | REF_CLOSE: (12), (13), (14), (17), (35), (49), (61), (63),
% 158.51/24.93  | | | | | | | | | | | |            (69), (92), (104), (132) are inconsistent by
% 158.51/24.93  | | | | | | | | | | | |            sub-proof #197.
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | End of split
% 158.51/24.93  | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | Case 2:
% 158.51/24.93  | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | |   (133)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.51/24.93  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.51/24.93  | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.51/24.93  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.51/24.93  | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.51/24.93  | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.51/24.93  | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 158.51/24.93  | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 158.51/24.93  | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 158.51/24.93  | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 158.51/24.93  | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.51/24.93  | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.51/24.93  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 158.51/24.93  | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.51/24.93  | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.51/24.93  | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.51/24.93  | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 158.51/24.93  | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 158.51/24.93  | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 158.51/24.93  | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.51/24.93  | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.51/24.93  | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.51/24.93  | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.51/24.93  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.51/24.93  | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.51/24.93  | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.51/24.93  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.51/24.93  | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.51/24.93  | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.51/24.93  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.51/24.93  | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.51/24.93  | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.51/24.93  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.51/24.93  | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.51/24.93  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.93  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.51/24.93  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.51/24.93  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.93  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.51/24.93  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.51/24.93  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.93  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.51/24.93  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.51/24.93  | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.51/24.93  | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.51/24.93  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.51/24.93  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.51/24.93  | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.51/24.93  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.51/24.93  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.51/24.93  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.51/24.93  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.51/24.93  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.51/24.93  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.51/24.93  | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.51/24.93  | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.51/24.93  | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.51/24.93  | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.51/24.93  | | | | | | | | | | |                e0)))
% 158.51/24.93  | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | BETA: splitting (133) gives:
% 158.51/24.93  | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | Case 1:
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | |   (134)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.51/24.93  | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.51/24.93  | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.51/24.93  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.51/24.93  | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.51/24.93  | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.51/24.93  | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 158.51/24.93  | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 158.51/24.93  | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 158.51/24.93  | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 158.51/24.93  | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.51/24.93  | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.51/24.93  | | | | | | | | | | | |            e3 & $i(all_57_10))
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | BETA: splitting (134) gives:
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | Case 1:
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | |   (135)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.51/24.93  | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.51/24.93  | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.51/24.93  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.51/24.93  | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.51/24.93  | | | | | | | | | | | | |              e1) = e2)
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | REF_CLOSE: (12), (21), (46), (60), (72), (135) are
% 158.51/24.93  | | | | | | | | | | | | |            inconsistent by sub-proof #412.
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | Case 2:
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | |   (136)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 158.51/24.93  | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 158.51/24.93  | | | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.51/24.93  | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 158.51/24.93  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 158.51/24.93  | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.51/24.93  | | | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.51/24.93  | | | | | | | | | | | | |            $i(all_57_10))
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | BETA: splitting (136) gives:
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | Case 1:
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | |   (137)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 158.51/24.93  | | | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 158.51/24.93  | | | | | | | | | | | | | |          = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.51/24.93  | | | | | | | | | | | | | |          $i(all_57_14)
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | | ALPHA: (137) implies:
% 158.51/24.93  | | | | | | | | | | | | | |   (138)  op(e2, e2) = e1
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | | REF_CLOSE: (2), (12), (32), (84), (87), (138) are
% 158.51/24.93  | | | | | | | | | | | | | |            inconsistent by sub-proof #691.
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | Case 2:
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | |   (139)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 158.51/24.93  | | | | | | | | | | | | | |          ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.51/24.93  | | | | | | | | | | | | | |          op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.51/24.93  | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | | ALPHA: (139) implies:
% 158.51/24.93  | | | | | | | | | | | | | |   (140)  op(e0, e3) = e0
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (63), (104), (140) are inconsistent by
% 158.51/24.93  | | | | | | | | | | | | | |            sub-proof #689.
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | End of split
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | End of split
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | Case 2:
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | |   (141)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 158.51/24.93  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.51/24.93  | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.51/24.93  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.51/24.93  | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.51/24.93  | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 158.51/24.93  | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 158.51/24.93  | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 158.51/24.93  | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 158.51/24.93  | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.51/24.93  | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.51/24.93  | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 158.51/24.93  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.51/24.93  | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 158.51/24.93  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 158.51/24.93  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.51/24.93  | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 158.51/24.93  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 158.51/24.93  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 158.51/24.93  | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 158.51/24.93  | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.51/24.93  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.51/24.93  | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.51/24.93  | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.51/24.93  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.51/24.93  | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 158.51/24.93  | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.51/24.93  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.51/24.93  | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.51/24.93  | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.51/24.93  | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 158.51/24.93  | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 158.51/24.93  | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.51/24.93  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.51/24.93  | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 158.51/24.93  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.51/24.93  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.51/24.93  | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.51/24.93  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.51/24.93  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.51/24.93  | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.51/24.93  | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.51/24.93  | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.51/24.93  | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 158.51/24.93  | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.51/24.93  | | | | | | | | | | | |                op(e0, e1) = e0)))
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | BETA: splitting (141) gives:
% 158.51/24.93  | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | Case 1:
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | |   (142)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 158.51/24.93  | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.51/24.93  | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.51/24.93  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.51/24.93  | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.51/24.93  | | | | | | | | | | | | |              e0) = e3)
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | REF_CLOSE: (12), (15), (21), (52), (72), (142) are
% 158.51/24.93  | | | | | | | | | | | | |            inconsistent by sub-proof #451.
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | Case 2:
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | |   (143)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.51/24.93  | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 158.51/24.93  | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 158.51/24.93  | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.51/24.93  | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.51/24.93  | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.51/24.93  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.51/24.93  | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.51/24.93  | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.51/24.93  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.51/24.93  | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.51/24.93  | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.51/24.93  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.51/24.93  | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.51/24.93  | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.51/24.93  | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.51/24.93  | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.93  | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.51/24.93  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.51/24.93  | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.93  | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.51/24.93  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.51/24.93  | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.93  | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.51/24.93  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.51/24.93  | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.51/24.93  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.51/24.93  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.51/24.93  | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.51/24.93  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.51/24.93  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.51/24.93  | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.51/24.93  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.51/24.93  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.51/24.93  | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.51/24.93  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.51/24.93  | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.51/24.93  | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.51/24.93  | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.51/24.93  | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.51/24.93  | | | | | | | | | | | | |                e0)))
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | BETA: splitting (143) gives:
% 158.51/24.93  | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | Case 1:
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | |   (144)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.51/24.93  | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | | ALPHA: (144) implies:
% 158.51/24.93  | | | | | | | | | | | | | |   (145)  op(e2, e0) = e2
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | | REF_CLOSE: (12), (49), (92), (145) are inconsistent by
% 158.51/24.93  | | | | | | | | | | | | | |            sub-proof #996.
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.93  | | | | | | | | | | | | | Case 2:
% 158.51/24.93  | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | |   (146)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.51/24.94  | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.51/24.94  | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.51/24.94  | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.51/24.94  | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.51/24.94  | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.51/24.94  | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.51/24.94  | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.51/24.94  | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.51/24.94  | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.51/24.94  | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.51/24.94  | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.51/24.94  | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.51/24.94  | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.94  | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.51/24.94  | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.51/24.94  | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.94  | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.51/24.94  | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.51/24.94  | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.94  | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.51/24.94  | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.51/24.94  | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.51/24.94  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.51/24.94  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.51/24.94  | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.51/24.94  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.51/24.94  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.51/24.94  | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.51/24.94  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.51/24.94  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.51/24.94  | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.51/24.94  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.51/24.94  | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.51/24.94  | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.51/24.94  | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.51/24.94  | | | | | | | | | | | | | |                e0)))
% 158.51/24.94  | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 158.51/24.94  | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | |   (147)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.51/24.94  | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 158.51/24.94  | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 158.51/24.94  | | | | | | | | | | | | | | |   (148)  op(e1, e1) = e1
% 158.51/24.94  | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (51), (148) are inconsistent by
% 158.51/24.94  | | | | | | | | | | | | | | |            sub-proof #986.
% 158.51/24.94  | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | |   (149)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.51/24.94  | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.51/24.94  | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.51/24.94  | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.51/24.94  | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.51/24.94  | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.51/24.94  | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.51/24.94  | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.51/24.94  | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.51/24.94  | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.51/24.94  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.51/24.94  | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 158.51/24.94  | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.51/24.94  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.51/24.94  | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.51/24.94  | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.51/24.94  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.51/24.94  | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.51/24.94  | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.51/24.94  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 158.51/24.94  | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.51/24.94  | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.51/24.94  | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.51/24.94  | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.51/24.94  | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 158.51/24.94  | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.51/24.94  | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 158.51/24.94  | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.51/24.94  | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.51/24.94  | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.51/24.94  | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.51/24.94  | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.51/24.94  | | | | | | | | | | | | | | |              e0))
% 158.51/24.94  | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 158.51/24.94  | | | | | | | | | | | | | | |   (150)  op(e0, e0) = all_57_15
% 158.51/24.94  | | | | | | | | | | | | | | |   (151)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.51/24.94  | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.51/24.94  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.51/24.94  | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.51/24.94  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.51/24.94  | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.51/24.94  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.51/24.94  | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.51/24.94  | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.51/24.94  | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.51/24.94  | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.51/24.94  | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.94  | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.51/24.94  | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.51/24.94  | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.51/24.94  | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.51/24.94  | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.51/24.94  | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.51/24.94  | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.51/24.94  | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.51/24.94  | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 158.51/24.94  | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 158.51/24.94  | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.51/24.94  | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.51/24.94  | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.51/24.94  | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.51/24.94  | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.51/24.94  | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | |   (152)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 158.51/24.94  | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 158.51/24.94  | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | |   (153)  all_56_1 = e2 & op(e3, e2) = e2
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (35), (44), (45), (51), (61), (63),
% 158.51/24.94  | | | | | | | | | | | | | | | | |            (64), (97), (153) are inconsistent by sub-proof
% 158.51/24.94  | | | | | | | | | | | | | | | | |            #301.
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with e3, all_57_15, e0, e0,
% 158.51/24.94  | | | | | | | | | | | | | | | | |              simplifying with (21), (150) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | |   (154)  all_57_15 = e3
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_52_3, e2, e3, e0,
% 158.51/24.94  | | | | | | | | | | | | | | | | |              simplifying with (13), (104) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | |   (155)  all_52_3 = e2
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_52_12, e2, e0, e3,
% 158.51/24.94  | | | | | | | | | | | | | | | | |              simplifying with (52), (98) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | |   (156)  all_52_12 = e2
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | REDUCE: (27), (156) imply:
% 158.51/24.94  | | | | | | | | | | | | | | | | |   (157)   ~ (all_52_13 = e2)
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | |   (158)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |   (159)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (17), (49), (63), (92), (104), (159)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #168.
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |   (160)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (35), (49), (63), (64), (92), (104),
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            (160) are inconsistent by sub-proof #195.
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | End of split
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | |   (161)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |   (162)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (35), (63), (64), (154), (162) are
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #143.
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |   (163)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |   (164)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (49), (63), (92), (164) are
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #164.
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |   (165)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (64), (154), (165) are inconsistent by
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |            sub-proof #142.
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | End of split
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | End of split
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | End of split
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | End of split
% 158.51/24.94  | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | |   (166)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 158.51/24.94  | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 158.51/24.94  | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | |   (167)  all_56_7 = e2 & op(e1, e2) = e2
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (72), (167) are inconsistent by sub-proof
% 158.51/24.94  | | | | | | | | | | | | | | | | |            #940.
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | |   (168)  all_56_13 = e2 & op(e0, e2) = e2
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 158.51/24.94  | | | | | | | | | | | | | | | | |   (169)  all_56_13 = e2
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | |   (170)  all_56_15 = e0 & op(e0, e0) = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 158.51/24.94  | | | | | | | | | | | | | | | | | |   (171)  all_56_15 = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (12), (35), (45), (48), (51), (53), (57),
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            (59), (61), (63), (64), (72), (103), (169), (171)
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #596.
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | |   (172)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 158.51/24.94  | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 158.51/24.94  | | | | | | | | | | | | | | | | | |   (173)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 158.51/24.94  | | | | | | | | | | | | | | | | | |              e1) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |   (174)  all_56_12 = e0 & op(e0, e3) = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |   (175)  op(e0, e3) = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (63), (104), (175) are inconsistent by
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            sub-proof #689.
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |   (176)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 158.51/24.94  | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |   (177)  all_56_13 = e0 & op(e0, e2) = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (169), (177) are inconsistent by sub-proof
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |            #141.
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |   (178)  all_56_14 = e0 & op(e0, e1) = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | |   (179)  all_56_14 = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | |   (180)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | |   (181)  all_56_1 = e0 & op(e3, e2) = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | |   (182)  all_56_1 = e0
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | |   (183)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (35), (45), (61), (182), (183) are
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #561.
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.51/24.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | |   (184)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | |   (185)  all_56_4 = e1 & op(e3, e1) = e1
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_56_4 = e1
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (187)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_56_12 = e1 & op(e0, e3) = e1
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (103), (188) are inconsistent by sub-proof
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            #769.
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (189)  all_56_13 = e1 & op(e0, e2) = e1
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (169), (189) are inconsistent by sub-proof
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            #938.
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (190)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (191)  all_56_14 = e1 & op(e0, e1) = e1
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  all_56_14 = e1
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (192) imply:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  e1 = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (193) implies:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  e1 = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (194) imply:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  all_56_4 = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (14), (35), (44), (45), (51), (56),
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            (61), (63), (72), (182), (195) are inconsistent by
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #514.
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  all_56_15 = e1 & op(e0, e0) = e1
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  op(e0, e0) = e1
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (21), (61), (197) are inconsistent by
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #473.
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | |   (198)  all_56_9 = e1 & op(e3, e0) = e1
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (97), (198) are inconsistent by sub-proof
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | |            #948.
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (199)  all_56_3 = e0 & op(e2, e2) = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (200)  op(e2, e2) = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with e2, all_10_1, e2, e2,
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (80), (94) gives:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (201)  all_10_1 = e2
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with e0, all_10_1, e2, e2,
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (80), (200) gives:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (202)  all_10_1 = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (202) imply:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (203)  e2 = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (203) imply:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (204)  $false
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | |   (205)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (206)  all_56_7 = e0 & op(e1, e2) = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (207)  all_56_7 = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (207) imply:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (208)  e3 = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (208) imply:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (209)  all_56_15 = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (12), (35), (45), (48), (51), (53), (57),
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |            (59), (61), (63), (64), (72), (103), (169), (209)
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #596.
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |   (210)  all_56_13 = e0 & op(e0, e2) = e0
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (169), (210) are inconsistent by sub-proof
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | |            #141.
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | | 
% 158.54/24.95  | | | | | | | | End of split
% 158.54/24.95  | | | | | | | | 
% 158.54/24.95  | | | | | | | End of split
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | Case 2:
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | |   (211)  all_56_10 = e2 & op(e2, e0) = e2
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | ALPHA: (211) implies:
% 158.54/24.95  | | | | | | |   (212)  op(e2, e0) = e2
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | REF_CLOSE: (12), (49), (92), (212) are inconsistent by sub-proof
% 158.54/24.95  | | | | | | |            #996.
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | End of split
% 158.54/24.95  | | | | | | 
% 158.54/24.95  | | | | | Case 2:
% 158.54/24.95  | | | | | | 
% 158.54/24.95  | | | | | |   (213)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 &
% 158.54/24.95  | | | | | |            op(e0, e0) = e2)
% 158.54/24.95  | | | | | | 
% 158.54/24.95  | | | | | | BETA: splitting (213) gives:
% 158.54/24.95  | | | | | | 
% 158.54/24.95  | | | | | | Case 1:
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | |   (214)  all_56_11 = e2 & op(e1, e0) = e2
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | ALPHA: (214) implies:
% 158.54/24.95  | | | | | | |   (215)  all_56_11 = e2
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | REF_CLOSE: (12), (19), (20), (36), (39), (41), (42), (45), (51),
% 158.54/24.95  | | | | | | |            (61), (63), (64), (67), (72), (215) are inconsistent by
% 158.54/24.95  | | | | | | |            sub-proof #183.
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | Case 2:
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | |   (216)  all_56_15 = e2 & op(e0, e0) = e2
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | ALPHA: (216) implies:
% 158.54/24.95  | | | | | | |   (217)  op(e0, e0) = e2
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | REF_CLOSE: (12), (21), (72), (217) are inconsistent by sub-proof
% 158.54/24.95  | | | | | | |            #878.
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | End of split
% 158.54/24.95  | | | | | | 
% 158.54/24.95  | | | | | End of split
% 158.54/24.95  | | | | | 
% 158.54/24.95  | | | | Case 2:
% 158.54/24.95  | | | | | 
% 158.54/24.95  | | | | |   (218)  all_54_5 = e1 | all_54_5 = e0
% 158.54/24.95  | | | | | 
% 158.54/24.95  | | | | | REF_CLOSE: (2), (82), (84), (218) are inconsistent by sub-proof #962.
% 158.54/24.95  | | | | | 
% 158.54/24.95  | | | | End of split
% 158.54/24.95  | | | | 
% 158.54/24.95  | | | End of split
% 158.54/24.95  | | | 
% 158.54/24.95  | | Case 2:
% 158.54/24.95  | | | 
% 158.54/24.95  | | |   (219)  all_24_2 = e1
% 158.54/24.95  | | |   (220)  ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 & $i(all_24_0)) | ( ~
% 158.54/24.95  | | |            (all_24_1 = e0) & op(e1, e1) = all_24_1 & $i(all_24_1))
% 158.54/24.95  | | | 
% 158.54/24.95  | | | COMBINE_EQS: (29), (219) imply:
% 158.54/24.95  | | |   (221)  all_4_2 = e1
% 158.54/24.95  | | | 
% 158.54/24.95  | | | SIMP: (221) implies:
% 158.54/24.95  | | |   (222)  all_4_2 = e1
% 158.54/24.95  | | | 
% 158.54/24.95  | | | REDUCE: (71), (222) imply:
% 158.54/24.95  | | |   (223)   ~ (e3 = e1)
% 158.54/24.95  | | | 
% 158.54/24.95  | | | REDUCE: (32), (222) imply:
% 158.54/24.95  | | |   (224)  op(e2, e2) = e1
% 158.54/24.95  | | | 
% 158.54/24.95  | | | BETA: splitting (220) gives:
% 158.54/24.95  | | | 
% 158.54/24.95  | | | Case 1:
% 158.54/24.95  | | | | 
% 158.54/24.95  | | | |   (225)   ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 & $i(all_24_0)
% 158.54/24.95  | | | | 
% 158.54/24.95  | | | | ALPHA: (225) implies:
% 158.54/24.95  | | | |   (226)   ~ (all_24_0 = e3)
% 158.54/24.95  | | | |   (227)  op(e1, e2) = all_24_0
% 158.54/24.95  | | | | 
% 158.54/24.95  | | | | REF_CLOSE: (12), (40), (226), (227) are inconsistent by sub-proof #610.
% 158.54/24.95  | | | | 
% 158.54/24.95  | | | Case 2:
% 158.54/24.95  | | | | 
% 158.54/24.95  | | | |   (228)   ~ (all_24_1 = e0) & op(e1, e1) = all_24_1 & $i(all_24_1)
% 158.54/24.95  | | | | 
% 158.54/24.95  | | | | ALPHA: (228) implies:
% 158.54/24.95  | | | |   (229)   ~ (all_24_1 = e0)
% 158.54/24.95  | | | |   (230)  op(e1, e1) = all_24_1
% 158.54/24.95  | | | | 
% 158.54/24.95  | | | | BETA: splitting (8) gives:
% 158.54/24.95  | | | | 
% 158.54/24.95  | | | | Case 1:
% 158.54/24.95  | | | | | 
% 158.54/24.95  | | | | |   (231)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2,
% 158.54/24.95  | | | | |                  e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 158.54/24.95  | | | | |                all_57_0 & $i(all_57_0))) & ((all_57_14 = e3 & op(e1,
% 158.54/24.95  | | | | |                  e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 158.54/24.95  | | | | |                all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 158.54/24.95  | | | | |                  e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 158.54/24.95  | | | | |                all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 158.54/24.95  | | | | |              e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 158.54/24.95  | | | | |                (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.54/24.95  | | | | |                $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) |
% 158.54/24.95  | | | | |              ( ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 158.54/24.95  | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.54/24.95  | | | | |              ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 158.54/24.95  | | | | |                $i(all_57_7))))
% 158.54/24.95  | | | | | 
% 158.54/24.95  | | | | | BETA: splitting (231) gives:
% 158.54/24.95  | | | | | 
% 158.54/24.95  | | | | | Case 1:
% 158.54/24.95  | | | | | | 
% 158.54/24.95  | | | | | |   (232)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 &
% 158.54/24.95  | | | | | |              op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 158.54/24.95  | | | | | |              all_57_0 & $i(all_57_0))) & ((all_57_14 = e3 & op(e1,
% 158.54/24.95  | | | | | |                e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 158.54/24.95  | | | | | |              all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 158.54/24.95  | | | | | |                e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 158.54/24.95  | | | | | |              all_57_6 & $i(all_57_6)))
% 158.54/24.95  | | | | | | 
% 158.54/24.95  | | | | | | ALPHA: (232) implies:
% 158.54/24.95  | | | | | |   (233)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 158.54/24.95  | | | | | |            op(e0, e3) = all_57_6 & $i(all_57_6))
% 158.54/24.95  | | | | | |   (234)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) &
% 158.54/24.95  | | | | | |            op(e1, e3) = all_57_2 & $i(all_57_2))
% 158.54/24.95  | | | | | |   (235)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 158.54/24.95  | | | | | |            op(e2, e3) = all_57_0 & $i(all_57_0))
% 158.54/24.95  | | | | | | 
% 158.54/24.95  | | | | | | BETA: splitting (235) gives:
% 158.54/24.95  | | | | | | 
% 158.54/24.95  | | | | | | Case 1:
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | |   (236)  all_57_12 = e3 & op(e2, e2) = e3
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | ALPHA: (236) implies:
% 158.54/24.95  | | | | | | |   (237)  op(e2, e2) = e3
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | REF_CLOSE: (12), (61), (224), (237) are inconsistent by sub-proof
% 158.54/24.95  | | | | | | |            #847.
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | Case 2:
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | |   (238)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0)
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | ALPHA: (238) implies:
% 158.54/24.95  | | | | | | |   (239)   ~ (all_57_0 = e2)
% 158.54/24.95  | | | | | | |   (240)  op(e2, e3) = all_57_0
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | BETA: splitting (58) gives:
% 158.54/24.95  | | | | | | | 
% 158.54/24.95  | | | | | | | Case 1:
% 158.54/24.95  | | | | | | | | 
% 158.54/24.95  | | | | | | | |   (241)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.54/24.95  | | | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.54/24.95  | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.54/24.95  | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.54/24.95  | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.54/24.95  | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.54/24.95  | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.54/24.95  | | | | | | | |            all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 158.54/24.95  | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1,
% 158.54/24.95  | | | | | | | |              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.54/24.95  | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.54/24.95  | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/24.95  | | | | | | | |              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.54/24.95  | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 158.54/24.95  | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 158.54/24.95  | | | | | | | |            e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 158.54/24.95  | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.54/24.95  | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 158.54/24.95  | | | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 158.54/24.95  | | | | | | | |              e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.54/24.95  | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2,
% 158.54/24.95  | | | | | | | |              e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 &
% 158.54/24.95  | | | | | | | |            all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 158.54/24.95  | | | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.54/24.95  | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.54/24.95  | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 158.54/24.95  | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.54/24.95  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.54/24.95  | | | | | | | |            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 &
% 158.54/24.95  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.54/24.95  | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 158.54/24.95  | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.54/24.95  | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 158.54/24.95  | | | | | | | |            op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 158.54/24.95  | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) =
% 158.54/24.95  | | | | | | | |            e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.54/24.95  | | | | | | | |            op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 158.54/24.95  | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 158.54/24.95  | | | | | | | |            & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1
% 158.54/24.95  | | | | | | | |            & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2
% 158.54/24.95  | | | | | | | |            = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10
% 158.54/24.95  | | | | | | | |              = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 158.54/24.95  | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.54/24.95  | | | | | | | |          (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.54/24.95  | | | | | | | |            (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2
% 158.54/24.95  | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.95  | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 158.54/24.95  | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 158.54/24.95  | | | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.54/24.95  | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.54/24.95  | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 158.54/24.95  | | | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1,
% 158.54/24.95  | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.54/24.95  | | | | | | | |          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1,
% 158.54/24.95  | | | | | | | |              e3) = e1 & op(e1, e1) = e1)
% 158.54/24.95  | | | | | | | | 
% 158.54/24.95  | | | | | | | | BETA: splitting (241) gives:
% 158.54/24.95  | | | | | | | | 
% 158.54/24.95  | | | | | | | | Case 1:
% 158.54/24.95  | | | | | | | | | 
% 158.54/24.95  | | | | | | | | |   (242)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.54/24.95  | | | | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) =
% 158.54/24.95  | | | | | | | | |            e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.54/24.95  | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.54/24.95  | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.54/24.95  | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.54/24.95  | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.54/24.95  | | | | | | | | |            all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 158.54/24.95  | | | | | | | | |              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.54/24.95  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 158.54/24.95  | | | | | | | | |          | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 158.54/24.95  | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.54/24.95  | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3
% 158.54/24.95  | | | | | | | | |            & $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 158.54/24.95  | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 158.54/24.95  | | | | | | | | |            e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 158.54/24.95  | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.54/24.95  | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.54/24.95  | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.54/24.95  | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 158.54/24.95  | | | | | | | | |          | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.54/24.95  | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3
% 158.54/24.95  | | | | | | | | |            & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.54/24.95  | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 158.54/24.95  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 158.54/24.95  | | | | | | | | |          | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 158.54/24.95  | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) =
% 158.54/24.95  | | | | | | | | |            e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.54/24.95  | | | | | | | | |            $i(all_57_12))
% 158.54/24.95  | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | BETA: splitting (242) gives:
% 158.54/24.95  | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | Case 1:
% 158.54/24.95  | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | |   (243)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 158.54/24.95  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 158.54/24.95  | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.54/24.95  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.54/24.95  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 158.54/24.95  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.54/24.95  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 158.54/24.95  | | | | | | | | | |            & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12
% 158.54/24.95  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.54/24.95  | | | | | | | | | |            all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.54/24.95  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.54/24.95  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.54/24.95  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 &
% 158.54/24.95  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10))
% 158.54/24.95  | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | | REF_CLOSE: (12), (239), (240), (243) are inconsistent by
% 158.54/24.95  | | | | | | | | | |            sub-proof #540.
% 158.54/24.95  | | | | | | | | | | 
% 158.54/24.95  | | | | | | | | | Case 2:
% 158.54/24.95  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | |   (244)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.54/24.96  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 158.54/24.96  | | | | | | | | | |            = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.54/24.96  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.54/24.96  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.54/24.96  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 158.54/24.96  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 158.54/24.96  | | | | | | | | | |            & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 158.54/24.96  | | | | | | | | | |            & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 158.54/24.96  | | | | | | | | | |            e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.54/24.96  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.54/24.96  | | | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.54/24.96  | | | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 158.54/24.96  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 158.54/24.96  | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.54/24.96  | | | | | | | | | |            $i(all_57_12))
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | BETA: splitting (244) gives:
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | Case 1:
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | |   (245)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.54/24.96  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 158.54/24.96  | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 158.54/24.96  | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.54/24.96  | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.54/24.96  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.54/24.96  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.54/24.96  | | | | | | | | | | |            $i(all_57_10))
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | REF_CLOSE: (12), (239), (240), (245) are inconsistent by
% 158.54/24.96  | | | | | | | | | | |            sub-proof #539.
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | Case 2:
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | |   (246)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.54/24.96  | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 158.54/24.96  | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.54/24.96  | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.54/24.96  | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.54/24.96  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 158.54/24.96  | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.54/24.96  | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.54/24.96  | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | BETA: splitting (246) gives:
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | Case 1:
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | |   (247)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.54/24.96  | | | | | | | | | | | |          op(e2, e3) = e2 & op(e2, e2) = e2
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | ALPHA: (247) implies:
% 158.54/24.96  | | | | | | | | | | | |   (248)  op(e2, e3) = e2
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | REF_CLOSE: (12), (239), (240), (248) are inconsistent by
% 158.54/24.96  | | | | | | | | | | | |            sub-proof #783.
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | Case 2:
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | |   (249)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.54/24.96  | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.54/24.96  | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.54/24.96  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 158.54/24.96  | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.54/24.96  | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.54/24.96  | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | REF_CLOSE: (12), (17), (46), (60), (72), (249) are
% 158.54/24.96  | | | | | | | | | | | |            inconsistent by sub-proof #140.
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | End of split
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | End of split
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | End of split
% 158.54/24.96  | | | | | | | | | 
% 158.54/24.96  | | | | | | | | Case 2:
% 158.54/24.96  | | | | | | | | | 
% 158.54/24.96  | | | | | | | | |   (250)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.54/24.96  | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/24.96  | | | | | | | | |              e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.54/24.96  | | | | | | | | |            $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 & 
% 158.54/24.96  | | | | | | | | |            ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.54/24.96  | | | | | | | | |          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.54/24.96  | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 158.54/24.96  | | | | | | | | |            e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.54/24.96  | | | | | | | | |            $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.54/24.96  | | | | | | | | |            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) =
% 158.54/24.96  | | | | | | | | |            e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.54/24.96  | | | | | | | | |            = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.54/24.96  | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.54/24.96  | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 158.54/24.96  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 158.54/24.96  | | | | | | | | |          | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 158.54/24.96  | | | | | | | | |            ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.54/24.96  | | | | | | | | |            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.96  | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 158.54/24.96  | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 158.54/24.96  | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.54/24.96  | | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.54/24.96  | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.54/24.96  | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.54/24.96  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 158.54/24.96  | | | | | | | | |          | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 158.54/24.96  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.54/24.96  | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | BETA: splitting (250) gives:
% 158.54/24.96  | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | Case 1:
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | |   (251)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.54/24.96  | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.54/24.96  | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.54/24.96  | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.54/24.96  | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 158.54/24.96  | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 158.54/24.96  | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3)
% 158.54/24.96  | | | | | | | | | |            = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.54/24.96  | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1
% 158.54/24.96  | | | | | | | | | |            & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14
% 158.54/24.96  | | | | | | | | | |              = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.54/24.96  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.96  | | | | | | | | | |            $i(all_57_14))
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | BETA: splitting (251) gives:
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | Case 1:
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | |   (252)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.54/24.96  | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.54/24.96  | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.54/24.96  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.54/24.96  | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 158.54/24.96  | | | | | | | | | | |              e2) = e3)
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | REF_CLOSE: (12), (43), (68), (252) are inconsistent by
% 158.54/24.96  | | | | | | | | | | |            sub-proof #792.
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | Case 2:
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | |   (253)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 158.54/24.96  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 158.54/24.96  | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.54/24.96  | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 158.54/24.96  | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 158.54/24.96  | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.54/24.96  | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.96  | | | | | | | | | | |            $i(all_57_14))
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | BETA: splitting (253) gives:
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | Case 1:
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | |   (254)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 & 
% 158.54/24.96  | | | | | | | | | | | |          ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 158.54/24.96  | | | | | | | | | | | |          = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.54/24.96  | | | | | | | | | | | |          $i(all_57_12)
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | ALPHA: (254) implies:
% 158.54/24.96  | | | | | | | | | | | |   (255)  op(e3, e3) = e2
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | REF_CLOSE: (12), (35), (72), (255) are inconsistent by
% 158.54/24.96  | | | | | | | | | | | |            sub-proof #958.
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | Case 2:
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | |   (256)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.54/24.96  | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 158.54/24.96  | | | | | | | | | | | |          = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.96  | | | | | | | | | | | |          $i(all_57_14)
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | ALPHA: (256) implies:
% 158.54/24.96  | | | | | | | | | | | |   (257)  op(e3, e3) = e1
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | REF_CLOSE: (3), (4), (8), (10), (12), (14), (17), (23), (28),
% 158.54/24.96  | | | | | | | | | | | |            (30), (37), (45), (46), (51), (54), (55), (56),
% 158.54/24.96  | | | | | | | | | | | |            (60), (61), (63), (64), (72), (224), (257) are
% 158.54/24.96  | | | | | | | | | | | |            inconsistent by sub-proof #145.
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | End of split
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | End of split
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | Case 2:
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | |   (258)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 158.54/24.96  | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.54/24.96  | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.54/24.96  | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 =
% 158.54/24.96  | | | | | | | | | |            e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.54/24.96  | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 158.54/24.96  | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.54/24.96  | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.54/24.96  | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 158.54/24.96  | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.54/24.96  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.54/24.96  | | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.54/24.96  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 158.54/24.96  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 158.54/24.96  | | | | | | | | | |            & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1
% 158.54/24.96  | | | | | | | | | |            & op(e1, e1) = e1)
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | BETA: splitting (258) gives:
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | Case 1:
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | |   (259)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 158.54/24.96  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.54/24.96  | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.54/24.96  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 158.54/24.96  | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.54/24.96  | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 158.54/24.96  | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | BETA: splitting (259) gives:
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | Case 1:
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | |   (260)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 158.54/24.96  | | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.54/24.96  | | | | | | | | | | | |          op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.54/24.96  | | | | | | | | | | | |          e3 & $i(all_57_10)
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | ALPHA: (260) implies:
% 158.54/24.96  | | | | | | | | | | | |   (261)  op(e1, e1) = e3
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | REF_CLOSE: (12), (17), (72), (261) are inconsistent by
% 158.54/24.96  | | | | | | | | | | | |            sub-proof #646.
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | Case 2:
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | |   (262)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 158.54/24.96  | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 158.54/24.96  | | | | | | | | | | | |          = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.96  | | | | | | | | | | | |          $i(all_57_14)
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | ALPHA: (262) implies:
% 158.54/24.96  | | | | | | | | | | | |   (263)  all_57_2 = e1
% 158.54/24.96  | | | | | | | | | | | |   (264)   ~ (all_57_14 = e3)
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | REF_CLOSE: (234), (263), (264) are inconsistent by sub-proof
% 158.54/24.96  | | | | | | | | | | | |            #749.
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | End of split
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | Case 2:
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | |   (265)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.54/24.96  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 158.54/24.96  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.54/24.96  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.54/24.96  | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.54/24.96  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.54/24.96  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.54/24.96  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.54/24.96  | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.54/24.96  | | | | | | | | | | |            e1)
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | BETA: splitting (265) gives:
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | Case 1:
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | |   (266)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.54/24.96  | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 158.54/24.96  | | | | | | | | | | | |          = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.54/24.96  | | | | | | | | | | | |          $i(all_57_14)
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | ALPHA: (266) implies:
% 158.54/24.96  | | | | | | | | | | | |   (267)  op(e0, e0) = e1
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | REF_CLOSE: (12), (21), (61), (267) are inconsistent by
% 158.54/24.96  | | | | | | | | | | | |            sub-proof #473.
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | Case 2:
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | |   (268)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 158.54/24.96  | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.54/24.96  | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.54/24.96  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 158.54/24.96  | | | | | | | | | | | |            = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 158.54/24.96  | | | | | | | | | | | |              e1) = e1)
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | | REF_CLOSE: (12), (17), (51), (72), (268) are inconsistent by
% 158.54/24.96  | | | | | | | | | | | |            sub-proof #139.
% 158.54/24.96  | | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | | End of split
% 158.54/24.96  | | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | | End of split
% 158.54/24.96  | | | | | | | | | | 
% 158.54/24.96  | | | | | | | | | End of split
% 158.54/24.96  | | | | | | | | | 
% 158.54/24.96  | | | | | | | | End of split
% 158.54/24.96  | | | | | | | | 
% 158.54/24.96  | | | | | | | Case 2:
% 158.54/24.96  | | | | | | | | 
% 158.54/24.96  | | | | | | | |   (269)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.54/24.96  | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3
% 158.54/24.96  | | | | | | | |            & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.96  | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.54/24.96  | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 158.54/24.96  | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.96  | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.54/24.96  | | | | | | | |            all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 158.54/24.96  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.54/24.96  | | | | | | | |              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.54/24.96  | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.54/24.96  | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.96  | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.54/24.96  | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 158.54/24.96  | | | | | | | |            all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 158.54/24.96  | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 158.54/24.96  | | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.54/24.96  | | | | | | | |            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.54/24.96  | | | | | | | |            op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.54/24.96  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.54/24.96  | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.54/24.97  | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 158.54/24.97  | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.54/24.97  | | | | | | | |            op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.54/24.97  | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.54/24.97  | | | | | | | |            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.54/24.97  | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 &
% 158.54/24.97  | | | | | | | |            all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 158.54/24.97  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.54/24.97  | | | | | | | |              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.54/24.97  | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2,
% 158.54/24.97  | | | | | | | |              e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 &
% 158.54/24.97  | | | | | | | |            all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 158.54/24.97  | | | | | | | |            & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 158.54/24.97  | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 158.54/24.97  | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~
% 158.54/24.97  | | | | | | | |            (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/24.97  | | | | | | | |              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.54/24.97  | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.54/24.97  | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 158.54/24.97  | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 &
% 158.54/24.97  | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 &
% 158.54/24.97  | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 158.54/24.97  | | | | | | | |            op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 158.54/24.97  | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.54/24.97  | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.54/24.97  | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.54/24.97  | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.54/24.97  | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.54/24.97  | | | | | | | |                  e3) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.54/24.97  | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 158.54/24.97  | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.54/24.97  | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 158.54/24.97  | | | | | | | |                e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 158.54/24.97  | | | | | | | |                = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 158.54/24.97  | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/24.97  | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.54/24.97  | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10
% 158.54/24.97  | | | | | | | |                = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 158.54/24.97  | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.54/24.97  | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.54/24.97  | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 158.54/24.97  | | | | | | | |                e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.54/24.97  | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.54/24.97  | | | | | | | |                  e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.54/24.97  | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.54/24.97  | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.54/24.97  | | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.54/24.97  | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) =
% 158.54/24.97  | | | | | | | |                e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.54/24.97  | | | | | | | |                all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.54/24.97  | | | | | | | |                  e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.54/24.97  | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.54/24.97  | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.54/24.97  | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.54/24.97  | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15
% 158.54/24.97  | | | | | | | |                = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.54/24.97  | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.54/24.97  | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 158.54/24.97  | | | | | | | |                &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.54/24.97  | | | | | | | | 
% 158.54/24.97  | | | | | | | | BETA: splitting (269) gives:
% 158.54/24.97  | | | | | | | | 
% 158.54/24.97  | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | 
% 158.54/24.97  | | | | | | | | |   (270)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.54/24.97  | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) =
% 158.54/24.97  | | | | | | | | |            e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.97  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.54/24.97  | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 158.54/24.97  | | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.54/24.97  | | | | | | | | |            = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.54/24.97  | | | | | | | | |            all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 158.54/24.97  | | | | | | | | |              e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.54/24.97  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 158.54/24.97  | | | | | | | | |          | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.54/24.97  | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.97  | | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.54/24.97  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 158.54/24.97  | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 158.54/24.97  | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 158.54/24.97  | | | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.54/24.97  | | | | | | | | |            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.54/24.97  | | | | | | | | |            op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.54/24.97  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.54/24.97  | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.54/24.97  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 158.54/24.97  | | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.54/24.97  | | | | | | | | |            op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 158.54/24.97  | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3)
% 158.54/24.97  | | | | | | | | |            = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.54/24.97  | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14))
% 158.54/24.97  | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | BETA: splitting (270) gives:
% 158.54/24.97  | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | |   (271)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.54/24.97  | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 158.54/24.97  | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.97  | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.54/24.97  | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 158.54/24.97  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 158.54/24.97  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 158.54/24.97  | | | | | | | | | |            e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.54/24.97  | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.54/24.97  | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.97  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 =
% 158.54/24.97  | | | | | | | | | |            e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.54/24.97  | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 158.54/24.97  | | | | | | | | | |              e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | BETA: splitting (271) gives:
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | |   (272)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.54/24.97  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 158.54/24.97  | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.97  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.54/24.97  | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 158.54/24.97  | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.54/24.97  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.97  | | | | | | | | | | |            $i(all_57_14))
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | REF_CLOSE: (3), (4), (8), (10), (12), (14), (17), (23), (28),
% 158.54/24.97  | | | | | | | | | | |            (30), (37), (45), (46), (51), (54), (55), (56),
% 158.54/24.97  | | | | | | | | | | |            (60), (61), (63), (64), (72), (224), (272) are
% 158.54/24.97  | | | | | | | | | | |            inconsistent by sub-proof #138.
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | |   (273)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 158.54/24.97  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.54/24.97  | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.97  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 158.54/24.97  | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.54/24.97  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.97  | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.54/24.97  | | | | | | | | | | |            $i(all_57_14))
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | REF_CLOSE: (12), (21), (46), (60), (61), (273) are
% 158.54/24.97  | | | | | | | | | | |            inconsistent by sub-proof #144.
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | End of split
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | |   (274)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 158.54/24.97  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.54/24.97  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.97  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.54/24.97  | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.54/24.97  | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.54/24.97  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.54/24.97  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.54/24.97  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3
% 158.54/24.97  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3
% 158.54/24.97  | | | | | | | | | |            & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 =
% 158.54/24.97  | | | | | | | | | |            e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.54/24.97  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.54/24.97  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | BETA: splitting (274) gives:
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | |   (275)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 158.54/24.97  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.54/24.97  | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.97  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.54/24.97  | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.54/24.97  | | | | | | | | | | |              e1) = e1)
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | BETA: splitting (275) gives:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | |   (276)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 158.54/24.97  | | | | | | | | | | | |          ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.54/24.97  | | | | | | | | | | | |          op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.97  | | | | | | | | | | | |          e2 & $i(all_57_12)
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | ALPHA: (276) implies:
% 158.54/24.97  | | | | | | | | | | | |   (277)  op(e1, e2) = e1
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | REF_CLOSE: (12), (40), (61), (277) are inconsistent by
% 158.54/24.97  | | | | | | | | | | | |            sub-proof #939.
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | |   (278)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) &
% 158.54/24.97  | | | | | | | | | | | |          op(e1, e2) = e1 & op(e1, e1) = e1
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | ALPHA: (278) implies:
% 158.54/24.97  | | | | | | | | | | | |   (279)  op(e1, e1) = e1
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | REF_CLOSE: (12), (17), (51), (279) are inconsistent by
% 158.54/24.97  | | | | | | | | | | | |            sub-proof #986.
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | End of split
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | |   (280)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.54/24.97  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.54/24.97  | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.54/24.97  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 158.54/24.97  | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 158.54/24.97  | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.54/24.97  | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 158.54/24.97  | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.54/24.97  | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | BETA: splitting (280) gives:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | |   (281)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.54/24.97  | | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.54/24.97  | | | | | | | | | | | |          op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.54/24.97  | | | | | | | | | | | |          e3 & $i(all_57_10)
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | ALPHA: (281) implies:
% 158.54/24.97  | | | | | | | | | | | |   (282)  op(e3, e1) = e3
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | REF_CLOSE: (12), (14), (69), (282) are inconsistent by
% 158.54/24.97  | | | | | | | | | | | |            sub-proof #982.
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | |   (283)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 158.54/24.97  | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 158.54/24.97  | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.54/24.97  | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 158.54/24.97  | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 158.54/24.97  | | | | | | | | | | | |            & $i(all_57_14))
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | BETA: splitting (283) gives:
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | |   (284)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 158.54/24.97  | | | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e1) = e3
% 158.54/24.97  | | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | | ALPHA: (284) implies:
% 158.54/24.97  | | | | | | | | | | | | |   (285)  op(e3, e1) = e3
% 158.54/24.97  | | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | | REF_CLOSE: (12), (14), (69), (285) are inconsistent by
% 158.54/24.97  | | | | | | | | | | | | |            sub-proof #982.
% 158.54/24.97  | | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | |   (286)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 158.54/24.97  | | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 158.54/24.97  | | | | | | | | | | | | |          = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.54/24.97  | | | | | | | | | | | | |          $i(all_57_14)
% 158.54/24.97  | | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | | ALPHA: (286) implies:
% 158.54/24.97  | | | | | | | | | | | | |   (287)  op(e3, e3) = e1
% 158.54/24.97  | | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | | REF_CLOSE: (3), (4), (8), (10), (12), (14), (17), (23), (28),
% 158.54/24.97  | | | | | | | | | | | | |            (30), (37), (45), (46), (51), (54), (55), (56),
% 158.54/24.97  | | | | | | | | | | | | |            (60), (61), (63), (64), (72), (224), (287) are
% 158.54/24.97  | | | | | | | | | | | | |            inconsistent by sub-proof #145.
% 158.54/24.97  | | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | End of split
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | End of split
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | End of split
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | End of split
% 158.54/24.97  | | | | | | | | | 
% 158.54/24.97  | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | 
% 158.54/24.97  | | | | | | | | |   (288)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.54/24.97  | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.54/24.97  | | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.54/24.97  | | | | | | | | |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 & 
% 158.54/24.97  | | | | | | | | |            ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.54/24.97  | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 158.54/24.97  | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 158.54/24.97  | | | | | | | | |            e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.54/24.97  | | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.54/24.97  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.54/24.97  | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 158.54/24.97  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 &
% 158.54/24.97  | | | | | | | | |            all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 158.54/24.97  | | | | | | | | |              e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.54/24.97  | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 158.54/24.97  | | | | | | | | |          | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 158.54/24.97  | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 158.54/24.97  | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 158.54/24.97  | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14
% 158.54/24.97  | | | | | | | | |            = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0)
% 158.54/24.97  | | | | | | | | |            = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.54/24.97  | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.54/24.97  | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.54/24.97  | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.54/24.97  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.54/24.97  | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 158.54/24.97  | | | | | | | | |                = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.54/24.97  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.54/24.97  | | | | | | | | |                  = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.54/24.97  | | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 158.54/24.97  | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.54/24.97  | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.54/24.97  | | | | | | | | |                 ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.54/24.97  | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 158.54/24.97  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.54/24.97  | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 158.54/24.97  | | | | | | | | |                = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.54/24.97  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.54/24.97  | | | | | | | | |                  = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.54/24.97  | | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.54/24.97  | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.54/24.97  | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.54/24.97  | | | | | | | | |                 ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.54/24.97  | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0
% 158.54/24.97  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.54/24.97  | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 158.54/24.97  | | | | | | | | |                = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.54/24.97  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.54/24.97  | | | | | | | | |                  = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.54/24.97  | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.54/24.97  | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.54/24.97  | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.54/24.97  | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 158.54/24.97  | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 158.54/24.97  | | | | | | | | |                = e0)))
% 158.54/24.97  | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | BETA: splitting (288) gives:
% 158.54/24.97  | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | |   (289)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.54/24.97  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.54/24.97  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.54/24.97  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.54/24.97  | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.54/24.97  | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.54/24.97  | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2)
% 158.54/24.97  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 &
% 158.54/24.97  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0
% 158.54/24.97  | | | | | | | | | |            & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10
% 158.54/24.97  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 158.54/24.97  | | | | | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.54/24.97  | | | | | | | | | |            $i(all_57_10))
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | BETA: splitting (289) gives:
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | |   (290)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.54/24.97  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.54/24.97  | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.54/24.97  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.54/24.97  | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.54/24.97  | | | | | | | | | | |              e1) = e2)
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | REF_CLOSE: (12), (21), (72), (224), (290) are inconsistent by
% 158.54/24.97  | | | | | | | | | | |            sub-proof #394.
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | |   (291)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 158.54/24.97  | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 158.54/24.97  | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.54/24.97  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 158.54/24.97  | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 158.54/24.97  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.54/24.97  | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.54/24.97  | | | | | | | | | | |            $i(all_57_10))
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | REF_CLOSE: (12), (15), (46), (52), (60), (291) are
% 158.54/24.97  | | | | | | | | | | |            inconsistent by sub-proof #746.
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | End of split
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | |   (292)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 158.54/24.97  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.54/24.97  | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.54/24.97  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.54/24.97  | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.54/24.97  | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 & 
% 158.54/24.97  | | | | | | | | | |            ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2)
% 158.54/24.97  | | | | | | | | | |          | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.54/24.97  | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.54/24.97  | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.54/24.97  | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.54/24.97  | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.54/24.97  | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/24.97  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.54/24.97  | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.54/24.97  | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/24.97  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.54/24.97  | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.54/24.97  | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/24.97  | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.54/24.97  | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.54/24.97  | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.97  | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.54/24.97  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 = e2
% 158.54/24.97  | | | | | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.97  | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.54/24.97  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 = e1
% 158.54/24.97  | | | | | | | | | |                & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.97  | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.54/24.97  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 = e0
% 158.54/24.97  | | | | | | | | | |                &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.54/24.97  | | | | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.54/24.97  | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.54/24.97  | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/24.97  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.54/24.97  | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.54/24.97  | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/24.97  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.54/24.97  | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.54/24.97  | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/24.97  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 158.54/24.97  | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.54/24.97  | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.54/24.97  | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 =
% 158.54/24.97  | | | | | | | | | |                e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | BETA: splitting (292) gives:
% 158.54/24.97  | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | |   (293)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 158.54/24.97  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.54/24.97  | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.54/24.97  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.54/24.97  | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.54/24.97  | | | | | | | | | | |              e0) = e3)
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | REF_CLOSE: (12), (15), (21), (52), (72), (293) are
% 158.54/24.97  | | | | | | | | | | |            inconsistent by sub-proof #451.
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | |   (294)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.54/24.97  | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 158.54/24.97  | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 158.54/24.97  | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.54/24.97  | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.54/24.97  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.54/24.97  | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.54/24.97  | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/24.97  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.54/24.97  | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.54/24.97  | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/24.97  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.54/24.97  | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.54/24.97  | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/24.97  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.54/24.97  | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.54/24.97  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.97  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.54/24.97  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.54/24.97  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.97  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.54/24.97  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.54/24.97  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.97  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.54/24.97  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.54/24.97  | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.54/24.97  | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.54/24.97  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.54/24.97  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.54/24.97  | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.54/24.97  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.54/24.97  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.54/24.97  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.54/24.97  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.54/24.97  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.54/24.97  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.54/24.97  | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.54/24.97  | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.54/24.97  | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.54/24.97  | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.54/24.97  | | | | | | | | | | |                e0)))
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | BETA: splitting (294) gives:
% 158.54/24.97  | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | Case 1:
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | |   (295)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.54/24.97  | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | ALPHA: (295) implies:
% 158.54/24.97  | | | | | | | | | | | |   (296)  op(e2, e2) = e2
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | | REF_CLOSE: (12), (51), (224), (296) are inconsistent by
% 158.54/24.97  | | | | | | | | | | | |            sub-proof #993.
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.97  | | | | | | | | | | | Case 2:
% 158.54/24.97  | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | |   (297)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.54/24.98  | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.54/24.98  | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.54/24.98  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.54/24.98  | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.54/24.98  | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/24.98  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.54/24.98  | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.54/24.98  | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/24.98  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.54/24.98  | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.54/24.98  | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/24.98  | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.54/24.98  | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.54/24.98  | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.98  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.54/24.98  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.54/24.98  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.98  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.54/24.98  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.54/24.98  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.98  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.54/24.98  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.54/24.98  | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.54/24.98  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.54/24.98  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.54/24.98  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.54/24.98  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.54/24.98  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.54/24.98  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.54/24.98  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.54/24.98  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.54/24.98  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.54/24.98  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.54/24.98  | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.54/24.98  | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.54/24.98  | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.54/24.98  | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.54/24.98  | | | | | | | | | | | |                e0)))
% 158.54/24.98  | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | BETA: splitting (297) gives:
% 158.54/24.98  | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | Case 1:
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | |   (298)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.54/24.98  | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | ALPHA: (298) implies:
% 158.54/24.98  | | | | | | | | | | | | |   (299)  op(e1, e1) = e1
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | REF_CLOSE: (12), (17), (51), (299) are inconsistent by
% 158.54/24.98  | | | | | | | | | | | | |            sub-proof #986.
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | Case 2:
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | |   (300)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.54/24.98  | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.54/24.98  | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.54/24.98  | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.54/24.98  | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.54/24.98  | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.54/24.98  | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.54/24.98  | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.54/24.98  | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.54/24.98  | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.54/24.98  | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.54/24.98  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.54/24.98  | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 158.54/24.98  | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.54/24.98  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.54/24.98  | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.54/24.98  | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.54/24.98  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.54/24.98  | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.54/24.98  | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.54/24.98  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 158.54/24.98  | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.54/24.98  | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.54/24.98  | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.54/24.98  | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.54/24.98  | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.54/24.98  | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 158.54/24.98  | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.54/24.98  | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 158.54/24.98  | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.54/24.98  | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.54/24.98  | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.54/24.98  | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.54/24.98  | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.54/24.98  | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.54/24.98  | | | | | | | | | | | | |              e0))
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | ALPHA: (300) implies:
% 158.54/24.98  | | | | | | | | | | | | |   (301)  op(e0, e0) = all_57_15
% 158.54/24.98  | | | | | | | | | | | | |   (302)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.54/24.98  | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.54/24.98  | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.54/24.98  | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.54/24.98  | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.54/24.98  | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.54/24.98  | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.54/24.98  | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.54/24.98  | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.54/24.98  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.54/24.98  | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.54/24.98  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.54/24.98  | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.98  | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.54/24.98  | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.54/24.98  | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.54/24.98  | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 158.54/24.98  | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.54/24.98  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.54/24.98  | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.54/24.98  | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.54/24.98  | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.54/24.98  | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 158.54/24.98  | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 158.54/24.98  | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 158.54/24.98  | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.54/24.98  | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.54/24.98  | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.54/24.98  | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.54/24.98  | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.54/24.98  | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.54/24.98  | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | GROUND_INST: instantiating (12) with e3, all_57_15, e0, e0,
% 158.54/24.98  | | | | | | | | | | | | |              simplifying with (21), (301) gives:
% 158.54/24.98  | | | | | | | | | | | | |   (303)  all_57_15 = e3
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | GROUND_INST: instantiating (12) with e2, all_24_1, e1, e1,
% 158.54/24.98  | | | | | | | | | | | | |              simplifying with (17), (230) gives:
% 158.54/24.98  | | | | | | | | | | | | |   (304)  all_24_1 = e2
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | BETA: splitting (302) gives:
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | Case 1:
% 158.54/24.98  | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | |   (305)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.54/24.98  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.54/24.98  | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.54/24.98  | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.54/24.98  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.54/24.98  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.54/24.98  | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.54/24.98  | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.54/24.98  | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.54/24.98  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.54/24.98  | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.98  | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.54/24.98  | | | | | | | | | | | | | |            e0)
% 158.54/24.98  | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 158.54/24.98  | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | Case 1:
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | |   (306)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.54/24.98  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.54/24.98  | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.54/24.98  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.54/24.98  | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.54/24.98  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.54/24.98  | | | | | | | | | | | | | | |            e0)
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | Case 1:
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | |   (307)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 158.54/24.98  | | | | | | | | | | | | | | | |          = e3 & op(e0, e3) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 158.54/24.98  | | | | | | | | | | | | | | | |   (308)  all_57_6 = e0
% 158.54/24.98  | | | | | | | | | | | | | | | |   (309)   ~ (all_57_15 = e3)
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | REF_CLOSE: (233), (308), (309) are inconsistent by sub-proof
% 158.54/24.98  | | | | | | | | | | | | | | | |            #684.
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | Case 2:
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | |   (310)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.54/24.98  | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.54/24.98  | | | | | | | | | | | | | | | |              = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.54/24.98  | | | | | | | | | | | | | | | |            op(e0, e3) = e0)
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | Case 1:
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (311)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 158.54/24.98  | | | | | | | | | | | | | | | | |          = e2 & op(e0, e3) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (312)  all_57_6 = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (313)   ~ (all_57_15 = e3)
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (233), (312), (313) are inconsistent by sub-proof
% 158.54/24.98  | | | | | | | | | | | | | | | | |            #684.
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | Case 2:
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (314)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 158.54/24.98  | | | | | | | | | | | | | | | | |          = e1 & op(e0, e3) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | ALPHA: (314) implies:
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (315)  op(e1, e1) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (63), (315) are inconsistent by
% 158.54/24.98  | | | | | | | | | | | | | | | | |            sub-proof #914.
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | Case 2:
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | |   (316)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.54/24.98  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 158.54/24.98  | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.98  | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.54/24.98  | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.54/24.98  | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.54/24.98  | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | Case 1:
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | |   (317)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.54/24.98  | | | | | | | | | | | | | | | |          op(e0, e3) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | REF_CLOSE: (303), (317) are inconsistent by sub-proof #450.
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | Case 2:
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | |   (318)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.54/24.98  | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.54/24.98  | | | | | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.54/24.98  | | | | | | | | | | | | | | | |            op(e0, e2) = e0)
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | Case 1:
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (319)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 158.54/24.98  | | | | | | | | | | | | | | | | |          = e3 & op(e0, e2) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (320)  op(e3, e3) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (35), (64), (320) are inconsistent by
% 158.54/24.98  | | | | | | | | | | | | | | | | |            sub-proof #971.
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | Case 2:
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (321)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 158.54/24.98  | | | | | | | | | | | | | | | | |          = e2 & op(e0, e2) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | ALPHA: (321) implies:
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (322)  op(e2, e2) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (79), (80), (322) are inconsistent by
% 158.54/24.98  | | | | | | | | | | | | | | | | |            sub-proof #172.
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | Case 2:
% 158.54/24.98  | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | |   (323)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.54/24.98  | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.54/24.98  | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.54/24.98  | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.54/24.98  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.54/24.98  | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.54/24.98  | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.54/24.98  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.54/24.98  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.54/24.98  | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.54/24.98  | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.54/24.98  | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 158.54/24.98  | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.54/24.98  | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 158.54/24.98  | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | Case 1:
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | |   (324)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.54/24.98  | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.54/24.98  | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.54/24.98  | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.54/24.98  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (35), (63), (64), (303), (324) are
% 158.54/24.98  | | | | | | | | | | | | | | |            inconsistent by sub-proof #143.
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | Case 2:
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | |   (325)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.54/24.98  | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.54/24.98  | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.54/24.98  | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.54/24.98  | | | | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.54/24.98  | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.54/24.98  | | | | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 158.54/24.98  | | | | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 158.54/24.98  | | | | | | | | | | | | | | |            = e0)
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | Case 1:
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | |   (326)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.54/24.98  | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.54/24.98  | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.54/24.98  | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | Case 1:
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (327)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 158.54/24.98  | | | | | | | | | | | | | | | | |          = e2 & op(e0, e1) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | ALPHA: (327) implies:
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (328)  op(e2, e2) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (79), (80), (328) are inconsistent by
% 158.54/24.98  | | | | | | | | | | | | | | | | |            sub-proof #172.
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | Case 2:
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (329)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 158.54/24.98  | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 158.54/24.98  | | | | | | | | | | | | | | | | |          = e1 & op(e0, e1) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 158.54/24.98  | | | | | | | | | | | | | | | | |   (330)  op(e1, e1) = e0
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (63), (330) are inconsistent by
% 158.54/24.98  | | | | | | | | | | | | | | | | |            sub-proof #914.
% 158.54/24.98  | | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | Case 2:
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | |   (331)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 158.54/24.98  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.54/24.98  | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.54/24.98  | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 158.54/24.98  | | | | | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | | REF_CLOSE: (61), (64), (303), (331) are inconsistent by
% 158.54/24.98  | | | | | | | | | | | | | | | |            sub-proof #142.
% 158.54/24.98  | | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | | 
% 158.54/24.98  | | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | | 
% 158.54/24.98  | | | | | | | | End of split
% 158.54/24.98  | | | | | | | | 
% 158.54/24.98  | | | | | | | End of split
% 158.54/24.98  | | | | | | | 
% 158.54/24.98  | | | | | | End of split
% 158.54/24.98  | | | | | | 
% 158.54/24.98  | | | | | Case 2:
% 158.54/24.98  | | | | | | 
% 158.54/24.98  | | | | | |   (332)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 &
% 158.54/24.98  | | | | | |              op(e3, e3) = e2) | ( ~ (all_57_1 = e3) & op(e3, e2) =
% 158.54/24.98  | | | | | |              all_57_1 & $i(all_57_1))) & ((all_57_14 = e2 & op(e1,
% 158.54/24.98  | | | | | |                e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 158.54/24.98  | | | | | |              all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 158.54/24.98  | | | | | |                e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 158.54/24.98  | | | | | |              all_57_7 & $i(all_57_7)))
% 158.54/24.98  | | | | | | 
% 158.54/24.98  | | | | | | ALPHA: (332) implies:
% 158.54/24.98  | | | | | |   (333)  op(e2, e2) = e2
% 158.54/24.98  | | | | | | 
% 158.54/24.98  | | | | | | REF_CLOSE: (12), (51), (224), (333) are inconsistent by sub-proof
% 158.54/24.98  | | | | | |            #993.
% 158.54/24.98  | | | | | | 
% 158.54/24.98  | | | | | End of split
% 158.54/24.98  | | | | | 
% 158.54/24.98  | | | | Case 2:
% 158.54/24.98  | | | | | 
% 158.54/24.98  | | | | |   (334)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 158.54/24.98  | | | | |                  e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) =
% 158.54/24.98  | | | | |                all_57_4 & $i(all_57_4))) & ((all_57_12 = e1 & op(e2,
% 158.54/24.98  | | | | |                  e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 158.54/24.98  | | | | |                all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 158.54/24.98  | | | | |                  e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 158.54/24.98  | | | | |                all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 158.54/24.98  | | | | |              e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 158.54/24.98  | | | | |                (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 158.54/24.98  | | | | |                $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) |
% 158.54/24.98  | | | | |              ( ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 158.54/24.98  | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0) |
% 158.54/24.98  | | | | |              ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.54/24.98  | | | | |                $i(all_57_13))))
% 158.54/24.98  | | | | | 
% 158.54/24.98  | | | | | REF_CLOSE: (12), (17), (21), (51), (64), (334) are inconsistent by
% 158.54/24.98  | | | | |            sub-proof #416.
% 158.54/24.98  | | | | | 
% 158.54/24.98  | | | | End of split
% 158.54/24.98  | | | | 
% 158.54/24.98  | | | End of split
% 158.54/24.98  | | | 
% 158.54/24.98  | | End of split
% 158.54/24.98  | | 
% 158.54/24.98  | End of split
% 158.54/24.98  | 
% 158.54/24.98  End of proof
% 158.54/24.98  
% 158.54/24.98  Sub-proof #138 shows that the following formulas are inconsistent:
% 158.54/24.98  ----------------------------------------------------------------
% 158.54/24.98    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.54/24.98         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.54/24.98    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.54/24.98         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.54/24.98    (3)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.54/24.98             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.54/24.98           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.54/24.98               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.54/24.98             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.54/24.98         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.54/24.98             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.54/24.98           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.54/24.98               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.54/24.98             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.54/24.98         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.54/24.98             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.54/24.98           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.54/24.98               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.54/24.98             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.54/24.98         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.54/24.98             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.54/24.98           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.54/24.98               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.54/24.98             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.54/24.98    (4)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.54/24.98         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/24.98    (5)   ~ (e3 = e2)
% 158.54/24.98    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/24.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/24.98    (7)  op(e3, e1) = all_52_8
% 158.54/24.98    (8)  op(e1, e1) = e2
% 158.54/24.98    (9)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 158.54/24.98           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.98           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 158.54/24.98           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 158.54/24.98             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.54/24.98    (10)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.54/24.98          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.54/24.98    (11)  op(e1, e0) = all_52_14
% 158.54/24.98    (12)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.54/24.98          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.54/24.98    (13)  op(e0, e0) = all_14_2
% 158.54/24.98    (14)  op(e2, e2) = e1
% 158.54/24.98    (15)   ~ (e1 = e0)
% 158.54/24.98    (16)  op(e2, e1) = all_52_9
% 158.54/24.99    (17)   ~ (e2 = e1)
% 158.54/24.99    (18)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.54/24.99          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.54/24.99    (19)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.54/24.99          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.54/24.99    (20)   ~ (all_52_8 = e2)
% 158.54/24.99    (21)   ~ (all_52_9 = e2)
% 158.54/24.99    (22)   ~ (e3 = e1)
% 158.54/24.99    (23)   ~ (e2 = e0)
% 158.54/24.99    (24)   ~ (e3 = e0)
% 158.54/24.99  
% 158.54/24.99  Begin of proof
% 158.54/24.99  | 
% 158.54/24.99  | BETA: splitting (9) gives:
% 158.54/24.99  | 
% 158.54/24.99  | Case 1:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (25)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 158.54/24.99  | |         & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.99  | |         all_57_14 & $i(all_57_14)
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (25) implies:
% 158.54/24.99  | |   (26)  op(e3, e3) = e1
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 158.54/24.99  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 158.54/24.99  | |            (26) are inconsistent by sub-proof #145.
% 158.54/24.99  | | 
% 158.54/24.99  | Case 2:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (27)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 158.54/24.99  | |         & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.54/24.99  | |         all_57_14 & $i(all_57_14)
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (27) implies:
% 158.54/24.99  | |   (28)  op(e2, e1) = e2
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (6), (16), (21), (28) are inconsistent by sub-proof #1002.
% 158.54/24.99  | | 
% 158.54/24.99  | End of split
% 158.54/24.99  | 
% 158.54/24.99  End of proof
% 158.54/24.99  
% 158.54/24.99  Sub-proof #139 shows that the following formulas are inconsistent:
% 158.54/24.99  ----------------------------------------------------------------
% 158.54/24.99    (1)   ~ (e3 = e2)
% 158.54/24.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/24.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/24.99    (3)  op(e1, e1) = e2
% 158.54/24.99    (4)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) &
% 158.54/24.99           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.54/24.99           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1)
% 158.54/24.99           & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.54/24.99    (5)   ~ (e2 = e1)
% 158.54/24.99  
% 158.54/24.99  Begin of proof
% 158.54/24.99  | 
% 158.54/24.99  | BETA: splitting (4) gives:
% 158.54/24.99  | 
% 158.54/24.99  | Case 1:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (6)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 158.54/24.99  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 158.54/24.99  | |          e1) = e3 & $i(all_57_10)
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (6) implies:
% 158.54/24.99  | |   (7)  op(e1, e1) = e3
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #646.
% 158.54/24.99  | | 
% 158.54/24.99  | Case 2:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (8)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.54/24.99  | |        op(e1, e1) = e1
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (8) implies:
% 158.54/24.99  | |   (9)  op(e1, e1) = e1
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #986.
% 158.54/24.99  | | 
% 158.54/24.99  | End of split
% 158.54/24.99  | 
% 158.54/24.99  End of proof
% 158.54/24.99  
% 158.54/24.99  Sub-proof #140 shows that the following formulas are inconsistent:
% 158.54/24.99  ----------------------------------------------------------------
% 158.54/24.99    (1)   ~ (e3 = e2)
% 158.54/24.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/24.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/24.99    (3)  op(e1, e1) = e2
% 158.54/24.99    (4)  op(e2, e1) = all_52_9
% 158.54/24.99    (5)   ~ (all_52_9 = e2)
% 158.54/24.99    (6)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.54/24.99           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.54/24.99           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 158.54/24.99           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 158.54/24.99           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.54/24.99  
% 158.54/24.99  Begin of proof
% 158.54/24.99  | 
% 158.54/24.99  | BETA: splitting (6) gives:
% 158.54/24.99  | 
% 158.54/24.99  | Case 1:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (7)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 158.54/24.99  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 158.54/24.99  | |          e1) = e3 & $i(all_57_10)
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (7) implies:
% 158.54/24.99  | |   (8)  op(e1, e1) = e3
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #646.
% 158.54/24.99  | | 
% 158.54/24.99  | Case 2:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (9)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 158.54/24.99  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.54/24.99  | |          e1) = e2 & $i(all_57_12)
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (9) implies:
% 158.54/24.99  | |   (10)  op(e2, e1) = e2
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #1002.
% 158.54/24.99  | | 
% 158.54/24.99  | End of split
% 158.54/24.99  | 
% 158.54/24.99  End of proof
% 158.54/24.99  
% 158.54/24.99  Sub-proof #141 shows that the following formulas are inconsistent:
% 158.54/24.99  ----------------------------------------------------------------
% 158.54/24.99    (1)  all_56_13 = e0 & op(e0, e2) = e0
% 158.54/24.99    (2)  all_56_13 = e2
% 158.54/24.99    (3)   ~ (e2 = e0)
% 158.54/24.99  
% 158.54/24.99  Begin of proof
% 158.54/24.99  | 
% 158.54/24.99  | ALPHA: (1) implies:
% 158.54/24.99  |   (4)  all_56_13 = e0
% 158.54/24.99  | 
% 158.54/24.99  | COMBINE_EQS: (2), (4) imply:
% 158.54/24.99  |   (5)  e2 = e0
% 158.54/24.99  | 
% 158.54/24.99  | SIMP: (5) implies:
% 158.54/24.99  |   (6)  e2 = e0
% 158.54/24.99  | 
% 158.54/24.99  | REDUCE: (3), (6) imply:
% 158.54/24.99  |   (7)  $false
% 158.54/24.99  | 
% 158.54/24.99  | CLOSE: (7) is inconsistent.
% 158.54/24.99  | 
% 158.54/24.99  End of proof
% 158.54/24.99  
% 158.54/24.99  Sub-proof #142 shows that the following formulas are inconsistent:
% 158.54/24.99  ----------------------------------------------------------------
% 158.54/24.99    (1)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.54/24.99           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.54/24.99           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.54/24.99           op(e0, e1) = e0)
% 158.54/24.99    (2)  all_57_15 = e3
% 158.54/24.99    (3)   ~ (e3 = e1)
% 158.54/24.99    (4)   ~ (e3 = e0)
% 158.54/24.99  
% 158.54/24.99  Begin of proof
% 158.54/24.99  | 
% 158.54/24.99  | BETA: splitting (1) gives:
% 158.54/24.99  | 
% 158.54/24.99  | Case 1:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (5)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 158.54/24.99  | |        & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.54/24.99  | |        $i(all_57_14)
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (5) implies:
% 158.54/24.99  | |   (6)  all_57_15 = e1
% 158.54/24.99  | | 
% 158.54/24.99  | | COMBINE_EQS: (2), (6) imply:
% 158.54/24.99  | |   (7)  e3 = e1
% 158.54/24.99  | | 
% 158.54/24.99  | | REDUCE: (3), (7) imply:
% 158.54/24.99  | |   (8)  $false
% 158.54/24.99  | | 
% 158.54/24.99  | | CLOSE: (8) is inconsistent.
% 158.54/24.99  | | 
% 158.54/24.99  | Case 2:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (9)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #447.
% 158.54/24.99  | | 
% 158.54/24.99  | End of split
% 158.54/24.99  | 
% 158.54/24.99  End of proof
% 158.54/24.99  
% 158.54/24.99  Sub-proof #143 shows that the following formulas are inconsistent:
% 158.54/24.99  ----------------------------------------------------------------
% 158.54/24.99    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/24.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/24.99    (2)  op(e1, e1) = e2
% 158.54/24.99    (3)  all_57_15 = e3
% 158.54/24.99    (4)  op(e3, e3) = e3
% 158.54/24.99    (5)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.54/24.99           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.54/24.99           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.54/24.99           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 158.54/24.99           & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.54/24.99    (6)   ~ (e2 = e0)
% 158.54/24.99    (7)   ~ (e3 = e0)
% 158.54/24.99  
% 158.54/24.99  Begin of proof
% 158.54/24.99  | 
% 158.54/24.99  | BETA: splitting (5) gives:
% 158.54/24.99  | 
% 158.54/24.99  | Case 1:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (8)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 158.54/24.99  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (8) implies:
% 158.54/24.99  | |   (9)  op(e1, e1) = e0
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #914.
% 158.54/24.99  | | 
% 158.54/24.99  | Case 2:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (10)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.54/24.99  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.54/24.99  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (1), (3), (4), (7), (10) are inconsistent by sub-proof #448.
% 158.54/24.99  | | 
% 158.54/24.99  | End of split
% 158.54/24.99  | 
% 158.54/24.99  End of proof
% 158.54/24.99  
% 158.54/24.99  Sub-proof #144 shows that the following formulas are inconsistent:
% 158.54/24.99  ----------------------------------------------------------------
% 158.54/24.99    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/24.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/24.99    (2)  op(e0, e0) = e3
% 158.54/24.99    (3)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 158.54/24.99           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.54/24.99           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 158.54/24.99           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.54/24.99           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 158.54/24.99    (4)  op(e2, e1) = all_52_9
% 158.54/24.99    (5)   ~ (all_52_9 = e2)
% 158.54/24.99    (6)   ~ (e3 = e1)
% 158.54/24.99  
% 158.54/24.99  Begin of proof
% 158.54/24.99  | 
% 158.54/24.99  | BETA: splitting (3) gives:
% 158.54/24.99  | 
% 158.54/24.99  | Case 1:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (7)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 158.54/24.99  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 158.54/24.99  | |          e1) = e2 & $i(all_57_12)
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (7) implies:
% 158.54/24.99  | |   (8)  op(e2, e1) = e2
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1002.
% 158.54/24.99  | | 
% 158.54/24.99  | Case 2:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (9)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 158.54/24.99  | |        & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.54/24.99  | |          e0) = e1 & $i(all_57_14)
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (9) implies:
% 158.54/24.99  | |   (10)  op(e0, e0) = e1
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #473.
% 158.54/24.99  | | 
% 158.54/24.99  | End of split
% 158.54/24.99  | 
% 158.54/24.99  End of proof
% 158.54/24.99  
% 158.54/24.99  Sub-proof #145 shows that the following formulas are inconsistent:
% 158.54/24.99  ----------------------------------------------------------------
% 158.54/24.99    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.54/24.99         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.54/24.99    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.54/24.99         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.54/24.99    (3)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.54/24.99             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.54/24.99           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.54/24.99               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.54/24.99             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.54/24.99         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.54/24.99             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.54/24.99           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.54/24.99               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.54/24.99             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.54/24.99         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.54/24.99             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.54/24.99           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.54/24.99               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.54/24.99             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.54/24.99         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.54/24.99             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.54/24.99           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.54/24.99               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.54/24.99             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.54/24.99    (4)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.54/24.99         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/24.99    (5)   ~ (e3 = e2)
% 158.54/24.99    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/24.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/24.99    (7)  op(e3, e1) = all_52_8
% 158.54/24.99    (8)  op(e1, e1) = e2
% 158.54/24.99    (9)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.54/24.99         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.54/24.99    (10)  op(e1, e0) = all_52_14
% 158.54/24.99    (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.54/24.99          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.54/24.99    (12)  op(e0, e0) = all_14_2
% 158.54/24.99    (13)  op(e3, e3) = e1
% 158.54/24.99    (14)  op(e2, e2) = e1
% 158.54/24.99    (15)   ~ (e1 = e0)
% 158.54/24.99    (16)  op(e2, e1) = all_52_9
% 158.54/24.99    (17)   ~ (e2 = e1)
% 158.54/24.99    (18)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.54/24.99          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.54/24.99    (19)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.54/24.99          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.54/24.99    (20)   ~ (all_52_8 = e2)
% 158.54/24.99    (21)   ~ (all_52_9 = e2)
% 158.54/24.99    (22)   ~ (e3 = e1)
% 158.54/24.99    (23)   ~ (e2 = e0)
% 158.54/24.99    (24)   ~ (e3 = e0)
% 158.54/24.99  
% 158.54/24.99  Begin of proof
% 158.54/24.99  | 
% 158.54/24.99  | BETA: splitting (1) gives:
% 158.54/24.99  | 
% 158.54/24.99  | Case 1:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (25)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 158.54/24.99  | |           e1)
% 158.54/24.99  | | 
% 158.54/24.99  | | BETA: splitting (25) gives:
% 158.54/24.99  | | 
% 158.54/24.99  | | Case 1:
% 158.54/24.99  | | | 
% 158.54/24.99  | | |   (26)  all_56_9 = e1 & op(e3, e0) = e1
% 158.54/24.99  | | | 
% 158.54/24.99  | | | ALPHA: (26) implies:
% 158.54/24.99  | | |   (27)  all_56_9 = e1
% 158.54/24.99  | | | 
% 158.54/24.99  | | | REF_CLOSE: (2), (4), (5), (6), (7), (11), (13), (15), (17), (20), (22),
% 158.54/24.99  | | |            (23), (24), (27) are inconsistent by sub-proof #147.
% 158.54/24.99  | | | 
% 158.54/24.99  | | Case 2:
% 158.54/24.99  | | | 
% 158.54/24.99  | | |   (28)  all_56_10 = e1 & op(e2, e0) = e1
% 158.54/24.99  | | | 
% 158.54/24.99  | | | ALPHA: (28) implies:
% 158.54/24.99  | | |   (29)  all_56_10 = e1
% 158.54/24.99  | | | 
% 158.54/24.99  | | | REF_CLOSE: (5), (6), (9), (14), (15), (16), (17), (18), (19), (21), (22),
% 158.54/24.99  | | |            (23), (24), (29) are inconsistent by sub-proof #842.
% 158.54/24.99  | | | 
% 158.54/24.99  | | End of split
% 158.54/24.99  | | 
% 158.54/24.99  | Case 2:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (30)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.54/24.99  | |           e1)
% 158.54/24.99  | | 
% 158.54/24.99  | | BETA: splitting (30) gives:
% 158.54/24.99  | | 
% 158.54/24.99  | | Case 1:
% 158.54/24.99  | | | 
% 158.54/24.99  | | |   (31)  all_56_11 = e1 & op(e1, e0) = e1
% 158.54/24.99  | | | 
% 158.54/24.99  | | | ALPHA: (31) implies:
% 158.54/24.99  | | |   (32)  op(e1, e0) = e1
% 158.54/24.99  | | | 
% 158.54/24.99  | | | BETA: splitting (3) gives:
% 158.54/24.99  | | | 
% 158.54/24.99  | | | Case 1:
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | |   (33)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2,
% 158.54/24.99  | | | |                 e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0
% 158.54/24.99  | | | |               & $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | (
% 158.54/24.99  | | | |               ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)))
% 158.54/24.99  | | | |           & ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 158.54/24.99  | | | |               op(e0, e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2
% 158.54/24.99  | | | |           & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 158.54/24.99  | | | |               (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.54/24.99  | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 158.54/24.99  | | | |               op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2
% 158.54/24.99  | | | |               & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 158.54/24.99  | | | |               all_57_7 & $i(all_57_7))))
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | | REF_CLOSE: (6), (13), (14), (17), (22), (33) are inconsistent by
% 158.54/24.99  | | | |            sub-proof #499.
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | Case 2:
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | |   (34)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 158.54/24.99  | | | |                 e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4
% 158.54/24.99  | | | |               & $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | (
% 158.54/24.99  | | | |               ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)))
% 158.54/24.99  | | | |           & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.54/24.99  | | | |               op(e0, e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0
% 158.54/24.99  | | | |           & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 158.54/24.99  | | | |               (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.54/24.99  | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 158.54/24.99  | | | |               op(e2, e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 =
% 158.54/24.99  | | | |               e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0)
% 158.54/24.99  | | | |               = all_57_13 & $i(all_57_13))))
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | | BETA: splitting (34) gives:
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | | Case 1:
% 158.54/24.99  | | | | | 
% 158.54/24.99  | | | | |   (35)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 158.54/24.99  | | | | |               e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4
% 158.54/24.99  | | | | |             & $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | (
% 158.54/24.99  | | | | |             ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)))
% 158.54/24.99  | | | | |         & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.54/24.99  | | | | |             op(e0, e1) = all_57_8 & $i(all_57_8)))
% 158.54/24.99  | | | | | 
% 158.54/24.99  | | | | | ALPHA: (35) implies:
% 158.54/24.99  | | | | |   (36)  op(e1, e1) = e1
% 158.54/24.99  | | | | | 
% 158.54/24.99  | | | | | REF_CLOSE: (6), (8), (17), (36) are inconsistent by sub-proof #986.
% 158.54/24.99  | | | | | 
% 158.54/24.99  | | | | Case 2:
% 158.54/24.99  | | | | | 
% 158.54/24.99  | | | | |   (37)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3,
% 158.54/24.99  | | | | |               e3) = e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9
% 158.54/24.99  | | | | |             & $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | (
% 158.54/24.99  | | | | |             ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 158.54/24.99  | | | | |             $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0) | (
% 158.54/24.99  | | | | |             ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.54/24.99  | | | | |             $i(all_57_13)))
% 158.54/24.99  | | | | | 
% 158.54/24.99  | | | | | ALPHA: (37) implies:
% 158.54/24.99  | | | | |   (38)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) &
% 158.54/24.99  | | | | |           op(e1, e0) = all_57_13 & $i(all_57_13))
% 158.54/24.99  | | | | | 
% 158.54/24.99  | | | | | REF_CLOSE: (6), (8), (10), (23), (32), (38) are inconsistent by
% 158.54/24.99  | | | | |            sub-proof #146.
% 158.54/24.99  | | | | | 
% 158.54/24.99  | | | | End of split
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | End of split
% 158.54/24.99  | | | 
% 158.54/24.99  | | Case 2:
% 158.54/24.99  | | | 
% 158.54/24.99  | | |   (39)  all_56_15 = e1 & op(e0, e0) = e1
% 158.54/24.99  | | | 
% 158.54/24.99  | | | ALPHA: (39) implies:
% 158.54/24.99  | | |   (40)  op(e0, e0) = e1
% 158.54/24.99  | | | 
% 158.54/24.99  | | | BETA: splitting (3) gives:
% 158.54/24.99  | | | 
% 158.54/24.99  | | | Case 1:
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | |   (41)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2,
% 158.54/24.99  | | | |                 e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0
% 158.54/24.99  | | | |               & $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | (
% 158.54/24.99  | | | |               ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)))
% 158.54/24.99  | | | |           & ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 158.54/24.99  | | | |               op(e0, e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2
% 158.54/24.99  | | | |           & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 158.54/24.99  | | | |               (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.54/24.99  | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 158.54/24.99  | | | |               op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2
% 158.54/24.99  | | | |               & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 158.54/24.99  | | | |               all_57_7 & $i(all_57_7))))
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | | REF_CLOSE: (6), (13), (14), (17), (22), (41) are inconsistent by
% 158.54/24.99  | | | |            sub-proof #499.
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | Case 2:
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | |   (42)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 158.54/24.99  | | | |                 e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4
% 158.54/24.99  | | | |               & $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | (
% 158.54/24.99  | | | |               ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)))
% 158.54/24.99  | | | |           & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.54/24.99  | | | |               op(e0, e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0
% 158.54/24.99  | | | |           & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 158.54/24.99  | | | |               (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.54/24.99  | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 158.54/24.99  | | | |               op(e2, e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 =
% 158.54/24.99  | | | |               e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0)
% 158.54/24.99  | | | |               = all_57_13 & $i(all_57_13))))
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | | REF_CLOSE: (6), (8), (12), (15), (17), (40), (42) are inconsistent by
% 158.54/24.99  | | | |            sub-proof #748.
% 158.54/24.99  | | | | 
% 158.54/24.99  | | | End of split
% 158.54/24.99  | | | 
% 158.54/24.99  | | End of split
% 158.54/24.99  | | 
% 158.54/24.99  | End of split
% 158.54/24.99  | 
% 158.54/24.99  End of proof
% 158.54/24.99  
% 158.54/24.99  Sub-proof #146 shows that the following formulas are inconsistent:
% 158.54/24.99  ----------------------------------------------------------------
% 158.54/24.99    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/24.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/24.99    (2)  op(e1, e1) = e2
% 158.54/24.99    (3)  op(e1, e0) = all_52_14
% 158.54/24.99    (4)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) =
% 158.54/24.99           all_57_13 & $i(all_57_13))
% 158.54/24.99    (5)  op(e1, e0) = e1
% 158.54/24.99    (6)   ~ (e2 = e0)
% 158.54/24.99  
% 158.54/24.99  Begin of proof
% 158.54/24.99  | 
% 158.54/24.99  | BETA: splitting (4) gives:
% 158.54/24.99  | 
% 158.54/24.99  | Case 1:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (7)  all_57_14 = e0 & op(e1, e1) = e0
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (7) implies:
% 158.54/24.99  | |   (8)  op(e1, e1) = e0
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #914.
% 158.54/24.99  | | 
% 158.54/24.99  | Case 2:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (9)   ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13)
% 158.54/24.99  | | 
% 158.54/24.99  | | ALPHA: (9) implies:
% 158.54/24.99  | |   (10)   ~ (all_57_13 = e1)
% 158.54/24.99  | |   (11)  op(e1, e0) = all_57_13
% 158.54/24.99  | | 
% 158.54/24.99  | | REF_CLOSE: (1), (3), (5), (10), (11) are inconsistent by sub-proof #637.
% 158.54/24.99  | | 
% 158.54/24.99  | End of split
% 158.54/24.99  | 
% 158.54/24.99  End of proof
% 158.54/24.99  
% 158.54/24.99  Sub-proof #147 shows that the following formulas are inconsistent:
% 158.54/24.99  ----------------------------------------------------------------
% 158.54/24.99    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.54/24.99         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.54/24.99    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.54/24.99         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/24.99    (3)   ~ (e3 = e2)
% 158.54/24.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/24.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/24.99    (5)  op(e3, e1) = all_52_8
% 158.54/24.99    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.54/24.99         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.54/24.99    (7)  all_56_9 = e1
% 158.54/24.99    (8)  op(e3, e3) = e1
% 158.54/24.99    (9)   ~ (e1 = e0)
% 158.54/24.99    (10)   ~ (e2 = e1)
% 158.54/24.99    (11)   ~ (all_52_8 = e2)
% 158.54/24.99    (12)   ~ (e3 = e1)
% 158.54/24.99    (13)   ~ (e2 = e0)
% 158.54/24.99    (14)   ~ (e3 = e0)
% 158.54/24.99  
% 158.54/24.99  Begin of proof
% 158.54/24.99  | 
% 158.54/24.99  | BETA: splitting (1) gives:
% 158.54/24.99  | 
% 158.54/24.99  | Case 1:
% 158.54/24.99  | | 
% 158.54/24.99  | |   (15)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) =
% 158.54/24.99  | |           e2)
% 158.54/24.99  | | 
% 158.54/24.99  | | BETA: splitting (15) gives:
% 158.54/24.99  | | 
% 158.54/24.99  | | Case 1:
% 158.54/24.99  | | | 
% 158.54/24.99  | | |   (16)  all_56_0 = e2 & op(e3, e3) = e2
% 158.54/24.99  | | | 
% 158.54/24.99  | | | ALPHA: (16) implies:
% 158.54/24.99  | | |   (17)  op(e3, e3) = e2
% 158.54/24.99  | | | 
% 158.54/24.99  | | | REF_CLOSE: (4), (8), (10), (17) are inconsistent by sub-proof #828.
% 158.54/24.99  | | | 
% 158.54/24.99  | | Case 2:
% 158.54/24.99  | | | 
% 158.54/24.99  | | |   (18)  all_56_1 = e2 & op(e3, e2) = e2
% 158.54/24.99  | | | 
% 158.54/24.99  | | | ALPHA: (18) implies:
% 158.54/24.99  | | |   (19)  all_56_1 = e2
% 158.54/24.99  | | |   (20)  op(e3, e2) = e2
% 158.54/24.99  | | | 
% 158.54/24.99  | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (12), (13), (14), (19), (20)
% 158.54/24.99  | | |            are inconsistent by sub-proof #148.
% 158.54/24.99  | | | 
% 158.54/24.99  | | End of split
% 158.54/24.99  | | 
% 158.54/24.99  | Case 2:
% 158.54/24.99  | | 
% 158.54/25.00  | |   (21)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 158.54/25.00  | |           e2)
% 158.54/25.00  | | 
% 158.54/25.00  | | REF_CLOSE: (4), (5), (7), (10), (11), (21) are inconsistent by sub-proof
% 158.54/25.00  | |            #177.
% 158.54/25.00  | | 
% 158.54/25.00  | End of split
% 158.54/25.00  | 
% 158.54/25.00  End of proof
% 158.54/25.00  
% 158.54/25.00  Sub-proof #148 shows that the following formulas are inconsistent:
% 158.54/25.00  ----------------------------------------------------------------
% 158.54/25.00    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.54/25.00         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/25.00    (2)   ~ (e3 = e2)
% 158.54/25.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/25.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/25.00    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.54/25.00         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.54/25.00    (5)  all_56_1 = e2
% 158.54/25.00    (6)  all_56_9 = e1
% 158.54/25.00    (7)  op(e3, e2) = e2
% 158.54/25.00    (8)  op(e3, e3) = e1
% 158.54/25.00    (9)   ~ (e1 = e0)
% 158.54/25.00    (10)   ~ (e3 = e1)
% 158.54/25.00    (11)   ~ (e2 = e0)
% 158.54/25.00    (12)   ~ (e3 = e0)
% 158.54/25.00  
% 158.54/25.00  Begin of proof
% 158.54/25.00  | 
% 158.54/25.00  | BETA: splitting (4) gives:
% 158.54/25.00  | 
% 158.54/25.00  | Case 1:
% 158.54/25.00  | | 
% 158.54/25.00  | |   (13)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 158.54/25.00  | |           e3)
% 158.54/25.00  | | 
% 158.54/25.00  | | BETA: splitting (13) gives:
% 158.54/25.00  | | 
% 158.54/25.00  | | Case 1:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (14)  all_56_0 = e3 & op(e3, e3) = e3
% 158.54/25.00  | | | 
% 158.54/25.00  | | | ALPHA: (14) implies:
% 158.54/25.00  | | |   (15)  op(e3, e3) = e3
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REF_CLOSE: (3), (8), (10), (15) are inconsistent by sub-proof #995.
% 158.54/25.00  | | | 
% 158.54/25.00  | | Case 2:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (16)  all_56_1 = e3 & op(e3, e2) = e3
% 158.54/25.00  | | | 
% 158.54/25.00  | | | ALPHA: (16) implies:
% 158.54/25.00  | | |   (17)  op(e3, e2) = e3
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REF_CLOSE: (2), (3), (7), (17) are inconsistent by sub-proof #433.
% 158.54/25.00  | | | 
% 158.54/25.00  | | End of split
% 158.54/25.00  | | 
% 158.54/25.00  | Case 2:
% 158.54/25.00  | | 
% 158.54/25.00  | |   (18)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 158.54/25.00  | |           e3)
% 158.54/25.00  | | 
% 158.54/25.00  | | BETA: splitting (18) gives:
% 158.54/25.00  | | 
% 158.54/25.00  | | Case 1:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (19)  all_56_4 = e3 & op(e3, e1) = e3
% 158.54/25.00  | | | 
% 158.54/25.00  | | | ALPHA: (19) implies:
% 158.54/25.00  | | |   (20)  all_56_4 = e3
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (20) are inconsistent
% 158.54/25.00  | | |            by sub-proof #149.
% 158.54/25.00  | | | 
% 158.54/25.00  | | Case 2:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (21)  all_56_9 = e3 & op(e3, e0) = e3
% 158.54/25.00  | | | 
% 158.54/25.00  | | | ALPHA: (21) implies:
% 158.54/25.00  | | |   (22)  all_56_9 = e3
% 158.54/25.00  | | | 
% 158.54/25.00  | | | COMBINE_EQS: (6), (22) imply:
% 158.54/25.00  | | |   (23)  e3 = e1
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REDUCE: (10), (23) imply:
% 158.54/25.00  | | |   (24)  $false
% 158.54/25.00  | | | 
% 158.54/25.00  | | | CLOSE: (24) is inconsistent.
% 158.54/25.00  | | | 
% 158.54/25.00  | | End of split
% 158.54/25.00  | | 
% 158.54/25.00  | End of split
% 158.54/25.00  | 
% 158.54/25.00  End of proof
% 158.54/25.00  
% 158.54/25.00  Sub-proof #149 shows that the following formulas are inconsistent:
% 158.54/25.00  ----------------------------------------------------------------
% 158.54/25.00    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.54/25.00         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/25.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/25.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/25.00    (3)  all_56_4 = e3
% 158.54/25.00    (4)  all_56_1 = e2
% 158.54/25.00    (5)  all_56_9 = e1
% 158.54/25.00    (6)  op(e3, e3) = e1
% 158.54/25.00    (7)   ~ (e1 = e0)
% 158.54/25.00    (8)   ~ (e2 = e0)
% 158.54/25.00    (9)   ~ (e3 = e0)
% 158.54/25.00  
% 158.54/25.00  Begin of proof
% 158.54/25.00  | 
% 158.54/25.00  | BETA: splitting (1) gives:
% 158.54/25.00  | 
% 158.54/25.00  | Case 1:
% 158.54/25.00  | | 
% 158.54/25.00  | |   (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 158.54/25.00  | |           e0)
% 158.54/25.00  | | 
% 158.54/25.00  | | BETA: splitting (10) gives:
% 158.54/25.00  | | 
% 158.54/25.00  | | Case 1:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (11)  all_56_0 = e0 & op(e3, e3) = e0
% 158.54/25.00  | | | 
% 158.54/25.00  | | | ALPHA: (11) implies:
% 158.54/25.00  | | |   (12)  op(e3, e3) = e0
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REF_CLOSE: (2), (6), (7), (12) are inconsistent by sub-proof #834.
% 158.54/25.00  | | | 
% 158.54/25.00  | | Case 2:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (13)  all_56_1 = e0 & op(e3, e2) = e0
% 158.54/25.00  | | | 
% 158.54/25.00  | | | ALPHA: (13) implies:
% 158.54/25.00  | | |   (14)  all_56_1 = e0
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REF_CLOSE: (4), (8), (14) are inconsistent by sub-proof #943.
% 158.54/25.00  | | | 
% 158.54/25.00  | | End of split
% 158.54/25.00  | | 
% 158.54/25.00  | Case 2:
% 158.54/25.00  | | 
% 158.54/25.00  | |   (15)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 158.54/25.00  | |           e0)
% 158.54/25.00  | | 
% 158.54/25.00  | | BETA: splitting (15) gives:
% 158.54/25.00  | | 
% 158.54/25.00  | | Case 1:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (16)  all_56_4 = e0 & op(e3, e1) = e0
% 158.54/25.00  | | | 
% 158.54/25.00  | | | ALPHA: (16) implies:
% 158.54/25.00  | | |   (17)  all_56_4 = e0
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REF_CLOSE: (3), (9), (17) are inconsistent by sub-proof #150.
% 158.54/25.00  | | | 
% 158.54/25.00  | | Case 2:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (18)  all_56_9 = e0 & op(e3, e0) = e0
% 158.54/25.00  | | | 
% 158.54/25.00  | | | ALPHA: (18) implies:
% 158.54/25.00  | | |   (19)  all_56_9 = e0
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REF_CLOSE: (5), (7), (19) are inconsistent by sub-proof #756.
% 158.54/25.00  | | | 
% 158.54/25.00  | | End of split
% 158.54/25.00  | | 
% 158.54/25.00  | End of split
% 158.54/25.00  | 
% 158.54/25.00  End of proof
% 158.54/25.00  
% 158.54/25.00  Sub-proof #150 shows that the following formulas are inconsistent:
% 158.54/25.00  ----------------------------------------------------------------
% 158.54/25.00    (1)  all_56_4 = e3
% 158.54/25.00    (2)  all_56_4 = e0
% 158.54/25.00    (3)   ~ (e3 = e0)
% 158.54/25.00  
% 158.54/25.00  Begin of proof
% 158.54/25.00  | 
% 158.54/25.00  | COMBINE_EQS: (1), (2) imply:
% 158.54/25.00  |   (4)  e3 = e0
% 158.54/25.00  | 
% 158.54/25.00  | SIMP: (4) implies:
% 158.54/25.00  |   (5)  e3 = e0
% 158.54/25.00  | 
% 158.54/25.00  | REDUCE: (3), (5) imply:
% 158.54/25.00  |   (6)  $false
% 158.54/25.00  | 
% 158.54/25.00  | CLOSE: (6) is inconsistent.
% 158.54/25.00  | 
% 158.54/25.00  End of proof
% 158.54/25.00  
% 158.54/25.00  Sub-proof #151 shows that the following formulas are inconsistent:
% 158.54/25.00  ----------------------------------------------------------------
% 158.54/25.00    (1)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.54/25.00    (2)   ~ (all_52_7 = all_14_2)
% 158.54/25.00    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.54/25.00         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.54/25.00    (4)   ~ (all_52_1 = all_52_3)
% 158.54/25.00    (5)  all_54_5 = all_4_2
% 158.54/25.00    (6)  all_56_0 = e2
% 158.54/25.00    (7)  all_54_9 = all_52_6
% 158.54/25.00    (8)   ~ (all_52_3 = all_14_2)
% 158.54/25.00    (9)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.54/25.00         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.54/25.00    (10)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.54/25.00          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.54/25.00    (11)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.54/25.00          (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.54/25.00    (12)  all_56_0 = e2 & op(e3, e3) = e2
% 158.54/25.00    (13)  all_54_12 = all_52_3
% 158.54/25.00    (14)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.54/25.00    (15)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 158.54/25.00              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.54/25.00            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.54/25.00                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 158.54/25.00              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.54/25.00          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 158.54/25.00              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.54/25.00            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.54/25.00                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 158.54/25.00              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.54/25.00          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 158.54/25.00              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.54/25.00            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.54/25.00                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 158.54/25.00              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.54/25.00          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 158.54/25.00              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.54/25.00            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 158.54/25.00                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 158.54/25.00                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.54/25.00                $i(all_57_13))))
% 158.54/25.00    (16)   ~ (all_52_4 = all_52_12)
% 158.54/25.00    (17)   ~ (all_52_4 = all_52_6)
% 158.54/25.00    (18)   ~ (all_52_6 = all_52_7)
% 158.54/25.00    (19)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.54/25.00          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/25.00    (20)  op(e0, e1) = all_52_11
% 158.54/25.00    (21)   ~ (all_52_2 = all_52_14)
% 158.54/25.00    (22)   ~ (e3 = e2)
% 158.54/25.00    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/25.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/25.00    (24)  op(e0, e3) = all_52_3
% 158.54/25.00    (25)  op(e3, e1) = all_52_8
% 158.54/25.00    (26)  all_28_2 = all_14_2
% 158.54/25.00    (27)   ~ (all_52_9 = all_4_2)
% 158.54/25.00    (28)  op(e1, e1) = e2
% 158.54/25.00    (29)   ~ (all_4_2 = e3)
% 158.54/25.00    (30)   ~ (all_52_4 = e1)
% 158.54/25.00    (31)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.54/25.00    (32)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/25.00              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 158.54/25.00                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.54/25.00                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.54/25.00    (33)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.54/25.00          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.54/25.00    (34)   ~ (all_52_11 = all_14_2)
% 158.54/25.00    (35)   ~ (all_52_12 = all_14_2)
% 158.54/25.00    (36)  op(e1, e3) = all_52_2
% 158.54/25.00    (37)  all_54_15 = all_14_2
% 158.54/25.00    (38)  op(e0, e2) = all_52_7
% 158.54/25.00    (39)   ~ (all_26_0 = e0)
% 158.54/25.00    (40)   ~ (all_52_13 = all_4_2)
% 158.54/25.00    (41)   ~ (all_52_14 = all_14_2)
% 158.54/25.00    (42)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 158.54/25.00    (43)  all_54_1 = all_52_4
% 158.54/25.00    (44)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.54/25.00    (45)   ~ (all_52_6 = all_52_14)
% 158.54/25.00    (46)   ~ (all_52_2 = e2)
% 158.54/25.00    (47)   ~ (all_52_2 = all_52_3)
% 158.54/25.00    (48)   ~ (all_52_2 = e1)
% 158.54/25.00    (49)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 158.54/25.00    (50)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.54/25.00    (51)   ~ (all_28_2 = e2) | ( ~ (all_28_0 = e1) & op(e2, e0) = all_28_0 &
% 158.54/25.00            $i(all_28_0)) | ( ~ (all_28_1 = e3) & op(e2, e2) = all_28_1 &
% 158.54/25.00            $i(all_28_1))
% 158.54/25.00    (52)   ~ (all_52_8 = e1)
% 158.54/25.00    (53)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.54/25.00          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.54/25.00    (54)   ~ (all_52_6 = all_4_2)
% 158.54/25.00    (55)   ~ (all_52_1 = e1)
% 158.54/25.00    (56)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.54/25.00          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.54/25.00    (57)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.54/25.00          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.54/25.00    (58)   ~ (all_52_3 = e1)
% 158.54/25.00    (59)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.54/25.00          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.54/25.00    (60)  op(e2, e2) = all_4_2
% 158.54/25.00    (61)   ~ (all_52_14 = e2)
% 158.54/25.00    (62)   ~ (all_52_4 = all_4_2)
% 158.54/25.00    (63)   ~ (all_52_2 = all_52_6)
% 158.54/25.00    (64)   ~ (all_52_1 = all_52_2)
% 158.54/25.00    (65)  all_56_8 = e2
% 158.54/25.00    (66)  op(e0, e0) = all_14_2
% 158.54/25.00    (67)  op(e3, e3) = e1
% 158.54/25.00    (68)  op(e2, e3) = all_52_1
% 158.54/25.00    (69)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.54/25.00          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.54/25.00    (70)   ~ (all_14_2 = e1)
% 158.54/25.00    (71)   ~ (all_4_2 = e1)
% 158.54/25.00    (72)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.54/25.00          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.54/25.00    (73)  op(e3, e2) = all_52_4
% 158.54/25.00    (74)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.54/25.00          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.54/25.00    (75)   ~ (e1 = e0)
% 158.54/25.00    (76)  op(e2, e1) = all_52_9
% 158.54/25.00    (77)  all_54_4 = all_52_1
% 158.54/25.00    (78)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.54/25.00          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.54/25.00    (79)  op(e2, e0) = all_52_13
% 158.54/25.00    (80)  op(e3, e3) = e2
% 158.54/25.00    (81)   ~ (e2 = e1)
% 158.54/25.00    (82)  op(e3, e0) = all_52_12
% 158.54/25.00    (83)   ~ (all_52_4 = all_52_8)
% 158.54/25.00    (84)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.54/25.00          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.54/25.00    (85)   ~ (all_52_8 = e2)
% 158.54/25.00    (86)  op(e1, e3) = all_26_0
% 158.54/25.00    (87)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.54/25.00            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.54/25.00            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.54/25.00            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.00              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.54/25.00          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.54/25.00            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.54/25.00              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.54/25.00            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.00              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.54/25.00          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.54/25.00            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.54/25.00              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.54/25.00            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.00              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.54/25.00          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.54/25.00            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.54/25.00            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.54/25.00              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.54/25.00            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.54/25.00            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.54/25.00            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.54/25.00            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.54/25.00              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.54/25.00            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.54/25.00          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.54/25.00            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.54/25.00              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.54/25.00            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.54/25.00            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.54/25.00          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.54/25.00            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.54/25.00              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.54/25.00            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.54/25.00            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.54/25.00          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.54/25.00            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.54/25.00              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.54/25.00            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.00              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.54/25.00          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.54/25.00            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.54/25.00            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.54/25.00            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.54/25.00            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.54/25.00            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.54/25.00            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.54/25.00            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.54/25.00              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.54/25.00            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.54/25.00            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.54/25.00            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.54/25.00            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.54/25.00              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.54/25.00            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.54/25.00          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.54/25.00            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.54/25.00              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.54/25.00              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.54/25.00            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.54/25.00            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.54/25.00            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.54/25.00            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.54/25.00              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.54/25.00            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.54/25.00          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.54/25.00            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.54/25.00              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.54/25.00            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.00              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.54/25.00          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.54/25.00            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.54/25.00              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.54/25.00              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.54/25.00            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.54/25.00          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.54/25.00            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.54/25.00            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.54/25.00                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.54/25.00                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.54/25.00                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/25.00                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.54/25.00                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/25.00                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.54/25.00                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.54/25.00                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.54/25.00                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.54/25.00                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.54/25.00                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.54/25.00                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.54/25.00                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.54/25.00                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.54/25.00                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/25.00                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.54/25.00                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/25.00                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.54/25.00                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/25.00                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.54/25.00                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.54/25.00                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.54/25.00                op(e0, e1) = e0)))
% 158.54/25.00    (88)  all_54_11 = all_52_14
% 158.54/25.00    (89)   ~ (e3 = e1)
% 158.54/25.00    (90)   ~ (all_52_1 = all_4_2)
% 158.54/25.00    (91)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.54/25.00    (92)   ~ (e2 = e0)
% 158.54/25.00    (93)   ~ (all_14_2 = e3)
% 158.54/25.00    (94)   ~ (e3 = e0)
% 158.54/25.00    (95)  all_54_8 = all_52_2
% 158.54/25.00  
% 158.54/25.00  Begin of proof
% 158.54/25.00  | 
% 158.54/25.00  | BETA: splitting (74) gives:
% 158.54/25.00  | 
% 158.54/25.00  | Case 1:
% 158.54/25.00  | | 
% 158.54/25.00  | |   (96)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 158.54/25.00  | |           e1)
% 158.54/25.00  | | 
% 158.54/25.00  | | BETA: splitting (96) gives:
% 158.54/25.00  | | 
% 158.54/25.00  | | Case 1:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (97)  all_56_0 = e1 & op(e3, e3) = e1
% 158.54/25.00  | | | 
% 158.54/25.00  | | | ALPHA: (97) implies:
% 158.54/25.00  | | |   (98)  all_56_0 = e1
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 158.54/25.00  | | |            (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 158.54/25.00  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 158.54/25.00  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 158.54/25.00  | | |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56),
% 158.54/25.00  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 158.54/25.00  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 158.54/25.00  | | |            (77), (78), (79), (81), (82), (83), (84), (85), (86), (87),
% 158.54/25.00  | | |            (88), (90), (91), (92), (93), (95), (98) are inconsistent by
% 158.54/25.00  | | |            sub-proof #155.
% 158.54/25.00  | | | 
% 158.54/25.00  | | Case 2:
% 158.54/25.00  | | | 
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 158.54/25.00  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 158.54/25.00  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 158.54/25.00  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 158.54/25.00  | | |            (45), (46), (47), (48), (49), (50), (51), (53), (54), (55),
% 158.54/25.00  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 158.54/25.00  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 158.54/25.00  | | |            (76), (77), (78), (79), (81), (82), (83), (84), (85), (86),
% 158.54/25.00  | | |            (87), (88), (90), (91), (92), (93), (95) are inconsistent by
% 158.54/25.00  | | |            sub-proof #154.
% 158.54/25.00  | | | 
% 158.54/25.00  | | End of split
% 158.54/25.00  | | 
% 158.54/25.00  | Case 2:
% 158.54/25.00  | | 
% 158.54/25.00  | |   (99)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 158.54/25.00  | |           e1)
% 158.54/25.00  | | 
% 158.54/25.00  | | BETA: splitting (99) gives:
% 158.54/25.00  | | 
% 158.54/25.00  | | Case 1:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (100)  all_56_4 = e1 & op(e3, e1) = e1
% 158.54/25.00  | | | 
% 158.54/25.00  | | | REF_CLOSE: (23), (25), (52), (100) are inconsistent by sub-proof #331.
% 158.54/25.00  | | | 
% 158.54/25.00  | | Case 2:
% 158.54/25.00  | | | 
% 158.54/25.00  | | |   (101)  all_56_9 = e1 & op(e3, e0) = e1
% 158.54/25.00  | | | 
% 158.54/25.00  | | | ALPHA: (101) implies:
% 158.54/25.00  | | |   (102)  all_56_9 = e1
% 158.54/25.00  | | | 
% 158.54/25.00  | | | BETA: splitting (11) gives:
% 158.54/25.00  | | | 
% 158.54/25.00  | | | Case 1:
% 158.54/25.00  | | | | 
% 158.54/25.00  | | | |   (103)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2)
% 158.54/25.00  | | | |            = e2)
% 158.54/25.00  | | | | 
% 158.54/25.00  | | | | BETA: splitting (103) gives:
% 158.54/25.00  | | | | 
% 158.54/25.00  | | | | Case 1:
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 158.54/25.00  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23),
% 158.54/25.00  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 158.54/25.00  | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 158.54/25.00  | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (53), (54),
% 158.54/25.00  | | | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 158.54/25.00  | | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 158.54/25.00  | | | | |            (75), (76), (77), (78), (79), (81), (82), (83), (84), (85),
% 158.54/25.00  | | | | |            (86), (87), (88), (90), (91), (92), (93), (95) are
% 158.54/25.00  | | | | |            inconsistent by sub-proof #154.
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | Case 2:
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | |   (104)  all_56_1 = e2 & op(e3, e2) = e2
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | ALPHA: (104) implies:
% 158.54/25.00  | | | | |   (105)  all_56_1 = e2
% 158.54/25.00  | | | | |   (106)  op(e3, e2) = e2
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | REF_CLOSE: (6), (19), (22), (23), (57), (75), (80), (89), (92), (94),
% 158.54/25.00  | | | | |            (102), (105), (106) are inconsistent by sub-proof #152.
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | End of split
% 158.54/25.00  | | | | 
% 158.54/25.00  | | | Case 2:
% 158.54/25.00  | | | | 
% 158.54/25.00  | | | |   (107)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0)
% 158.54/25.00  | | | |            = e2)
% 158.54/25.00  | | | | 
% 158.54/25.00  | | | | BETA: splitting (107) gives:
% 158.54/25.00  | | | | 
% 158.54/25.00  | | | | Case 1:
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | |   (108)  all_56_4 = e2 & op(e3, e1) = e2
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | ALPHA: (108) implies:
% 158.54/25.00  | | | | |   (109)  op(e3, e1) = e2
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | REF_CLOSE: (23), (25), (85), (109) are inconsistent by sub-proof #670.
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | Case 2:
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | |   (110)  all_56_9 = e2 & op(e3, e0) = e2
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | ALPHA: (110) implies:
% 158.54/25.00  | | | | |   (111)  all_56_9 = e2
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | COMBINE_EQS: (102), (111) imply:
% 158.54/25.00  | | | | |   (112)  e2 = e1
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | SIMP: (112) implies:
% 158.54/25.00  | | | | |   (113)  e2 = e1
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | COMBINE_EQS: (6), (113) imply:
% 158.54/25.00  | | | | |   (114)  all_56_0 = e1
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13),
% 158.54/25.00  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 158.54/25.00  | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 158.54/25.00  | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 158.54/25.00  | | | | |            (45), (46), (47), (48), (49), (50), (51), (53), (54), (55),
% 158.54/25.00  | | | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 158.54/25.00  | | | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 158.54/25.00  | | | | |            (76), (77), (78), (79), (81), (82), (83), (84), (85), (86),
% 158.54/25.00  | | | | |            (87), (88), (90), (91), (92), (93), (95), (114) are
% 158.54/25.00  | | | | |            inconsistent by sub-proof #155.
% 158.54/25.00  | | | | | 
% 158.54/25.00  | | | | End of split
% 158.54/25.00  | | | | 
% 158.54/25.00  | | | End of split
% 158.54/25.00  | | | 
% 158.54/25.00  | | End of split
% 158.54/25.00  | | 
% 158.54/25.00  | End of split
% 158.54/25.00  | 
% 158.54/25.00  End of proof
% 158.54/25.00  
% 158.54/25.00  Sub-proof #152 shows that the following formulas are inconsistent:
% 158.54/25.00  ----------------------------------------------------------------
% 158.54/25.00    (1)  all_56_0 = e2
% 158.54/25.00    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.54/25.00         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/25.00    (3)   ~ (e3 = e2)
% 158.54/25.00    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/25.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/25.01    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.54/25.01         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.54/25.01    (6)  all_56_1 = e2
% 158.54/25.01    (7)  all_56_9 = e1
% 158.54/25.01    (8)  op(e3, e2) = e2
% 158.54/25.01    (9)   ~ (e1 = e0)
% 158.54/25.01    (10)  op(e3, e3) = e2
% 158.54/25.01    (11)   ~ (e3 = e1)
% 158.54/25.01    (12)   ~ (e2 = e0)
% 158.54/25.01    (13)   ~ (e3 = e0)
% 158.54/25.01  
% 158.54/25.01  Begin of proof
% 158.54/25.01  | 
% 158.54/25.01  | BETA: splitting (5) gives:
% 158.54/25.01  | 
% 158.54/25.01  | Case 1:
% 158.54/25.01  | | 
% 158.54/25.01  | |   (14)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 158.54/25.01  | |           e3)
% 158.54/25.01  | | 
% 158.54/25.01  | | BETA: splitting (14) gives:
% 158.54/25.01  | | 
% 158.54/25.01  | | Case 1:
% 158.54/25.01  | | | 
% 158.54/25.01  | | |   (15)  all_56_0 = e3 & op(e3, e3) = e3
% 158.54/25.01  | | | 
% 158.54/25.01  | | | ALPHA: (15) implies:
% 158.54/25.01  | | |   (16)  op(e3, e3) = e3
% 158.54/25.01  | | | 
% 158.54/25.01  | | | REF_CLOSE: (3), (4), (10), (16) are inconsistent by sub-proof #958.
% 158.54/25.01  | | | 
% 158.54/25.01  | | Case 2:
% 158.54/25.01  | | | 
% 158.54/25.01  | | |   (17)  all_56_1 = e3 & op(e3, e2) = e3
% 158.54/25.01  | | | 
% 158.54/25.01  | | | ALPHA: (17) implies:
% 158.54/25.01  | | |   (18)  op(e3, e2) = e3
% 158.54/25.01  | | | 
% 158.54/25.01  | | | REF_CLOSE: (3), (4), (8), (18) are inconsistent by sub-proof #433.
% 158.54/25.01  | | | 
% 158.54/25.01  | | End of split
% 158.54/25.01  | | 
% 158.54/25.01  | Case 2:
% 158.54/25.01  | | 
% 158.54/25.01  | |   (19)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 158.54/25.01  | |           e3)
% 158.54/25.01  | | 
% 158.54/25.01  | | BETA: splitting (19) gives:
% 158.54/25.01  | | 
% 158.54/25.01  | | Case 1:
% 158.54/25.01  | | | 
% 158.54/25.01  | | |   (20)  all_56_4 = e3 & op(e3, e1) = e3
% 158.54/25.01  | | | 
% 158.54/25.01  | | | ALPHA: (20) implies:
% 158.54/25.01  | | |   (21)  all_56_4 = e3
% 158.54/25.01  | | | 
% 158.54/25.01  | | | REF_CLOSE: (1), (2), (6), (7), (9), (12), (13), (21) are inconsistent by
% 158.54/25.01  | | |            sub-proof #153.
% 158.54/25.01  | | | 
% 158.54/25.01  | | Case 2:
% 158.54/25.01  | | | 
% 158.54/25.01  | | |   (22)  all_56_9 = e3 & op(e3, e0) = e3
% 158.54/25.01  | | | 
% 158.54/25.01  | | | REF_CLOSE: (7), (11), (22) are inconsistent by sub-proof #895.
% 158.54/25.01  | | | 
% 158.54/25.01  | | End of split
% 158.54/25.01  | | 
% 158.54/25.01  | End of split
% 158.54/25.01  | 
% 158.54/25.01  End of proof
% 158.54/25.01  
% 158.54/25.01  Sub-proof #153 shows that the following formulas are inconsistent:
% 158.54/25.01  ----------------------------------------------------------------
% 158.54/25.01    (1)  all_56_0 = e2
% 158.54/25.01    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.54/25.01         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/25.01    (3)  all_56_4 = e3
% 158.54/25.01    (4)  all_56_1 = e2
% 158.54/25.01    (5)  all_56_9 = e1
% 158.54/25.01    (6)   ~ (e1 = e0)
% 158.54/25.01    (7)   ~ (e2 = e0)
% 158.54/25.01    (8)   ~ (e3 = e0)
% 158.54/25.01  
% 158.54/25.01  Begin of proof
% 158.54/25.01  | 
% 158.54/25.01  | BETA: splitting (2) gives:
% 158.54/25.01  | 
% 158.54/25.01  | Case 1:
% 158.54/25.01  | | 
% 158.54/25.01  | |   (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 158.54/25.01  | | 
% 158.54/25.01  | | BETA: splitting (9) gives:
% 158.54/25.01  | | 
% 158.54/25.01  | | Case 1:
% 158.54/25.01  | | | 
% 158.54/25.01  | | |   (10)  all_56_0 = e0 & op(e3, e3) = e0
% 158.54/25.01  | | | 
% 158.54/25.01  | | | ALPHA: (10) implies:
% 158.54/25.01  | | |   (11)  all_56_0 = e0
% 158.54/25.01  | | | 
% 158.54/25.01  | | | COMBINE_EQS: (1), (11) imply:
% 158.54/25.01  | | |   (12)  e2 = e0
% 158.54/25.01  | | | 
% 158.54/25.01  | | | REDUCE: (7), (12) imply:
% 158.54/25.01  | | |   (13)  $false
% 158.54/25.01  | | | 
% 158.54/25.01  | | | CLOSE: (13) is inconsistent.
% 158.54/25.01  | | | 
% 158.54/25.01  | | Case 2:
% 158.54/25.01  | | | 
% 158.54/25.01  | | |   (14)  all_56_1 = e0 & op(e3, e2) = e0
% 158.54/25.01  | | | 
% 158.54/25.01  | | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #910.
% 158.54/25.01  | | | 
% 158.54/25.01  | | End of split
% 158.54/25.01  | | 
% 158.54/25.01  | Case 2:
% 158.54/25.01  | | 
% 158.54/25.01  | |   (15)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 158.54/25.01  | |           e0)
% 158.54/25.01  | | 
% 158.54/25.01  | | BETA: splitting (15) gives:
% 158.54/25.01  | | 
% 158.54/25.01  | | Case 1:
% 158.54/25.01  | | | 
% 158.54/25.01  | | |   (16)  all_56_4 = e0 & op(e3, e1) = e0
% 158.54/25.01  | | | 
% 158.54/25.01  | | | REF_CLOSE: (3), (8), (16) are inconsistent by sub-proof #248.
% 158.54/25.01  | | | 
% 158.54/25.01  | | Case 2:
% 158.54/25.01  | | | 
% 158.54/25.01  | | |   (17)  all_56_9 = e0 & op(e3, e0) = e0
% 158.54/25.01  | | | 
% 158.54/25.01  | | | REF_CLOSE: (5), (6), (17) are inconsistent by sub-proof #952.
% 158.54/25.01  | | | 
% 158.54/25.01  | | End of split
% 158.54/25.01  | | 
% 158.54/25.01  | End of split
% 158.54/25.01  | 
% 158.54/25.01  End of proof
% 158.54/25.01  
% 158.54/25.01  Sub-proof #154 shows that the following formulas are inconsistent:
% 158.54/25.01  ----------------------------------------------------------------
% 158.54/25.01    (1)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.54/25.01    (2)   ~ (all_52_7 = all_14_2)
% 158.54/25.01    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.54/25.01         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.54/25.01    (4)   ~ (all_52_1 = all_52_3)
% 158.54/25.01    (5)  all_54_5 = all_4_2
% 158.54/25.01    (6)  all_54_9 = all_52_6
% 158.54/25.01    (7)   ~ (all_52_3 = all_14_2)
% 158.54/25.01    (8)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.54/25.01         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.54/25.01    (9)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.54/25.01         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.54/25.01    (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.54/25.01          (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.54/25.01    (11)  all_56_0 = e2 & op(e3, e3) = e2
% 158.54/25.01    (12)  all_54_12 = all_52_3
% 158.54/25.01    (13)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.54/25.01    (14)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 158.54/25.01              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.54/25.01            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.54/25.01                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 158.54/25.01              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.54/25.01          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 158.54/25.01              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.54/25.01            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.54/25.01                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 158.54/25.01              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.54/25.01          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 158.54/25.01              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.54/25.01            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.54/25.01                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 158.54/25.01              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.54/25.01          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 158.54/25.01              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.54/25.01            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 158.54/25.01                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 158.54/25.01                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.54/25.01                $i(all_57_13))))
% 158.54/25.01    (15)   ~ (all_52_4 = all_52_12)
% 158.54/25.01    (16)   ~ (all_52_4 = all_52_6)
% 158.54/25.01    (17)   ~ (all_52_6 = all_52_7)
% 158.54/25.01    (18)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.54/25.01          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/25.01    (19)  op(e0, e1) = all_52_11
% 158.54/25.01    (20)   ~ (all_52_2 = all_52_14)
% 158.54/25.01    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/25.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/25.01    (22)  op(e0, e3) = all_52_3
% 158.54/25.01    (23)  op(e3, e1) = all_52_8
% 158.54/25.01    (24)  all_28_2 = all_14_2
% 158.54/25.01    (25)   ~ (all_52_9 = all_4_2)
% 158.54/25.01    (26)  op(e1, e1) = e2
% 158.54/25.01    (27)   ~ (all_4_2 = e3)
% 158.54/25.01    (28)   ~ (all_52_4 = e1)
% 158.54/25.01    (29)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.54/25.01    (30)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/25.01              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 158.54/25.01                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.54/25.01                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.54/25.01    (31)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.54/25.01          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.54/25.01    (32)   ~ (all_52_11 = all_14_2)
% 158.54/25.01    (33)   ~ (all_52_12 = all_14_2)
% 158.54/25.01    (34)  op(e1, e3) = all_52_2
% 158.54/25.01    (35)  all_54_15 = all_14_2
% 158.54/25.01    (36)  op(e0, e2) = all_52_7
% 158.54/25.01    (37)   ~ (all_26_0 = e0)
% 158.54/25.01    (38)   ~ (all_52_13 = all_4_2)
% 158.54/25.01    (39)   ~ (all_52_14 = all_14_2)
% 158.54/25.01    (40)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 158.54/25.01    (41)  all_54_1 = all_52_4
% 158.54/25.01    (42)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.54/25.01    (43)   ~ (all_52_6 = all_52_14)
% 158.54/25.01    (44)   ~ (all_52_2 = e2)
% 158.54/25.01    (45)   ~ (all_52_2 = all_52_3)
% 158.54/25.01    (46)   ~ (all_52_2 = e1)
% 158.54/25.01    (47)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 158.54/25.01    (48)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.54/25.01    (49)   ~ (all_28_2 = e2) | ( ~ (all_28_0 = e1) & op(e2, e0) = all_28_0 &
% 158.54/25.01            $i(all_28_0)) | ( ~ (all_28_1 = e3) & op(e2, e2) = all_28_1 &
% 158.54/25.01            $i(all_28_1))
% 158.54/25.01    (50)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.54/25.01          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.54/25.01    (51)   ~ (all_52_6 = all_4_2)
% 158.54/25.01    (52)   ~ (all_52_1 = e1)
% 158.54/25.01    (53)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.54/25.01          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.54/25.01    (54)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.54/25.01          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.54/25.01    (55)   ~ (all_52_3 = e1)
% 158.54/25.01    (56)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.54/25.01          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.54/25.01    (57)  op(e2, e2) = all_4_2
% 158.54/25.01    (58)   ~ (all_52_14 = e2)
% 158.54/25.01    (59)   ~ (all_52_4 = all_4_2)
% 158.54/25.01    (60)   ~ (all_52_2 = all_52_6)
% 158.54/25.01    (61)   ~ (all_52_1 = all_52_2)
% 158.54/25.01    (62)  all_56_8 = e2
% 158.54/25.01    (63)  op(e0, e0) = all_14_2
% 158.54/25.01    (64)  op(e3, e3) = e1
% 158.54/25.01    (65)  op(e2, e3) = all_52_1
% 158.54/25.01    (66)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.54/25.01          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.54/25.01    (67)   ~ (all_14_2 = e1)
% 158.54/25.01    (68)   ~ (all_4_2 = e1)
% 158.54/25.01    (69)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.54/25.01          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.54/25.01    (70)  op(e3, e2) = all_52_4
% 158.54/25.01    (71)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.54/25.01          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.54/25.01    (72)   ~ (e1 = e0)
% 158.54/25.01    (73)  op(e2, e1) = all_52_9
% 158.54/25.01    (74)  all_54_4 = all_52_1
% 158.54/25.01    (75)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.54/25.01          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.54/25.01    (76)  op(e2, e0) = all_52_13
% 158.54/25.01    (77)   ~ (e2 = e1)
% 158.54/25.01    (78)  op(e3, e0) = all_52_12
% 158.54/25.01    (79)   ~ (all_52_4 = all_52_8)
% 158.54/25.01    (80)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.54/25.01          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.54/25.01    (81)   ~ (all_52_8 = e2)
% 158.54/25.01    (82)  op(e1, e3) = all_26_0
% 158.54/25.01    (83)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.54/25.01            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.54/25.01            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.54/25.01            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.01              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.54/25.01          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.54/25.01            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.54/25.01              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.54/25.01            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.01              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.54/25.01          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.54/25.01            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.54/25.01              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.54/25.01            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.01              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.54/25.01          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.54/25.01            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.54/25.01            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.54/25.01              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.54/25.01            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.54/25.01            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.54/25.01            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.54/25.01            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.54/25.01              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.54/25.01            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.54/25.01          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.54/25.01            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.54/25.01              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.54/25.01            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.54/25.01            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.54/25.01          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.54/25.01            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.54/25.01              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.54/25.01            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.54/25.01            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.54/25.01          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.54/25.01            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.54/25.01              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.54/25.01            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.01              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.54/25.01          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.54/25.01            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.54/25.01            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.54/25.01            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.54/25.01            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.54/25.01            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.54/25.01            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.54/25.01            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.54/25.01              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.54/25.01            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.54/25.01            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.54/25.01            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.54/25.01            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.54/25.01              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.54/25.01            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.54/25.01          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.54/25.01            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.54/25.01              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.54/25.01              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.54/25.01            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.54/25.01            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.54/25.01            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.54/25.01            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.54/25.01              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.54/25.01            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.54/25.01          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.54/25.01            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.54/25.01              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.54/25.01            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.01              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.54/25.01          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.54/25.01            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.54/25.01              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.54/25.01              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.54/25.01            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.54/25.01          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.54/25.01            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.54/25.01            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.54/25.01                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.54/25.01                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.54/25.01                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/25.01                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.54/25.01                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/25.01                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.54/25.01                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.54/25.01                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.54/25.01                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.54/25.01                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.54/25.01                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.54/25.01                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.54/25.01                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.54/25.01                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.54/25.01                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/25.01                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.54/25.01                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/25.01                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.54/25.01                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/25.01                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.54/25.01                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.54/25.01                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.54/25.01                op(e0, e1) = e0)))
% 158.54/25.01    (84)  all_54_11 = all_52_14
% 158.54/25.01    (85)   ~ (all_52_1 = all_4_2)
% 158.54/25.01    (86)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.54/25.01    (87)   ~ (e2 = e0)
% 158.54/25.01    (88)   ~ (all_14_2 = e3)
% 158.54/25.01    (89)  all_54_8 = all_52_2
% 158.54/25.01  
% 158.54/25.01  Begin of proof
% 158.54/25.01  | 
% 158.54/25.01  | ALPHA: (11) implies:
% 158.54/25.01  |   (90)  all_56_0 = e2
% 158.54/25.01  |   (91)  op(e3, e3) = e2
% 158.54/25.01  | 
% 158.54/25.01  | GROUND_INST: instantiating (21) with e1, e2, e3, e3, simplifying with (64),
% 158.54/25.01  |              (91) gives:
% 158.54/25.01  |   (92)  e2 = e1
% 158.54/25.01  | 
% 158.54/25.01  | COMBINE_EQS: (90), (92) imply:
% 158.54/25.01  |   (93)  all_56_0 = e1
% 158.54/25.01  | 
% 158.54/25.01  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 158.54/25.01  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 158.54/25.01  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 158.54/25.01  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 158.54/25.01  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 158.54/25.01  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 158.54/25.01  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 158.54/25.01  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (93)
% 158.54/25.01  |            are inconsistent by sub-proof #155.
% 158.54/25.01  | 
% 158.54/25.01  End of proof
% 158.54/25.01  
% 158.54/25.01  Sub-proof #155 shows that the following formulas are inconsistent:
% 158.54/25.01  ----------------------------------------------------------------
% 158.54/25.01    (1)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.54/25.01    (2)   ~ (all_52_7 = all_14_2)
% 158.54/25.01    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.54/25.01         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.54/25.01    (4)   ~ (all_52_1 = all_52_3)
% 158.54/25.01    (5)  all_54_5 = all_4_2
% 158.54/25.01    (6)  all_54_9 = all_52_6
% 158.54/25.01    (7)   ~ (all_52_3 = all_14_2)
% 158.54/25.01    (8)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.54/25.01         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.54/25.01    (9)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.54/25.01         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.54/25.01    (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.54/25.01          (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.54/25.01    (11)  all_54_12 = all_52_3
% 158.54/25.01    (12)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.54/25.01    (13)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 158.54/25.01              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.54/25.01            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.54/25.01                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 158.54/25.01              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.54/25.01          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 158.54/25.01              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.54/25.01            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.54/25.01                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 158.54/25.01              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.54/25.01          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 158.54/25.01              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.54/25.01            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.54/25.01                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 158.54/25.01              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.54/25.01          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 158.54/25.01              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.54/25.01            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 158.54/25.01                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 158.54/25.01                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.54/25.01                $i(all_57_13))))
% 158.54/25.01    (14)   ~ (all_52_4 = all_52_12)
% 158.54/25.01    (15)   ~ (all_52_4 = all_52_6)
% 158.54/25.01    (16)   ~ (all_52_6 = all_52_7)
% 158.54/25.01    (17)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.54/25.01          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/25.01    (18)  op(e0, e1) = all_52_11
% 158.54/25.01    (19)   ~ (all_52_2 = all_52_14)
% 158.54/25.01    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.54/25.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.54/25.01    (21)  op(e0, e3) = all_52_3
% 158.54/25.01    (22)  op(e3, e1) = all_52_8
% 158.54/25.01    (23)  all_28_2 = all_14_2
% 158.54/25.01    (24)   ~ (all_52_9 = all_4_2)
% 158.54/25.01    (25)  op(e1, e1) = e2
% 158.54/25.01    (26)   ~ (all_4_2 = e3)
% 158.54/25.01    (27)   ~ (all_52_4 = e1)
% 158.54/25.01    (28)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.54/25.01    (29)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.54/25.01              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 158.54/25.01                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.54/25.01                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.54/25.01    (30)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.54/25.01          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.54/25.01    (31)   ~ (all_52_11 = all_14_2)
% 158.54/25.01    (32)   ~ (all_52_12 = all_14_2)
% 158.54/25.01    (33)  op(e1, e3) = all_52_2
% 158.54/25.01    (34)  all_54_15 = all_14_2
% 158.54/25.01    (35)  op(e0, e2) = all_52_7
% 158.54/25.01    (36)   ~ (all_26_0 = e0)
% 158.54/25.01    (37)   ~ (all_52_13 = all_4_2)
% 158.54/25.01    (38)   ~ (all_52_14 = all_14_2)
% 158.54/25.01    (39)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 158.54/25.01    (40)  all_54_1 = all_52_4
% 158.54/25.01    (41)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.54/25.01    (42)   ~ (all_52_6 = all_52_14)
% 158.54/25.01    (43)   ~ (all_52_2 = e2)
% 158.54/25.01    (44)   ~ (all_52_2 = all_52_3)
% 158.54/25.01    (45)   ~ (all_52_2 = e1)
% 158.54/25.01    (46)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 158.54/25.01    (47)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.54/25.01    (48)   ~ (all_28_2 = e2) | ( ~ (all_28_0 = e1) & op(e2, e0) = all_28_0 &
% 158.54/25.01            $i(all_28_0)) | ( ~ (all_28_1 = e3) & op(e2, e2) = all_28_1 &
% 158.54/25.01            $i(all_28_1))
% 158.54/25.01    (49)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.54/25.01          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.54/25.01    (50)   ~ (all_52_6 = all_4_2)
% 158.54/25.01    (51)   ~ (all_52_1 = e1)
% 158.54/25.02    (52)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.54/25.02          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.54/25.02    (53)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.54/25.02          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.54/25.02    (54)   ~ (all_52_3 = e1)
% 158.54/25.02    (55)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.54/25.02          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.54/25.02    (56)  op(e2, e2) = all_4_2
% 158.54/25.02    (57)   ~ (all_52_14 = e2)
% 158.54/25.02    (58)   ~ (all_52_4 = all_4_2)
% 158.54/25.02    (59)   ~ (all_52_2 = all_52_6)
% 158.54/25.02    (60)   ~ (all_52_1 = all_52_2)
% 158.54/25.02    (61)  all_56_8 = e2
% 158.54/25.02    (62)  op(e0, e0) = all_14_2
% 158.54/25.02    (63)  op(e3, e3) = e1
% 158.54/25.02    (64)  op(e2, e3) = all_52_1
% 158.54/25.02    (65)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.54/25.02          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.54/25.02    (66)   ~ (all_14_2 = e1)
% 158.54/25.02    (67)   ~ (all_4_2 = e1)
% 158.54/25.02    (68)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.54/25.02          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.54/25.02    (69)  op(e3, e2) = all_52_4
% 158.54/25.02    (70)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.54/25.02          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.54/25.02    (71)  all_56_0 = e1
% 158.54/25.02    (72)   ~ (e1 = e0)
% 158.54/25.02    (73)  op(e2, e1) = all_52_9
% 158.54/25.02    (74)  all_54_4 = all_52_1
% 158.54/25.02    (75)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.54/25.02          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.54/25.02    (76)  op(e2, e0) = all_52_13
% 158.54/25.02    (77)   ~ (e2 = e1)
% 158.54/25.02    (78)  op(e3, e0) = all_52_12
% 158.54/25.02    (79)   ~ (all_52_4 = all_52_8)
% 158.54/25.02    (80)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.54/25.02          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.54/25.02    (81)   ~ (all_52_8 = e2)
% 158.54/25.02    (82)  op(e1, e3) = all_26_0
% 158.54/25.02    (83)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.54/25.02            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.54/25.02            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.54/25.02            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.02              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.54/25.02          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.54/25.02            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.54/25.02              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.54/25.02            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.02              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.54/25.02          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.54/25.02            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.54/25.02              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.54/25.02            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.02              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.54/25.02          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.54/25.02            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.54/25.02            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.54/25.02              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.54/25.02            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.54/25.02            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.54/25.02            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.54/25.02            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.54/25.02              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.54/25.02            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.54/25.02          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.54/25.02            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.54/25.02              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.54/25.02            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.54/25.02            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.54/25.02          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.54/25.02            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.54/25.02              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.54/25.02            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.54/25.02            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.54/25.02          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.54/25.02            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.54/25.02              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.54/25.02            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.02              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.54/25.02          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.54/25.02            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.54/25.02            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.54/25.02            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.54/25.02            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.54/25.02            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.54/25.02            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.54/25.02            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.54/25.02              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.54/25.02            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.54/25.02            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.54/25.02            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.54/25.02            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.54/25.02              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.54/25.02            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.54/25.02          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.54/25.02            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.54/25.02              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.54/25.02              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.54/25.02            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.54/25.02            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.54/25.02            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.54/25.02            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.54/25.02              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.54/25.02            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.54/25.02          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.54/25.02            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.54/25.02              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.54/25.02            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.54/25.02              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.54/25.02          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.54/25.02            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.54/25.02              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.54/25.02              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.54/25.02            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.54/25.02          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.54/25.02            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.54/25.02            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.54/25.02                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.54/25.02                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.54/25.02                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/25.02                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.54/25.02                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.54/25.02                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.54/25.02                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.54/25.02                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.54/25.02                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.54/25.02                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.54/25.02                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.54/25.02                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.54/25.02                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.54/25.02                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.54/25.02                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/25.02                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.54/25.02                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/25.02                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.54/25.02                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.54/25.02                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.54/25.02                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.54/25.02                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.54/25.02                op(e0, e1) = e0)))
% 158.54/25.02    (84)  all_54_11 = all_52_14
% 158.54/25.02    (85)   ~ (all_52_1 = all_4_2)
% 158.54/25.02    (86)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.54/25.02    (87)   ~ (e2 = e0)
% 158.54/25.02    (88)   ~ (all_14_2 = e3)
% 158.54/25.02    (89)  all_54_8 = all_52_2
% 158.54/25.02  
% 158.54/25.02  Begin of proof
% 158.54/25.02  | 
% 158.54/25.02  | GROUND_INST: instantiating (20) with all_52_2, all_26_0, e3, e1, simplifying
% 158.54/25.02  |              with (33), (82) gives:
% 158.54/25.02  |   (90)  all_52_2 = all_26_0
% 158.54/25.02  | 
% 158.54/25.02  | COMBINE_EQS: (89), (90) imply:
% 158.54/25.02  |   (91)  all_54_8 = all_26_0
% 158.54/25.02  | 
% 158.54/25.02  | REDUCE: (60), (90) imply:
% 158.54/25.02  |   (92)   ~ (all_52_1 = all_26_0)
% 158.54/25.02  | 
% 158.54/25.02  | REDUCE: (44), (90) imply:
% 158.54/25.02  |   (93)   ~ (all_52_3 = all_26_0)
% 158.54/25.02  | 
% 158.54/25.02  | SIMP: (93) implies:
% 158.54/25.02  |   (94)   ~ (all_52_3 = all_26_0)
% 158.54/25.02  | 
% 158.54/25.02  | REDUCE: (59), (90) imply:
% 158.54/25.02  |   (95)   ~ (all_52_6 = all_26_0)
% 158.54/25.02  | 
% 158.54/25.02  | SIMP: (95) implies:
% 158.54/25.02  |   (96)   ~ (all_52_6 = all_26_0)
% 158.54/25.02  | 
% 158.54/25.02  | REDUCE: (19), (90) imply:
% 158.54/25.02  |   (97)   ~ (all_52_14 = all_26_0)
% 158.54/25.02  | 
% 158.54/25.02  | SIMP: (97) implies:
% 158.54/25.02  |   (98)   ~ (all_52_14 = all_26_0)
% 158.54/25.02  | 
% 158.54/25.02  | REDUCE: (43), (90) imply:
% 158.54/25.02  |   (99)   ~ (all_26_0 = e2)
% 158.54/25.02  | 
% 158.54/25.02  | REDUCE: (45), (90) imply:
% 158.54/25.02  |   (100)   ~ (all_26_0 = e1)
% 158.54/25.02  | 
% 158.54/25.02  | BETA: splitting (86) gives:
% 158.54/25.02  | 
% 158.54/25.02  | Case 1:
% 158.54/25.02  | | 
% 158.54/25.02  | |   (101)  all_54_8 = e3
% 158.54/25.02  | | 
% 158.54/25.02  | | COMBINE_EQS: (91), (101) imply:
% 158.54/25.02  | |   (102)  all_26_0 = e3
% 158.54/25.02  | | 
% 158.54/25.02  | | REDUCE: (92), (102) imply:
% 158.54/25.02  | |   (103)   ~ (all_52_1 = e3)
% 158.54/25.02  | | 
% 158.54/25.02  | | REDUCE: (94), (102) imply:
% 158.54/25.02  | |   (104)   ~ (all_52_3 = e3)
% 158.54/25.02  | | 
% 158.54/25.02  | | REDUCE: (96), (102) imply:
% 158.54/25.02  | |   (105)   ~ (all_52_6 = e3)
% 158.54/25.02  | | 
% 158.54/25.02  | | REDUCE: (98), (102) imply:
% 158.54/25.02  | |   (106)   ~ (all_52_14 = e3)
% 158.54/25.02  | | 
% 158.54/25.02  | | REDUCE: (99), (102) imply:
% 158.54/25.02  | |   (107)   ~ (e3 = e2)
% 158.54/25.02  | | 
% 158.54/25.02  | | REDUCE: (100), (102) imply:
% 158.54/25.02  | |   (108)   ~ (e3 = e1)
% 158.54/25.02  | | 
% 158.54/25.02  | | REDUCE: (36), (102) imply:
% 158.54/25.02  | |   (109)   ~ (e3 = e0)
% 158.54/25.02  | | 
% 158.54/25.02  | | REDUCE: (82), (102) imply:
% 158.54/25.02  | |   (110)  op(e1, e3) = e3
% 158.54/25.02  | | 
% 158.54/25.02  | | BETA: splitting (68) gives:
% 158.54/25.02  | | 
% 158.54/25.02  | | Case 1:
% 158.54/25.02  | | | 
% 158.54/25.02  | | |   (111)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) =
% 158.54/25.02  | | |            e3)
% 158.54/25.02  | | | 
% 158.54/25.02  | | | BETA: splitting (111) gives:
% 158.54/25.02  | | | 
% 158.54/25.02  | | | Case 1:
% 158.54/25.02  | | | | 
% 158.54/25.02  | | | |   (112)  all_56_6 = e3 & op(e1, e3) = e3
% 158.54/25.02  | | | | 
% 158.54/25.02  | | | | ALPHA: (112) implies:
% 158.54/25.02  | | | |   (113)  all_56_6 = e3
% 158.54/25.02  | | | | 
% 158.54/25.02  | | | | BETA: splitting (48) gives:
% 158.54/25.02  | | | | 
% 158.54/25.02  | | | | Case 1:
% 158.54/25.02  | | | | | 
% 158.54/25.02  | | | | |   (114)   ~ (all_28_2 = e2)
% 158.54/25.02  | | | | | 
% 158.54/25.02  | | | | | REDUCE: (23), (114) imply:
% 158.54/25.02  | | | | |   (115)   ~ (all_14_2 = e2)
% 158.54/25.02  | | | | | 
% 158.54/25.02  | | | | | BETA: splitting (28) gives:
% 158.54/25.02  | | | | | 
% 158.54/25.02  | | | | | Case 1:
% 158.54/25.02  | | | | | | 
% 158.54/25.02  | | | | | |   (116)  all_54_15 = e3
% 158.54/25.02  | | | | | | 
% 158.54/25.02  | | | | | | REF_CLOSE: (34), (88), (116) are inconsistent by sub-proof #1010.
% 158.54/25.02  | | | | | | 
% 158.54/25.02  | | | | | Case 2:
% 158.54/25.02  | | | | | | 
% 158.54/25.02  | | | | | |   (117)   ~ (all_54_15 = e3)
% 158.54/25.02  | | | | | |   (118)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.54/25.02  | | | | | | 
% 158.54/25.02  | | | | | | BETA: splitting (118) gives:
% 158.54/25.02  | | | | | | 
% 158.54/25.02  | | | | | | Case 1:
% 158.54/25.02  | | | | | | | 
% 158.54/25.02  | | | | | | |   (119)  all_54_15 = e2
% 158.54/25.02  | | | | | | | 
% 158.54/25.02  | | | | | | | REF_CLOSE: (34), (115), (119) are inconsistent by sub-proof #1009.
% 158.54/25.02  | | | | | | | 
% 158.54/25.02  | | | | | | Case 2:
% 158.54/25.02  | | | | | | | 
% 158.54/25.02  | | | | | | |   (120)   ~ (all_54_15 = e2)
% 158.54/25.02  | | | | | | |   (121)  all_54_15 = e1 | all_54_15 = e0
% 158.54/25.02  | | | | | | | 
% 158.54/25.02  | | | | | | | BETA: splitting (121) gives:
% 158.54/25.02  | | | | | | | 
% 158.54/25.02  | | | | | | | Case 1:
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | |   (122)  all_54_15 = e1
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | REF_CLOSE: (34), (66), (122) are inconsistent by sub-proof
% 158.54/25.02  | | | | | | | |            #1008.
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | Case 2:
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | |   (123)  all_54_15 = e0
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | COMBINE_EQS: (34), (123) imply:
% 158.54/25.02  | | | | | | | |   (124)  all_14_2 = e0
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | SIMP: (124) implies:
% 158.54/25.02  | | | | | | | |   (125)  all_14_2 = e0
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | REDUCE: (7), (125) imply:
% 158.54/25.02  | | | | | | | |   (126)   ~ (all_52_3 = e0)
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | REDUCE: (2), (125) imply:
% 158.54/25.02  | | | | | | | |   (127)   ~ (all_52_7 = e0)
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | REDUCE: (31), (125) imply:
% 158.54/25.02  | | | | | | | |   (128)   ~ (all_52_11 = e0)
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | REDUCE: (38), (125) imply:
% 158.54/25.02  | | | | | | | |   (129)   ~ (all_52_14 = e0)
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | REDUCE: (88), (125) imply:
% 158.54/25.02  | | | | | | | |   (130)   ~ (e3 = e0)
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | REDUCE: (115), (125) imply:
% 158.54/25.02  | | | | | | | |   (131)   ~ (e2 = e0)
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | REDUCE: (66), (125) imply:
% 158.54/25.02  | | | | | | | |   (132)   ~ (e1 = e0)
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | BETA: splitting (29) gives:
% 158.54/25.02  | | | | | | | | 
% 158.54/25.02  | | | | | | | | Case 1:
% 158.54/25.02  | | | | | | | | | 
% 158.54/25.02  | | | | | | | | |   (133)  all_56_15 = e0 & op(e0, e0) = e0
% 158.54/25.02  | | | | | | | | | 
% 158.54/25.02  | | | | | | | | | ALPHA: (133) implies:
% 158.54/25.02  | | | | | | | | |   (134)  all_56_15 = e0
% 158.54/25.02  | | | | | | | | |   (135)  op(e0, e0) = e0
% 158.54/25.02  | | | | | | | | | 
% 158.54/25.02  | | | | | | | | | BETA: splitting (39) gives:
% 158.54/25.02  | | | | | | | | | 
% 158.54/25.02  | | | | | | | | | Case 1:
% 158.54/25.02  | | | | | | | | | | 
% 158.54/25.02  | | | | | | | | | |   (136)  all_54_12 = e3
% 158.54/25.02  | | | | | | | | | | 
% 158.54/25.02  | | | | | | | | | | REF_CLOSE: (11), (104), (136) are inconsistent by sub-proof
% 158.54/25.02  | | | | | | | | | |            #697.
% 158.54/25.02  | | | | | | | | | | 
% 158.54/25.02  | | | | | | | | | Case 2:
% 158.54/25.02  | | | | | | | | | | 
% 158.54/25.02  | | | | | | | | | |   (137)   ~ (all_54_12 = e3)
% 158.62/25.02  | | | | | | | | | |   (138)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 158.62/25.02  | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | BETA: splitting (138) gives:
% 158.62/25.02  | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | |   (139)  all_54_12 = e2
% 158.62/25.02  | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | COMBINE_EQS: (11), (139) imply:
% 158.62/25.02  | | | | | | | | | | |   (140)  all_52_3 = e2
% 158.62/25.02  | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | SIMP: (140) implies:
% 158.62/25.02  | | | | | | | | | | |   (141)  all_52_3 = e2
% 158.62/25.02  | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | REDUCE: (4), (141) imply:
% 158.62/25.02  | | | | | | | | | | |   (142)   ~ (all_52_1 = e2)
% 158.62/25.02  | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | REDUCE: (104), (141) imply:
% 158.62/25.02  | | | | | | | | | | |   (143)   ~ (e3 = e2)
% 158.62/25.02  | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | REDUCE: (21), (141) imply:
% 158.62/25.02  | | | | | | | | | | |   (144)  op(e0, e3) = e2
% 158.62/25.02  | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | BETA: splitting (65) gives:
% 158.62/25.02  | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | |   (145)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 158.62/25.02  | | | | | | | | | | | |            & op(e1, e2) = e0)
% 158.62/25.02  | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | BETA: splitting (145) gives:
% 158.62/25.02  | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | |   (146)  all_56_6 = e0 & op(e1, e3) = e0
% 158.62/25.02  | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | REF_CLOSE: (109), (113), (146) are inconsistent by sub-proof
% 158.62/25.02  | | | | | | | | | | | | |            #171.
% 158.62/25.02  | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | |   (147)  all_56_7 = e0 & op(e1, e2) = e0
% 158.62/25.02  | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | ALPHA: (147) implies:
% 158.62/25.02  | | | | | | | | | | | | |   (148)  all_56_7 = e0
% 158.62/25.02  | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | BETA: splitting (30) gives:
% 158.62/25.02  | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | |   (149)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 158.62/25.02  | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 158.62/25.02  | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | REF_CLOSE: (20), (33), (45), (72), (148), (149) are
% 158.62/25.02  | | | | | | | | | | | | | |            inconsistent by sub-proof #170.
% 158.62/25.02  | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | |   (150)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 158.62/25.02  | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 158.62/25.02  | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 158.62/25.02  | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | |   (151)  all_56_8 = e1 & op(e1, e1) = e1
% 158.62/25.02  | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 158.62/25.02  | | | | | | | | | | | | | | |   (152)  op(e1, e1) = e1
% 158.62/25.02  | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | REF_CLOSE: (20), (25), (77), (152) are inconsistent by
% 158.62/25.02  | | | | | | | | | | | | | | |            sub-proof #986.
% 158.62/25.02  | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | |   (153)  all_56_11 = e1 & op(e1, e0) = e1
% 158.62/25.02  | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 158.62/25.02  | | | | | | | | | | | | | | |   (154)  all_56_11 = e1
% 158.62/25.02  | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | |   (155)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 158.62/25.02  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 158.62/25.02  | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | |   (156)  all_56_1 = e1 & op(e3, e2) = e1
% 158.62/25.02  | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | |   (157)  all_56_1 = e1
% 158.62/25.02  | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | |   (158)  all_54_4 = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (158) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | |   (159)  all_52_1 = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | REDUCE: (103), (159) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | |   (160)  $false
% 158.62/25.02  | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | |   (161)   ~ (all_54_4 = e3)
% 158.62/25.02  | | | | | | | | | | | | | | | | | |   (162)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | |   (163)  all_54_4 = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (163) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | |   (164)  all_52_1 = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | REDUCE: (142), (164) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | |   (165)  $false
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | |   (166)   ~ (all_54_4 = e2)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | |   (167)  all_54_4 = e1 | all_54_4 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | |   (168)  all_54_4 = e1
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (168) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | |   (169)  all_52_1 = e1
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (169) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | |   (170)  $false
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | |   (171)  all_54_4 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (171) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | |   (172)  all_52_1 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (172) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | |   (173)   ~ (all_4_2 = e0)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | SIMP: (173) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | |   (174)   ~ (all_4_2 = e0)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | |   (175)  all_54_5 = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (26), (175) are inconsistent by sub-proof
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | |            #930.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | |   (176)   ~ (all_54_5 = e3)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | |   (177)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | |   (178)  all_54_5 = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (178) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | |   (179)  all_4_2 = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | SIMP: (179) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | |   (180)  all_4_2 = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (180) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | |   (181)   ~ (all_52_6 = e2)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (180) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | |   (182)   ~ (all_52_9 = e2)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (180) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | |   (183)   ~ (all_52_13 = e2)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (180) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | |   (184)  op(e2, e2) = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | |   (185)  all_54_11 = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (106), (185) are inconsistent by sub-proof
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | |            #655.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | |   (187)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_56_9 = e2 & op(e3, e0) = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (189)  all_56_9 = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (190)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (191)  all_56_0 = e3 & op(e3, e3) = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  op(e3, e3) = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (63), (108), (192) are inconsistent by
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #995.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  all_56_1 = e3 & op(e3, e2) = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  all_56_1 = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  op(e3, e2) = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (14), (15), (16), (17), (18), (20),
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21), (22), (25), (27), (33), (35), (40), (41),
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (42), (45), (57), (64), (69), (70), (73), (76),
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (83), (84), (105), (128), (129),
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (142), (144), (181), (182), (183), (184),
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (186), (189), (194), (195) are inconsistent by
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #162.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  all_56_4 = e3 & op(e3, e1) = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  all_56_4 = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (199)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_56_0 = e0 & op(e3, e3) = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (52), (55), (71), (72), (77), (87),
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (108), (109), (134), (135), (154), (200)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #489.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_56_1 = e0 & op(e3, e2) = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (202)  all_56_1 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (202) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (203)  e1 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (203) imply:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (204)  all_56_11 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (52), (55), (72), (77), (87), (107),
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (109), (134), (135), (204) are inconsistent
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #883.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (206)  all_56_4 = e0 & op(e3, e1) = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (198), (206) are inconsistent by sub-proof
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #248.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  all_56_9 = e0 & op(e3, e0) = e0
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (189), (207) are inconsistent by sub-proof
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #950.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_56_9 = e3 & op(e3, e0) = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_56_9 = e3
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (189), (209) are inconsistent by sub-proof
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #888.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_56_10 = e2 & op(e2, e0) = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  op(e2, e0) = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (76), (183), (211) are inconsistent by
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #996.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | |   (212)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_56_11 = e2 & op(e1, e0) = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_56_11 = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (154), (214) are inconsistent by sub-proof
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |            #621.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_56_15 = e2 & op(e0, e0) = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  op(e0, e0) = e2
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (87), (135), (216) are inconsistent by
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #979.
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.02  | | | | | | | | | | | | | | | | | | | | | |   (217)  all_54_5 = e1 | all_54_5 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (67), (174), (217) are inconsistent by
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (218)  all_56_3 = e1 & op(e2, e2) = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (219)  op(e2, e2) = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (20), (26), (56), (67), (219) are
% 158.62/25.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #690.
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | |   (220)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 158.62/25.03  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (221)  all_56_7 = e1 & op(e1, e2) = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (222)  all_56_7 = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (222) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (223)  e1 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | SIMP: (223) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (224)  e1 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (224) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (225)  all_56_11 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (52), (55), (72), (77), (87), (107),
% 158.62/25.03  | | | | | | | | | | | | | | | | |            (108), (109), (134), (135), (225) are inconsistent
% 158.62/25.03  | | | | | | | | | | | | | | | | |            by sub-proof #883.
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (226)  all_56_13 = e1 & op(e0, e2) = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (227)  all_56_13 = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | |   (228)  all_54_4 = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (228) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | |   (229)  all_52_1 = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | REDUCE: (103), (229) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | |   (230)  $false
% 158.62/25.03  | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | |   (231)   ~ (all_54_4 = e3)
% 158.62/25.03  | | | | | | | | | | | | | | | | | |   (232)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | |   (233)  all_54_4 = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (233) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | |   (234)  all_52_1 = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | REDUCE: (142), (234) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | |   (235)  $false
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | |   (236)   ~ (all_54_4 = e2)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | |   (237)  all_54_4 = e1 | all_54_4 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | |   (238)  all_54_4 = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (238) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | |   (239)  all_52_1 = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (239) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | |   (240)  $false
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | |   (241)  all_54_4 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (241) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | |   (242)  all_52_1 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (242) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | |   (243)   ~ (all_4_2 = e0)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | SIMP: (243) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | |   (244)   ~ (all_4_2 = e0)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | |   (245)  all_54_5 = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (26), (245) are inconsistent by sub-proof
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | |            #930.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | |   (246)   ~ (all_54_5 = e3)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | |   (247)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | |   (248)  all_54_5 = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (248) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | |   (249)  all_4_2 = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | SIMP: (249) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | |   (250)  all_4_2 = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (250) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | |   (251)   ~ (all_52_6 = e2)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (250) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | |   (252)   ~ (all_52_9 = e2)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (250) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | |   (253)   ~ (all_52_13 = e2)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | |   (254)  all_54_11 = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (106), (254) are inconsistent by sub-proof
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | |            #655.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | |   (255)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | |   (256)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_56_2 = e2 & op(e2, e3) = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  op(e2, e3) = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (64), (142), (258) are inconsistent by
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1007.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  all_56_3 = e2 & op(e2, e2) = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_56_3 = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  op(e2, e2) = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_56_9 = e2 & op(e3, e0) = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_56_9 = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_56_1 = e3 & op(e3, e2) = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_56_1 = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  op(e3, e2) = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (14), (15), (16), (17), (18), (20),
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21), (22), (25), (27), (33), (35), (40), (41),
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (42), (45), (57), (64), (69), (70), (73), (76),
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (83), (84), (105), (128), (129),
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (142), (144), (251), (252), (253), (255),
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (261), (264), (267), (268) are inconsistent by
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #162.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_56_3 = e3 & op(e2, e2) = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_56_3 = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (270) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  e3 = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (271) imply:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  $false
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (272) is inconsistent.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_56_7 = e3 & op(e1, e2) = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (148), (274) are inconsistent by sub-proof
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #333.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_56_13 = e3 & op(e0, e2) = e3
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (227), (275) are inconsistent by sub-proof
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #161.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  all_56_10 = e2 & op(e2, e0) = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  op(e2, e0) = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (76), (253), (277) are inconsistent by
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #996.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_56_11 = e2 & op(e1, e0) = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (154), (279) are inconsistent by sub-proof
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #658.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_56_15 = e2 & op(e0, e0) = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  op(e0, e0) = e2
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (87), (135), (281) are inconsistent by
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #979.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | |   (282)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (73), (76), (252), (253), (282) are
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #160.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | |   (283)  all_54_5 = e1 | all_54_5 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (67), (244), (283) are inconsistent by
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | |   (284)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 158.62/25.03  | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | REF_CLOSE: (9), (20), (25), (52), (55), (72), (77), (87),
% 158.62/25.03  | | | | | | | | | | | |            (107), (108), (109), (134), (135), (284) are
% 158.62/25.03  | | | | | | | | | | | |            inconsistent by sub-proof #159.
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | |   (285)   ~ (all_54_12 = e2)
% 158.62/25.03  | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | REDUCE: (11), (285) imply:
% 158.62/25.03  | | | | | | | | | | |   (286)   ~ (all_52_3 = e2)
% 158.62/25.03  | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | BETA: splitting (3) gives:
% 158.62/25.03  | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | |   (287)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 158.62/25.03  | | | | | | | | | | | |            & op(e2, e3) = e2)
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | BETA: splitting (287) gives:
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | |   (288)  all_56_0 = e2 & op(e3, e3) = e2
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | REF_CLOSE: (71), (77), (288) are inconsistent by sub-proof
% 158.62/25.03  | | | | | | | | | | | | |            #490.
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | |   (289)  all_56_2 = e2 & op(e2, e3) = e2
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | ALPHA: (289) implies:
% 158.62/25.03  | | | | | | | | | | | | |   (290)  all_56_2 = e2
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | BETA: splitting (65) gives:
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | |   (291)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 158.62/25.03  | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 158.62/25.03  | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | BETA: splitting (291) gives:
% 158.62/25.03  | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | |   (292)  all_56_6 = e0 & op(e1, e3) = e0
% 158.62/25.03  | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | REF_CLOSE: (109), (113), (292) are inconsistent by sub-proof
% 158.62/25.03  | | | | | | | | | | | | | | |            #171.
% 158.62/25.03  | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | |   (293)  all_56_7 = e0 & op(e1, e2) = e0
% 158.62/25.03  | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 158.62/25.03  | | | | | | | | | | | | | | |   (294)  all_56_7 = e0
% 158.62/25.03  | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | |   (295)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 158.62/25.03  | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | REF_CLOSE: (20), (33), (45), (72), (294), (295) are
% 158.62/25.03  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #170.
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | |   (296)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 158.62/25.03  | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (297)  all_56_8 = e1 & op(e1, e1) = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (298)  op(e1, e1) = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (25), (77), (298) are inconsistent by
% 158.62/25.03  | | | | | | | | | | | | | | | | |            sub-proof #986.
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (299)  all_56_11 = e1 & op(e1, e0) = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 158.62/25.03  | | | | | | | | | | | | | | | | |   (300)  all_56_11 = e1
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (21), (52), (55), (71), (72), (75),
% 158.62/25.03  | | | | | | | | | | | | | | | | |            (77), (87), (107), (108), (109), (113), (126),
% 158.62/25.03  | | | | | | | | | | | | | | | | |            (134), (135), (290), (300) are inconsistent by
% 158.62/25.03  | | | | | | | | | | | | | | | | |            sub-proof #488.
% 158.62/25.03  | | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | |   (301)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 158.62/25.03  | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 158.62/25.03  | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (25), (52), (55), (72), (77), (87),
% 158.62/25.03  | | | | | | | | | | | | | |            (107), (108), (109), (134), (135), (301) are
% 158.62/25.03  | | | | | | | | | | | | | |            inconsistent by sub-proof #159.
% 158.62/25.03  | | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | |   (302)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 158.62/25.03  | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | BETA: splitting (302) gives:
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | Case 1:
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | |   (303)  all_56_6 = e2 & op(e1, e3) = e2
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | REF_CLOSE: (20), (33), (43), (303) are inconsistent by
% 158.62/25.03  | | | | | | | | | | | | |            sub-proof #761.
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | |   (304)  all_56_12 = e2 & op(e0, e3) = e2
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | | REF_CLOSE: (20), (21), (286), (304) are inconsistent by
% 158.62/25.03  | | | | | | | | | | | | |            sub-proof #858.
% 158.62/25.03  | | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | | 
% 158.62/25.03  | | | | | | | | Case 2:
% 158.62/25.03  | | | | | | | | | 
% 158.62/25.03  | | | | | | | | |   (305)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0
% 158.62/25.03  | | | | | | | | |              & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 158.62/25.03  | | | | | | | | |              = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) |
% 158.62/25.03  | | | | | | | | |            (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 158.62/25.03  | | | | | | | | |              e0 & op(e0, e1) = e0))
% 158.62/25.03  | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | ALPHA: (305) implies:
% 158.62/25.03  | | | | | | | | |   (306)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0
% 158.62/25.03  | | | | | | | | |            & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 158.62/25.03  | | | | | | | | |            e0)
% 158.62/25.03  | | | | | | | | | 
% 158.62/25.03  | | | | | | | | | REF_CLOSE: (18), (20), (21), (35), (126), (127), (128), (306)
% 158.62/25.03  | | | | | | | | |            are inconsistent by sub-proof #881.
% 158.62/25.03  | | | | | | | | | 
% 158.62/25.03  | | | | | | | | End of split
% 158.62/25.03  | | | | | | | | 
% 158.62/25.03  | | | | | | | End of split
% 158.62/25.03  | | | | | | | 
% 158.62/25.03  | | | | | | End of split
% 158.62/25.03  | | | | | | 
% 158.62/25.03  | | | | | End of split
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | Case 2:
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | |   (307)  all_28_2 = e2
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | | COMBINE_EQS: (23), (307) imply:
% 158.62/25.03  | | | | |   (308)  all_14_2 = e2
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | | SIMP: (308) implies:
% 158.62/25.03  | | | | |   (309)  all_14_2 = e2
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | | REDUCE: (7), (309) imply:
% 158.62/25.03  | | | | |   (310)   ~ (all_52_3 = e2)
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | | REDUCE: (32), (309) imply:
% 158.62/25.03  | | | | |   (311)   ~ (all_52_12 = e2)
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | | REDUCE: (62), (309) imply:
% 158.62/25.03  | | | | |   (312)  op(e0, e0) = e2
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | | REF_CLOSE: (3), (5), (10), (12), (13), (20), (21), (22), (25), (26),
% 158.62/25.03  | | | | |            (33), (43), (56), (58), (64), (67), (69), (71), (77), (78),
% 158.62/25.03  | | | | |            (81), (87), (310), (311), (312) are inconsistent by
% 158.62/25.03  | | | | |            sub-proof #158.
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | End of split
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | Case 2:
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | |   (313)  all_56_7 = e3 & op(e1, e2) = e3
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | REF_CLOSE: (20), (25), (30), (33), (45), (65), (72), (77), (87), (108),
% 158.62/25.03  | | | |            (109), (110), (313) are inconsistent by sub-proof #157.
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | End of split
% 158.62/25.03  | | | 
% 158.62/25.03  | | Case 2:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (314)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0)
% 158.62/25.03  | | |            = e3)
% 158.62/25.03  | | | 
% 158.62/25.03  | | | BETA: splitting (314) gives:
% 158.62/25.03  | | | 
% 158.62/25.03  | | | Case 1:
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | |   (315)  all_56_8 = e3 & op(e1, e1) = e3
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | REF_CLOSE: (61), (107), (315) are inconsistent by sub-proof #193.
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | Case 2:
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | |   (316)  all_56_11 = e3 & op(e1, e0) = e3
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | ALPHA: (316) implies:
% 158.62/25.03  | | | |   (317)  all_56_11 = e3
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | BETA: splitting (30) gives:
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | Case 1:
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | |   (318)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1,
% 158.62/25.03  | | | | |              e2) = e1)
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | | BETA: splitting (318) gives:
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | | Case 1:
% 158.62/25.03  | | | | | | 
% 158.62/25.03  | | | | | |   (319)  all_56_6 = e1 & op(e1, e3) = e1
% 158.62/25.03  | | | | | | 
% 158.62/25.03  | | | | | | ALPHA: (319) implies:
% 158.62/25.03  | | | | | |   (320)  op(e1, e3) = e1
% 158.62/25.03  | | | | | | 
% 158.62/25.03  | | | | | | REF_CLOSE: (20), (33), (45), (320) are inconsistent by sub-proof
% 158.62/25.03  | | | | | |            #990.
% 158.62/25.03  | | | | | | 
% 158.62/25.03  | | | | | Case 2:
% 158.62/25.03  | | | | | | 
% 158.62/25.03  | | | | | |   (321)  all_56_7 = e1 & op(e1, e2) = e1
% 158.62/25.03  | | | | | | 
% 158.62/25.03  | | | | | | ALPHA: (321) implies:
% 158.62/25.03  | | | | | |   (322)  all_56_7 = e1
% 158.62/25.03  | | | | | | 
% 158.62/25.03  | | | | | | REF_CLOSE: (20), (25), (65), (72), (87), (109), (110), (317), (322)
% 158.62/25.03  | | | | | |            are inconsistent by sub-proof #156.
% 158.62/25.03  | | | | | | 
% 158.62/25.03  | | | | | End of split
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | Case 2:
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | |   (323)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1,
% 158.62/25.03  | | | | |              e0) = e1)
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | | REF_CLOSE: (20), (25), (77), (108), (317), (323) are inconsistent by
% 158.62/25.03  | | | | |            sub-proof #180.
% 158.62/25.03  | | | | | 
% 158.62/25.03  | | | | End of split
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | End of split
% 158.62/25.03  | | | 
% 158.62/25.03  | | End of split
% 158.62/25.03  | | 
% 158.62/25.03  | Case 2:
% 158.62/25.03  | | 
% 158.62/25.03  | |   (324)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.62/25.03  | | 
% 158.62/25.03  | | BETA: splitting (324) gives:
% 158.62/25.03  | | 
% 158.62/25.03  | | Case 1:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (325)  all_54_8 = e2
% 158.62/25.03  | | | 
% 158.62/25.03  | | | COMBINE_EQS: (91), (325) imply:
% 158.62/25.03  | | |   (326)  all_26_0 = e2
% 158.62/25.03  | | | 
% 158.62/25.03  | | | REDUCE: (99), (326) imply:
% 158.62/25.03  | | |   (327)  $false
% 158.62/25.03  | | | 
% 158.62/25.03  | | | CLOSE: (327) is inconsistent.
% 158.62/25.03  | | | 
% 158.62/25.03  | | Case 2:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (328)  all_54_8 = e1 | all_54_8 = e0
% 158.62/25.03  | | | 
% 158.62/25.03  | | | BETA: splitting (328) gives:
% 158.62/25.03  | | | 
% 158.62/25.03  | | | Case 1:
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | |   (329)  all_54_8 = e1
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | COMBINE_EQS: (91), (329) imply:
% 158.62/25.03  | | | |   (330)  all_26_0 = e1
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | REDUCE: (100), (330) imply:
% 158.62/25.03  | | | |   (331)  $false
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | CLOSE: (331) is inconsistent.
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | Case 2:
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | |   (332)  all_54_8 = e0
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | COMBINE_EQS: (91), (332) imply:
% 158.62/25.03  | | | |   (333)  all_26_0 = e0
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | REDUCE: (36), (333) imply:
% 158.62/25.03  | | | |   (334)  $false
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | | CLOSE: (334) is inconsistent.
% 158.62/25.03  | | | | 
% 158.62/25.03  | | | End of split
% 158.62/25.03  | | | 
% 158.62/25.03  | | End of split
% 158.62/25.03  | | 
% 158.62/25.03  | End of split
% 158.62/25.03  | 
% 158.62/25.03  End of proof
% 158.62/25.03  
% 158.62/25.03  Sub-proof #156 shows that the following formulas are inconsistent:
% 158.62/25.03  ----------------------------------------------------------------
% 158.62/25.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.03    (2)  op(e1, e1) = e2
% 158.62/25.03    (3)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.62/25.03         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.62/25.03    (4)  all_56_7 = e1
% 158.62/25.03    (5)  op(e1, e3) = e3
% 158.62/25.03    (6)   ~ (e1 = e0)
% 158.62/25.03    (7)  all_56_11 = e3
% 158.62/25.03    (8)   ~ (e2 = e0)
% 158.62/25.03    (9)   ~ (e3 = e0)
% 158.62/25.03  
% 158.62/25.03  Begin of proof
% 158.62/25.03  | 
% 158.62/25.03  | BETA: splitting (3) gives:
% 158.62/25.03  | 
% 158.62/25.03  | Case 1:
% 158.62/25.03  | | 
% 158.62/25.03  | |   (10)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) =
% 158.62/25.03  | |           e0)
% 158.62/25.03  | | 
% 158.62/25.03  | | BETA: splitting (10) gives:
% 158.62/25.03  | | 
% 158.62/25.03  | | Case 1:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (11)  all_56_6 = e0 & op(e1, e3) = e0
% 158.62/25.03  | | | 
% 158.62/25.03  | | | ALPHA: (11) implies:
% 158.62/25.03  | | |   (12)  op(e1, e3) = e0
% 158.62/25.03  | | | 
% 158.62/25.03  | | | REF_CLOSE: (1), (5), (9), (12) are inconsistent by sub-proof #913.
% 158.62/25.03  | | | 
% 158.62/25.03  | | Case 2:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (13)  all_56_7 = e0 & op(e1, e2) = e0
% 158.62/25.03  | | | 
% 158.62/25.03  | | | ALPHA: (13) implies:
% 158.62/25.03  | | |   (14)  all_56_7 = e0
% 158.62/25.03  | | | 
% 158.62/25.03  | | | REF_CLOSE: (4), (6), (14) are inconsistent by sub-proof #560.
% 158.62/25.03  | | | 
% 158.62/25.03  | | End of split
% 158.62/25.03  | | 
% 158.62/25.03  | Case 2:
% 158.62/25.03  | | 
% 158.62/25.03  | |   (15)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 158.62/25.03  | |           e0)
% 158.62/25.03  | | 
% 158.62/25.03  | | BETA: splitting (15) gives:
% 158.62/25.03  | | 
% 158.62/25.03  | | Case 1:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (16)  all_56_8 = e0 & op(e1, e1) = e0
% 158.62/25.03  | | | 
% 158.62/25.03  | | | ALPHA: (16) implies:
% 158.62/25.03  | | |   (17)  op(e1, e1) = e0
% 158.62/25.03  | | | 
% 158.62/25.03  | | | REF_CLOSE: (1), (2), (8), (17) are inconsistent by sub-proof #914.
% 158.62/25.03  | | | 
% 158.62/25.03  | | Case 2:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (18)  all_56_11 = e0 & op(e1, e0) = e0
% 158.62/25.03  | | | 
% 158.62/25.03  | | | ALPHA: (18) implies:
% 158.62/25.03  | | |   (19)  all_56_11 = e0
% 158.62/25.03  | | | 
% 158.62/25.03  | | | REF_CLOSE: (7), (9), (19) are inconsistent by sub-proof #893.
% 158.62/25.03  | | | 
% 158.62/25.03  | | End of split
% 158.62/25.03  | | 
% 158.62/25.03  | End of split
% 158.62/25.03  | 
% 158.62/25.03  End of proof
% 158.62/25.03  
% 158.62/25.03  Sub-proof #157 shows that the following formulas are inconsistent:
% 158.62/25.03  ----------------------------------------------------------------
% 158.62/25.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.03    (2)  op(e1, e1) = e2
% 158.62/25.03    (3)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.62/25.03         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.62/25.03    (4)  op(e1, e3) = all_52_2
% 158.62/25.03    (5)   ~ (all_52_2 = e1)
% 158.62/25.03    (6)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.62/25.03         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.62/25.03    (7)  op(e1, e3) = e3
% 158.62/25.03    (8)   ~ (e1 = e0)
% 158.62/25.03    (9)   ~ (e2 = e1)
% 158.62/25.03    (10)  all_56_7 = e3 & op(e1, e2) = e3
% 158.62/25.03    (11)   ~ (e3 = e1)
% 158.62/25.03    (12)   ~ (e2 = e0)
% 158.62/25.03    (13)   ~ (e3 = e0)
% 158.62/25.03  
% 158.62/25.03  Begin of proof
% 158.62/25.03  | 
% 158.62/25.03  | ALPHA: (10) implies:
% 158.62/25.03  |   (14)  all_56_7 = e3
% 158.62/25.03  | 
% 158.62/25.03  | BETA: splitting (3) gives:
% 158.62/25.03  | 
% 158.62/25.03  | Case 1:
% 158.62/25.03  | | 
% 158.62/25.03  | |   (15)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 158.62/25.03  | |           e1)
% 158.62/25.03  | | 
% 158.62/25.03  | | BETA: splitting (15) gives:
% 158.62/25.03  | | 
% 158.62/25.03  | | Case 1:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (16)  all_56_6 = e1 & op(e1, e3) = e1
% 158.62/25.03  | | | 
% 158.62/25.03  | | | ALPHA: (16) implies:
% 158.62/25.03  | | |   (17)  op(e1, e3) = e1
% 158.62/25.03  | | | 
% 158.62/25.03  | | | REF_CLOSE: (1), (4), (5), (17) are inconsistent by sub-proof #990.
% 158.62/25.03  | | | 
% 158.62/25.03  | | Case 2:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (18)  all_56_7 = e1 & op(e1, e2) = e1
% 158.62/25.03  | | | 
% 158.62/25.03  | | | REF_CLOSE: (11), (14), (18) are inconsistent by sub-proof #173.
% 158.62/25.03  | | | 
% 158.62/25.03  | | End of split
% 158.62/25.03  | | 
% 158.62/25.03  | Case 2:
% 158.62/25.03  | | 
% 158.62/25.03  | |   (19)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 158.62/25.03  | |           e1)
% 158.62/25.03  | | 
% 158.62/25.03  | | BETA: splitting (19) gives:
% 158.62/25.03  | | 
% 158.62/25.03  | | Case 1:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (20)  all_56_8 = e1 & op(e1, e1) = e1
% 158.62/25.03  | | | 
% 158.62/25.03  | | | ALPHA: (20) implies:
% 158.62/25.03  | | |   (21)  op(e1, e1) = e1
% 158.62/25.03  | | | 
% 158.62/25.03  | | | REF_CLOSE: (1), (2), (9), (21) are inconsistent by sub-proof #986.
% 158.62/25.03  | | | 
% 158.62/25.03  | | Case 2:
% 158.62/25.03  | | | 
% 158.62/25.03  | | |   (22)  all_56_11 = e1 & op(e1, e0) = e1
% 158.62/25.03  | | | 
% 158.62/25.03  | | | ALPHA: (22) implies:
% 158.62/25.03  | | |   (23)  all_56_11 = e1
% 158.62/25.03  | | | 
% 158.62/25.03  | | | REF_CLOSE: (1), (2), (6), (7), (8), (12), (13), (14), (23) are
% 158.62/25.03  | | |            inconsistent by sub-proof #659.
% 158.62/25.03  | | | 
% 158.62/25.03  | | End of split
% 158.62/25.03  | | 
% 158.62/25.03  | End of split
% 158.62/25.03  | 
% 158.62/25.03  End of proof
% 158.62/25.03  
% 158.62/25.03  Sub-proof #158 shows that the following formulas are inconsistent:
% 158.62/25.03  ----------------------------------------------------------------
% 158.62/25.03    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.62/25.03         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.62/25.03    (2)  all_54_5 = all_4_2
% 158.62/25.03    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.62/25.03         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.62/25.03    (4)   ~ (all_52_12 = e2)
% 158.62/25.03    (5)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.62/25.03    (6)  op(e0, e0) = e2
% 158.62/25.03    (7)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.62/25.03             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.62/25.03           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.62/25.03               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.62/25.03             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.62/25.03         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.62/25.03             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.62/25.03           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.62/25.03               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.62/25.03             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.62/25.03         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.62/25.03             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.62/25.03           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.62/25.03               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.62/25.03             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.62/25.03         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.62/25.03             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.62/25.03           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.62/25.03               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.62/25.03             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.62/25.03    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.04    (9)  op(e0, e3) = all_52_3
% 158.62/25.04    (10)  op(e3, e1) = all_52_8
% 158.62/25.04    (11)  op(e1, e1) = e2
% 158.62/25.04    (12)   ~ (all_4_2 = e3)
% 158.62/25.04    (13)  op(e1, e3) = all_52_2
% 158.62/25.04    (14)   ~ (all_52_2 = e2)
% 158.62/25.04    (15)  op(e2, e2) = all_4_2
% 158.62/25.04    (16)   ~ (all_52_4 = all_4_2)
% 158.62/25.04    (17)   ~ (all_52_3 = e2)
% 158.62/25.04    (18)  op(e2, e3) = all_52_1
% 158.62/25.04    (19)   ~ (all_4_2 = e1)
% 158.62/25.04    (20)  op(e3, e2) = all_52_4
% 158.62/25.04    (21)  all_56_0 = e1
% 158.62/25.04    (22)   ~ (e2 = e1)
% 158.62/25.04    (23)  op(e3, e0) = all_52_12
% 158.62/25.04    (24)   ~ (all_52_8 = e2)
% 158.62/25.04    (25)   ~ (e2 = e0)
% 158.62/25.04  
% 158.62/25.04  Begin of proof
% 158.62/25.04  | 
% 158.62/25.04  | BETA: splitting (1) gives:
% 158.62/25.04  | 
% 158.62/25.04  | Case 1:
% 158.62/25.04  | | 
% 158.62/25.04  | |   (26)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 158.62/25.04  | |           e2)
% 158.62/25.04  | | 
% 158.62/25.04  | | BETA: splitting (26) gives:
% 158.62/25.04  | | 
% 158.62/25.04  | | Case 1:
% 158.62/25.04  | | | 
% 158.62/25.04  | | |   (27)  all_56_0 = e2 & op(e3, e3) = e2
% 158.62/25.04  | | | 
% 158.62/25.04  | | | REF_CLOSE: (21), (22), (27) are inconsistent by sub-proof #490.
% 158.62/25.04  | | | 
% 158.62/25.04  | | Case 2:
% 158.62/25.04  | | | 
% 158.62/25.04  | | |   (28)  all_56_2 = e2 & op(e2, e3) = e2
% 158.62/25.04  | | | 
% 158.62/25.04  | | | ALPHA: (28) implies:
% 158.62/25.04  | | |   (29)  op(e2, e3) = e2
% 158.62/25.04  | | | 
% 158.62/25.04  | | | BETA: splitting (3) gives:
% 158.62/25.04  | | | 
% 158.62/25.04  | | | Case 1:
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | |   (30)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2)
% 158.62/25.04  | | | |           = e2)
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | | BETA: splitting (30) gives:
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | | Case 1:
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | |   (31)  all_56_0 = e2 & op(e3, e3) = e2
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | | REF_CLOSE: (21), (22), (31) are inconsistent by sub-proof #490.
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | Case 2:
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | |   (32)  all_56_1 = e2 & op(e3, e2) = e2
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | | ALPHA: (32) implies:
% 158.62/25.04  | | | | |   (33)  op(e3, e2) = e2
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | | REF_CLOSE: (2), (5), (6), (7), (8), (11), (12), (15), (16), (18),
% 158.62/25.04  | | | | |            (19), (20), (22), (25), (29), (33) are inconsistent by
% 158.62/25.04  | | | | |            sub-proof #182.
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | End of split
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | Case 2:
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | |   (34)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0)
% 158.62/25.04  | | | |           = e2)
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | | REF_CLOSE: (4), (8), (10), (23), (24), (34) are inconsistent by
% 158.62/25.04  | | | |            sub-proof #511.
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | End of split
% 158.62/25.04  | | | 
% 158.62/25.04  | | End of split
% 158.62/25.04  | | 
% 158.62/25.04  | Case 2:
% 158.62/25.04  | | 
% 158.62/25.04  | |   (35)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 158.62/25.04  | |           e2)
% 158.62/25.04  | | 
% 158.62/25.04  | | BETA: splitting (35) gives:
% 158.62/25.04  | | 
% 158.62/25.04  | | Case 1:
% 158.62/25.04  | | | 
% 158.62/25.04  | | |   (36)  all_56_6 = e2 & op(e1, e3) = e2
% 158.62/25.04  | | | 
% 158.62/25.04  | | | REF_CLOSE: (8), (13), (14), (36) are inconsistent by sub-proof #761.
% 158.62/25.04  | | | 
% 158.62/25.04  | | Case 2:
% 158.62/25.04  | | | 
% 158.62/25.04  | | |   (37)  all_56_12 = e2 & op(e0, e3) = e2
% 158.62/25.04  | | | 
% 158.62/25.04  | | | REF_CLOSE: (8), (9), (17), (37) are inconsistent by sub-proof #858.
% 158.62/25.04  | | | 
% 158.62/25.04  | | End of split
% 158.62/25.04  | | 
% 158.62/25.04  | End of split
% 158.62/25.04  | 
% 158.62/25.04  End of proof
% 158.62/25.04  
% 158.62/25.04  Sub-proof #159 shows that the following formulas are inconsistent:
% 158.62/25.04  ----------------------------------------------------------------
% 158.62/25.04    (1)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.62/25.04    (2)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.62/25.04         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.62/25.04    (3)   ~ (e3 = e2)
% 158.62/25.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.04    (5)  op(e1, e1) = e2
% 158.62/25.04    (6)  op(e0, e0) = e0
% 158.62/25.04    (7)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.62/25.04         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.62/25.04    (8)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.62/25.04         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.62/25.04    (9)   ~ (e1 = e0)
% 158.62/25.04    (10)   ~ (e2 = e1)
% 158.62/25.04    (11)  all_56_15 = e0
% 158.62/25.04    (12)   ~ (e3 = e1)
% 158.62/25.04    (13)   ~ (e2 = e0)
% 158.62/25.04    (14)   ~ (e3 = e0)
% 158.62/25.04  
% 158.62/25.04  Begin of proof
% 158.62/25.04  | 
% 158.62/25.04  | BETA: splitting (1) gives:
% 158.62/25.04  | 
% 158.62/25.04  | Case 1:
% 158.62/25.04  | | 
% 158.62/25.04  | |   (15)  all_56_8 = e0 & op(e1, e1) = e0
% 158.62/25.04  | | 
% 158.62/25.04  | | ALPHA: (15) implies:
% 158.62/25.04  | |   (16)  op(e1, e1) = e0
% 158.62/25.04  | | 
% 158.62/25.04  | | REF_CLOSE: (4), (5), (13), (16) are inconsistent by sub-proof #914.
% 158.62/25.04  | | 
% 158.62/25.04  | Case 2:
% 158.62/25.04  | | 
% 158.62/25.04  | |   (17)  all_56_11 = e0 & op(e1, e0) = e0
% 158.62/25.04  | | 
% 158.62/25.04  | | ALPHA: (17) implies:
% 158.62/25.04  | |   (18)  all_56_11 = e0
% 158.62/25.04  | | 
% 158.62/25.04  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 158.62/25.04  | |            (18) are inconsistent by sub-proof #883.
% 158.62/25.04  | | 
% 158.62/25.04  | End of split
% 158.62/25.04  | 
% 158.62/25.04  End of proof
% 158.62/25.04  
% 158.62/25.04  Sub-proof #160 shows that the following formulas are inconsistent:
% 158.62/25.04  ----------------------------------------------------------------
% 158.62/25.04    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.04    (2)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.62/25.04    (3)  op(e2, e1) = all_52_9
% 158.62/25.04    (4)  op(e2, e0) = all_52_13
% 158.62/25.04    (5)   ~ (all_52_9 = e2)
% 158.62/25.04    (6)   ~ (all_52_13 = e2)
% 158.62/25.04  
% 158.62/25.04  Begin of proof
% 158.62/25.04  | 
% 158.62/25.04  | BETA: splitting (2) gives:
% 158.62/25.04  | 
% 158.62/25.04  | Case 1:
% 158.62/25.04  | | 
% 158.62/25.04  | |   (7)  all_56_5 = e2 & op(e2, e1) = e2
% 158.62/25.04  | | 
% 158.62/25.04  | | ALPHA: (7) implies:
% 158.62/25.04  | |   (8)  op(e2, e1) = e2
% 158.62/25.04  | | 
% 158.62/25.04  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1002.
% 158.62/25.04  | | 
% 158.62/25.04  | Case 2:
% 158.62/25.04  | | 
% 158.62/25.04  | |   (9)  all_56_10 = e2 & op(e2, e0) = e2
% 158.62/25.04  | | 
% 158.62/25.04  | | ALPHA: (9) implies:
% 158.62/25.04  | |   (10)  op(e2, e0) = e2
% 158.62/25.04  | | 
% 158.62/25.04  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #996.
% 158.62/25.04  | | 
% 158.62/25.04  | End of split
% 158.62/25.04  | 
% 158.62/25.04  End of proof
% 158.62/25.04  
% 158.62/25.04  Sub-proof #161 shows that the following formulas are inconsistent:
% 158.62/25.04  ----------------------------------------------------------------
% 158.62/25.04    (1)  all_56_13 = e3 & op(e0, e2) = e3
% 158.62/25.04    (2)  all_56_13 = e1
% 158.62/25.04    (3)   ~ (e3 = e1)
% 158.62/25.04  
% 158.62/25.04  Begin of proof
% 158.62/25.04  | 
% 158.62/25.04  | ALPHA: (1) implies:
% 158.62/25.04  |   (4)  all_56_13 = e3
% 158.62/25.04  | 
% 158.62/25.04  | COMBINE_EQS: (2), (4) imply:
% 158.62/25.04  |   (5)  e3 = e1
% 158.62/25.04  | 
% 158.62/25.04  | REDUCE: (3), (5) imply:
% 158.62/25.04  |   (6)  $false
% 158.62/25.04  | 
% 158.62/25.04  | CLOSE: (6) is inconsistent.
% 158.62/25.04  | 
% 158.62/25.04  End of proof
% 158.62/25.04  
% 158.62/25.04  Sub-proof #162 shows that the following formulas are inconsistent:
% 158.62/25.04  ----------------------------------------------------------------
% 158.62/25.04    (1)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.62/25.04    (2)  all_54_9 = all_52_6
% 158.62/25.04    (3)   ~ (all_52_1 = e2)
% 158.62/25.04    (4)   ~ (all_52_6 = e2)
% 158.62/25.04    (5)   ~ (all_52_14 = e0)
% 158.62/25.04    (6)   ~ (all_52_4 = all_52_12)
% 158.62/25.04    (7)   ~ (all_52_4 = all_52_6)
% 158.62/25.04    (8)  all_56_9 = e2
% 158.62/25.04    (9)   ~ (all_52_6 = all_52_7)
% 158.62/25.04    (10)  op(e0, e3) = e2
% 158.62/25.04    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.62/25.04          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.62/25.04    (12)  op(e0, e1) = all_52_11
% 158.62/25.04    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.04            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.04    (14)  op(e0, e3) = all_52_3
% 158.62/25.04    (15)  op(e3, e1) = all_52_8
% 158.62/25.04    (16)  op(e1, e1) = e2
% 158.62/25.04    (17)   ~ (all_52_4 = e1)
% 158.62/25.04    (18)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.62/25.04    (19)  op(e2, e2) = e2
% 158.62/25.04    (20)   ~ (all_52_6 = e3)
% 158.62/25.04    (21)  op(e1, e3) = all_52_2
% 158.62/25.04    (22)  op(e0, e2) = all_52_7
% 158.62/25.04    (23)  all_54_1 = all_52_4
% 158.62/25.04    (24)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.62/25.04    (25)   ~ (all_52_6 = all_52_14)
% 158.62/25.04    (26)   ~ (all_52_2 = e1)
% 158.62/25.04    (27)  op(e0, e0) = e0
% 158.62/25.04    (28)   ~ (all_52_14 = e2)
% 158.62/25.04    (29)  op(e2, e3) = all_52_1
% 158.62/25.04    (30)  op(e3, e2) = all_52_4
% 158.62/25.04    (31)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.62/25.04          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.62/25.04    (32)  op(e2, e1) = all_52_9
% 158.62/25.04    (33)  op(e2, e0) = all_52_13
% 158.62/25.04    (34)   ~ (all_52_11 = e0)
% 158.62/25.04    (35)  op(e3, e0) = all_52_12
% 158.62/25.04    (36)   ~ (all_52_4 = all_52_8)
% 158.62/25.04    (37)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.62/25.04            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.62/25.04            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.62/25.04            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.62/25.04              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.62/25.04          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.62/25.04            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.62/25.04              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.62/25.04            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.62/25.04              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.62/25.04          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.62/25.04            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.62/25.04              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.62/25.04            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.62/25.04              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.62/25.04          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.62/25.04            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.62/25.04            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.62/25.04              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.62/25.04            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.62/25.04            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.62/25.04            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.62/25.04            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.62/25.04              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.62/25.04            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.62/25.04          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.62/25.04            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.62/25.04              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.62/25.04            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.62/25.04            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.62/25.04          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.62/25.04            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.62/25.04              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.62/25.04            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.62/25.04            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.62/25.04          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.62/25.04            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.62/25.04              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.62/25.04            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.62/25.04              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.62/25.04          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.62/25.04            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.62/25.04            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.62/25.04            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.62/25.04            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.62/25.04            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.04            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.62/25.04            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.62/25.04              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.62/25.04            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.62/25.04            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.62/25.04            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.62/25.04            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.62/25.04              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.62/25.04            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.62/25.04          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.62/25.04            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.62/25.04              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.62/25.04              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.62/25.04            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.62/25.04            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.62/25.04            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.62/25.04            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.62/25.04              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.62/25.04            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.62/25.04          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.62/25.04            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.62/25.04              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.62/25.04            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.62/25.04              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.62/25.04          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.62/25.04            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.62/25.04              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.62/25.04              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.62/25.04            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.62/25.04          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.62/25.04            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.62/25.04            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.62/25.04                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.62/25.04                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.62/25.04                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.04                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.62/25.04                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.04                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.62/25.04                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.04                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.62/25.04                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.04                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.62/25.04                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.04                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.62/25.04                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.62/25.04                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.62/25.04                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.62/25.04                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.62/25.04                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.62/25.04                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.62/25.04                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.62/25.04                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.62/25.04                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.62/25.04                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.62/25.04                op(e0, e1) = e0)))
% 158.62/25.04    (38)   ~ (all_52_9 = e2)
% 158.62/25.04    (39)  all_54_11 = all_52_14
% 158.62/25.04    (40)  op(e3, e2) = e3
% 158.62/25.04    (41)  all_56_1 = e3
% 158.62/25.04    (42)   ~ (all_52_13 = e2)
% 158.62/25.04  
% 158.62/25.04  Begin of proof
% 158.62/25.04  | 
% 158.62/25.04  | BETA: splitting (18) gives:
% 158.62/25.04  | 
% 158.62/25.04  | Case 1:
% 158.62/25.04  | | 
% 158.62/25.04  | |   (43)  all_54_11 = e2
% 158.62/25.04  | | 
% 158.62/25.04  | | REF_CLOSE: (28), (39), (43) are inconsistent by sub-proof #588.
% 158.62/25.04  | | 
% 158.62/25.04  | Case 2:
% 158.62/25.04  | | 
% 158.62/25.04  | |   (44)   ~ (all_54_11 = e2)
% 158.62/25.04  | |   (45)  all_54_11 = e1 | all_54_11 = e0
% 158.62/25.04  | | 
% 158.62/25.04  | | BETA: splitting (45) gives:
% 158.62/25.04  | | 
% 158.62/25.04  | | Case 1:
% 158.62/25.04  | | | 
% 158.62/25.04  | | |   (46)  all_54_11 = e1
% 158.62/25.04  | | | 
% 158.62/25.04  | | | COMBINE_EQS: (39), (46) imply:
% 158.62/25.04  | | |   (47)  all_52_14 = e1
% 158.62/25.04  | | | 
% 158.62/25.04  | | | SIMP: (47) implies:
% 158.62/25.04  | | |   (48)  all_52_14 = e1
% 158.62/25.04  | | | 
% 158.62/25.04  | | | REDUCE: (25), (48) imply:
% 158.62/25.04  | | |   (49)   ~ (all_52_6 = e1)
% 158.62/25.04  | | | 
% 158.62/25.04  | | | REDUCE: (28), (48) imply:
% 158.62/25.04  | | |   (50)   ~ (e2 = e1)
% 158.62/25.04  | | | 
% 158.62/25.04  | | | SIMP: (50) implies:
% 158.62/25.04  | | |   (51)   ~ (e2 = e1)
% 158.62/25.04  | | | 
% 158.62/25.04  | | | BETA: splitting (1) gives:
% 158.62/25.04  | | | 
% 158.62/25.04  | | | Case 1:
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | |   (52)  all_54_9 = e3
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | | REF_CLOSE: (2), (20), (52) are inconsistent by sub-proof #656.
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | Case 2:
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | |   (53)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | | BETA: splitting (53) gives:
% 158.62/25.04  | | | | 
% 158.62/25.04  | | | | Case 1:
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | |   (54)  all_54_9 = e2
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | | REF_CLOSE: (2), (4), (54) are inconsistent by sub-proof #676.
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | Case 2:
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | |   (55)   ~ (all_54_9 = e2)
% 158.62/25.04  | | | | |   (56)  all_54_9 = e1 | all_54_9 = e0
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | | BETA: splitting (56) gives:
% 158.62/25.04  | | | | | 
% 158.62/25.04  | | | | | Case 1:
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | |   (57)  all_54_9 = e1
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | REF_CLOSE: (2), (49), (57) are inconsistent by sub-proof #675.
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | Case 2:
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | |   (58)  all_54_9 = e0
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | COMBINE_EQS: (2), (58) imply:
% 158.62/25.04  | | | | | |   (59)  all_52_6 = e0
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | SIMP: (59) implies:
% 158.62/25.04  | | | | | |   (60)  all_52_6 = e0
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | REDUCE: (7), (60) imply:
% 158.62/25.04  | | | | | |   (61)   ~ (all_52_4 = e0)
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | REDUCE: (9), (60) imply:
% 158.62/25.04  | | | | | |   (62)   ~ (all_52_7 = e0)
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | SIMP: (62) implies:
% 158.62/25.04  | | | | | |   (63)   ~ (all_52_7 = e0)
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | REDUCE: (4), (60) imply:
% 158.62/25.04  | | | | | |   (64)   ~ (e2 = e0)
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | SIMP: (64) implies:
% 158.62/25.04  | | | | | |   (65)   ~ (e2 = e0)
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | REDUCE: (49), (60) imply:
% 158.62/25.04  | | | | | |   (66)   ~ (e1 = e0)
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | SIMP: (66) implies:
% 158.62/25.04  | | | | | |   (67)   ~ (e1 = e0)
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | BETA: splitting (24) gives:
% 158.62/25.04  | | | | | | 
% 158.62/25.04  | | | | | | Case 1:
% 158.62/25.04  | | | | | | | 
% 158.62/25.04  | | | | | | |   (68)  all_54_1 = e3
% 158.62/25.04  | | | | | | | 
% 158.62/25.04  | | | | | | | COMBINE_EQS: (23), (68) imply:
% 158.62/25.04  | | | | | | |   (69)  all_52_4 = e3
% 158.62/25.04  | | | | | | | 
% 158.62/25.04  | | | | | | | REDUCE: (6), (69) imply:
% 158.62/25.04  | | | | | | |   (70)   ~ (all_52_12 = e3)
% 158.62/25.04  | | | | | | | 
% 158.62/25.04  | | | | | | | SIMP: (70) implies:
% 158.62/25.04  | | | | | | |   (71)   ~ (all_52_12 = e3)
% 158.62/25.04  | | | | | | | 
% 158.62/25.04  | | | | | | | REDUCE: (17), (69) imply:
% 158.62/25.04  | | | | | | |   (72)   ~ (e3 = e1)
% 158.62/25.04  | | | | | | | 
% 158.62/25.04  | | | | | | | REDUCE: (61), (69) imply:
% 158.62/25.04  | | | | | | |   (73)   ~ (e3 = e0)
% 158.62/25.04  | | | | | | | 
% 158.62/25.04  | | | | | | | BETA: splitting (37) gives:
% 158.62/25.04  | | | | | | | 
% 158.62/25.04  | | | | | | | Case 1:
% 158.62/25.04  | | | | | | | | 
% 158.62/25.04  | | | | | | | |   (74)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.62/25.04  | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.62/25.04  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.62/25.04  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.62/25.04  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.62/25.04  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 158.62/25.04  | | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.62/25.04  | | | | | | | |           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.62/25.04  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 158.62/25.04  | | | | | | | |           = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 =
% 158.62/25.04  | | | | | | | |           e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.62/25.04  | | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 158.62/25.04  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.62/25.04  | | | | | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.62/25.04  | | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.62/25.04  | | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.62/25.04  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.62/25.04  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.62/25.04  | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.62/25.04  | | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.62/25.04  | | | | | | | |           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.62/25.04  | | | | | | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 158.62/25.04  | | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.62/25.04  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 158.62/25.04  | | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.62/25.04  | | | | | | | |           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.62/25.04  | | | | | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.62/25.04  | | | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 158.62/25.04  | | | | | | | |         (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.62/25.04  | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2)
% 158.62/25.04  | | | | | | | |           = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.62/25.04  | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~
% 158.62/25.04  | | | | | | | |           (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.62/25.04  | | | | | | | |         (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.62/25.04  | | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.62/25.04  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.62/25.04  | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.62/25.04  | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1
% 158.62/25.04  | | | | | | | |           & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.62/25.04  | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_4
% 158.62/25.04  | | | | | | | |           = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 158.62/25.04  | | | | | | | |             e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1
% 158.62/25.04  | | | | | | | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 158.62/25.04  | | | | | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.62/25.04  | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 158.62/25.04  | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2 =
% 158.62/25.04  | | | | | | | |           e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.62/25.04  | | | | | | | |             e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.04  | | | | | | | |           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 158.62/25.04  | | | | | | | |         (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~
% 158.62/25.04  | | | | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0)
% 158.62/25.04  | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.62/25.04  | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~
% 158.62/25.04  | | | | | | | |           (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.62/25.04  | | | | | | | | 
% 158.62/25.04  | | | | | | | | BETA: splitting (74) gives:
% 158.62/25.04  | | | | | | | | 
% 158.62/25.04  | | | | | | | | Case 1:
% 158.62/25.04  | | | | | | | | | 
% 158.62/25.04  | | | | | | | | |   (75)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.62/25.04  | | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.62/25.04  | | | | | | | | |           & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.62/25.04  | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.62/25.04  | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.62/25.04  | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.62/25.04  | | | | | | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.62/25.04  | | | | | | | | |           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 158.62/25.04  | | | | | | | | |           & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1,
% 158.62/25.04  | | | | | | | | |             e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.62/25.04  | | | | | | | | |         (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.62/25.04  | | | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.62/25.04  | | | | | | | | |             e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.62/25.04  | | | | | | | | |           $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 158.62/25.04  | | | | | | | | |           all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 158.62/25.04  | | | | | | | | |           e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 158.62/25.04  | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.62/25.04  | | | | | | | | |           all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 158.62/25.04  | | | | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 158.62/25.04  | | | | | | | | |             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.62/25.04  | | | | | | | | |         (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.62/25.04  | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3
% 158.62/25.04  | | | | | | | | |           & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.62/25.04  | | | | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 158.62/25.04  | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.62/25.04  | | | | | | | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 158.62/25.04  | | | | | | | | |           (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.62/25.04  | | | | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.62/25.04  | | | | | | | | |           $i(all_57_12))
% 158.62/25.04  | | | | | | | | | 
% 158.62/25.04  | | | | | | | | | REF_CLOSE: (3), (13), (21), (26), (29), (32), (38), (75) are
% 158.62/25.04  | | | | | | | | |            inconsistent by sub-proof #652.
% 158.62/25.04  | | | | | | | | | 
% 158.62/25.04  | | | | | | | | Case 2:
% 158.62/25.04  | | | | | | | | | 
% 158.62/25.04  | | | | | | | | |   (76)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.62/25.04  | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.62/25.04  | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.62/25.04  | | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 & 
% 158.62/25.04  | | | | | | | | |           ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.62/25.04  | | | | | | | | |         (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.62/25.04  | | | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.62/25.04  | | | | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.62/25.04  | | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.62/25.04  | | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) =
% 158.62/25.04  | | | | | | | | |           e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.62/25.04  | | | | | | | | |           = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.62/25.04  | | | | | | | | |           all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 158.62/25.04  | | | | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1,
% 158.62/25.04  | | | | | | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.62/25.04  | | | | | | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.62/25.04  | | | | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2
% 158.62/25.04  | | | | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.04  | | | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 158.62/25.04  | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 158.62/25.04  | | | | | | | | |           e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.62/25.04  | | | | | | | | |           op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.62/25.04  | | | | | | | | |           all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 158.62/25.04  | | | | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1,
% 158.62/25.04  | | | | | | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.62/25.04  | | | | | | | | |         (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 158.62/25.04  | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.62/25.04  | | | | | | | | | 
% 158.62/25.04  | | | | | | | | | BETA: splitting (76) gives:
% 158.62/25.04  | | | | | | | | | 
% 158.62/25.04  | | | | | | | | | Case 1:
% 158.62/25.04  | | | | | | | | | | 
% 158.62/25.04  | | | | | | | | | |   (77)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.62/25.04  | | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.62/25.04  | | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.62/25.04  | | | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &
% 158.62/25.04  | | | | | | | | | |            ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 158.62/25.04  | | | | | | | | | |         | (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 158.62/25.04  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 158.62/25.04  | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.62/25.04  | | | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.62/25.04  | | | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3)
% 158.62/25.04  | | | | | | | | | |           = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.62/25.04  | | | | | | | | | |             e1) = all_57_14 & $i(all_57_14))
% 158.62/25.04  | | | | | | | | | | 
% 158.62/25.04  | | | | | | | | | | BETA: splitting (77) gives:
% 158.62/25.04  | | | | | | | | | | 
% 158.62/25.04  | | | | | | | | | | Case 1:
% 158.62/25.04  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (78)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.62/25.05  | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.62/25.05  | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.62/25.05  | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.62/25.05  | | | | | | | | | | |           = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 158.62/25.05  | | | | | | | | | | |             e2) = e3)
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | BETA: splitting (78) gives:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | |   (79)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.62/25.05  | | | | | | | | | | | |         ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.62/25.05  | | | | | | | | | | | |         op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.62/25.05  | | | | | | | | | | | |         e3 & $i(all_57_10)
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | ALPHA: (79) implies:
% 158.62/25.05  | | | | | | | | | | | |   (80)  op(e0, e3) = e0
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | REF_CLOSE: (10), (13), (14), (65), (80) are inconsistent by
% 158.62/25.05  | | | | | | | | | | | |            sub-proof #689.
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | |   (81)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) &
% 158.62/25.05  | | | | | | | | | | | |         op(e3, e3) = e3 & op(e3, e2) = e3
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | ALPHA: (81) implies:
% 158.62/25.05  | | | | | | | | | | | |   (82)  op(e3, e3) = e3
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | REF_CLOSE: (8), (11), (13), (31), (41), (51), (65), (67),
% 158.62/25.05  | | | | | | | | | | | |            (72), (73), (82) are inconsistent by sub-proof
% 158.62/25.05  | | | | | | | | | | | |            #947.
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (83)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 158.62/25.05  | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 158.62/25.05  | | | | | | | | | | |             e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.62/25.05  | | | | | | | | | | |           = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 158.62/25.05  | | | | | | | | | | |           all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 158.62/25.05  | | | | | | | | | | |             e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.62/25.05  | | | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | | | | |           $i(all_57_14))
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | REF_CLOSE: (13), (21), (26), (33), (42), (83) are
% 158.62/25.05  | | | | | | | | | | |            inconsistent by sub-proof #651.
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | |   (84)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.62/25.05  | | | | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.62/25.05  | | | | | | | | | |             e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.62/25.05  | | | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.62/25.05  | | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2)
% 158.62/25.05  | | | | | | | | | |           = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1,
% 158.62/25.05  | | | | | | | | | |             e1) = all_57_14 & $i(all_57_14)) | (all_57_2 =
% 158.62/25.05  | | | | | | | | | |           e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.62/25.05  | | | | | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.62/25.05  | | | | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.62/25.05  | | | | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.62/25.05  | | | | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 158.62/25.05  | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 158.62/25.05  | | | | | | | | | |           & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1
% 158.62/25.05  | | | | | | | | | |           & op(e1, e1) = e1)
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | BETA: splitting (84) gives:
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (85)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 158.62/25.05  | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.62/25.05  | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 158.62/25.05  | | | | | | | | | | |           = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.62/25.05  | | | | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 158.62/25.05  | | | | | | | | | | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | REF_CLOSE: (13), (19), (21), (26), (51), (85) are
% 158.62/25.05  | | | | | | | | | | |            inconsistent by sub-proof #650.
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (86)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.62/25.05  | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 158.62/25.05  | | | | | | | | | | |             e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.62/25.05  | | | | | | | | | | |           = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.62/25.05  | | | | | | | | | | |           all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.62/25.05  | | | | | | | | | | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.62/25.05  | | | | | | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.62/25.05  | | | | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.62/25.05  | | | | | | | | | | |           &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | | |           e1)
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | BETA: splitting (86) gives:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | |   (87)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.62/25.05  | | | | | | | | | | | |         ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 158.62/25.05  | | | | | | | | | | | |         = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.62/25.05  | | | | | | | | | | | |         $i(all_57_14)
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | ALPHA: (87) implies:
% 158.62/25.05  | | | | | | | | | | | |   (88)  op(e0, e1) = e0
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | REF_CLOSE: (12), (13), (34), (88) are inconsistent by
% 158.62/25.05  | | | | | | | | | | | |            sub-proof #966.
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | |   (89)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 158.62/25.05  | | | | | | | | | | | |           ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.62/25.05  | | | | | | | | | | | |           op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 158.62/25.05  | | | | | | | | | | | |           = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 158.62/25.05  | | | | | | | | | | | |             e1) = e1)
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | BETA: splitting (89) gives:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | |   (90)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 158.62/25.05  | | | | | | | | | | | | |         ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.62/25.05  | | | | | | | | | | | | |         op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | | | | |         e3 & $i(all_57_10)
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | | ALPHA: (90) implies:
% 158.62/25.05  | | | | | | | | | | | | |   (91)  op(e1, e3) = e1
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | | REF_CLOSE: (13), (21), (26), (91) are inconsistent by
% 158.62/25.05  | | | | | | | | | | | | |            sub-proof #990.
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | |   (92)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 158.62/25.05  | | | | | | | | | | | | |         op(e1, e3) = e1 & op(e1, e1) = e1
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | | ALPHA: (92) implies:
% 158.62/25.05  | | | | | | | | | | | | |   (93)  op(e1, e1) = e1
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | | REF_CLOSE: (13), (16), (51), (93) are inconsistent by
% 158.62/25.05  | | | | | | | | | | | | |            sub-proof #986.
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | 
% 158.62/25.05  | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | 
% 158.62/25.05  | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | 
% 158.62/25.05  | | | | | | | |   (94)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.62/25.05  | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.62/25.05  | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.62/25.05  | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.62/25.05  | | | | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5
% 158.62/25.05  | | | | | | | |           = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 158.62/25.05  | | | | | | | |             e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1
% 158.62/25.05  | | | | | | | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.62/25.05  | | | | | | | |           all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.62/25.05  | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1)
% 158.62/25.05  | | | | | | | |           = e0 & op(e0, e0) = e1 & $i(all_57_14)) | (all_57_3 =
% 158.62/25.05  | | | | | | | |           e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 158.62/25.05  | | | | | | | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.62/25.05  | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.62/25.05  | | | | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1,
% 158.62/25.05  | | | | | | | |             e2) = e1 & op(e1, e1) = e1) | (all_57_4 = e3 &
% 158.62/25.05  | | | | | | | |           all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.62/25.05  | | | | | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 158.62/25.05  | | | | | | | |           = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 158.62/25.05  | | | | | | | |           e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.62/25.05  | | | | | | | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.62/25.05  | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1
% 158.62/25.05  | | | | | | | |           & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 158.62/25.05  | | | | | | | |             e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 &
% 158.62/25.05  | | | | | | | |           all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 158.62/25.05  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 158.62/25.05  | | | | | | | |           = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 =
% 158.62/25.05  | | | | | | | |           e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 158.62/25.05  | | | | | | | |           op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.62/25.05  | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1
% 158.62/25.05  | | | | | | | |           & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.62/25.05  | | | | | | | |             e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 158.62/25.05  | | | | | | | |           all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 158.62/25.05  | | | | | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3)
% 158.62/25.05  | | | | | | | |           = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 =
% 158.62/25.05  | | | | | | | |           e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 158.62/25.05  | | | | | | | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.62/25.05  | | | | | | | |           op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.62/25.05  | | | | | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3,
% 158.62/25.05  | | | | | | | |             e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.62/25.05  | | | | | | | |           all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 &
% 158.62/25.05  | | | | | | | |           op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1 & 
% 158.62/25.05  | | | | | | | |           ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 158.62/25.05  | | | | | | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 =
% 158.62/25.05  | | | | | | | |               e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.62/25.05  | | | | | | | |               (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 158.62/25.05  | | | | | | | |               e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 158.62/25.05  | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.62/25.05  | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 158.62/25.05  | | | | | | | |               e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 158.62/25.05  | | | | | | | |               = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 158.62/25.05  | | | | | | | |               op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.05  | | | | | | | |               e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.62/25.05  | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 158.62/25.05  | | | | | | | |               e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 158.62/25.05  | | | | | | | |               op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.62/25.05  | | | | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.62/25.05  | | | | | | | |               (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 158.62/25.05  | | | | | | | |               e2 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_13
% 158.62/25.05  | | | | | | | |               = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.05  | | | | | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.62/25.05  | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 =
% 158.62/25.05  | | | | | | | |                 e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.62/25.05  | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.62/25.05  | | | | | | | |                 e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.62/25.05  | | | | | | | |                 e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.62/25.05  | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2)
% 158.62/25.05  | | | | | | | |               = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.62/25.05  | | | | | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 158.62/25.05  | | | | | | | |               ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 158.62/25.05  | | | | | | | |               = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.62/25.05  | | | | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.62/25.05  | | | | | | | |                 e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.62/25.05  | | | | | | | |               op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0
% 158.62/25.05  | | | | | | | |               & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.62/25.05  | | | | | | | |               e0)))
% 158.62/25.05  | | | | | | | | 
% 158.62/25.05  | | | | | | | | BETA: splitting (94) gives:
% 158.62/25.05  | | | | | | | | 
% 158.62/25.05  | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | 
% 158.62/25.05  | | | | | | | | |   (95)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.62/25.05  | | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3
% 158.62/25.05  | | | | | | | | |           & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.62/25.05  | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 158.62/25.05  | | | | | | | | |           e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.62/25.05  | | | | | | | | |           = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.62/25.05  | | | | | | | | |           all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 158.62/25.05  | | | | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.62/25.05  | | | | | | | | |             e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.62/25.05  | | | | | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.62/25.05  | | | | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.62/25.05  | | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 158.62/25.05  | | | | | | | | |           all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 158.62/25.05  | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 158.62/25.05  | | | | | | | | |           op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.62/25.05  | | | | | | | | |           all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.62/25.05  | | | | | | | | |           op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.62/25.05  | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.62/25.05  | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.62/25.05  | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 158.62/25.05  | | | | | | | | |           all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.62/25.05  | | | | | | | | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.62/25.05  | | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.62/25.05  | | | | | | | | |           e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_14))
% 158.62/25.05  | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | BETA: splitting (95) gives:
% 158.62/25.05  | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | |   (96)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.62/25.05  | | | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) =
% 158.62/25.05  | | | | | | | | | |           e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.62/25.05  | | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 158.62/25.05  | | | | | | | | | |           = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 158.62/25.05  | | | | | | | | | |             e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 158.62/25.05  | | | | | | | | | |           e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.62/25.05  | | | | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.62/25.05  | | | | | | | | | |             e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.62/25.05  | | | | | | | | | |           $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 &
% 158.62/25.05  | | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2)
% 158.62/25.05  | | | | | | | | | |           = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.62/25.05  | | | | | | | | | |           op(e0, e0) = e1 & $i(all_57_14))
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | BETA: splitting (96) gives:
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (97)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.62/25.05  | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 158.62/25.05  | | | | | | | | | | |             e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.62/25.05  | | | | | | | | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 158.62/25.05  | | | | | | | | | | |             e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.62/25.05  | | | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | | | | |           $i(all_57_14))
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | BETA: splitting (97) gives:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | |   (98)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.62/25.05  | | | | | | | | | | | |         ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 158.62/25.05  | | | | | | | | | | | |         = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | | | | | |         $i(all_57_14)
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | ALPHA: (98) implies:
% 158.62/25.05  | | | | | | | | | | | |   (99)  op(e3, e1) = e3
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | REF_CLOSE: (13), (15), (23), (24), (30), (36), (40), (99) are
% 158.62/25.05  | | | | | | | | | | | |            inconsistent by sub-proof #403.
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | |   (100)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 158.62/25.05  | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 158.62/25.05  | | | | | | | | | | | |          = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | | | | | |          $i(all_57_14)
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | ALPHA: (100) implies:
% 158.62/25.05  | | | | | | | | | | | |   (101)  op(e2, e2) = e1
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | REF_CLOSE: (13), (19), (51), (101) are inconsistent by
% 158.62/25.05  | | | | | | | | | | | |            sub-proof #993.
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (102)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 158.62/25.05  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.62/25.05  | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 158.62/25.05  | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.62/25.05  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.62/25.05  | | | | | | | | | | |            $i(all_57_14))
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | REF_CLOSE: (12), (13), (32), (34), (38), (102) are
% 158.62/25.05  | | | | | | | | | | |            inconsistent by sub-proof #199.
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | |   (103)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 158.62/25.05  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.62/25.05  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.62/25.05  | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.62/25.05  | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.62/25.05  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.62/25.05  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.62/25.05  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3
% 158.62/25.05  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3
% 158.62/25.05  | | | | | | | | | |            & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 =
% 158.62/25.05  | | | | | | | | | |            e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.62/25.05  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | BETA: splitting (103) gives:
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (104)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 158.62/25.05  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.62/25.05  | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.62/25.05  | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.62/25.05  | | | | | | | | | | |              e1) = e1)
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | REF_CLOSE: (13), (16), (33), (42), (104) are inconsistent by
% 158.62/25.05  | | | | | | | | | | |            sub-proof #198.
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (105)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.62/25.05  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.62/25.05  | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.62/25.05  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 158.62/25.05  | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 158.62/25.05  | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.62/25.05  | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 158.62/25.05  | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.62/25.05  | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | BETA: splitting (105) gives:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | |   (106)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.62/25.05  | | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.62/25.05  | | | | | | | | | | | |          op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.62/25.05  | | | | | | | | | | | |          e3 & $i(all_57_10)
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | ALPHA: (106) implies:
% 158.62/25.05  | | | | | | | | | | | |   (107)  op(e0, e3) = e0
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | REF_CLOSE: (10), (13), (14), (65), (107) are inconsistent by
% 158.62/25.05  | | | | | | | | | | | |            sub-proof #689.
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | |   (108)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 158.62/25.05  | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 158.62/25.05  | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.62/25.05  | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 158.62/25.05  | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 158.62/25.05  | | | | | | | | | | | |            & $i(all_57_14))
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | BETA: splitting (108) gives:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | |   (109)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 158.62/25.05  | | | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e1) = e3
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | | ALPHA: (109) implies:
% 158.62/25.05  | | | | | | | | | | | | |   (110)  op(e3, e3) = e3
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | | REF_CLOSE: (8), (11), (13), (31), (41), (51), (65), (67),
% 158.62/25.05  | | | | | | | | | | | | |            (72), (73), (110) are inconsistent by sub-proof
% 158.62/25.05  | | | | | | | | | | | | |            #947.
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | |   (111)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 158.62/25.05  | | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 158.62/25.05  | | | | | | | | | | | | |          = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.62/25.05  | | | | | | | | | | | | |          $i(all_57_14)
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | | ALPHA: (111) implies:
% 158.62/25.05  | | | | | | | | | | | | |   (112)  op(e3, e1) = e3
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | | REF_CLOSE: (13), (15), (23), (24), (30), (36), (40), (112)
% 158.62/25.05  | | | | | | | | | | | | |            are inconsistent by sub-proof #403.
% 158.62/25.05  | | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | 
% 158.62/25.05  | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | 
% 158.62/25.05  | | | | | | | | |   (113)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.62/25.05  | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.62/25.05  | | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.62/25.05  | | | | | | | | |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 & 
% 158.62/25.05  | | | | | | | | |            ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.62/25.05  | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 158.62/25.05  | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 158.62/25.05  | | | | | | | | |            e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.62/25.05  | | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.62/25.05  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.62/25.05  | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 158.62/25.05  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 &
% 158.62/25.05  | | | | | | | | |            all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 158.62/25.05  | | | | | | | | |              e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.62/25.05  | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 158.62/25.05  | | | | | | | | |          | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 158.62/25.05  | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 158.62/25.05  | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 158.62/25.05  | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14
% 158.62/25.05  | | | | | | | | |            = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0)
% 158.62/25.05  | | | | | | | | |            = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.62/25.05  | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.62/25.05  | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.62/25.05  | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.62/25.05  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.62/25.05  | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 158.62/25.05  | | | | | | | | |                = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.62/25.05  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.62/25.05  | | | | | | | | |                  = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.62/25.05  | | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 158.62/25.05  | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.62/25.05  | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.62/25.05  | | | | | | | | |                 ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.62/25.05  | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 158.62/25.05  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.62/25.05  | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 158.62/25.05  | | | | | | | | |                = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.62/25.05  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.62/25.05  | | | | | | | | |                  = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.62/25.05  | | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.62/25.05  | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.62/25.05  | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.62/25.05  | | | | | | | | |                 ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.62/25.05  | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0
% 158.62/25.05  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.62/25.05  | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 158.62/25.05  | | | | | | | | |                = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.62/25.05  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.62/25.05  | | | | | | | | |                  = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.62/25.05  | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.62/25.05  | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.62/25.05  | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.62/25.05  | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 158.62/25.05  | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 158.62/25.05  | | | | | | | | |                = e0)))
% 158.62/25.05  | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | BETA: splitting (113) gives:
% 158.62/25.05  | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | |   (114)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.62/25.05  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.62/25.05  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.62/25.05  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.62/25.05  | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.62/25.05  | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.62/25.05  | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2)
% 158.62/25.05  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0
% 158.62/25.05  | | | | | | | | | |            & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10
% 158.62/25.05  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 158.62/25.05  | | | | | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.62/25.05  | | | | | | | | | |            $i(all_57_10))
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | BETA: splitting (114) gives:
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (115)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.62/25.05  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.62/25.05  | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.62/25.05  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.62/25.05  | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.62/25.05  | | | | | | | | | | |              e1) = e2)
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | REF_CLOSE: (13), (27), (32), (38), (65), (115) are
% 158.62/25.05  | | | | | | | | | | |            inconsistent by sub-proof #978.
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (116)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 158.62/25.05  | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 158.62/25.05  | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.62/25.05  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 158.62/25.05  | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 158.62/25.05  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.62/25.05  | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.62/25.05  | | | | | | | | | | |            $i(all_57_10))
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | REF_CLOSE: (10), (13), (14), (19), (51), (65), (116) are
% 158.62/25.05  | | | | | | | | | | |            inconsistent by sub-proof #196.
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | |   (117)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 158.62/25.05  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.62/25.05  | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.62/25.05  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.62/25.05  | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.62/25.05  | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 & 
% 158.62/25.05  | | | | | | | | | |            ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2)
% 158.62/25.05  | | | | | | | | | |          | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.62/25.05  | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.62/25.05  | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.62/25.05  | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.62/25.05  | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.62/25.05  | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.05  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.62/25.05  | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.62/25.05  | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.05  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.62/25.05  | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.62/25.05  | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.05  | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.62/25.05  | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.62/25.05  | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.05  | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.62/25.05  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 = e2
% 158.62/25.05  | | | | | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.05  | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.62/25.05  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 = e1
% 158.62/25.05  | | | | | | | | | |                & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.05  | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.62/25.05  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 = e0
% 158.62/25.05  | | | | | | | | | |                &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.62/25.05  | | | | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.62/25.05  | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.62/25.05  | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.62/25.05  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.62/25.05  | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.62/25.05  | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.62/25.05  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.62/25.05  | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.62/25.05  | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.62/25.05  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 158.62/25.05  | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.62/25.05  | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.62/25.05  | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 =
% 158.62/25.05  | | | | | | | | | |                e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | BETA: splitting (117) gives:
% 158.62/25.05  | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | |   (118)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 158.62/25.05  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.62/25.05  | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.62/25.05  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.62/25.05  | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.62/25.05  | | | | | | | | | | |              e0) = e3)
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | BETA: splitting (118) gives:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | Case 1:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | |   (119)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 158.62/25.05  | | | | | | | | | | | |          ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.62/25.05  | | | | | | | | | | | |          op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.62/25.05  | | | | | | | | | | | |          e2 & $i(all_57_12)
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | ALPHA: (119) implies:
% 158.62/25.05  | | | | | | | | | | | |   (120)  op(e0, e0) = e2
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | REF_CLOSE: (13), (27), (65), (120) are inconsistent by
% 158.62/25.05  | | | | | | | | | | | |            sub-proof #979.
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | |   (121)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 158.62/25.05  | | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e0) = e3
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | ALPHA: (121) implies:
% 158.62/25.05  | | | | | | | | | | | |   (122)  op(e3, e3) = e3
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | | REF_CLOSE: (8), (11), (13), (31), (41), (51), (65), (67),
% 158.62/25.05  | | | | | | | | | | | |            (72), (73), (122) are inconsistent by sub-proof
% 158.62/25.05  | | | | | | | | | | | |            #947.
% 158.62/25.05  | | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | | End of split
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.05  | | | | | | | | | | Case 2:
% 158.62/25.05  | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | |   (123)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.62/25.06  | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 158.62/25.06  | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 158.62/25.06  | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.62/25.06  | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.62/25.06  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.62/25.06  | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.62/25.06  | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.06  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.62/25.06  | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.62/25.06  | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.06  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.62/25.06  | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.62/25.06  | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.06  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.62/25.06  | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.62/25.06  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.62/25.06  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.62/25.06  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.62/25.06  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.62/25.06  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.62/25.06  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.62/25.06  | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.62/25.06  | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.62/25.06  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.62/25.06  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.62/25.06  | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.62/25.06  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.62/25.06  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.62/25.06  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.62/25.06  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.62/25.06  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.62/25.06  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.62/25.06  | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.62/25.06  | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.62/25.06  | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.62/25.06  | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.62/25.06  | | | | | | | | | | |                e0)))
% 158.62/25.06  | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | BETA: splitting (123) gives:
% 158.62/25.06  | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | Case 1:
% 158.62/25.06  | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | |   (124)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.62/25.06  | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 158.62/25.06  | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | ALPHA: (124) implies:
% 158.62/25.06  | | | | | | | | | | | |   (125)  op(e2, e0) = e2
% 158.62/25.06  | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | REF_CLOSE: (13), (33), (42), (125) are inconsistent by
% 158.62/25.06  | | | | | | | | | | | |            sub-proof #996.
% 158.62/25.06  | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | Case 2:
% 158.62/25.06  | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | |   (126)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.62/25.06  | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.62/25.06  | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.62/25.06  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.62/25.06  | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.62/25.06  | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.06  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.62/25.06  | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.62/25.06  | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.06  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.62/25.06  | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.62/25.06  | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.62/25.06  | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.62/25.06  | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.62/25.06  | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.62/25.06  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.62/25.06  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.62/25.06  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.62/25.06  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.62/25.06  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.62/25.06  | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.62/25.06  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.62/25.06  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.62/25.06  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.62/25.06  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.62/25.06  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.62/25.06  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.62/25.06  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.62/25.06  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.62/25.06  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.62/25.06  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.62/25.06  | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.62/25.06  | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.62/25.06  | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.62/25.06  | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.62/25.06  | | | | | | | | | | | |                e0)))
% 158.62/25.06  | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | BETA: splitting (126) gives:
% 158.62/25.06  | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | Case 1:
% 158.62/25.06  | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | |   (127)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.62/25.06  | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 158.62/25.06  | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | ALPHA: (127) implies:
% 158.62/25.06  | | | | | | | | | | | | |   (128)  op(e1, e1) = e1
% 158.62/25.06  | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | REF_CLOSE: (13), (16), (51), (128) are inconsistent by
% 158.62/25.06  | | | | | | | | | | | | |            sub-proof #986.
% 158.62/25.06  | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | Case 2:
% 158.62/25.06  | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | |   (129)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.62/25.06  | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.62/25.06  | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.62/25.06  | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.62/25.06  | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.62/25.06  | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.62/25.06  | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.62/25.06  | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.62/25.06  | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.62/25.06  | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.62/25.06  | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.62/25.06  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.62/25.06  | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 158.62/25.06  | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.62/25.06  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.62/25.06  | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.62/25.06  | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.62/25.06  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.62/25.06  | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.62/25.06  | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.62/25.06  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 158.62/25.06  | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.62/25.06  | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.62/25.06  | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.62/25.06  | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.62/25.06  | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.62/25.06  | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 158.62/25.06  | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.62/25.06  | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 158.62/25.06  | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.62/25.06  | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.62/25.06  | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.62/25.06  | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.62/25.06  | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.62/25.06  | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.62/25.06  | | | | | | | | | | | | |              e0))
% 158.62/25.06  | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | ALPHA: (129) implies:
% 158.62/25.06  | | | | | | | | | | | | |   (130)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.62/25.06  | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.62/25.06  | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.62/25.06  | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.62/25.06  | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.62/25.06  | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.62/25.06  | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.62/25.06  | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.62/25.06  | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.62/25.06  | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.62/25.06  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.62/25.06  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.62/25.06  | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06  | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.62/25.06  | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.62/25.06  | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.62/25.06  | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 158.62/25.06  | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.62/25.06  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.62/25.06  | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.62/25.06  | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.62/25.06  | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.62/25.06  | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 158.62/25.06  | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 158.62/25.06  | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 158.62/25.06  | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.62/25.06  | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.62/25.06  | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.62/25.06  | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.62/25.06  | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.62/25.06  | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.62/25.06  | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.62/25.06  | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | BETA: splitting (130) gives:
% 158.62/25.06  | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | Case 1:
% 158.62/25.06  | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | |   (131)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.62/25.06  | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.62/25.06  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.62/25.06  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.62/25.06  | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.62/25.06  | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.62/25.06  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.62/25.06  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.62/25.06  | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.62/25.06  | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.62/25.06  | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.62/25.06  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.62/25.06  | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06  | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.62/25.06  | | | | | | | | | | | | | |            e0)
% 158.62/25.06  | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 158.62/25.06  | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | Case 1:
% 158.62/25.06  | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | |   (132)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.62/25.06  | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.62/25.06  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.62/25.06  | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.62/25.06  | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.62/25.06  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.62/25.06  | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.62/25.06  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.62/25.06  | | | | | | | | | | | | | | |            e0)
% 158.62/25.06  | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (14), (16), (33), (42), (65), (132)
% 158.62/25.06  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #168.
% 158.62/25.06  | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | Case 2:
% 158.62/25.06  | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | |   (133)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.62/25.06  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 158.62/25.06  | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06  | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.62/25.06  | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.62/25.06  | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.62/25.06  | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.62/25.06  | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 158.62/25.06  | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | | Case 1:
% 158.62/25.06  | | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | | |   (134)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.62/25.06  | | | | | | | | | | | | | | | |          op(e0, e3) = e0
% 158.62/25.06  | | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 158.62/25.06  | | | | | | | | | | | | | | | |   (135)  op(e0, e3) = e0
% 158.62/25.06  | | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (14), (65), (135) are inconsistent by
% 158.62/25.06  | | | | | | | | | | | | | | | |            sub-proof #689.
% 158.62/25.06  | | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | | Case 2:
% 158.62/25.06  | | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | | |   (136)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.62/25.06  | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.62/25.06  | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.62/25.06  | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.62/25.06  | | | | | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.62/25.06  | | | | | | | | | | | | | | | |            op(e0, e2) = e0)
% 158.62/25.06  | | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (33), (35), (42), (71), (136) are
% 158.62/25.06  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #167.
% 158.62/25.06  | | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | | End of split
% 158.62/25.06  | | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | End of split
% 158.62/25.06  | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | Case 2:
% 158.62/25.06  | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | |   (137)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.62/25.06  | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.62/25.06  | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.62/25.06  | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.62/25.06  | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.62/25.06  | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.62/25.06  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.62/25.06  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.62/25.06  | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.62/25.06  | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.62/25.06  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.62/25.06  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.62/25.06  | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.62/25.06  | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.62/25.06  | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 158.62/25.06  | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.62/25.06  | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.62/25.06  | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (16), (22), (33), (34), (42), (63),
% 158.62/25.06  | | | | | | | | | | | | | |            (65), (137) are inconsistent by sub-proof #163.
% 158.62/25.06  | | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | | End of split
% 158.62/25.06  | | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | | End of split
% 158.62/25.06  | | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | | End of split
% 158.62/25.06  | | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | | End of split
% 158.62/25.06  | | | | | | | | | | 
% 158.62/25.06  | | | | | | | | | End of split
% 158.62/25.06  | | | | | | | | | 
% 158.62/25.06  | | | | | | | | End of split
% 158.62/25.06  | | | | | | | | 
% 158.62/25.06  | | | | | | | End of split
% 158.62/25.06  | | | | | | | 
% 158.62/25.06  | | | | | | Case 2:
% 158.62/25.06  | | | | | | | 
% 158.62/25.06  | | | | | | |   (138)   ~ (all_54_1 = e3)
% 158.62/25.06  | | | | | | | 
% 158.62/25.06  | | | | | | | REDUCE: (23), (138) imply:
% 158.62/25.06  | | | | | | |   (139)   ~ (all_52_4 = e3)
% 158.62/25.06  | | | | | | | 
% 158.62/25.06  | | | | | | | REF_CLOSE: (13), (30), (40), (139) are inconsistent by sub-proof
% 158.62/25.06  | | | | | | |            #998.
% 158.62/25.06  | | | | | | | 
% 158.62/25.06  | | | | | | End of split
% 158.62/25.06  | | | | | | 
% 158.62/25.06  | | | | | End of split
% 158.62/25.06  | | | | | 
% 158.62/25.06  | | | | End of split
% 158.62/25.06  | | | | 
% 158.62/25.06  | | | End of split
% 158.62/25.06  | | | 
% 158.62/25.06  | | Case 2:
% 158.62/25.06  | | | 
% 158.62/25.06  | | |   (140)  all_54_11 = e0
% 158.62/25.06  | | | 
% 158.62/25.06  | | | REF_CLOSE: (5), (39), (140) are inconsistent by sub-proof #624.
% 158.62/25.06  | | | 
% 158.62/25.06  | | End of split
% 158.62/25.06  | | 
% 158.62/25.06  | End of split
% 158.62/25.06  | 
% 158.62/25.06  End of proof
% 158.62/25.06  
% 158.62/25.06  Sub-proof #163 shows that the following formulas are inconsistent:
% 158.62/25.06  ----------------------------------------------------------------
% 158.62/25.06    (1)   ~ (all_52_7 = e0)
% 158.62/25.06    (2)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.62/25.06           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.62/25.06           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 158.62/25.06           & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 = e2
% 158.62/25.06           & all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 158.62/25.06           e2 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.62/25.06           e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.62/25.06             e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 158.62/25.06           (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.62/25.06             e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1
% 158.62/25.06             = e0) & op(e0, e1) = e0)
% 158.62/25.06    (3)  op(e0, e1) = all_52_11
% 158.62/25.06    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.06    (5)  op(e1, e1) = e2
% 158.62/25.06    (6)  op(e0, e2) = all_52_7
% 158.62/25.06    (7)  op(e2, e0) = all_52_13
% 158.62/25.06    (8)   ~ (all_52_11 = e0)
% 158.62/25.06    (9)   ~ (e2 = e0)
% 158.62/25.06    (10)   ~ (all_52_13 = e2)
% 158.62/25.06  
% 158.62/25.06  Begin of proof
% 158.62/25.06  | 
% 158.62/25.06  | BETA: splitting (2) gives:
% 158.62/25.06  | 
% 158.62/25.06  | Case 1:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (11)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.62/25.06  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.62/25.06  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (11) are inconsistent by
% 158.62/25.06  | |            sub-proof #165.
% 158.62/25.06  | | 
% 158.62/25.06  | Case 2:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (12)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.62/25.06  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.62/25.06  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.62/25.06  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 158.62/25.06  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 158.62/25.06  | |           & op(e0, e1) = e0)
% 158.62/25.06  | | 
% 158.62/25.06  | | BETA: splitting (12) gives:
% 158.62/25.06  | | 
% 158.62/25.06  | | Case 1:
% 158.62/25.06  | | | 
% 158.62/25.06  | | |   (13)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.62/25.06  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0)
% 158.62/25.06  | | | 
% 158.62/25.06  | | | REF_CLOSE: (4), (5), (7), (9), (10), (13) are inconsistent by sub-proof
% 158.62/25.06  | | |            #164.
% 158.62/25.06  | | | 
% 158.62/25.06  | | Case 2:
% 158.62/25.06  | | | 
% 158.62/25.06  | | |   (14)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.62/25.06  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.62/25.06  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 158.62/25.06  | | |             e0) & op(e0, e1) = e0)
% 158.62/25.06  | | | 
% 158.62/25.06  | | | REF_CLOSE: (3), (4), (8), (14) are inconsistent by sub-proof #965.
% 158.62/25.06  | | | 
% 158.62/25.06  | | End of split
% 158.62/25.06  | | 
% 158.62/25.06  | End of split
% 158.62/25.06  | 
% 158.62/25.06  End of proof
% 158.62/25.06  
% 158.62/25.06  Sub-proof #164 shows that the following formulas are inconsistent:
% 158.62/25.06  ----------------------------------------------------------------
% 158.62/25.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.06    (2)  op(e1, e1) = e2
% 158.62/25.06    (3)  op(e2, e0) = all_52_13
% 158.62/25.06    (4)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.62/25.06           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.62/25.06           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 158.62/25.06           & op(e1, e0) = e1 & op(e0, e1) = e0)
% 158.62/25.06    (5)   ~ (e2 = e0)
% 158.62/25.06    (6)   ~ (all_52_13 = e2)
% 158.62/25.06  
% 158.62/25.06  Begin of proof
% 158.62/25.06  | 
% 158.62/25.06  | BETA: splitting (4) gives:
% 158.62/25.06  | 
% 158.62/25.06  | Case 1:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (7)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1)
% 158.62/25.06  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (7) implies:
% 158.62/25.06  | |   (8)  op(e2, e0) = e2
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #996.
% 158.62/25.06  | | 
% 158.62/25.06  | Case 2:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (9)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1)
% 158.62/25.06  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (9) implies:
% 158.62/25.06  | |   (10)  op(e1, e1) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #914.
% 158.62/25.06  | | 
% 158.62/25.06  | End of split
% 158.62/25.06  | 
% 158.62/25.06  End of proof
% 158.62/25.06  
% 158.62/25.06  Sub-proof #165 shows that the following formulas are inconsistent:
% 158.62/25.06  ----------------------------------------------------------------
% 158.62/25.06    (1)   ~ (all_52_7 = e0)
% 158.62/25.06    (2)  op(e0, e1) = all_52_11
% 158.62/25.06    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.06    (4)  op(e1, e1) = e2
% 158.62/25.06    (5)  op(e0, e2) = all_52_7
% 158.62/25.06    (6)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.62/25.06           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.62/25.06           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 158.62/25.06           & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.62/25.06    (7)   ~ (all_52_11 = e0)
% 158.62/25.06    (8)   ~ (e2 = e0)
% 158.62/25.06  
% 158.62/25.06  Begin of proof
% 158.62/25.06  | 
% 158.62/25.06  | BETA: splitting (6) gives:
% 158.62/25.06  | 
% 158.62/25.06  | Case 1:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (9)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 158.62/25.06  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (9) implies:
% 158.62/25.06  | |   (10)  op(e1, e1) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (3), (4), (8), (10) are inconsistent by sub-proof #914.
% 158.62/25.06  | | 
% 158.62/25.06  | Case 2:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (11)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.62/25.06  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (2), (3), (5), (7), (11) are inconsistent by sub-proof #166.
% 158.62/25.06  | | 
% 158.62/25.06  | End of split
% 158.62/25.06  | 
% 158.62/25.06  End of proof
% 158.62/25.06  
% 158.62/25.06  Sub-proof #166 shows that the following formulas are inconsistent:
% 158.62/25.06  ----------------------------------------------------------------
% 158.62/25.06    (1)   ~ (all_52_7 = e0)
% 158.62/25.06    (2)  op(e0, e1) = all_52_11
% 158.62/25.06    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.06    (4)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.62/25.06         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.62/25.06           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.62/25.06    (5)  op(e0, e2) = all_52_7
% 158.62/25.06    (6)   ~ (all_52_11 = e0)
% 158.62/25.06  
% 158.62/25.06  Begin of proof
% 158.62/25.06  | 
% 158.62/25.06  | BETA: splitting (4) gives:
% 158.62/25.06  | 
% 158.62/25.06  | Case 1:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (7)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (7) implies:
% 158.62/25.06  | |   (8)  op(e0, e2) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #969.
% 158.62/25.06  | | 
% 158.62/25.06  | Case 2:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (9)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 158.62/25.06  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (9) implies:
% 158.62/25.06  | |   (10)  op(e0, e1) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #966.
% 158.62/25.06  | | 
% 158.62/25.06  | End of split
% 158.62/25.06  | 
% 158.62/25.06  End of proof
% 158.62/25.06  
% 158.62/25.06  Sub-proof #167 shows that the following formulas are inconsistent:
% 158.62/25.06  ----------------------------------------------------------------
% 158.62/25.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.06    (2)   ~ (all_52_12 = e3)
% 158.62/25.06    (3)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.62/25.06           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.62/25.06           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 158.62/25.06           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.62/25.06    (4)  op(e2, e0) = all_52_13
% 158.62/25.06    (5)  op(e3, e0) = all_52_12
% 158.62/25.06    (6)   ~ (all_52_13 = e2)
% 158.62/25.06  
% 158.62/25.06  Begin of proof
% 158.62/25.06  | 
% 158.62/25.06  | BETA: splitting (3) gives:
% 158.62/25.06  | 
% 158.62/25.06  | Case 1:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (7)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 158.62/25.06  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (7) implies:
% 158.62/25.06  | |   (8)  op(e3, e0) = e3
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #976.
% 158.62/25.06  | | 
% 158.62/25.06  | Case 2:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (9)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2)
% 158.62/25.06  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (9) implies:
% 158.62/25.06  | |   (10)  op(e2, e0) = e2
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #996.
% 158.62/25.06  | | 
% 158.62/25.06  | End of split
% 158.62/25.06  | 
% 158.62/25.06  End of proof
% 158.62/25.06  
% 158.62/25.06  Sub-proof #168 shows that the following formulas are inconsistent:
% 158.62/25.06  ----------------------------------------------------------------
% 158.62/25.06    (1)  op(e0, e3) = e2
% 158.62/25.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.06    (3)  op(e0, e3) = all_52_3
% 158.62/25.06    (4)  op(e1, e1) = e2
% 158.62/25.06    (5)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.62/25.06           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.62/25.06           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 158.62/25.06           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 158.62/25.06           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 158.62/25.06           e1 & op(e0, e3) = e0)
% 158.62/25.06    (6)  op(e2, e0) = all_52_13
% 158.62/25.06    (7)   ~ (e2 = e0)
% 158.62/25.06    (8)   ~ (all_52_13 = e2)
% 158.62/25.06  
% 158.62/25.06  Begin of proof
% 158.62/25.06  | 
% 158.62/25.06  | BETA: splitting (5) gives:
% 158.62/25.06  | 
% 158.62/25.06  | Case 1:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.62/25.06  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (9) implies:
% 158.62/25.06  | |   (10)  op(e0, e3) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (2), (3), (7), (10) are inconsistent by sub-proof #689.
% 158.62/25.06  | | 
% 158.62/25.06  | Case 2:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (11)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.62/25.06  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.62/25.06  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (2), (4), (6), (7), (8), (11) are inconsistent by sub-proof #169.
% 158.62/25.06  | | 
% 158.62/25.06  | End of split
% 158.62/25.06  | 
% 158.62/25.06  End of proof
% 158.62/25.06  
% 158.62/25.06  Sub-proof #169 shows that the following formulas are inconsistent:
% 158.62/25.06  ----------------------------------------------------------------
% 158.62/25.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.06    (2)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.62/25.06           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.62/25.06           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 158.62/25.06           & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.62/25.06    (3)  op(e1, e1) = e2
% 158.62/25.06    (4)  op(e2, e0) = all_52_13
% 158.62/25.06    (5)   ~ (e2 = e0)
% 158.62/25.06    (6)   ~ (all_52_13 = e2)
% 158.62/25.06  
% 158.62/25.06  Begin of proof
% 158.62/25.06  | 
% 158.62/25.06  | BETA: splitting (2) gives:
% 158.62/25.06  | 
% 158.62/25.06  | Case 1:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (7)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3)
% 158.62/25.06  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (7) implies:
% 158.62/25.06  | |   (8)  op(e2, e0) = e2
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #996.
% 158.62/25.06  | | 
% 158.62/25.06  | Case 2:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (9)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3)
% 158.62/25.06  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (9) implies:
% 158.62/25.06  | |   (10)  op(e1, e1) = e0
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #914.
% 158.62/25.06  | | 
% 158.62/25.06  | End of split
% 158.62/25.06  | 
% 158.62/25.06  End of proof
% 158.62/25.06  
% 158.62/25.06  Sub-proof #170 shows that the following formulas are inconsistent:
% 158.62/25.06  ----------------------------------------------------------------
% 158.62/25.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.06    (2)  op(e1, e3) = all_52_2
% 158.62/25.06    (3)   ~ (all_52_2 = e1)
% 158.62/25.06    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1)
% 158.62/25.06    (5)   ~ (e1 = e0)
% 158.62/25.06    (6)  all_56_7 = e0
% 158.62/25.06  
% 158.62/25.06  Begin of proof
% 158.62/25.06  | 
% 158.62/25.06  | BETA: splitting (4) gives:
% 158.62/25.06  | 
% 158.62/25.06  | Case 1:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (7)  all_56_6 = e1 & op(e1, e3) = e1
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (7) implies:
% 158.62/25.06  | |   (8)  op(e1, e3) = e1
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #990.
% 158.62/25.06  | | 
% 158.62/25.06  | Case 2:
% 158.62/25.06  | | 
% 158.62/25.06  | |   (9)  all_56_7 = e1 & op(e1, e2) = e1
% 158.62/25.06  | | 
% 158.62/25.06  | | ALPHA: (9) implies:
% 158.62/25.06  | |   (10)  all_56_7 = e1
% 158.62/25.06  | | 
% 158.62/25.06  | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #560.
% 158.62/25.06  | | 
% 158.62/25.06  | End of split
% 158.62/25.06  | 
% 158.62/25.06  End of proof
% 158.62/25.06  
% 158.62/25.06  Sub-proof #171 shows that the following formulas are inconsistent:
% 158.62/25.06  ----------------------------------------------------------------
% 158.62/25.06    (1)  all_56_6 = e0 & op(e1, e3) = e0
% 158.62/25.06    (2)  all_56_6 = e3
% 158.62/25.06    (3)   ~ (e3 = e0)
% 158.62/25.06  
% 158.62/25.06  Begin of proof
% 158.62/25.06  | 
% 158.62/25.06  | ALPHA: (1) implies:
% 158.62/25.06  |   (4)  all_56_6 = e0
% 158.62/25.06  | 
% 158.62/25.06  | COMBINE_EQS: (2), (4) imply:
% 158.62/25.06  |   (5)  e3 = e0
% 158.62/25.06  | 
% 158.62/25.06  | REDUCE: (3), (5) imply:
% 158.62/25.06  |   (6)  $false
% 158.62/25.06  | 
% 158.62/25.06  | CLOSE: (6) is inconsistent.
% 158.62/25.06  | 
% 158.62/25.06  End of proof
% 158.62/25.06  
% 158.62/25.06  Sub-proof #172 shows that the following formulas are inconsistent:
% 158.62/25.06  ----------------------------------------------------------------
% 158.62/25.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.06    (2)  op(e2, e2) = all_10_1
% 158.62/25.06    (3)  op(e2, e2) = e0
% 158.62/25.06    (4)   ~ (all_10_1 = e0)
% 158.62/25.06  
% 158.62/25.06  Begin of proof
% 158.62/25.06  | 
% 158.62/25.06  | GROUND_INST: instantiating (1) with e0, all_10_1, e2, e2, simplifying with
% 158.62/25.07  |              (2), (3) gives:
% 158.62/25.07  |   (5)  all_10_1 = e0
% 158.62/25.07  | 
% 158.62/25.07  | REDUCE: (4), (5) imply:
% 158.62/25.07  |   (6)  $false
% 158.62/25.07  | 
% 158.62/25.07  | CLOSE: (6) is inconsistent.
% 158.62/25.07  | 
% 158.62/25.07  End of proof
% 158.62/25.07  
% 158.62/25.07  Sub-proof #173 shows that the following formulas are inconsistent:
% 158.62/25.07  ----------------------------------------------------------------
% 158.62/25.07    (1)  all_56_7 = e1 & op(e1, e2) = e1
% 158.62/25.07    (2)  all_56_7 = e3
% 158.62/25.07    (3)   ~ (e3 = e1)
% 158.62/25.07  
% 158.62/25.07  Begin of proof
% 158.62/25.07  | 
% 158.62/25.07  | ALPHA: (1) implies:
% 158.62/25.07  |   (4)  all_56_7 = e1
% 158.62/25.07  | 
% 158.62/25.07  | COMBINE_EQS: (2), (4) imply:
% 158.62/25.07  |   (5)  e3 = e1
% 158.62/25.07  | 
% 158.62/25.07  | REDUCE: (3), (5) imply:
% 158.62/25.07  |   (6)  $false
% 158.62/25.07  | 
% 158.62/25.07  | CLOSE: (6) is inconsistent.
% 158.62/25.07  | 
% 158.62/25.07  End of proof
% 158.62/25.07  
% 158.62/25.07  Sub-proof #174 shows that the following formulas are inconsistent:
% 158.62/25.07  ----------------------------------------------------------------
% 158.62/25.07    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 158.62/25.07         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.62/25.07    (2)  all_56_14 = e3
% 158.62/25.07    (3)  all_56_8 = e2
% 158.62/25.07    (4)   ~ (e1 = e0)
% 158.62/25.07    (5)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.62/25.07         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.62/25.07    (6)  all_56_5 = e3 & op(e2, e1) = e3
% 158.62/25.07    (7)   ~ (e2 = e1)
% 158.62/25.07    (8)   ~ (e3 = e1)
% 158.62/25.07    (9)   ~ (e2 = e0)
% 158.62/25.07    (10)   ~ (e3 = e0)
% 158.62/25.07  
% 158.62/25.07  Begin of proof
% 158.62/25.07  | 
% 158.62/25.07  | ALPHA: (6) implies:
% 158.62/25.07  |   (11)  all_56_5 = e3
% 158.62/25.07  | 
% 158.62/25.07  | BETA: splitting (1) gives:
% 158.62/25.07  | 
% 158.62/25.07  | Case 1:
% 158.62/25.07  | | 
% 158.62/25.07  | |   (12)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 158.62/25.07  | |           e0)
% 158.62/25.07  | | 
% 158.62/25.07  | | BETA: splitting (12) gives:
% 158.62/25.07  | | 
% 158.62/25.07  | | Case 1:
% 158.62/25.07  | | | 
% 158.62/25.07  | | |   (13)  all_56_4 = e0 & op(e3, e1) = e0
% 158.62/25.07  | | | 
% 158.62/25.07  | | | ALPHA: (13) implies:
% 158.62/25.07  | | |   (14)  all_56_4 = e0
% 158.62/25.07  | | | 
% 158.62/25.07  | | | BETA: splitting (5) gives:
% 158.62/25.07  | | | 
% 158.62/25.07  | | | Case 1:
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | |   (15)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1)
% 158.62/25.07  | | | |           = e1)
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | | BETA: splitting (15) gives:
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | | Case 1:
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | |   (16)  all_56_4 = e1 & op(e3, e1) = e1
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | REF_CLOSE: (4), (14), (16) are inconsistent by sub-proof #232.
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | Case 2:
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | |   (17)  all_56_5 = e1 & op(e2, e1) = e1
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | ALPHA: (17) implies:
% 158.62/25.07  | | | | |   (18)  all_56_5 = e1
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | REF_CLOSE: (8), (11), (18) are inconsistent by sub-proof #531.
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | End of split
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | Case 2:
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | |   (19)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1)
% 158.62/25.07  | | | |           = e1)
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | | BETA: splitting (19) gives:
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | | Case 1:
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | |   (20)  all_56_8 = e1 & op(e1, e1) = e1
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | REF_CLOSE: (3), (7), (20) are inconsistent by sub-proof #184.
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | Case 2:
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | |   (21)  all_56_14 = e1 & op(e0, e1) = e1
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | ALPHA: (21) implies:
% 158.62/25.07  | | | | |   (22)  all_56_14 = e1
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | REF_CLOSE: (2), (8), (22) are inconsistent by sub-proof #669.
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | End of split
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | End of split
% 158.62/25.07  | | | 
% 158.62/25.07  | | Case 2:
% 158.62/25.07  | | | 
% 158.62/25.07  | | |   (23)  all_56_5 = e0 & op(e2, e1) = e0
% 158.62/25.07  | | | 
% 158.62/25.07  | | | ALPHA: (23) implies:
% 158.62/25.07  | | |   (24)  all_56_5 = e0
% 158.62/25.07  | | | 
% 158.62/25.07  | | | REF_CLOSE: (10), (11), (24) are inconsistent by sub-proof #591.
% 158.62/25.07  | | | 
% 158.62/25.07  | | End of split
% 158.62/25.07  | | 
% 158.62/25.07  | Case 2:
% 158.62/25.07  | | 
% 158.62/25.07  | |   (25)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 158.62/25.07  | |           e0)
% 158.62/25.07  | | 
% 158.62/25.07  | | BETA: splitting (25) gives:
% 158.62/25.07  | | 
% 158.62/25.07  | | Case 1:
% 158.62/25.07  | | | 
% 158.62/25.07  | | |   (26)  all_56_8 = e0 & op(e1, e1) = e0
% 158.62/25.07  | | | 
% 158.62/25.07  | | | REF_CLOSE: (3), (9), (26) are inconsistent by sub-proof #187.
% 158.62/25.07  | | | 
% 158.62/25.07  | | Case 2:
% 158.62/25.07  | | | 
% 158.62/25.07  | | |   (27)  all_56_14 = e0 & op(e0, e1) = e0
% 158.62/25.07  | | | 
% 158.62/25.07  | | | REF_CLOSE: (2), (10), (27) are inconsistent by sub-proof #175.
% 158.62/25.07  | | | 
% 158.62/25.07  | | End of split
% 158.62/25.07  | | 
% 158.62/25.07  | End of split
% 158.62/25.07  | 
% 158.62/25.07  End of proof
% 158.62/25.07  
% 158.62/25.07  Sub-proof #175 shows that the following formulas are inconsistent:
% 158.62/25.07  ----------------------------------------------------------------
% 158.62/25.07    (1)  all_56_14 = e0 & op(e0, e1) = e0
% 158.62/25.07    (2)  all_56_14 = e3
% 158.62/25.07    (3)   ~ (e3 = e0)
% 158.62/25.07  
% 158.62/25.07  Begin of proof
% 158.62/25.07  | 
% 158.62/25.07  | ALPHA: (1) implies:
% 158.62/25.07  |   (4)  all_56_14 = e0
% 158.62/25.07  | 
% 158.62/25.07  | COMBINE_EQS: (2), (4) imply:
% 158.62/25.07  |   (5)  e3 = e0
% 158.62/25.07  | 
% 158.62/25.07  | SIMP: (5) implies:
% 158.62/25.07  |   (6)  e3 = e0
% 158.62/25.07  | 
% 158.62/25.07  | REDUCE: (3), (6) imply:
% 158.62/25.07  |   (7)  $false
% 158.62/25.07  | 
% 158.62/25.07  | CLOSE: (7) is inconsistent.
% 158.62/25.07  | 
% 158.62/25.07  End of proof
% 158.62/25.07  
% 158.62/25.07  Sub-proof #176 shows that the following formulas are inconsistent:
% 158.62/25.07  ----------------------------------------------------------------
% 158.62/25.07    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.62/25.07         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.62/25.07    (2)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.62/25.07         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.62/25.07    (3)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.62/25.07         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.62/25.07    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.62/25.07         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.62/25.07    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.62/25.07         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.62/25.07    (6)   ~ (e3 = e2)
% 158.62/25.07    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.07    (8)  op(e3, e1) = all_52_8
% 158.62/25.07    (9)  op(e1, e3) = all_52_2
% 158.62/25.07    (10)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.62/25.07          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.62/25.07    (11)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.62/25.07          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.62/25.07    (12)   ~ (all_52_2 = e2)
% 158.62/25.07    (13)  op(e0, e0) = e0
% 158.62/25.07    (14)  all_56_2 = e2
% 158.62/25.07    (15)  op(e2, e1) = all_10_0
% 158.62/25.07    (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.62/25.07          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.62/25.07    (17)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.62/25.07          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.62/25.07    (18)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.62/25.07          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.62/25.07    (19)  op(e3, e3) = e3
% 158.62/25.07    (20)   ~ (all_52_2 = e3)
% 158.62/25.07    (21)  all_56_8 = e2
% 158.62/25.07    (22)  op(e2, e2) = e0
% 158.62/25.07    (23)  all_56_1 = e0
% 158.62/25.07    (24)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.62/25.07          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.62/25.07    (25)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.62/25.07          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.62/25.07    (26)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.62/25.07          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.62/25.07    (27)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.62/25.07          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 158.62/25.07    (28)   ~ (e1 = e0)
% 158.62/25.07    (29)  op(e2, e1) = all_52_9
% 158.62/25.07    (30)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.62/25.07          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.62/25.07    (31)   ~ (e2 = e1)
% 158.62/25.07    (32)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.62/25.07          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.62/25.07            e3)
% 158.62/25.07    (33)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.62/25.07          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.62/25.07    (34)   ~ (all_52_8 = e2)
% 158.62/25.07    (35)  all_56_15 = e0
% 158.62/25.07    (36)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.62/25.07          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.62/25.07    (37)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.62/25.07          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.62/25.07            e1)
% 158.62/25.07    (38)   ~ (all_52_9 = e2)
% 158.62/25.07    (39)   ~ (e3 = e1)
% 158.62/25.07    (40)   ~ (e2 = e0)
% 158.62/25.07    (41)   ~ (e3 = e0)
% 158.62/25.07    (42)  all_56_4 = e0
% 158.62/25.07  
% 158.62/25.07  Begin of proof
% 158.62/25.07  | 
% 158.62/25.07  | BETA: splitting (26) gives:
% 158.62/25.07  | 
% 158.62/25.07  | Case 1:
% 158.62/25.07  | | 
% 158.62/25.07  | |   (43)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 158.62/25.07  | |           e1)
% 158.62/25.07  | | 
% 158.62/25.07  | | REF_CLOSE: (7), (19), (23), (28), (39), (43) are inconsistent by sub-proof
% 158.62/25.07  | |            #561.
% 158.62/25.07  | | 
% 158.62/25.07  | Case 2:
% 158.62/25.07  | | 
% 158.62/25.07  | |   (44)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 158.62/25.07  | |           e1)
% 158.62/25.07  | | 
% 158.62/25.07  | | BETA: splitting (44) gives:
% 158.62/25.07  | | 
% 158.62/25.07  | | Case 1:
% 158.62/25.07  | | | 
% 158.62/25.07  | | |   (45)  all_56_4 = e1 & op(e3, e1) = e1
% 158.62/25.07  | | | 
% 158.62/25.07  | | | ALPHA: (45) implies:
% 158.62/25.07  | | |   (46)  all_56_4 = e1
% 158.62/25.07  | | | 
% 158.62/25.07  | | | REF_CLOSE: (28), (42), (46) are inconsistent by sub-proof #526.
% 158.62/25.07  | | | 
% 158.62/25.07  | | Case 2:
% 158.62/25.07  | | | 
% 158.62/25.07  | | |   (47)  all_56_9 = e1 & op(e3, e0) = e1
% 158.62/25.07  | | | 
% 158.62/25.07  | | | ALPHA: (47) implies:
% 158.62/25.07  | | |   (48)  all_56_9 = e1
% 158.62/25.07  | | | 
% 158.62/25.07  | | | BETA: splitting (4) gives:
% 158.62/25.07  | | | 
% 158.62/25.07  | | | Case 1:
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | |   (49)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2)
% 158.62/25.07  | | | |           = e2)
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | | BETA: splitting (49) gives:
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | | Case 1:
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | |   (50)  all_56_0 = e2 & op(e3, e3) = e2
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | ALPHA: (50) implies:
% 158.62/25.07  | | | | |   (51)  op(e3, e3) = e2
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | REF_CLOSE: (6), (7), (19), (51) are inconsistent by sub-proof #958.
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | Case 2:
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | |   (52)  all_56_1 = e2 & op(e3, e2) = e2
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | ALPHA: (52) implies:
% 158.62/25.07  | | | | |   (53)  all_56_1 = e2
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | COMBINE_EQS: (23), (53) imply:
% 158.62/25.07  | | | | |   (54)  e2 = e0
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | SIMP: (54) implies:
% 158.62/25.07  | | | | |   (55)  e2 = e0
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | COMBINE_EQS: (14), (55) imply:
% 158.62/25.07  | | | | |   (56)  all_56_2 = e0
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 158.62/25.07  | | | | |            (12), (13), (15), (16), (17), (18), (19), (20), (21), (22),
% 158.62/25.07  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 158.62/25.07  | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (56)
% 158.62/25.07  | | | | |            are inconsistent by sub-proof #188.
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | End of split
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | Case 2:
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | |   (57)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0)
% 158.62/25.07  | | | |           = e2)
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | | REF_CLOSE: (7), (8), (31), (34), (48), (57) are inconsistent by
% 158.62/25.07  | | | |            sub-proof #177.
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | End of split
% 158.62/25.07  | | | 
% 158.62/25.07  | | End of split
% 158.62/25.07  | | 
% 158.62/25.07  | End of split
% 158.62/25.07  | 
% 158.62/25.07  End of proof
% 158.62/25.07  
% 158.62/25.07  Sub-proof #177 shows that the following formulas are inconsistent:
% 158.62/25.07  ----------------------------------------------------------------
% 158.62/25.07    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.07    (2)  op(e3, e1) = all_52_8
% 158.62/25.07    (3)  all_56_9 = e1
% 158.62/25.07    (4)   ~ (e2 = e1)
% 158.62/25.07    (5)   ~ (all_52_8 = e2)
% 158.62/25.07    (6)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.62/25.07  
% 158.62/25.07  Begin of proof
% 158.62/25.07  | 
% 158.62/25.07  | BETA: splitting (6) gives:
% 158.62/25.07  | 
% 158.62/25.07  | Case 1:
% 158.62/25.07  | | 
% 158.62/25.07  | |   (7)  all_56_4 = e2 & op(e3, e1) = e2
% 158.62/25.07  | | 
% 158.62/25.07  | | ALPHA: (7) implies:
% 158.62/25.07  | |   (8)  op(e3, e1) = e2
% 158.62/25.07  | | 
% 158.62/25.07  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #670.
% 158.62/25.07  | | 
% 158.62/25.07  | Case 2:
% 158.62/25.07  | | 
% 158.62/25.07  | |   (9)  all_56_9 = e2 & op(e3, e0) = e2
% 158.62/25.07  | | 
% 158.62/25.07  | | ALPHA: (9) implies:
% 158.62/25.07  | |   (10)  all_56_9 = e2
% 158.62/25.07  | | 
% 158.62/25.07  | | REF_CLOSE: (3), (4), (10) are inconsistent by sub-proof #896.
% 158.62/25.07  | | 
% 158.62/25.07  | End of split
% 158.62/25.07  | 
% 158.62/25.07  End of proof
% 158.62/25.07  
% 158.62/25.07  Sub-proof #178 shows that the following formulas are inconsistent:
% 158.62/25.07  ----------------------------------------------------------------
% 158.62/25.07    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 158.62/25.07         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.62/25.07    (2)   ~ (e3 = e2)
% 158.62/25.07    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.62/25.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.62/25.07    (4)  op(e3, e1) = all_52_8
% 158.62/25.07    (5)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 158.62/25.07         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.62/25.07    (6)  all_56_8 = e2
% 158.62/25.07    (7)   ~ (e1 = e0)
% 158.62/25.07    (8)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.62/25.07         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.62/25.07    (9)  all_56_14 = e2
% 158.62/25.07    (10)   ~ (e2 = e1)
% 158.62/25.07    (11)   ~ (e3 = e1)
% 158.62/25.07    (12)   ~ (e2 = e0)
% 158.62/25.07    (13)   ~ (all_52_8 = e3)
% 158.62/25.07    (14)   ~ (e3 = e0)
% 158.62/25.07  
% 158.62/25.07  Begin of proof
% 158.62/25.07  | 
% 158.62/25.07  | BETA: splitting (5) gives:
% 158.62/25.07  | 
% 158.62/25.07  | Case 1:
% 158.62/25.07  | | 
% 158.62/25.07  | |   (15)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) =
% 158.62/25.07  | |           e3)
% 158.62/25.07  | | 
% 158.62/25.07  | | BETA: splitting (15) gives:
% 158.62/25.07  | | 
% 158.62/25.07  | | Case 1:
% 158.62/25.07  | | | 
% 158.62/25.07  | | |   (16)  all_56_4 = e3 & op(e3, e1) = e3
% 158.62/25.07  | | | 
% 158.62/25.07  | | | ALPHA: (16) implies:
% 158.62/25.07  | | |   (17)  op(e3, e1) = e3
% 158.62/25.07  | | | 
% 158.62/25.07  | | | REF_CLOSE: (3), (4), (13), (17) are inconsistent by sub-proof #982.
% 158.62/25.07  | | | 
% 158.62/25.07  | | Case 2:
% 158.62/25.07  | | | 
% 158.62/25.07  | | |   (18)  all_56_5 = e3 & op(e2, e1) = e3
% 158.62/25.07  | | | 
% 158.62/25.07  | | | ALPHA: (18) implies:
% 158.62/25.07  | | |   (19)  all_56_5 = e3
% 158.62/25.07  | | | 
% 158.62/25.07  | | | BETA: splitting (8) gives:
% 158.62/25.07  | | | 
% 158.62/25.07  | | | Case 1:
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | |   (20)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1)
% 158.62/25.07  | | | |           = e1)
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | | BETA: splitting (20) gives:
% 158.62/25.07  | | | | 
% 158.62/25.07  | | | | Case 1:
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | |   (21)  all_56_4 = e1 & op(e3, e1) = e1
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | ALPHA: (21) implies:
% 158.62/25.07  | | | | |   (22)  all_56_4 = e1
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | BETA: splitting (1) gives:
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | | Case 1:
% 158.62/25.07  | | | | | | 
% 158.62/25.07  | | | | | |   (23)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2,
% 158.62/25.07  | | | | | |             e1) = e0)
% 158.62/25.07  | | | | | | 
% 158.62/25.07  | | | | | | BETA: splitting (23) gives:
% 158.62/25.07  | | | | | | 
% 158.62/25.07  | | | | | | Case 1:
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | |   (24)  all_56_4 = e0 & op(e3, e1) = e0
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | | ALPHA: (24) implies:
% 158.62/25.07  | | | | | | |   (25)  all_56_4 = e0
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | | REF_CLOSE: (7), (22), (25) are inconsistent by sub-proof #526.
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | Case 2:
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | |   (26)  all_56_5 = e0 & op(e2, e1) = e0
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | | ALPHA: (26) implies:
% 158.62/25.07  | | | | | | |   (27)  all_56_5 = e0
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | | REF_CLOSE: (14), (19), (27) are inconsistent by sub-proof #591.
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | End of split
% 158.62/25.07  | | | | | | 
% 158.62/25.07  | | | | | Case 2:
% 158.62/25.07  | | | | | | 
% 158.62/25.07  | | | | | |   (28)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0,
% 158.62/25.07  | | | | | |             e1) = e0)
% 158.62/25.07  | | | | | | 
% 158.62/25.07  | | | | | | BETA: splitting (28) gives:
% 158.62/25.07  | | | | | | 
% 158.62/25.07  | | | | | | Case 1:
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | |   (29)  all_56_8 = e0 & op(e1, e1) = e0
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | | REF_CLOSE: (6), (12), (29) are inconsistent by sub-proof #191.
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | Case 2:
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | |   (30)  all_56_14 = e0 & op(e0, e1) = e0
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | | ALPHA: (30) implies:
% 158.62/25.07  | | | | | | |   (31)  all_56_14 = e0
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | | REF_CLOSE: (9), (12), (31) are inconsistent by sub-proof #214.
% 158.62/25.07  | | | | | | | 
% 158.62/25.07  | | | | | | End of split
% 158.62/25.07  | | | | | | 
% 158.62/25.07  | | | | | End of split
% 158.62/25.07  | | | | | 
% 158.62/25.07  | | | | Case 2:
% 158.62/25.07  | | | | | 
% 158.68/25.07  | | | | |   (32)  all_56_5 = e1 & op(e2, e1) = e1
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | | ALPHA: (32) implies:
% 158.68/25.07  | | | | |   (33)  all_56_5 = e1
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | | REF_CLOSE: (11), (19), (33) are inconsistent by sub-proof #531.
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | End of split
% 158.68/25.07  | | | | 
% 158.68/25.07  | | | Case 2:
% 158.68/25.07  | | | | 
% 158.68/25.07  | | | |   (34)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1)
% 158.68/25.07  | | | |           = e1)
% 158.68/25.07  | | | | 
% 158.68/25.07  | | | | BETA: splitting (34) gives:
% 158.68/25.07  | | | | 
% 158.68/25.07  | | | | Case 1:
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | |   (35)  all_56_8 = e1 & op(e1, e1) = e1
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | | REF_CLOSE: (6), (10), (35) are inconsistent by sub-proof #184.
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | Case 2:
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | |   (36)  all_56_14 = e1 & op(e0, e1) = e1
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | | ALPHA: (36) implies:
% 158.68/25.07  | | | | |   (37)  all_56_14 = e1
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | | COMBINE_EQS: (9), (37) imply:
% 158.68/25.07  | | | | |   (38)  e2 = e1
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | | SIMP: (38) implies:
% 158.68/25.07  | | | | |   (39)  e2 = e1
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | | REDUCE: (10), (39) imply:
% 158.68/25.07  | | | | |   (40)  $false
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | | CLOSE: (40) is inconsistent.
% 158.68/25.07  | | | | | 
% 158.68/25.07  | | | | End of split
% 158.68/25.07  | | | | 
% 158.68/25.07  | | | End of split
% 158.68/25.07  | | | 
% 158.68/25.07  | | End of split
% 158.68/25.07  | | 
% 158.68/25.07  | Case 2:
% 158.68/25.07  | | 
% 158.68/25.07  | |   (41)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 158.68/25.07  | |           e3)
% 158.68/25.07  | | 
% 158.68/25.07  | | BETA: splitting (41) gives:
% 158.68/25.07  | | 
% 158.68/25.07  | | Case 1:
% 158.68/25.07  | | | 
% 158.68/25.07  | | |   (42)  all_56_8 = e3 & op(e1, e1) = e3
% 158.68/25.07  | | | 
% 158.68/25.07  | | | REF_CLOSE: (2), (6), (42) are inconsistent by sub-proof #193.
% 158.68/25.07  | | | 
% 158.68/25.07  | | Case 2:
% 158.68/25.07  | | | 
% 158.68/25.07  | | |   (43)  all_56_14 = e3 & op(e0, e1) = e3
% 158.68/25.07  | | | 
% 158.68/25.07  | | | ALPHA: (43) implies:
% 158.68/25.07  | | |   (44)  all_56_14 = e3
% 158.68/25.07  | | | 
% 158.68/25.07  | | | REF_CLOSE: (2), (9), (44) are inconsistent by sub-proof #723.
% 158.68/25.07  | | | 
% 158.68/25.07  | | End of split
% 158.68/25.07  | | 
% 158.68/25.07  | End of split
% 158.68/25.07  | 
% 158.68/25.07  End of proof
% 158.68/25.07  
% 158.68/25.07  Sub-proof #179 shows that the following formulas are inconsistent:
% 158.68/25.07  ----------------------------------------------------------------
% 158.68/25.07    (1)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 158.68/25.07           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.68/25.07           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1)
% 158.68/25.07           & op(e1, e2) = e1 & op(e1, e1) = e1)
% 158.68/25.07    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.07    (3)  op(e2, e2) = e0
% 158.68/25.07    (4)  op(e1, e1) = e2
% 158.68/25.07  
% 158.68/25.07  Begin of proof
% 158.68/25.07  | 
% 158.68/25.07  | BETA: splitting (1) gives:
% 158.68/25.07  | 
% 158.68/25.07  | Case 1:
% 158.68/25.07  | | 
% 158.68/25.07  | |   (5)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0)
% 158.68/25.07  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1,
% 158.68/25.07  | |          e1) = e2 & $i(all_57_12)
% 158.68/25.07  | | 
% 158.68/25.07  | | ALPHA: (5) implies:
% 158.68/25.07  | |   (6)   ~ (all_57_12 = e0)
% 158.68/25.07  | |   (7)  op(e2, e2) = all_57_12
% 158.68/25.07  | | 
% 158.68/25.07  | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #811.
% 158.68/25.07  | | 
% 158.68/25.07  | Case 2:
% 158.68/25.07  | | 
% 158.68/25.07  | |   (8)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.68/25.07  | |        op(e1, e1) = e1
% 158.68/25.07  | | 
% 158.68/25.07  | | ALPHA: (8) implies:
% 158.68/25.07  | |   (9)   ~ (e2 = e1)
% 158.68/25.07  | |   (10)  op(e1, e1) = e1
% 158.68/25.07  | | 
% 158.68/25.07  | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #986.
% 158.68/25.07  | | 
% 158.68/25.07  | End of split
% 158.68/25.07  | 
% 158.68/25.07  End of proof
% 158.68/25.07  
% 158.68/25.07  Sub-proof #180 shows that the following formulas are inconsistent:
% 158.68/25.07  ----------------------------------------------------------------
% 158.68/25.07    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.07    (2)  op(e1, e1) = e2
% 158.68/25.07    (3)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.68/25.07    (4)  all_56_11 = e3
% 158.68/25.07    (5)   ~ (e2 = e1)
% 158.68/25.07    (6)   ~ (e3 = e1)
% 158.68/25.07  
% 158.68/25.07  Begin of proof
% 158.68/25.07  | 
% 158.68/25.07  | BETA: splitting (3) gives:
% 158.68/25.07  | 
% 158.68/25.07  | Case 1:
% 158.68/25.07  | | 
% 158.68/25.07  | |   (7)  all_56_8 = e1 & op(e1, e1) = e1
% 158.68/25.07  | | 
% 158.68/25.07  | | ALPHA: (7) implies:
% 158.68/25.07  | |   (8)  op(e1, e1) = e1
% 158.68/25.07  | | 
% 158.68/25.07  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #986.
% 158.68/25.07  | | 
% 158.68/25.07  | Case 2:
% 158.68/25.07  | | 
% 158.68/25.07  | |   (9)  all_56_11 = e1 & op(e1, e0) = e1
% 158.68/25.07  | | 
% 158.68/25.07  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #754.
% 158.68/25.07  | | 
% 158.68/25.07  | End of split
% 158.68/25.07  | 
% 158.68/25.07  End of proof
% 158.68/25.07  
% 158.68/25.07  Sub-proof #181 shows that the following formulas are inconsistent:
% 158.68/25.07  ----------------------------------------------------------------
% 158.68/25.07    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.68/25.07         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.68/25.07    (2)  all_54_5 = all_4_2
% 158.68/25.07    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.68/25.07         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.68/25.07    (4)   ~ (all_52_12 = e2)
% 158.68/25.07    (5)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.68/25.07    (6)  op(e0, e0) = e2
% 158.68/25.07    (7)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.68/25.07             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.68/25.07           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.68/25.07               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.68/25.07             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.68/25.07         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.68/25.07             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.68/25.07           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.68/25.07               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.68/25.07             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.68/25.07         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.68/25.07             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.68/25.07           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.68/25.07               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.68/25.07             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.68/25.07         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.68/25.07             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.68/25.07           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.68/25.07               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.68/25.07             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.68/25.07    (8)   ~ (e3 = e2)
% 158.68/25.07    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.07    (10)  op(e0, e3) = all_52_3
% 158.68/25.07    (11)  op(e3, e1) = all_52_8
% 158.68/25.07    (12)  op(e1, e1) = e2
% 158.68/25.07    (13)   ~ (all_4_2 = e3)
% 158.68/25.07    (14)  op(e1, e3) = all_52_2
% 158.68/25.07    (15)   ~ (all_52_2 = e2)
% 158.68/25.07    (16)  op(e2, e2) = all_4_2
% 158.68/25.07    (17)   ~ (all_52_4 = all_4_2)
% 158.68/25.07    (18)   ~ (all_52_3 = e2)
% 158.68/25.07    (19)  op(e3, e3) = e3
% 158.68/25.07    (20)  op(e2, e3) = all_52_1
% 158.68/25.07    (21)   ~ (all_4_2 = e1)
% 158.68/25.07    (22)  op(e3, e2) = all_52_4
% 158.68/25.07    (23)   ~ (e2 = e1)
% 158.68/25.07    (24)  op(e3, e0) = all_52_12
% 158.68/25.07    (25)   ~ (all_52_8 = e2)
% 158.68/25.07    (26)   ~ (e2 = e0)
% 158.68/25.07  
% 158.68/25.07  Begin of proof
% 158.68/25.07  | 
% 158.68/25.07  | BETA: splitting (1) gives:
% 158.68/25.07  | 
% 158.68/25.07  | Case 1:
% 158.68/25.07  | | 
% 158.68/25.07  | |   (27)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 158.68/25.07  | |           e2)
% 158.68/25.07  | | 
% 158.68/25.07  | | BETA: splitting (27) gives:
% 158.68/25.07  | | 
% 158.68/25.07  | | Case 1:
% 158.68/25.07  | | | 
% 158.68/25.07  | | |   (28)  all_56_0 = e2 & op(e3, e3) = e2
% 158.68/25.07  | | | 
% 158.68/25.07  | | | ALPHA: (28) implies:
% 158.68/25.07  | | |   (29)  op(e3, e3) = e2
% 158.68/25.07  | | | 
% 158.68/25.07  | | | REF_CLOSE: (8), (9), (19), (29) are inconsistent by sub-proof #958.
% 158.68/25.07  | | | 
% 158.68/25.07  | | Case 2:
% 158.68/25.07  | | | 
% 158.68/25.07  | | |   (30)  all_56_2 = e2 & op(e2, e3) = e2
% 158.68/25.07  | | | 
% 158.68/25.07  | | | ALPHA: (30) implies:
% 158.68/25.07  | | |   (31)  op(e2, e3) = e2
% 158.68/25.07  | | | 
% 158.68/25.07  | | | BETA: splitting (3) gives:
% 158.68/25.07  | | | 
% 158.68/25.07  | | | Case 1:
% 158.68/25.07  | | | | 
% 158.68/25.07  | | | |   (32)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2)
% 158.68/25.07  | | | |           = e2)
% 158.68/25.07  | | | | 
% 158.68/25.07  | | | | BETA: splitting (32) gives:
% 158.68/25.07  | | | | 
% 158.68/25.07  | | | | Case 1:
% 158.68/25.07  | | | | | 
% 158.68/25.08  | | | | |   (33)  all_56_0 = e2 & op(e3, e3) = e2
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | | ALPHA: (33) implies:
% 158.68/25.08  | | | | |   (34)  op(e3, e3) = e2
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | | REF_CLOSE: (8), (9), (19), (34) are inconsistent by sub-proof #958.
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | Case 2:
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | |   (35)  all_56_1 = e2 & op(e3, e2) = e2
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | | ALPHA: (35) implies:
% 158.68/25.08  | | | | |   (36)  op(e3, e2) = e2
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | | REF_CLOSE: (2), (5), (6), (7), (9), (12), (13), (16), (17), (20),
% 158.68/25.08  | | | | |            (21), (22), (23), (26), (31), (36) are inconsistent by
% 158.68/25.08  | | | | |            sub-proof #182.
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | End of split
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | Case 2:
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | |   (37)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0)
% 158.68/25.08  | | | |           = e2)
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | | REF_CLOSE: (4), (9), (11), (24), (25), (37) are inconsistent by
% 158.68/25.08  | | | |            sub-proof #511.
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | End of split
% 158.68/25.08  | | | 
% 158.68/25.08  | | End of split
% 158.68/25.08  | | 
% 158.68/25.08  | Case 2:
% 158.68/25.08  | | 
% 158.68/25.08  | |   (38)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 158.68/25.08  | |           e2)
% 158.68/25.08  | | 
% 158.68/25.08  | | BETA: splitting (38) gives:
% 158.68/25.08  | | 
% 158.68/25.08  | | Case 1:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (39)  all_56_6 = e2 & op(e1, e3) = e2
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REF_CLOSE: (9), (14), (15), (39) are inconsistent by sub-proof #761.
% 158.68/25.08  | | | 
% 158.68/25.08  | | Case 2:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (40)  all_56_12 = e2 & op(e0, e3) = e2
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REF_CLOSE: (9), (10), (18), (40) are inconsistent by sub-proof #858.
% 158.68/25.08  | | | 
% 158.68/25.08  | | End of split
% 158.68/25.08  | | 
% 158.68/25.08  | End of split
% 158.68/25.08  | 
% 158.68/25.08  End of proof
% 158.68/25.08  
% 158.68/25.08  Sub-proof #182 shows that the following formulas are inconsistent:
% 158.68/25.08  ----------------------------------------------------------------
% 158.68/25.08    (1)  op(e2, e3) = e2
% 158.68/25.08    (2)  all_54_5 = all_4_2
% 158.68/25.08    (3)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.68/25.08    (4)  op(e0, e0) = e2
% 158.68/25.08    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.68/25.08             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.68/25.08           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.68/25.08               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.68/25.08             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.68/25.08         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.68/25.08             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.68/25.08           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.68/25.08               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.68/25.08             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.68/25.08         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.68/25.08             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.68/25.08           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.68/25.08               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.68/25.08             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.68/25.08         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.68/25.08             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.68/25.08           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.68/25.08               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.68/25.08             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.68/25.08    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.08    (7)  op(e1, e1) = e2
% 158.68/25.08    (8)   ~ (all_4_2 = e3)
% 158.68/25.08    (9)  op(e2, e2) = all_4_2
% 158.68/25.08    (10)   ~ (all_52_4 = all_4_2)
% 158.68/25.08    (11)  op(e3, e2) = e2
% 158.68/25.08    (12)  op(e2, e3) = all_52_1
% 158.68/25.08    (13)   ~ (all_4_2 = e1)
% 158.68/25.08    (14)  op(e3, e2) = all_52_4
% 158.68/25.08    (15)   ~ (e2 = e1)
% 158.68/25.08    (16)   ~ (e2 = e0)
% 158.68/25.08  
% 158.68/25.08  Begin of proof
% 158.68/25.08  | 
% 158.68/25.08  | GROUND_INST: instantiating (6) with all_52_1, e2, e3, e2, simplifying with
% 158.68/25.08  |              (1), (12) gives:
% 158.68/25.08  |   (17)  all_52_1 = e2
% 158.68/25.08  | 
% 158.68/25.08  | GROUND_INST: instantiating (6) with all_52_4, e2, e2, e3, simplifying with
% 158.68/25.08  |              (11), (14) gives:
% 158.68/25.08  |   (18)  all_52_4 = e2
% 158.68/25.08  | 
% 158.68/25.08  | REDUCE: (10), (18) imply:
% 158.68/25.08  |   (19)   ~ (all_4_2 = e2)
% 158.68/25.08  | 
% 158.68/25.08  | SIMP: (19) implies:
% 158.68/25.08  |   (20)   ~ (all_4_2 = e2)
% 158.68/25.08  | 
% 158.68/25.08  | BETA: splitting (3) gives:
% 158.68/25.08  | 
% 158.68/25.08  | Case 1:
% 158.68/25.08  | | 
% 158.68/25.08  | |   (21)  all_54_5 = e3
% 158.68/25.08  | | 
% 158.68/25.08  | | COMBINE_EQS: (2), (21) imply:
% 158.68/25.08  | |   (22)  all_4_2 = e3
% 158.68/25.08  | | 
% 158.68/25.08  | | REDUCE: (8), (22) imply:
% 158.68/25.08  | |   (23)  $false
% 158.68/25.08  | | 
% 158.68/25.08  | | CLOSE: (23) is inconsistent.
% 158.68/25.08  | | 
% 158.68/25.08  | Case 2:
% 158.68/25.08  | | 
% 158.68/25.08  | |   (24)   ~ (all_54_5 = e3)
% 158.68/25.08  | |   (25)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.68/25.08  | | 
% 158.68/25.08  | | BETA: splitting (5) gives:
% 158.68/25.08  | | 
% 158.68/25.08  | | Case 1:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (26)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2)
% 158.68/25.08  | | |               = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.68/25.08  | | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.68/25.08  | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.68/25.08  | | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 158.68/25.08  | | |               op(e0, e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 &
% 158.68/25.08  | | |           op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 158.68/25.08  | | |               (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.68/25.08  | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 158.68/25.08  | | |               op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 &
% 158.68/25.08  | | |               op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 158.68/25.08  | | |               all_57_7 & $i(all_57_7))))
% 158.68/25.08  | | | 
% 158.68/25.08  | | | BETA: splitting (26) gives:
% 158.68/25.08  | | | 
% 158.68/25.08  | | | Case 1:
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | |   (27)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2)
% 158.68/25.08  | | | |             = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.68/25.08  | | | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.68/25.08  | | | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.68/25.08  | | | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 158.68/25.08  | | | |             op(e0, e3) = all_57_6 & $i(all_57_6)))
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | | ALPHA: (27) implies:
% 158.68/25.08  | | | |   (28)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 158.68/25.08  | | | |           op(e2, e3) = all_57_0 & $i(all_57_0))
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | | BETA: splitting (28) gives:
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | | Case 1:
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | |   (29)  all_57_12 = e3 & op(e2, e2) = e3
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | | ALPHA: (29) implies:
% 158.68/25.08  | | | | |   (30)  op(e2, e2) = e3
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | | BETA: splitting (25) gives:
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | | Case 1:
% 158.68/25.08  | | | | | | 
% 158.68/25.08  | | | | | |   (31)  all_54_5 = e2
% 158.68/25.08  | | | | | | 
% 158.68/25.08  | | | | | | COMBINE_EQS: (2), (31) imply:
% 158.68/25.08  | | | | | |   (32)  all_4_2 = e2
% 158.68/25.08  | | | | | | 
% 158.68/25.08  | | | | | | REDUCE: (20), (32) imply:
% 158.68/25.08  | | | | | |   (33)  $false
% 158.68/25.08  | | | | | | 
% 158.68/25.08  | | | | | | CLOSE: (33) is inconsistent.
% 158.68/25.08  | | | | | | 
% 158.68/25.08  | | | | | Case 2:
% 158.68/25.08  | | | | | | 
% 158.68/25.08  | | | | | |   (34)  all_54_5 = e1 | all_54_5 = e0
% 158.68/25.08  | | | | | | 
% 158.68/25.08  | | | | | | BETA: splitting (34) gives:
% 158.68/25.08  | | | | | | 
% 158.68/25.08  | | | | | | Case 1:
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | |   (35)  all_54_5 = e1
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | | COMBINE_EQS: (2), (35) imply:
% 158.68/25.08  | | | | | | |   (36)  all_4_2 = e1
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | | REDUCE: (13), (36) imply:
% 158.68/25.08  | | | | | | |   (37)  $false
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | | CLOSE: (37) is inconsistent.
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | Case 2:
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | |   (38)  all_54_5 = e0
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | | COMBINE_EQS: (2), (38) imply:
% 158.68/25.08  | | | | | | |   (39)  all_4_2 = e0
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | | REDUCE: (8), (39) imply:
% 158.68/25.08  | | | | | | |   (40)   ~ (e3 = e0)
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | | SIMP: (40) implies:
% 158.68/25.08  | | | | | | |   (41)   ~ (e3 = e0)
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | | REDUCE: (9), (39) imply:
% 158.68/25.08  | | | | | | |   (42)  op(e2, e2) = e0
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | | REF_CLOSE: (6), (30), (41), (42) are inconsistent by sub-proof
% 158.68/25.08  | | | | | | |            #945.
% 158.68/25.08  | | | | | | | 
% 158.68/25.08  | | | | | | End of split
% 158.68/25.08  | | | | | | 
% 158.68/25.08  | | | | | End of split
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | Case 2:
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | |   (43)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0)
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | | ALPHA: (43) implies:
% 158.68/25.08  | | | | |   (44)   ~ (all_57_0 = e2)
% 158.68/25.08  | | | | |   (45)  op(e2, e3) = all_57_0
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | | REF_CLOSE: (1), (6), (44), (45) are inconsistent by sub-proof #783.
% 158.68/25.08  | | | | | 
% 158.68/25.08  | | | | End of split
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | Case 2:
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | |   (46)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3)
% 158.68/25.08  | | | |             = e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.68/25.08  | | | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 158.68/25.08  | | | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 158.68/25.08  | | | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) &
% 158.68/25.08  | | | |             op(e0, e2) = all_57_7 & $i(all_57_7)))
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | | ALPHA: (46) implies:
% 158.68/25.08  | | | |   (47)  op(e2, e2) = e2
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | | REF_CLOSE: (2), (6), (9), (13), (20), (25), (47) are inconsistent by
% 158.68/25.08  | | | |            sub-proof #928.
% 158.68/25.08  | | | | 
% 158.68/25.08  | | | End of split
% 158.68/25.08  | | | 
% 158.68/25.08  | | Case 2:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (48)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3)
% 158.68/25.08  | | |               = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 158.68/25.08  | | |               $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 158.68/25.08  | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 158.68/25.08  | | |           ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.68/25.08  | | |               op(e0, e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 &
% 158.68/25.08  | | |           op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 158.68/25.08  | | |               (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.68/25.08  | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 158.68/25.08  | | |               op(e2, e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0
% 158.68/25.08  | | |               & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) =
% 158.68/25.08  | | |               all_57_13 & $i(all_57_13))))
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REF_CLOSE: (4), (6), (7), (15), (16), (48) are inconsistent by sub-proof
% 158.68/25.08  | | |            #780.
% 158.68/25.08  | | | 
% 158.68/25.08  | | End of split
% 158.68/25.08  | | 
% 158.68/25.08  | End of split
% 158.68/25.08  | 
% 158.68/25.08  End of proof
% 158.68/25.08  
% 158.68/25.08  Sub-proof #183 shows that the following formulas are inconsistent:
% 158.68/25.08  ----------------------------------------------------------------
% 158.68/25.08    (1)   ~ (e3 = e2)
% 158.68/25.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.08    (3)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.68/25.08         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.68/25.08    (4)  op(e1, e3) = all_52_2
% 158.68/25.08    (5)   ~ (all_52_2 = e3)
% 158.68/25.08    (6)  all_56_8 = e2
% 158.68/25.08    (7)  all_56_11 = e2
% 158.68/25.08    (8)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.68/25.08         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.68/25.08    (9)  all_56_7 = e3
% 158.68/25.08    (10)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.68/25.08          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.68/25.08    (11)   ~ (e1 = e0)
% 158.68/25.08    (12)   ~ (e2 = e1)
% 158.68/25.08    (13)   ~ (e3 = e1)
% 158.68/25.08    (14)   ~ (e2 = e0)
% 158.68/25.08    (15)   ~ (e3 = e0)
% 158.68/25.08  
% 158.68/25.08  Begin of proof
% 158.68/25.08  | 
% 158.68/25.08  | BETA: splitting (3) gives:
% 158.68/25.08  | 
% 158.68/25.08  | Case 1:
% 158.68/25.08  | | 
% 158.68/25.08  | |   (16)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 158.68/25.08  | |           e1)
% 158.68/25.08  | | 
% 158.68/25.08  | | BETA: splitting (16) gives:
% 158.68/25.08  | | 
% 158.68/25.08  | | Case 1:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (17)  all_56_6 = e1 & op(e1, e3) = e1
% 158.68/25.08  | | | 
% 158.68/25.08  | | | ALPHA: (17) implies:
% 158.68/25.08  | | |   (18)  all_56_6 = e1
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REF_CLOSE: (6), (7), (8), (9), (11), (14), (15), (18) are inconsistent by
% 158.68/25.08  | | |            sub-proof #190.
% 158.68/25.08  | | | 
% 158.68/25.08  | | Case 2:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (19)  all_56_7 = e1 & op(e1, e2) = e1
% 158.68/25.08  | | | 
% 158.68/25.08  | | | ALPHA: (19) implies:
% 158.68/25.08  | | |   (20)  all_56_7 = e1
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (13), (20) are inconsistent
% 158.68/25.08  | | |            by sub-proof #185.
% 158.68/25.08  | | | 
% 158.68/25.08  | | End of split
% 158.68/25.08  | | 
% 158.68/25.08  | Case 2:
% 158.68/25.08  | | 
% 158.68/25.08  | |   (21)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 158.68/25.08  | |           e1)
% 158.68/25.08  | | 
% 158.68/25.08  | | BETA: splitting (21) gives:
% 158.68/25.08  | | 
% 158.68/25.08  | | Case 1:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (22)  all_56_8 = e1 & op(e1, e1) = e1
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REF_CLOSE: (6), (12), (22) are inconsistent by sub-proof #184.
% 158.68/25.08  | | | 
% 158.68/25.08  | | Case 2:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (23)  all_56_11 = e1 & op(e1, e0) = e1
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REF_CLOSE: (7), (12), (23) are inconsistent by sub-proof #469.
% 158.68/25.08  | | | 
% 158.68/25.08  | | End of split
% 158.68/25.08  | | 
% 158.68/25.08  | End of split
% 158.68/25.08  | 
% 158.68/25.08  End of proof
% 158.68/25.08  
% 158.68/25.08  Sub-proof #184 shows that the following formulas are inconsistent:
% 158.68/25.08  ----------------------------------------------------------------
% 158.68/25.08    (1)  all_56_8 = e1 & op(e1, e1) = e1
% 158.68/25.08    (2)  all_56_8 = e2
% 158.68/25.08    (3)   ~ (e2 = e1)
% 158.68/25.08  
% 158.68/25.08  Begin of proof
% 158.68/25.08  | 
% 158.68/25.08  | ALPHA: (1) implies:
% 158.68/25.08  |   (4)  all_56_8 = e1
% 158.68/25.08  | 
% 158.68/25.08  | COMBINE_EQS: (2), (4) imply:
% 158.68/25.08  |   (5)  e2 = e1
% 158.68/25.08  | 
% 158.68/25.08  | REDUCE: (3), (5) imply:
% 158.68/25.08  |   (6)  $false
% 158.68/25.08  | 
% 158.68/25.08  | CLOSE: (6) is inconsistent.
% 158.68/25.08  | 
% 158.68/25.08  End of proof
% 158.68/25.08  
% 158.68/25.08  Sub-proof #185 shows that the following formulas are inconsistent:
% 158.68/25.08  ----------------------------------------------------------------
% 158.68/25.08    (1)   ~ (e3 = e2)
% 158.68/25.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.08    (3)  op(e1, e3) = all_52_2
% 158.68/25.08    (4)   ~ (all_52_2 = e3)
% 158.68/25.08    (5)  all_56_8 = e2
% 158.68/25.08    (6)  all_56_11 = e2
% 158.68/25.08    (7)  all_56_7 = e1
% 158.68/25.08    (8)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.68/25.08         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.68/25.08    (9)   ~ (e3 = e1)
% 158.68/25.08  
% 158.68/25.08  Begin of proof
% 158.68/25.08  | 
% 158.68/25.08  | BETA: splitting (8) gives:
% 158.68/25.08  | 
% 158.68/25.08  | Case 1:
% 158.68/25.08  | | 
% 158.68/25.08  | |   (10)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) =
% 158.68/25.08  | |           e3)
% 158.68/25.08  | | 
% 158.68/25.08  | | BETA: splitting (10) gives:
% 158.68/25.08  | | 
% 158.68/25.08  | | Case 1:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (11)  all_56_6 = e3 & op(e1, e3) = e3
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REF_CLOSE: (2), (3), (4), (11) are inconsistent by sub-proof #681.
% 158.68/25.08  | | | 
% 158.68/25.08  | | Case 2:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (12)  all_56_7 = e3 & op(e1, e2) = e3
% 158.68/25.08  | | | 
% 158.68/25.08  | | | ALPHA: (12) implies:
% 158.68/25.08  | | |   (13)  all_56_7 = e3
% 158.68/25.08  | | | 
% 158.68/25.08  | | | COMBINE_EQS: (7), (13) imply:
% 158.68/25.08  | | |   (14)  e3 = e1
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REDUCE: (9), (14) imply:
% 158.68/25.08  | | |   (15)  $false
% 158.68/25.08  | | | 
% 158.68/25.08  | | | CLOSE: (15) is inconsistent.
% 158.68/25.08  | | | 
% 158.68/25.08  | | End of split
% 158.68/25.08  | | 
% 158.68/25.08  | Case 2:
% 158.68/25.08  | | 
% 158.68/25.08  | |   (16)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) =
% 158.68/25.08  | |           e3)
% 158.68/25.08  | | 
% 158.68/25.08  | | BETA: splitting (16) gives:
% 158.68/25.08  | | 
% 158.68/25.08  | | Case 1:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (17)  all_56_8 = e3 & op(e1, e1) = e3
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REF_CLOSE: (1), (5), (17) are inconsistent by sub-proof #193.
% 158.68/25.08  | | | 
% 158.68/25.08  | | Case 2:
% 158.68/25.08  | | | 
% 158.68/25.08  | | |   (18)  all_56_11 = e3 & op(e1, e0) = e3
% 158.68/25.08  | | | 
% 158.68/25.08  | | | ALPHA: (18) implies:
% 158.68/25.08  | | |   (19)  all_56_11 = e3
% 158.68/25.08  | | | 
% 158.68/25.08  | | | COMBINE_EQS: (6), (19) imply:
% 158.68/25.08  | | |   (20)  e3 = e2
% 158.68/25.08  | | | 
% 158.68/25.08  | | | REDUCE: (1), (20) imply:
% 158.68/25.08  | | |   (21)  $false
% 158.68/25.08  | | | 
% 158.68/25.08  | | | CLOSE: (21) is inconsistent.
% 158.68/25.08  | | | 
% 158.68/25.08  | | End of split
% 158.68/25.08  | | 
% 158.68/25.08  | End of split
% 158.68/25.08  | 
% 158.68/25.08  End of proof
% 158.68/25.08  
% 158.68/25.08  Sub-proof #186 shows that the following formulas are inconsistent:
% 158.68/25.08  ----------------------------------------------------------------
% 158.68/25.08    (1)  op(e0, e1) = all_52_11
% 158.68/25.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.08    (3)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 158.68/25.08    (4)  all_56_8 = e2
% 158.68/25.08    (5)   ~ (all_52_11 = e0)
% 158.68/25.08    (6)   ~ (e2 = e0)
% 158.68/25.08  
% 158.68/25.08  Begin of proof
% 158.68/25.08  | 
% 158.68/25.08  | BETA: splitting (3) gives:
% 158.68/25.08  | 
% 158.68/25.08  | Case 1:
% 158.68/25.08  | | 
% 158.68/25.08  | |   (7)  all_56_8 = e0 & op(e1, e1) = e0
% 158.68/25.08  | | 
% 158.68/25.08  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #187.
% 158.68/25.08  | | 
% 158.68/25.08  | Case 2:
% 158.68/25.08  | | 
% 158.68/25.08  | |   (8)  all_56_14 = e0 & op(e0, e1) = e0
% 158.68/25.08  | | 
% 158.68/25.08  | | ALPHA: (8) implies:
% 158.68/25.08  | |   (9)  op(e0, e1) = e0
% 158.68/25.08  | | 
% 158.68/25.08  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #966.
% 158.68/25.08  | | 
% 158.68/25.08  | End of split
% 158.68/25.08  | 
% 158.68/25.08  End of proof
% 158.68/25.08  
% 158.68/25.08  Sub-proof #187 shows that the following formulas are inconsistent:
% 158.68/25.08  ----------------------------------------------------------------
% 158.68/25.09    (1)  all_56_8 = e0 & op(e1, e1) = e0
% 158.68/25.09    (2)  all_56_8 = e2
% 158.68/25.09    (3)   ~ (e2 = e0)
% 158.68/25.09  
% 158.68/25.09  Begin of proof
% 158.68/25.09  | 
% 158.68/25.09  | ALPHA: (1) implies:
% 158.68/25.09  |   (4)  all_56_8 = e0
% 158.68/25.09  | 
% 158.68/25.09  | COMBINE_EQS: (2), (4) imply:
% 158.68/25.09  |   (5)  e2 = e0
% 158.68/25.09  | 
% 158.68/25.09  | SIMP: (5) implies:
% 158.68/25.09  |   (6)  e2 = e0
% 158.68/25.09  | 
% 158.68/25.09  | REDUCE: (3), (6) imply:
% 158.68/25.09  |   (7)  $false
% 158.68/25.09  | 
% 158.68/25.09  | CLOSE: (7) is inconsistent.
% 158.68/25.09  | 
% 158.68/25.09  End of proof
% 158.68/25.09  
% 158.68/25.09  Sub-proof #188 shows that the following formulas are inconsistent:
% 158.68/25.09  ----------------------------------------------------------------
% 158.68/25.09    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.68/25.09         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.68/25.09    (2)  all_56_2 = e0
% 158.68/25.09    (3)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.68/25.09         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.68/25.09    (4)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.68/25.09         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.68/25.09    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.68/25.09         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.68/25.09    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.68/25.09         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.68/25.09    (7)   ~ (e3 = e2)
% 158.68/25.09    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.09    (9)  op(e3, e1) = all_52_8
% 158.68/25.09    (10)  op(e1, e3) = all_52_2
% 158.68/25.09    (11)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.68/25.09          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.68/25.09    (12)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.68/25.09          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.68/25.09    (13)   ~ (all_52_2 = e2)
% 158.68/25.09    (14)  op(e0, e0) = e0
% 158.68/25.09    (15)  op(e2, e1) = all_10_0
% 158.68/25.09    (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.68/25.09          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.68/25.09    (17)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.68/25.09          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.68/25.09    (18)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.68/25.09          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.68/25.09    (19)  op(e3, e3) = e3
% 158.68/25.09    (20)   ~ (all_52_2 = e3)
% 158.68/25.09    (21)  all_56_8 = e2
% 158.68/25.09    (22)  op(e2, e2) = e0
% 158.68/25.09    (23)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.68/25.09          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.68/25.09    (24)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.68/25.09          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.68/25.09    (25)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.68/25.09          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.68/25.09    (26)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.68/25.09          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 158.68/25.09    (27)   ~ (e1 = e0)
% 158.68/25.09    (28)  op(e2, e1) = all_52_9
% 158.68/25.09    (29)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.68/25.09          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.68/25.09    (30)   ~ (e2 = e1)
% 158.68/25.09    (31)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.68/25.09          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.68/25.09            e3)
% 158.68/25.09    (32)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.68/25.09          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.68/25.09    (33)   ~ (all_52_8 = e2)
% 158.68/25.09    (34)  all_56_15 = e0
% 158.68/25.09    (35)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.68/25.09          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.68/25.09    (36)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.68/25.09          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.68/25.09            e1)
% 158.68/25.09    (37)   ~ (all_52_9 = e2)
% 158.68/25.09    (38)   ~ (e3 = e1)
% 158.68/25.09    (39)   ~ (e2 = e0)
% 158.68/25.09    (40)   ~ (e3 = e0)
% 158.68/25.09    (41)  all_56_4 = e0
% 158.68/25.09  
% 158.68/25.09  Begin of proof
% 158.68/25.09  | 
% 158.68/25.09  | BETA: splitting (1) gives:
% 158.68/25.09  | 
% 158.68/25.09  | Case 1:
% 158.68/25.09  | | 
% 158.68/25.09  | |   (42)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 158.68/25.09  | |           e2)
% 158.68/25.09  | | 
% 158.68/25.09  | | REF_CLOSE: (2), (7), (8), (19), (39), (42) are inconsistent by sub-proof
% 158.68/25.09  | |            #534.
% 158.68/25.09  | | 
% 158.68/25.09  | Case 2:
% 158.68/25.09  | | 
% 158.68/25.09  | |   (43)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 158.68/25.09  | |           e2)
% 158.68/25.09  | | 
% 158.68/25.09  | | BETA: splitting (43) gives:
% 158.68/25.09  | | 
% 158.68/25.09  | | Case 1:
% 158.68/25.09  | | | 
% 158.68/25.09  | | |   (44)  all_56_6 = e2 & op(e1, e3) = e2
% 158.68/25.09  | | | 
% 158.68/25.09  | | | REF_CLOSE: (8), (10), (13), (44) are inconsistent by sub-proof #761.
% 158.68/25.09  | | | 
% 158.68/25.09  | | Case 2:
% 158.68/25.09  | | | 
% 158.68/25.09  | | |   (45)  all_56_12 = e2 & op(e0, e3) = e2
% 158.68/25.09  | | | 
% 158.68/25.09  | | | ALPHA: (45) implies:
% 158.68/25.09  | | |   (46)  all_56_12 = e2
% 158.68/25.09  | | | 
% 158.68/25.09  | | | BETA: splitting (23) gives:
% 158.68/25.09  | | | 
% 158.68/25.09  | | | Case 1:
% 158.68/25.09  | | | | 
% 158.68/25.09  | | | |   (47)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2)
% 158.68/25.09  | | | |           = e0)
% 158.68/25.09  | | | | 
% 158.68/25.09  | | | | BETA: splitting (47) gives:
% 158.68/25.09  | | | | 
% 158.68/25.09  | | | | Case 1:
% 158.68/25.09  | | | | | 
% 158.68/25.09  | | | | |   (48)  all_56_6 = e0 & op(e1, e3) = e0
% 158.68/25.09  | | | | | 
% 158.68/25.09  | | | | | ALPHA: (48) implies:
% 158.68/25.09  | | | | |   (49)  all_56_6 = e0
% 158.68/25.09  | | | | | 
% 158.68/25.09  | | | | | BETA: splitting (32) gives:
% 158.68/25.09  | | | | | 
% 158.68/25.09  | | | | | Case 1:
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | |   (50)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2,
% 158.68/25.09  | | | | | |             e2) = e2)
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | | BETA: splitting (50) gives:
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | | Case 1:
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | |   (51)  all_56_2 = e2 & op(e2, e3) = e2
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | ALPHA: (51) implies:
% 158.68/25.09  | | | | | | |   (52)  all_56_2 = e2
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | REF_CLOSE: (8), (19), (27), (30), (35), (38), (46), (49), (52) are
% 158.68/25.09  | | | | | | |            inconsistent by sub-proof #598.
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | Case 2:
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | |   (53)  all_56_3 = e2 & op(e2, e2) = e2
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | ALPHA: (53) implies:
% 158.68/25.09  | | | | | | |   (54)  op(e2, e2) = e2
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | REF_CLOSE: (8), (22), (39), (54) are inconsistent by sub-proof
% 158.68/25.09  | | | | | | |            #942.
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | End of split
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | Case 2:
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | |   (55)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2,
% 158.68/25.09  | | | | | |             e0) = e2)
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | | BETA: splitting (55) gives:
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | | Case 1:
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | |   (56)  all_56_5 = e2 & op(e2, e1) = e2
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | ALPHA: (56) implies:
% 158.68/25.09  | | | | | | |   (57)  op(e2, e1) = e2
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | REF_CLOSE: (8), (15), (28), (37), (57) are inconsistent by
% 158.68/25.09  | | | | | | |            sub-proof #194.
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | Case 2:
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | |   (58)  all_56_10 = e2 & op(e2, e0) = e2
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | ALPHA: (58) implies:
% 158.68/25.09  | | | | | | |   (59)  all_56_10 = e2
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | BETA: splitting (12) gives:
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | |   (60)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 &
% 158.68/25.09  | | | | | | | |           op(e2, e2) = e3)
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | | BETA: splitting (60) gives:
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | |   (61)  all_56_2 = e3 & op(e2, e3) = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | ALPHA: (61) implies:
% 158.68/25.09  | | | | | | | | |   (62)  all_56_2 = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | REF_CLOSE: (8), (19), (27), (30), (35), (38), (46), (49), (62)
% 158.68/25.09  | | | | | | | | |            are inconsistent by sub-proof #768.
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | Case 2:
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | |   (63)  all_56_3 = e3 & op(e2, e2) = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | ALPHA: (63) implies:
% 158.68/25.09  | | | | | | | | |   (64)  op(e2, e2) = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | REF_CLOSE: (8), (22), (40), (64) are inconsistent by sub-proof
% 158.68/25.09  | | | | | | | | |            #945.
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | End of split
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | Case 2:
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | |   (65)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 &
% 158.68/25.09  | | | | | | | |           op(e2, e0) = e3)
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | | BETA: splitting (65) gives:
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | |   (66)  all_56_5 = e3 & op(e2, e1) = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | ALPHA: (66) implies:
% 158.68/25.09  | | | | | | | | |   (67)  all_56_5 = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | REF_CLOSE: (2), (8), (22), (26), (27), (30), (38), (59), (67)
% 158.68/25.09  | | | | | | | | |            are inconsistent by sub-proof #436.
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | Case 2:
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | |   (68)  all_56_10 = e3 & op(e2, e0) = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | REF_CLOSE: (7), (59), (68) are inconsistent by sub-proof #894.
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | End of split
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | End of split
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | End of split
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | End of split
% 158.68/25.09  | | | | | 
% 158.68/25.09  | | | | Case 2:
% 158.68/25.09  | | | | | 
% 158.68/25.09  | | | | |   (69)  all_56_7 = e0 & op(e1, e2) = e0
% 158.68/25.09  | | | | | 
% 158.68/25.09  | | | | | ALPHA: (69) implies:
% 158.68/25.09  | | | | |   (70)  all_56_7 = e0
% 158.68/25.09  | | | | | 
% 158.68/25.09  | | | | | BETA: splitting (24) gives:
% 158.68/25.09  | | | | | 
% 158.68/25.09  | | | | | Case 1:
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | |   (71)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1,
% 158.68/25.09  | | | | | |             e2) = e3)
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | | BETA: splitting (71) gives:
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | | Case 1:
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | |   (72)  all_56_6 = e3 & op(e1, e3) = e3
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | REF_CLOSE: (8), (10), (20), (72) are inconsistent by sub-proof
% 158.68/25.09  | | | | | | |            #681.
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | Case 2:
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | |   (73)  all_56_7 = e3 & op(e1, e2) = e3
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | REF_CLOSE: (40), (70), (73) are inconsistent by sub-proof #522.
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | End of split
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | Case 2:
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | |   (74)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1,
% 158.68/25.09  | | | | | |             e0) = e3)
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | | BETA: splitting (74) gives:
% 158.68/25.09  | | | | | | 
% 158.68/25.09  | | | | | | Case 1:
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | |   (75)  all_56_8 = e3 & op(e1, e1) = e3
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | REF_CLOSE: (7), (21), (75) are inconsistent by sub-proof #193.
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | Case 2:
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | |   (76)  all_56_11 = e3 & op(e1, e0) = e3
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | ALPHA: (76) implies:
% 158.68/25.09  | | | | | | |   (77)  all_56_11 = e3
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | BETA: splitting (16) gives:
% 158.68/25.09  | | | | | | | 
% 158.68/25.09  | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | |   (78)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 &
% 158.68/25.09  | | | | | | | |           op(e2, e2) = e3)
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (19), (22), (25), (27), (30),
% 158.68/25.09  | | | | | | | |            (38), (39), (40), (78) are inconsistent by sub-proof
% 158.68/25.09  | | | | | | | |            #944.
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | Case 2:
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | |   (79)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 &
% 158.68/25.09  | | | | | | | |           op(e0, e2) = e3)
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | | BETA: splitting (79) gives:
% 158.68/25.09  | | | | | | | | 
% 158.68/25.09  | | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | |   (80)  all_56_7 = e3 & op(e1, e2) = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | ALPHA: (80) implies:
% 158.68/25.09  | | | | | | | | |   (81)  all_56_7 = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | COMBINE_EQS: (70), (81) imply:
% 158.68/25.09  | | | | | | | | |   (82)  e3 = e0
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | SIMP: (82) implies:
% 158.68/25.09  | | | | | | | | |   (83)  e3 = e0
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | COMBINE_EQS: (77), (83) imply:
% 158.68/25.09  | | | | | | | | |   (84)  all_56_11 = e0
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (11), (14), (17),
% 158.68/25.09  | | | | | | | | |            (18), (19), (21), (22), (23), (25), (27), (29),
% 158.68/25.09  | | | | | | | | |            (30), (31), (34), (35), (36), (38), (39), (40),
% 158.68/25.09  | | | | | | | | |            (41), (46), (81), (84) are inconsistent by
% 158.68/25.09  | | | | | | | | |            sub-proof #189.
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | Case 2:
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | |   (85)  all_56_13 = e3 & op(e0, e2) = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | ALPHA: (85) implies:
% 158.68/25.09  | | | | | | | | |   (86)  all_56_13 = e3
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | BETA: splitting (32) gives:
% 158.68/25.09  | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | |   (87)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 &
% 158.68/25.09  | | | | | | | | | |           op(e2, e2) = e2)
% 158.68/25.09  | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | REF_CLOSE: (8), (19), (22), (27), (29), (30), (35), (38),
% 158.68/25.09  | | | | | | | | | |            (39), (40), (46), (87) are inconsistent by
% 158.68/25.09  | | | | | | | | | |            sub-proof #549.
% 158.68/25.09  | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | Case 2:
% 158.68/25.09  | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | |   (88)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2
% 158.68/25.09  | | | | | | | | | |           & op(e2, e0) = e2)
% 158.68/25.09  | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | BETA: splitting (88) gives:
% 158.68/25.09  | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | |   (89)  all_56_5 = e2 & op(e2, e1) = e2
% 158.68/25.09  | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | ALPHA: (89) implies:
% 158.68/25.09  | | | | | | | | | | |   (90)  op(e2, e1) = e2
% 158.68/25.09  | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | REF_CLOSE: (8), (15), (28), (37), (90) are inconsistent by
% 158.68/25.09  | | | | | | | | | | |            sub-proof #194.
% 158.68/25.09  | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | Case 2:
% 158.68/25.09  | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | |   (91)  all_56_10 = e2 & op(e2, e0) = e2
% 158.68/25.09  | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | ALPHA: (91) implies:
% 158.68/25.09  | | | | | | | | | | |   (92)  all_56_10 = e2
% 158.68/25.09  | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | BETA: splitting (3) gives:
% 158.68/25.09  | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | |   (93)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 158.68/25.09  | | | | | | | | | | | |           & op(e2, e2) = e1)
% 158.68/25.09  | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | BETA: splitting (93) gives:
% 158.68/25.09  | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | |   (94)  all_56_1 = e1 & op(e3, e2) = e1
% 158.68/25.09  | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | ALPHA: (94) implies:
% 158.68/25.09  | | | | | | | | | | | | |   (95)  all_56_1 = e1
% 158.68/25.09  | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | BETA: splitting (5) gives:
% 158.68/25.09  | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | |   (96)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 158.68/25.09  | | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 158.68/25.09  | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 158.68/25.09  | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | |   (97)  all_56_0 = e2 & op(e3, e3) = e2
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 158.68/25.09  | | | | | | | | | | | | | | |   (98)  op(e3, e3) = e2
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (19), (98) are inconsistent by sub-proof
% 158.68/25.09  | | | | | | | | | | | | | | |            #958.
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | Case 2:
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | |   (99)  all_56_1 = e2 & op(e3, e2) = e2
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 158.68/25.09  | | | | | | | | | | | | | | |   (100)  all_56_1 = e2
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | | COMBINE_EQS: (95), (100) imply:
% 158.68/25.09  | | | | | | | | | | | | | | |   (101)  e2 = e1
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | | REDUCE: (30), (101) imply:
% 158.68/25.09  | | | | | | | | | | | | | | |   (102)  $false
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | | CLOSE: (102) is inconsistent.
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | End of split
% 158.68/25.09  | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | Case 2:
% 158.68/25.09  | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | |   (103)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 158.68/25.09  | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 158.68/25.09  | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 158.68/25.09  | | | | | | | | | | | | | | 
% 158.68/25.09  | | | | | | | | | | | | | | Case 1:
% 158.68/25.09  | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | |   (104)  all_56_4 = e2 & op(e3, e1) = e2
% 158.68/25.10  | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 158.68/25.10  | | | | | | | | | | | | | | |   (105)  op(e3, e1) = e2
% 158.68/25.10  | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (33), (105) are inconsistent by
% 158.68/25.10  | | | | | | | | | | | | | | |            sub-proof #670.
% 158.68/25.10  | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | |   (106)  all_56_9 = e2 & op(e3, e0) = e2
% 158.68/25.10  | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 158.68/25.10  | | | | | | | | | | | | | | |   (107)  all_56_9 = e2
% 158.68/25.10  | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 158.68/25.10  | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | Case 1:
% 158.68/25.10  | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | |   (108)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 158.68/25.10  | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 158.68/25.10  | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19), (22), (27), (29), (30), (35), (38),
% 158.68/25.10  | | | | | | | | | | | | | | | |            (39), (40), (46), (108) are inconsistent by
% 158.68/25.10  | | | | | | | | | | | | | | | |            sub-proof #532.
% 158.68/25.10  | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | |   (109)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 158.68/25.10  | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 158.68/25.10  | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 158.68/25.10  | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | Case 1:
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | |   (110)  all_56_5 = e3 & op(e2, e1) = e3
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 158.68/25.10  | | | | | | | | | | | | | | | | |   (111)  all_56_5 = e3
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | Case 1:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | |   (112)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 158.68/25.10  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 158.68/25.10  | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | Case 1:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |   (113)  all_56_2 = e1 & op(e2, e3) = e1
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |   (114)  all_56_2 = e1
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (114) imply:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |   (115)  e1 = e0
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (115) imply:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |   (116)  all_56_1 = e0
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (22), (27), (38), (70), (86), (116) are
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #558.
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |   (117)  all_56_3 = e1 & op(e2, e2) = e1
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |   (118)  op(e2, e2) = e1
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22), (27), (118) are inconsistent by
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |            sub-proof #960.
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | |   (119)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 158.68/25.10  | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 158.68/25.10  | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | Case 1:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |   (120)  all_56_5 = e1 & op(e2, e1) = e1
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |   (121)  all_56_5 = e1
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (111), (121) are inconsistent by sub-proof
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |            #531.
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |   (122)  all_56_10 = e1 & op(e2, e0) = e1
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |   (123)  all_56_10 = e1
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (92), (123) are inconsistent by sub-proof
% 158.68/25.10  | | | | | | | | | | | | | | | | | | |            #886.
% 158.68/25.10  | | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | |   (124)  all_56_10 = e3 & op(e2, e0) = e3
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 158.68/25.10  | | | | | | | | | | | | | | | | |   (125)  all_56_10 = e3
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (125) imply:
% 158.68/25.10  | | | | | | | | | | | | | | | | |   (126)  e3 = e2
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (126) imply:
% 158.68/25.10  | | | | | | | | | | | | | | | | |   (127)  all_56_11 = e2
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (17), (19), (25), (27),
% 158.68/25.10  | | | | | | | | | | | | | | | | |            (30), (34), (38), (39), (40), (107), (127) are
% 158.68/25.10  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #302.
% 158.68/25.10  | | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | |   (128)  all_56_3 = e1 & op(e2, e2) = e1
% 158.68/25.10  | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | ALPHA: (128) implies:
% 158.68/25.10  | | | | | | | | | | | | |   (129)  op(e2, e2) = e1
% 158.68/25.10  | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | | REF_CLOSE: (8), (22), (27), (129) are inconsistent by
% 158.68/25.10  | | | | | | | | | | | | |            sub-proof #960.
% 158.68/25.10  | | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | |   (130)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 158.68/25.10  | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 158.68/25.10  | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | | REF_CLOSE: (27), (38), (70), (86), (130) are inconsistent by
% 158.68/25.10  | | | | | | | | | | | |            sub-proof #559.
% 158.68/25.10  | | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | 
% 158.68/25.10  | | | | | | | End of split
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | End of split
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | End of split
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | End of split
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | Case 2:
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | |   (131)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1,
% 158.68/25.10  | | | |              e0) = e0)
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | | BETA: splitting (131) gives:
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | | Case 1:
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | |   (132)  all_56_8 = e0 & op(e1, e1) = e0
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | | REF_CLOSE: (21), (39), (132) are inconsistent by sub-proof #191.
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | Case 2:
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | |   (133)  all_56_11 = e0 & op(e1, e0) = e0
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | | ALPHA: (133) implies:
% 158.68/25.10  | | | | |   (134)  all_56_11 = e0
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | | BETA: splitting (24) gives:
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | | Case 1:
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | |   (135)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1,
% 158.68/25.10  | | | | | |              e2) = e3)
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | | BETA: splitting (135) gives:
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | | Case 1:
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | |   (136)  all_56_6 = e3 & op(e1, e3) = e3
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | REF_CLOSE: (8), (10), (20), (136) are inconsistent by sub-proof
% 158.68/25.10  | | | | | | |            #681.
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | Case 2:
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | |   (137)  all_56_7 = e3 & op(e1, e2) = e3
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | ALPHA: (137) implies:
% 158.68/25.10  | | | | | | |   (138)  all_56_7 = e3
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (11), (14), (17), (18),
% 158.68/25.10  | | | | | | |            (19), (21), (22), (23), (25), (27), (29), (30), (31),
% 158.68/25.10  | | | | | | |            (34), (35), (36), (38), (39), (40), (41), (46), (134),
% 158.68/25.10  | | | | | | |            (138) are inconsistent by sub-proof #189.
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | End of split
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | Case 2:
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | |   (139)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 &
% 158.68/25.10  | | | | | |            op(e1, e0) = e3)
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | | BETA: splitting (139) gives:
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | | Case 1:
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | |   (140)  all_56_8 = e3 & op(e1, e1) = e3
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | REF_CLOSE: (7), (21), (140) are inconsistent by sub-proof #193.
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | Case 2:
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | |   (141)  all_56_11 = e3 & op(e1, e0) = e3
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | ALPHA: (141) implies:
% 158.68/25.10  | | | | | | |   (142)  all_56_11 = e3
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | REF_CLOSE: (40), (134), (142) are inconsistent by sub-proof #893.
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | End of split
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | End of split
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | End of split
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | End of split
% 158.68/25.10  | | | 
% 158.68/25.10  | | End of split
% 158.68/25.10  | | 
% 158.68/25.10  | End of split
% 158.68/25.10  | 
% 158.68/25.10  End of proof
% 158.68/25.10  
% 158.68/25.10  Sub-proof #189 shows that the following formulas are inconsistent:
% 158.68/25.10  ----------------------------------------------------------------
% 158.68/25.10    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.68/25.10         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.68/25.10    (2)  all_56_2 = e0
% 158.68/25.10    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.68/25.10         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.68/25.10    (4)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.68/25.10         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.68/25.10    (5)   ~ (e3 = e2)
% 158.68/25.10    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.10    (7)  all_56_11 = e0
% 158.68/25.10    (8)  all_56_12 = e2
% 158.68/25.10    (9)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.68/25.10         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.68/25.10    (10)  op(e0, e0) = e0
% 158.68/25.10    (11)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.68/25.10          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.68/25.10    (12)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.68/25.10          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.68/25.10    (13)  op(e3, e3) = e3
% 158.68/25.10    (14)  all_56_8 = e2
% 158.68/25.10    (15)  op(e2, e2) = e0
% 158.68/25.10    (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.68/25.10          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.68/25.10    (17)  all_56_7 = e3
% 158.68/25.10    (18)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.68/25.10          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.68/25.10    (19)   ~ (e1 = e0)
% 158.68/25.10    (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.68/25.10          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.68/25.10    (21)   ~ (e2 = e1)
% 158.68/25.10    (22)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.68/25.10          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.68/25.10            e3)
% 158.68/25.10    (23)  all_56_15 = e0
% 158.68/25.10    (24)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.68/25.10          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.68/25.10    (25)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.68/25.10          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.68/25.10            e1)
% 158.68/25.10    (26)   ~ (e3 = e1)
% 158.68/25.10    (27)   ~ (e2 = e0)
% 158.68/25.10    (28)   ~ (e3 = e0)
% 158.68/25.10    (29)  all_56_4 = e0
% 158.68/25.10  
% 158.68/25.10  Begin of proof
% 158.68/25.10  | 
% 158.68/25.10  | BETA: splitting (11) gives:
% 158.68/25.10  | 
% 158.68/25.10  | Case 1:
% 158.68/25.10  | | 
% 158.68/25.10  | |   (30)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 158.68/25.10  | |           e3)
% 158.68/25.10  | | 
% 158.68/25.10  | | BETA: splitting (30) gives:
% 158.68/25.10  | | 
% 158.68/25.10  | | Case 1:
% 158.68/25.10  | | | 
% 158.68/25.10  | | |   (31)  all_56_9 = e3 & op(e3, e0) = e3
% 158.68/25.10  | | | 
% 158.68/25.10  | | | ALPHA: (31) implies:
% 158.68/25.10  | | |   (32)  all_56_9 = e3
% 158.68/25.10  | | | 
% 158.68/25.10  | | | REF_CLOSE: (3), (4), (5), (6), (13), (18), (19), (21), (26), (27), (28),
% 158.68/25.10  | | |            (32) are inconsistent by sub-proof #632.
% 158.68/25.10  | | | 
% 158.68/25.10  | | Case 2:
% 158.68/25.10  | | | 
% 158.68/25.10  | | |   (33)  all_56_10 = e3 & op(e2, e0) = e3
% 158.68/25.10  | | | 
% 158.68/25.10  | | | ALPHA: (33) implies:
% 158.68/25.10  | | |   (34)  all_56_10 = e3
% 158.68/25.10  | | | 
% 158.68/25.10  | | | BETA: splitting (24) gives:
% 158.68/25.10  | | | 
% 158.68/25.10  | | | Case 1:
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | |   (35)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3)
% 158.68/25.10  | | | |           = e1)
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | | REF_CLOSE: (2), (6), (13), (19), (26), (35) are inconsistent by
% 158.68/25.10  | | | |            sub-proof #732.
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | Case 2:
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | |   (36)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3)
% 158.68/25.10  | | | |           = e1)
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | | BETA: splitting (36) gives:
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | | Case 1:
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | |   (37)  all_56_6 = e1 & op(e1, e3) = e1
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | | ALPHA: (37) implies:
% 158.68/25.10  | | | | |   (38)  all_56_6 = e1
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | | BETA: splitting (12) gives:
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | | Case 1:
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | |   (39)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2,
% 158.68/25.10  | | | | | |             e0) = e2)
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | | BETA: splitting (39) gives:
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | | Case 1:
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | |   (40)  all_56_9 = e2 & op(e3, e0) = e2
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | ALPHA: (40) implies:
% 158.68/25.10  | | | | | | |   (41)  all_56_9 = e2
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | BETA: splitting (18) gives:
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | Case 1:
% 158.68/25.10  | | | | | | | | 
% 158.68/25.10  | | | | | | | |   (42)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 &
% 158.68/25.10  | | | | | | | |           op(e3, e2) = e1)
% 158.68/25.10  | | | | | | | | 
% 158.68/25.10  | | | | | | | | BETA: splitting (42) gives:
% 158.68/25.10  | | | | | | | | 
% 158.68/25.10  | | | | | | | | Case 1:
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | |   (43)  all_56_0 = e1 & op(e3, e3) = e1
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | ALPHA: (43) implies:
% 158.68/25.10  | | | | | | | | |   (44)  op(e3, e3) = e1
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | REF_CLOSE: (6), (13), (26), (44) are inconsistent by sub-proof
% 158.68/25.10  | | | | | | | | |            #995.
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | |   (45)  all_56_1 = e1 & op(e3, e2) = e1
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | ALPHA: (45) implies:
% 158.68/25.10  | | | | | | | | |   (46)  all_56_1 = e1
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | BETA: splitting (9) gives:
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | Case 1:
% 158.68/25.10  | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | |   (47)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 &
% 158.68/25.10  | | | | | | | | | |           op(e2, e2) = e2)
% 158.68/25.10  | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | REF_CLOSE: (6), (15), (21), (27), (46), (47) are inconsistent
% 158.68/25.10  | | | | | | | | | |            by sub-proof #192.
% 158.68/25.10  | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | |   (48)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2
% 158.68/25.10  | | | | | | | | | |           & op(e0, e2) = e2)
% 158.68/25.10  | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | BETA: splitting (48) gives:
% 158.68/25.10  | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | Case 1:
% 158.68/25.10  | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | |   (49)  all_56_7 = e2 & op(e1, e2) = e2
% 158.68/25.10  | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | REF_CLOSE: (5), (17), (49) are inconsistent by sub-proof
% 158.68/25.10  | | | | | | | | | | |            #940.
% 158.68/25.10  | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | |   (50)  all_56_13 = e2 & op(e0, e2) = e2
% 158.68/25.10  | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | ALPHA: (50) implies:
% 158.68/25.10  | | | | | | | | | | |   (51)  all_56_13 = e2
% 158.68/25.10  | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (8), (13), (19), (20), (21), (22),
% 158.68/25.10  | | | | | | | | | | |            (23), (24), (25), (26), (27), (28), (51) are
% 158.68/25.10  | | | | | | | | | | |            inconsistent by sub-proof #596.
% 158.68/25.10  | | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | 
% 158.68/25.10  | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | 
% 158.68/25.10  | | | | | | | |   (52)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 &
% 158.68/25.10  | | | | | | | |           op(e3, e0) = e1)
% 158.68/25.10  | | | | | | | | 
% 158.68/25.10  | | | | | | | | BETA: splitting (52) gives:
% 158.68/25.10  | | | | | | | | 
% 158.68/25.10  | | | | | | | | Case 1:
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | |   (53)  all_56_4 = e1 & op(e3, e1) = e1
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | ALPHA: (53) implies:
% 158.68/25.10  | | | | | | | | |   (54)  all_56_4 = e1
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | REF_CLOSE: (19), (29), (54) are inconsistent by sub-proof
% 158.68/25.10  | | | | | | | | |            #526.
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | Case 2:
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | |   (55)  all_56_9 = e1 & op(e3, e0) = e1
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | | REF_CLOSE: (21), (41), (55) are inconsistent by sub-proof
% 158.68/25.10  | | | | | | | | |            #948.
% 158.68/25.10  | | | | | | | | | 
% 158.68/25.10  | | | | | | | | End of split
% 158.68/25.10  | | | | | | | | 
% 158.68/25.10  | | | | | | | End of split
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | Case 2:
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | |   (56)  all_56_10 = e2 & op(e2, e0) = e2
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | REF_CLOSE: (5), (34), (56) are inconsistent by sub-proof #470.
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | End of split
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | Case 2:
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | |   (57)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 &
% 158.68/25.10  | | | | | |           op(e0, e0) = e2)
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | | BETA: splitting (57) gives:
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | | Case 1:
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | |   (58)  all_56_11 = e2 & op(e1, e0) = e2
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | ALPHA: (58) implies:
% 158.68/25.10  | | | | | | |   (59)  all_56_11 = e2
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | REF_CLOSE: (14), (16), (17), (19), (27), (28), (38), (59) are
% 158.68/25.10  | | | | | | |            inconsistent by sub-proof #190.
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | Case 2:
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | |   (60)  all_56_15 = e2 & op(e0, e0) = e2
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | ALPHA: (60) implies:
% 158.68/25.10  | | | | | | |   (61)  op(e0, e0) = e2
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | | REF_CLOSE: (6), (10), (27), (61) are inconsistent by sub-proof
% 158.68/25.10  | | | | | | |            #979.
% 158.68/25.10  | | | | | | | 
% 158.68/25.10  | | | | | | End of split
% 158.68/25.10  | | | | | | 
% 158.68/25.10  | | | | | End of split
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | Case 2:
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | |   (62)  all_56_12 = e1 & op(e0, e3) = e1
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | | REF_CLOSE: (8), (21), (62) are inconsistent by sub-proof #769.
% 158.68/25.10  | | | | | 
% 158.68/25.10  | | | | End of split
% 158.68/25.10  | | | | 
% 158.68/25.10  | | | End of split
% 158.68/25.10  | | | 
% 158.68/25.10  | | End of split
% 158.68/25.10  | | 
% 158.68/25.10  | Case 2:
% 158.68/25.10  | | 
% 158.68/25.10  | |   (63)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.68/25.10  | |           e3)
% 158.68/25.10  | | 
% 158.68/25.10  | | BETA: splitting (63) gives:
% 158.68/25.10  | | 
% 158.68/25.10  | | Case 1:
% 158.68/25.10  | | | 
% 158.68/25.10  | | |   (64)  all_56_11 = e3 & op(e1, e0) = e3
% 158.68/25.10  | | | 
% 158.68/25.10  | | | ALPHA: (64) implies:
% 158.68/25.10  | | |   (65)  all_56_11 = e3
% 158.68/25.10  | | | 
% 158.68/25.10  | | | COMBINE_EQS: (7), (65) imply:
% 158.68/25.10  | | |   (66)  e3 = e0
% 158.68/25.10  | | | 
% 158.68/25.10  | | | REDUCE: (28), (66) imply:
% 158.68/25.10  | | |   (67)  $false
% 158.68/25.10  | | | 
% 158.68/25.10  | | | CLOSE: (67) is inconsistent.
% 158.68/25.10  | | | 
% 158.68/25.10  | | Case 2:
% 158.68/25.10  | | | 
% 158.68/25.10  | | |   (68)  all_56_15 = e3 & op(e0, e0) = e3
% 158.68/25.10  | | | 
% 158.68/25.10  | | | REF_CLOSE: (23), (28), (68) are inconsistent by sub-proof #892.
% 158.68/25.10  | | | 
% 158.68/25.10  | | End of split
% 158.68/25.10  | | 
% 158.68/25.10  | End of split
% 158.68/25.10  | 
% 158.68/25.10  End of proof
% 158.68/25.10  
% 158.68/25.10  Sub-proof #190 shows that the following formulas are inconsistent:
% 158.68/25.10  ----------------------------------------------------------------
% 158.68/25.10    (1)  all_56_8 = e2
% 158.68/25.10    (2)  all_56_11 = e2
% 158.68/25.10    (3)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 158.68/25.10         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.68/25.10    (4)  all_56_7 = e3
% 158.68/25.11    (5)   ~ (e1 = e0)
% 158.68/25.11    (6)  all_56_6 = e1
% 158.68/25.11    (7)   ~ (e2 = e0)
% 158.68/25.11    (8)   ~ (e3 = e0)
% 158.68/25.11  
% 158.68/25.11  Begin of proof
% 158.68/25.11  | 
% 158.68/25.11  | BETA: splitting (3) gives:
% 158.68/25.11  | 
% 158.68/25.11  | Case 1:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (9)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0)
% 158.68/25.11  | | 
% 158.68/25.11  | | BETA: splitting (9) gives:
% 158.68/25.11  | | 
% 158.68/25.11  | | Case 1:
% 158.68/25.11  | | | 
% 158.68/25.11  | | |   (10)  all_56_6 = e0 & op(e1, e3) = e0
% 158.68/25.11  | | | 
% 158.68/25.11  | | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #459.
% 158.68/25.11  | | | 
% 158.68/25.11  | | Case 2:
% 158.68/25.11  | | | 
% 158.68/25.11  | | |   (11)  all_56_7 = e0 & op(e1, e2) = e0
% 158.68/25.11  | | | 
% 158.68/25.11  | | | REF_CLOSE: (4), (8), (11) are inconsistent by sub-proof #909.
% 158.68/25.11  | | | 
% 158.68/25.11  | | End of split
% 158.68/25.11  | | 
% 158.68/25.11  | Case 2:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (12)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 158.68/25.11  | |           e0)
% 158.68/25.11  | | 
% 158.68/25.11  | | BETA: splitting (12) gives:
% 158.68/25.11  | | 
% 158.68/25.11  | | Case 1:
% 158.68/25.11  | | | 
% 158.68/25.11  | | |   (13)  all_56_8 = e0 & op(e1, e1) = e0
% 158.68/25.11  | | | 
% 158.68/25.11  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #191.
% 158.68/25.11  | | | 
% 158.68/25.11  | | Case 2:
% 158.68/25.11  | | | 
% 158.68/25.11  | | |   (14)  all_56_11 = e0 & op(e1, e0) = e0
% 158.68/25.11  | | | 
% 158.68/25.11  | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #739.
% 158.68/25.11  | | | 
% 158.68/25.11  | | End of split
% 158.68/25.11  | | 
% 158.68/25.11  | End of split
% 158.68/25.11  | 
% 158.68/25.11  End of proof
% 158.68/25.11  
% 158.68/25.11  Sub-proof #191 shows that the following formulas are inconsistent:
% 158.68/25.11  ----------------------------------------------------------------
% 158.68/25.11    (1)  all_56_8 = e0 & op(e1, e1) = e0
% 158.68/25.11    (2)  all_56_8 = e2
% 158.68/25.11    (3)   ~ (e2 = e0)
% 158.68/25.11  
% 158.68/25.11  Begin of proof
% 158.68/25.11  | 
% 158.68/25.11  | ALPHA: (1) implies:
% 158.68/25.11  |   (4)  all_56_8 = e0
% 158.68/25.11  | 
% 158.68/25.11  | COMBINE_EQS: (2), (4) imply:
% 158.68/25.11  |   (5)  e2 = e0
% 158.68/25.11  | 
% 158.68/25.11  | REDUCE: (3), (5) imply:
% 158.68/25.11  |   (6)  $false
% 158.68/25.11  | 
% 158.68/25.11  | CLOSE: (6) is inconsistent.
% 158.68/25.11  | 
% 158.68/25.11  End of proof
% 158.68/25.11  
% 158.68/25.11  Sub-proof #192 shows that the following formulas are inconsistent:
% 158.68/25.11  ----------------------------------------------------------------
% 158.68/25.11    (1)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 158.68/25.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.11    (3)  all_56_1 = e1
% 158.68/25.11    (4)  op(e2, e2) = e0
% 158.68/25.11    (5)   ~ (e2 = e1)
% 158.68/25.11    (6)   ~ (e2 = e0)
% 158.68/25.11  
% 158.68/25.11  Begin of proof
% 158.68/25.11  | 
% 158.68/25.11  | BETA: splitting (1) gives:
% 158.68/25.11  | 
% 158.68/25.11  | Case 1:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (7)  all_56_1 = e2 & op(e3, e2) = e2
% 158.68/25.11  | | 
% 158.68/25.11  | | ALPHA: (7) implies:
% 158.68/25.11  | |   (8)  all_56_1 = e2
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #680.
% 158.68/25.11  | | 
% 158.68/25.11  | Case 2:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (9)  all_56_3 = e2 & op(e2, e2) = e2
% 158.68/25.11  | | 
% 158.68/25.11  | | ALPHA: (9) implies:
% 158.68/25.11  | |   (10)  op(e2, e2) = e2
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #942.
% 158.68/25.11  | | 
% 158.68/25.11  | End of split
% 158.68/25.11  | 
% 158.68/25.11  End of proof
% 158.68/25.11  
% 158.68/25.11  Sub-proof #193 shows that the following formulas are inconsistent:
% 158.68/25.11  ----------------------------------------------------------------
% 158.68/25.11    (1)  all_56_8 = e3 & op(e1, e1) = e3
% 158.68/25.11    (2)  all_56_8 = e2
% 158.68/25.11    (3)   ~ (e3 = e2)
% 158.68/25.11  
% 158.68/25.11  Begin of proof
% 158.68/25.11  | 
% 158.68/25.11  | ALPHA: (1) implies:
% 158.68/25.11  |   (4)  all_56_8 = e3
% 158.68/25.11  | 
% 158.68/25.11  | COMBINE_EQS: (2), (4) imply:
% 158.68/25.11  |   (5)  e3 = e2
% 158.68/25.11  | 
% 158.68/25.11  | SIMP: (5) implies:
% 158.68/25.11  |   (6)  e3 = e2
% 158.68/25.11  | 
% 158.68/25.11  | REDUCE: (3), (6) imply:
% 158.68/25.11  |   (7)  $false
% 158.68/25.11  | 
% 158.68/25.11  | CLOSE: (7) is inconsistent.
% 158.68/25.11  | 
% 158.68/25.11  End of proof
% 158.68/25.11  
% 158.68/25.11  Sub-proof #194 shows that the following formulas are inconsistent:
% 158.68/25.11  ----------------------------------------------------------------
% 158.68/25.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.11    (2)  op(e2, e1) = all_10_0
% 158.68/25.11    (3)  op(e2, e1) = all_52_9
% 158.68/25.11    (4)  op(e2, e1) = e2
% 158.68/25.11    (5)   ~ (all_52_9 = e2)
% 158.68/25.11  
% 158.68/25.11  Begin of proof
% 158.68/25.11  | 
% 158.68/25.11  | GROUND_INST: instantiating (1) with all_52_9, e2, e1, e2, simplifying with
% 158.68/25.11  |              (3), (4) gives:
% 158.68/25.11  |   (6)  all_52_9 = e2
% 158.68/25.11  | 
% 158.68/25.11  | GROUND_INST: instantiating (1) with all_52_9, all_10_0, e1, e2, simplifying
% 158.68/25.11  |              with (2), (3) gives:
% 158.68/25.11  |   (7)  all_52_9 = all_10_0
% 158.68/25.11  | 
% 158.68/25.11  | COMBINE_EQS: (6), (7) imply:
% 158.68/25.11  |   (8)  all_10_0 = e2
% 158.68/25.11  | 
% 158.68/25.11  | REDUCE: (5), (6) imply:
% 158.68/25.11  |   (9)  $false
% 158.68/25.11  | 
% 158.68/25.11  | CLOSE: (9) is inconsistent.
% 158.68/25.11  | 
% 158.68/25.11  End of proof
% 158.68/25.11  
% 158.68/25.11  Sub-proof #195 shows that the following formulas are inconsistent:
% 158.68/25.11  ----------------------------------------------------------------
% 158.68/25.11    (1)  op(e0, e3) = e2
% 158.68/25.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.11    (3)  op(e0, e3) = all_52_3
% 158.68/25.11    (4)  op(e3, e3) = e3
% 158.68/25.11    (5)  op(e2, e0) = all_52_13
% 158.68/25.11    (6)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.68/25.11         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.68/25.11           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.68/25.11           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 158.68/25.11           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.68/25.11    (7)   ~ (e2 = e0)
% 158.68/25.11    (8)   ~ (e3 = e0)
% 158.68/25.11    (9)   ~ (all_52_13 = e2)
% 158.68/25.11  
% 158.68/25.11  Begin of proof
% 158.68/25.11  | 
% 158.68/25.11  | BETA: splitting (6) gives:
% 158.68/25.11  | 
% 158.68/25.11  | Case 1:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (10)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 158.68/25.11  | | 
% 158.68/25.11  | | ALPHA: (10) implies:
% 158.68/25.11  | |   (11)  op(e0, e3) = e0
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (1), (2), (3), (7), (11) are inconsistent by sub-proof #689.
% 158.68/25.11  | | 
% 158.68/25.11  | Case 2:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (12)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.68/25.11  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.68/25.11  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.68/25.11  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (2), (4), (5), (8), (9), (12) are inconsistent by sub-proof #864.
% 158.68/25.11  | | 
% 158.68/25.11  | End of split
% 158.68/25.11  | 
% 158.68/25.11  End of proof
% 158.68/25.11  
% 158.68/25.11  Sub-proof #196 shows that the following formulas are inconsistent:
% 158.68/25.11  ----------------------------------------------------------------
% 158.68/25.11    (1)  op(e0, e3) = e2
% 158.68/25.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.11    (3)  op(e0, e3) = all_52_3
% 158.68/25.11    (4)  op(e2, e2) = e2
% 158.68/25.11    (5)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.68/25.11           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.68/25.11           = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3
% 158.68/25.11           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.68/25.11           op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 158.68/25.11    (6)   ~ (e2 = e1)
% 158.68/25.11    (7)   ~ (e2 = e0)
% 158.68/25.11  
% 158.68/25.11  Begin of proof
% 158.68/25.11  | 
% 158.68/25.11  | BETA: splitting (5) gives:
% 158.68/25.11  | 
% 158.68/25.11  | Case 1:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (8)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 158.68/25.11  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.68/25.11  | |          e0) = e1 & $i(all_57_14)
% 158.68/25.11  | | 
% 158.68/25.11  | | ALPHA: (8) implies:
% 158.68/25.11  | |   (9)  op(e2, e2) = e1
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #993.
% 158.68/25.11  | | 
% 158.68/25.11  | Case 2:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (10)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0)
% 158.68/25.11  | |         & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 158.68/25.11  | |         op(e0, e0) = e3 & $i(all_57_10)
% 158.68/25.11  | | 
% 158.68/25.11  | | ALPHA: (10) implies:
% 158.68/25.11  | |   (11)  op(e0, e3) = e0
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (1), (2), (3), (7), (11) are inconsistent by sub-proof #689.
% 158.68/25.11  | | 
% 158.68/25.11  | End of split
% 158.68/25.11  | 
% 158.68/25.11  End of proof
% 158.68/25.11  
% 158.68/25.11  Sub-proof #197 shows that the following formulas are inconsistent:
% 158.68/25.11  ----------------------------------------------------------------
% 158.68/25.11    (1)  op(e0, e3) = e2
% 158.68/25.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.11    (3)  op(e0, e3) = all_52_3
% 158.68/25.11    (4)  op(e3, e1) = all_52_8
% 158.68/25.11    (5)  op(e1, e1) = e2
% 158.68/25.11    (6)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 158.68/25.11           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.68/25.11           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1)
% 158.68/25.11           & op(e1, e2) = e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.68/25.11           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.68/25.11             e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.68/25.11         (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 158.68/25.11             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.68/25.11           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.68/25.11           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.68/25.11    (7)  op(e3, e3) = e3
% 158.68/25.11    (8)  op(e2, e0) = all_52_13
% 158.68/25.11    (9)   ~ (e3 = e1)
% 158.68/25.11    (10)   ~ (e2 = e0)
% 158.68/25.11    (11)   ~ (all_52_8 = e3)
% 158.68/25.11    (12)   ~ (all_52_13 = e2)
% 158.68/25.11  
% 158.68/25.11  Begin of proof
% 158.68/25.11  | 
% 158.68/25.11  | BETA: splitting (6) gives:
% 158.68/25.11  | 
% 158.68/25.11  | Case 1:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (13)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 158.68/25.11  | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1
% 158.68/25.11  | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 =
% 158.68/25.11  | |           e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1)
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (2), (5), (8), (12), (13) are inconsistent by sub-proof #198.
% 158.68/25.11  | | 
% 158.68/25.11  | Case 2:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (14)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 158.68/25.11  | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0
% 158.68/25.11  | |           & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 =
% 158.68/25.11  | |           e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4
% 158.68/25.11  | |           = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.68/25.11  | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.68/25.11  | |           op(e1, e0) = e1 & $i(all_57_14))
% 158.68/25.11  | | 
% 158.68/25.11  | | BETA: splitting (14) gives:
% 158.68/25.11  | | 
% 158.68/25.11  | | Case 1:
% 158.68/25.11  | | | 
% 158.68/25.11  | | |   (15)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 158.68/25.11  | | |           e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0
% 158.68/25.11  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 158.68/25.11  | | | 
% 158.68/25.11  | | | ALPHA: (15) implies:
% 158.68/25.11  | | |   (16)  op(e0, e3) = e0
% 158.68/25.11  | | | 
% 158.68/25.11  | | | REF_CLOSE: (1), (2), (3), (10), (16) are inconsistent by sub-proof #689.
% 158.68/25.11  | | | 
% 158.68/25.11  | | Case 2:
% 158.68/25.11  | | | 
% 158.68/25.11  | | |   (17)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.68/25.11  | | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 =
% 158.68/25.11  | | |           e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.68/25.11  | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.68/25.11  | | | 
% 158.68/25.11  | | | REF_CLOSE: (2), (4), (7), (9), (11), (17) are inconsistent by sub-proof
% 158.68/25.11  | | |            #981.
% 158.68/25.11  | | | 
% 158.68/25.11  | | End of split
% 158.68/25.11  | | 
% 158.68/25.11  | End of split
% 158.68/25.11  | 
% 158.68/25.11  End of proof
% 158.68/25.11  
% 158.68/25.11  Sub-proof #198 shows that the following formulas are inconsistent:
% 158.68/25.11  ----------------------------------------------------------------
% 158.68/25.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.11    (2)  op(e1, e1) = e2
% 158.68/25.11    (3)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 158.68/25.11           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.68/25.11           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1)
% 158.68/25.11           & op(e1, e2) = e1 & op(e1, e1) = e1)
% 158.68/25.11    (4)  op(e2, e0) = all_52_13
% 158.68/25.11    (5)   ~ (all_52_13 = e2)
% 158.68/25.11  
% 158.68/25.11  Begin of proof
% 158.68/25.11  | 
% 158.68/25.11  | BETA: splitting (3) gives:
% 158.68/25.11  | 
% 158.68/25.11  | Case 1:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (6)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0)
% 158.68/25.11  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1,
% 158.68/25.11  | |          e1) = e2 & $i(all_57_12)
% 158.68/25.11  | | 
% 158.68/25.11  | | ALPHA: (6) implies:
% 158.68/25.11  | |   (7)  op(e2, e0) = e2
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #996.
% 158.68/25.11  | | 
% 158.68/25.11  | Case 2:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (8)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.68/25.11  | |        op(e1, e1) = e1
% 158.68/25.11  | | 
% 158.68/25.11  | | ALPHA: (8) implies:
% 158.68/25.11  | |   (9)   ~ (e2 = e1)
% 158.68/25.11  | |   (10)  op(e1, e1) = e1
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #986.
% 158.68/25.11  | | 
% 158.68/25.11  | End of split
% 158.68/25.11  | 
% 158.68/25.11  End of proof
% 158.68/25.11  
% 158.68/25.11  Sub-proof #199 shows that the following formulas are inconsistent:
% 158.68/25.11  ----------------------------------------------------------------
% 158.68/25.11    (1)  op(e0, e1) = all_52_11
% 158.68/25.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.11    (3)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 158.68/25.11           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.68/25.11           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 158.68/25.11           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.68/25.11           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 158.68/25.11    (4)  op(e2, e1) = all_52_9
% 158.68/25.11    (5)   ~ (all_52_11 = e0)
% 158.68/25.11    (6)   ~ (all_52_9 = e2)
% 158.68/25.11  
% 158.68/25.11  Begin of proof
% 158.68/25.11  | 
% 158.68/25.11  | BETA: splitting (3) gives:
% 158.68/25.11  | 
% 158.68/25.11  | Case 1:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (7)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 158.68/25.11  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 158.68/25.11  | |          e1) = e2 & $i(all_57_12)
% 158.68/25.11  | | 
% 158.68/25.11  | | ALPHA: (7) implies:
% 158.68/25.11  | |   (8)  op(e2, e1) = e2
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1002.
% 158.68/25.11  | | 
% 158.68/25.11  | Case 2:
% 158.68/25.11  | | 
% 158.68/25.11  | |   (9)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 158.68/25.11  | |        & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.68/25.11  | |          e0) = e1 & $i(all_57_14)
% 158.68/25.11  | | 
% 158.68/25.11  | | ALPHA: (9) implies:
% 158.68/25.11  | |   (10)  op(e0, e1) = e0
% 158.68/25.11  | | 
% 158.68/25.11  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #966.
% 158.68/25.11  | | 
% 158.68/25.11  | End of split
% 158.68/25.11  | 
% 158.68/25.11  End of proof
% 158.68/25.11  
% 158.68/25.11  Sub-proof #200 shows that the following formulas are inconsistent:
% 158.68/25.11  ----------------------------------------------------------------
% 158.68/25.11    (1)  op(e0, e1) = all_52_11
% 158.68/25.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.11    (3)   ~ (all_52_12 = e3)
% 158.68/25.11    (4)  op(e1, e1) = e2
% 158.68/25.11    (5)   ~ (all_52_11 = e0)
% 158.68/25.11    (6)   ~ (e2 = e1)
% 158.68/25.11    (7)  op(e3, e0) = all_52_12
% 158.68/25.12    (8)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.68/25.12           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.68/25.12           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 158.68/25.12           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.68/25.12           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 158.68/25.12           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.68/25.12  
% 158.68/25.12  Begin of proof
% 158.68/25.12  | 
% 158.68/25.12  | BETA: splitting (8) gives:
% 158.68/25.12  | 
% 158.68/25.12  | Case 1:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (9)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 158.68/25.12  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.68/25.12  | |          e0) = e1 & $i(all_57_14)
% 158.68/25.12  | | 
% 158.68/25.12  | | ALPHA: (9) implies:
% 158.68/25.12  | |   (10)  op(e0, e1) = e0
% 158.68/25.12  | | 
% 158.68/25.12  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #966.
% 158.68/25.12  | | 
% 158.68/25.12  | Case 2:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (11)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.68/25.12  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 158.68/25.12  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 158.68/25.12  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.68/25.12  | | 
% 158.68/25.12  | | REF_CLOSE: (2), (3), (4), (6), (7), (11) are inconsistent by sub-proof #747.
% 158.68/25.12  | | 
% 158.68/25.12  | End of split
% 158.68/25.12  | 
% 158.68/25.12  End of proof
% 158.68/25.12  
% 158.68/25.12  Sub-proof #201 shows that the following formulas are inconsistent:
% 158.68/25.12  ----------------------------------------------------------------
% 158.68/25.12    (1)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.68/25.12    (2)  op(e0, e0) = e1
% 158.68/25.12    (3)  all_54_9 = all_52_6
% 158.68/25.12    (4)  all_54_13 = all_52_7
% 158.68/25.12    (5)  op(e1, e1) = e0
% 158.68/25.12    (6)   ~ (all_52_6 = all_52_7)
% 158.68/25.12    (7)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.68/25.12    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.12    (9)   ~ (all_52_6 = e0)
% 158.68/25.12    (10)  op(e0, e2) = all_52_7
% 158.68/25.12    (11)  op(e1, e2) = all_52_6
% 158.68/25.12    (12)   ~ (all_52_6 = all_4_2)
% 158.68/25.12    (13)  op(e2, e2) = all_4_2
% 158.68/25.12    (14)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.68/25.12            ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.68/25.12          ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 158.68/25.12              all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) | (
% 158.68/25.12              ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))
% 158.68/25.12    (15)   ~ (all_52_7 = all_4_2)
% 158.68/25.12    (16)   ~ (e2 = e1)
% 158.68/25.12    (17)   ~ (all_52_7 = e1)
% 158.68/25.12    (18)   ~ (e2 = e0)
% 158.68/25.12  
% 158.68/25.12  Begin of proof
% 158.68/25.12  | 
% 158.68/25.12  | ALPHA: (14) implies:
% 158.68/25.12  |   (19)  op(e2, e2) = e2
% 158.68/25.12  |   (20)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2)
% 158.68/25.12  |           = all_57_7 & $i(all_57_7))
% 158.68/25.12  |   (21)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.68/25.12  |           = all_57_3 & $i(all_57_3))
% 158.68/25.12  | 
% 158.68/25.12  | BETA: splitting (20) gives:
% 158.68/25.12  | 
% 158.68/25.12  | Case 1:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (22)  all_57_15 = e2 & op(e0, e0) = e2
% 158.68/25.12  | | 
% 158.68/25.12  | | ALPHA: (22) implies:
% 158.68/25.12  | |   (23)  op(e0, e0) = e2
% 158.68/25.12  | | 
% 158.68/25.12  | | REF_CLOSE: (2), (8), (16), (23) are inconsistent by sub-proof #875.
% 158.68/25.12  | | 
% 158.68/25.12  | Case 2:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (24)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)
% 158.68/25.12  | | 
% 158.68/25.12  | | ALPHA: (24) implies:
% 158.68/25.12  | |   (25)   ~ (all_57_7 = e0)
% 158.68/25.12  | |   (26)  op(e0, e2) = all_57_7
% 158.68/25.12  | | 
% 158.68/25.12  | | BETA: splitting (21) gives:
% 158.68/25.12  | | 
% 158.68/25.12  | | Case 1:
% 158.68/25.12  | | | 
% 158.68/25.12  | | |   (27)  all_57_14 = e2 & op(e1, e1) = e2
% 158.68/25.12  | | | 
% 158.68/25.12  | | | ALPHA: (27) implies:
% 158.68/25.12  | | |   (28)  op(e1, e1) = e2
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REF_CLOSE: (5), (8), (18), (28) are inconsistent by sub-proof #914.
% 158.68/25.12  | | | 
% 158.68/25.12  | | Case 2:
% 158.68/25.12  | | | 
% 158.68/25.12  | | |   (29)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | ALPHA: (29) implies:
% 158.68/25.12  | | |   (30)   ~ (all_57_3 = e1)
% 158.68/25.12  | | |   (31)  op(e1, e2) = all_57_3
% 158.68/25.12  | | | 
% 158.68/25.12  | | | GROUND_INST: instantiating (8) with all_52_7, all_57_7, e2, e0,
% 158.68/25.12  | | |              simplifying with (10), (26) gives:
% 158.68/25.12  | | |   (32)  all_57_7 = all_52_7
% 158.68/25.12  | | | 
% 158.68/25.12  | | | GROUND_INST: instantiating (8) with all_52_6, all_57_3, e2, e1,
% 158.68/25.12  | | |              simplifying with (11), (31) gives:
% 158.68/25.12  | | |   (33)  all_57_3 = all_52_6
% 158.68/25.12  | | | 
% 158.68/25.12  | | | GROUND_INST: instantiating (8) with all_4_2, e2, e2, e2, simplifying with
% 158.68/25.12  | | |              (13), (19) gives:
% 158.68/25.12  | | |   (34)  all_4_2 = e2
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REDUCE: (30), (33) imply:
% 158.68/25.12  | | |   (35)   ~ (all_52_6 = e1)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REDUCE: (25), (32) imply:
% 158.68/25.12  | | |   (36)   ~ (all_52_7 = e0)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REDUCE: (12), (34) imply:
% 158.68/25.12  | | |   (37)   ~ (all_52_6 = e2)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REDUCE: (15), (34) imply:
% 158.68/25.12  | | |   (38)   ~ (all_52_7 = e2)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | BETA: splitting (1) gives:
% 158.68/25.12  | | | 
% 158.68/25.12  | | | Case 1:
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | |   (39)  all_54_9 = e3
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | | COMBINE_EQS: (3), (39) imply:
% 158.68/25.12  | | | |   (40)  all_52_6 = e3
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | | SIMP: (40) implies:
% 158.68/25.12  | | | |   (41)  all_52_6 = e3
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | | REDUCE: (6), (41) imply:
% 158.68/25.12  | | | |   (42)   ~ (all_52_7 = e3)
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | | SIMP: (42) implies:
% 158.68/25.12  | | | |   (43)   ~ (all_52_7 = e3)
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | | REF_CLOSE: (4), (7), (17), (36), (38), (43) are inconsistent by
% 158.68/25.12  | | | |            sub-proof #207.
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | Case 2:
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | |   (44)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | | REF_CLOSE: (3), (9), (35), (37), (44) are inconsistent by sub-proof
% 158.68/25.12  | | | |            #673.
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | End of split
% 158.68/25.12  | | | 
% 158.68/25.12  | | End of split
% 158.68/25.12  | | 
% 158.68/25.12  | End of split
% 158.68/25.12  | 
% 158.68/25.12  End of proof
% 158.68/25.12  
% 158.68/25.12  Sub-proof #202 shows that the following formulas are inconsistent:
% 158.68/25.12  ----------------------------------------------------------------
% 158.68/25.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.12    (2)  op(e0, e3) = all_52_3
% 158.68/25.12    (3)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.68/25.12    (4)  op(e1, e3) = all_52_2
% 158.68/25.12    (5)   ~ (all_52_2 = e1)
% 158.68/25.12    (6)   ~ (all_52_3 = e1)
% 158.68/25.12  
% 158.68/25.12  Begin of proof
% 158.68/25.12  | 
% 158.68/25.12  | BETA: splitting (3) gives:
% 158.68/25.12  | 
% 158.68/25.12  | Case 1:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (7)  all_56_6 = e1 & op(e1, e3) = e1
% 158.68/25.12  | | 
% 158.68/25.12  | | ALPHA: (7) implies:
% 158.68/25.12  | |   (8)  op(e1, e3) = e1
% 158.68/25.12  | | 
% 158.68/25.12  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #990.
% 158.68/25.12  | | 
% 158.68/25.12  | Case 2:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (9)  all_56_12 = e1 & op(e0, e3) = e1
% 158.68/25.12  | | 
% 158.68/25.12  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #852.
% 158.68/25.12  | | 
% 158.68/25.12  | End of split
% 158.68/25.12  | 
% 158.68/25.12  End of proof
% 158.68/25.12  
% 158.68/25.12  Sub-proof #203 shows that the following formulas are inconsistent:
% 158.68/25.12  ----------------------------------------------------------------
% 158.68/25.12    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.68/25.12         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.68/25.12    (2)  all_56_2 = e3
% 158.68/25.12    (3)   ~ (e3 = e2)
% 158.68/25.12    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.12    (5)  op(e0, e3) = all_52_3
% 158.68/25.12    (6)  op(e1, e3) = all_52_2
% 158.68/25.12    (7)   ~ (all_52_2 = e2)
% 158.68/25.12    (8)  op(e0, e3) = e0
% 158.68/25.12    (9)  all_56_0 = e1
% 158.68/25.12    (10)   ~ (e2 = e1)
% 158.68/25.12    (11)   ~ (e2 = e0)
% 158.68/25.12  
% 158.68/25.12  Begin of proof
% 158.68/25.12  | 
% 158.68/25.12  | BETA: splitting (1) gives:
% 158.68/25.12  | 
% 158.68/25.12  | Case 1:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (12)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 158.68/25.12  | |           e2)
% 158.68/25.12  | | 
% 158.68/25.12  | | BETA: splitting (12) gives:
% 158.68/25.12  | | 
% 158.68/25.12  | | Case 1:
% 158.68/25.12  | | | 
% 158.68/25.12  | | |   (13)  all_56_0 = e2 & op(e3, e3) = e2
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REF_CLOSE: (9), (10), (13) are inconsistent by sub-proof #490.
% 158.68/25.12  | | | 
% 158.68/25.12  | | Case 2:
% 158.68/25.12  | | | 
% 158.68/25.12  | | |   (14)  all_56_2 = e2 & op(e2, e3) = e2
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REF_CLOSE: (2), (3), (14) are inconsistent by sub-proof #778.
% 158.68/25.12  | | | 
% 158.68/25.12  | | End of split
% 158.68/25.12  | | 
% 158.68/25.12  | Case 2:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (15)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 158.68/25.12  | |           e2)
% 158.68/25.12  | | 
% 158.68/25.12  | | REF_CLOSE: (4), (5), (6), (7), (8), (11), (15) are inconsistent by sub-proof
% 158.68/25.12  | |            #589.
% 158.68/25.12  | | 
% 158.68/25.12  | End of split
% 158.68/25.12  | 
% 158.68/25.12  End of proof
% 158.68/25.12  
% 158.68/25.12  Sub-proof #204 shows that the following formulas are inconsistent:
% 158.68/25.12  ----------------------------------------------------------------
% 158.68/25.12    (1)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.68/25.12    (2)  all_54_13 = all_52_7
% 158.68/25.12    (3)  op(e0, e1) = all_52_11
% 158.68/25.12    (4)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.68/25.12    (5)   ~ (e3 = e2)
% 158.68/25.12    (6)   ~ (all_52_7 = e3)
% 158.68/25.12    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.12    (8)  op(e0, e0) = e3
% 158.68/25.12    (9)  op(e0, e2) = all_52_7
% 158.68/25.12    (10)  op(e2, e2) = all_4_2
% 158.68/25.12    (11)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.68/25.12            ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.68/25.12          ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 158.68/25.12              all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) | (
% 158.68/25.12              ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))
% 158.68/25.12    (12)  ( ~ (all_22_0 = e2) & op(e0, e1) = all_22_0 & $i(all_22_0)) | ( ~
% 158.68/25.12            (all_22_1 = e3) & op(e0, e0) = all_22_1 & $i(all_22_1))
% 158.68/25.12    (13)   ~ (all_52_7 = all_4_2)
% 158.68/25.12    (14)  all_54_14 = all_52_11
% 158.68/25.12    (15)   ~ (all_52_11 = e0)
% 158.68/25.12    (16)   ~ (all_52_7 = all_52_11)
% 158.68/25.12    (17)   ~ (all_52_11 = e3)
% 158.68/25.12  
% 158.68/25.12  Begin of proof
% 158.68/25.12  | 
% 158.68/25.12  | ALPHA: (11) implies:
% 158.68/25.12  |   (18)  op(e2, e2) = e2
% 158.68/25.12  |   (19)  (all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2)
% 158.68/25.12  |           = all_57_7 & $i(all_57_7))
% 158.68/25.12  | 
% 158.68/25.12  | BETA: splitting (19) gives:
% 158.68/25.12  | 
% 158.68/25.12  | Case 1:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (20)  all_57_15 = e2 & op(e0, e0) = e2
% 158.68/25.12  | | 
% 158.68/25.12  | | ALPHA: (20) implies:
% 158.68/25.12  | |   (21)  op(e0, e0) = e2
% 158.68/25.12  | | 
% 158.68/25.12  | | REF_CLOSE: (5), (7), (8), (21) are inconsistent by sub-proof #878.
% 158.68/25.12  | | 
% 158.68/25.12  | Case 2:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (22)   ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)
% 158.68/25.12  | | 
% 158.68/25.12  | | ALPHA: (22) implies:
% 158.68/25.12  | |   (23)   ~ (all_57_7 = e0)
% 158.68/25.12  | |   (24)  op(e0, e2) = all_57_7
% 158.68/25.12  | | 
% 158.68/25.12  | | BETA: splitting (12) gives:
% 158.68/25.12  | | 
% 158.68/25.12  | | Case 1:
% 158.68/25.12  | | | 
% 158.68/25.12  | | |   (25)   ~ (all_22_0 = e2) & op(e0, e1) = all_22_0 & $i(all_22_0)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | ALPHA: (25) implies:
% 158.68/25.12  | | |   (26)   ~ (all_22_0 = e2)
% 158.68/25.12  | | |   (27)  op(e0, e1) = all_22_0
% 158.68/25.12  | | | 
% 158.68/25.12  | | | GROUND_INST: instantiating (7) with all_52_11, all_22_0, e1, e0,
% 158.68/25.12  | | |              simplifying with (3), (27) gives:
% 158.68/25.12  | | |   (28)  all_52_11 = all_22_0
% 158.68/25.12  | | | 
% 158.68/25.12  | | | GROUND_INST: instantiating (7) with all_52_7, all_57_7, e2, e0,
% 158.68/25.12  | | |              simplifying with (9), (24) gives:
% 158.68/25.12  | | |   (29)  all_57_7 = all_52_7
% 158.68/25.12  | | | 
% 158.68/25.12  | | | GROUND_INST: instantiating (7) with all_4_2, e2, e2, e2, simplifying with
% 158.68/25.12  | | |              (10), (18) gives:
% 158.68/25.12  | | |   (30)  all_4_2 = e2
% 158.68/25.12  | | | 
% 158.68/25.12  | | | COMBINE_EQS: (14), (28) imply:
% 158.68/25.12  | | |   (31)  all_54_14 = all_22_0
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REDUCE: (23), (29) imply:
% 158.68/25.12  | | |   (32)   ~ (all_52_7 = e0)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REDUCE: (16), (28) imply:
% 158.68/25.12  | | |   (33)   ~ (all_52_7 = all_22_0)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REDUCE: (13), (30) imply:
% 158.68/25.12  | | |   (34)   ~ (all_52_7 = e2)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REDUCE: (17), (28) imply:
% 158.68/25.12  | | |   (35)   ~ (all_22_0 = e3)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REDUCE: (15), (28) imply:
% 158.68/25.12  | | |   (36)   ~ (all_22_0 = e0)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | BETA: splitting (1) gives:
% 158.68/25.12  | | | 
% 158.68/25.12  | | | Case 1:
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | |   (37)  all_54_14 = e3
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | | REF_CLOSE: (31), (35), (37) are inconsistent by sub-proof #387.
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | Case 2:
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | |   (38)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | | BETA: splitting (38) gives:
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | | Case 1:
% 158.68/25.12  | | | | | 
% 158.68/25.12  | | | | |   (39)  all_54_14 = e2
% 158.68/25.12  | | | | | 
% 158.68/25.12  | | | | | REF_CLOSE: (26), (31), (39) are inconsistent by sub-proof #386.
% 158.68/25.12  | | | | | 
% 158.68/25.12  | | | | Case 2:
% 158.68/25.12  | | | | | 
% 158.68/25.12  | | | | |   (40)  all_54_14 = e1 | all_54_14 = e0
% 158.68/25.12  | | | | | 
% 158.68/25.12  | | | | | BETA: splitting (4) gives:
% 158.68/25.12  | | | | | 
% 158.68/25.12  | | | | | Case 1:
% 158.68/25.12  | | | | | | 
% 158.68/25.12  | | | | | |   (41)  all_54_13 = e3
% 158.68/25.12  | | | | | | 
% 158.68/25.12  | | | | | | REF_CLOSE: (2), (6), (41) are inconsistent by sub-proof #385.
% 158.68/25.12  | | | | | | 
% 158.68/25.12  | | | | | Case 2:
% 158.68/25.12  | | | | | | 
% 158.68/25.12  | | | | | |   (42)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.68/25.12  | | | | | | 
% 158.68/25.12  | | | | | | BETA: splitting (40) gives:
% 158.68/25.12  | | | | | | 
% 158.68/25.12  | | | | | | Case 1:
% 158.68/25.12  | | | | | | | 
% 158.68/25.12  | | | | | | |   (43)  all_54_14 = e1
% 158.68/25.12  | | | | | | | 
% 158.68/25.12  | | | | | | | COMBINE_EQS: (31), (43) imply:
% 158.68/25.12  | | | | | | |   (44)  all_22_0 = e1
% 158.68/25.12  | | | | | | | 
% 158.68/25.12  | | | | | | | SIMP: (44) implies:
% 158.68/25.12  | | | | | | |   (45)  all_22_0 = e1
% 158.68/25.12  | | | | | | | 
% 158.68/25.12  | | | | | | | REDUCE: (33), (45) imply:
% 158.68/25.12  | | | | | | |   (46)   ~ (all_52_7 = e1)
% 158.68/25.12  | | | | | | | 
% 158.68/25.12  | | | | | | | REF_CLOSE: (2), (32), (34), (42), (46) are inconsistent by
% 158.68/25.12  | | | | | | |            sub-proof #502.
% 158.68/25.12  | | | | | | | 
% 158.68/25.12  | | | | | | Case 2:
% 158.68/25.12  | | | | | | | 
% 158.68/25.12  | | | | | | |   (47)  all_54_14 = e0
% 158.68/25.12  | | | | | | | 
% 158.68/25.12  | | | | | | | REF_CLOSE: (31), (36), (47) are inconsistent by sub-proof #363.
% 158.68/25.12  | | | | | | | 
% 158.68/25.12  | | | | | | End of split
% 158.68/25.12  | | | | | | 
% 158.68/25.12  | | | | | End of split
% 158.68/25.12  | | | | | 
% 158.68/25.12  | | | | End of split
% 158.68/25.12  | | | | 
% 158.68/25.12  | | | End of split
% 158.68/25.12  | | | 
% 158.68/25.12  | | Case 2:
% 158.68/25.12  | | | 
% 158.68/25.12  | | |   (48)   ~ (all_22_1 = e3) & op(e0, e0) = all_22_1 & $i(all_22_1)
% 158.68/25.12  | | | 
% 158.68/25.12  | | | REF_CLOSE: (7), (8), (48) are inconsistent by sub-proof #362.
% 158.68/25.12  | | | 
% 158.68/25.12  | | End of split
% 158.68/25.12  | | 
% 158.68/25.12  | End of split
% 158.68/25.12  | 
% 158.68/25.12  End of proof
% 158.68/25.12  
% 158.68/25.12  Sub-proof #205 shows that the following formulas are inconsistent:
% 158.68/25.12  ----------------------------------------------------------------
% 158.68/25.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.12    (2)  op(e0, e0) = e3
% 158.68/25.12    (3)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.68/25.12           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.68/25.12           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.68/25.12           op(e0, e1) = e0)
% 158.68/25.12    (4)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 158.68/25.12           all_57_8 & $i(all_57_8))
% 158.68/25.12    (5)   ~ (e3 = e1)
% 158.68/25.12  
% 158.68/25.12  Begin of proof
% 158.68/25.12  | 
% 158.68/25.12  | BETA: splitting (3) gives:
% 158.68/25.12  | 
% 158.68/25.12  | Case 1:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (6)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 158.68/25.12  | |        & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.68/25.12  | |        $i(all_57_14)
% 158.68/25.12  | | 
% 158.68/25.12  | | ALPHA: (6) implies:
% 158.68/25.12  | |   (7)  all_57_8 = e0
% 158.68/25.12  | | 
% 158.68/25.12  | | REF_CLOSE: (1), (2), (4), (5), (7) are inconsistent by sub-proof #430.
% 158.68/25.12  | | 
% 158.68/25.12  | Case 2:
% 158.68/25.12  | | 
% 158.68/25.12  | |   (8)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0
% 158.68/25.12  | | 
% 158.68/25.12  | | ALPHA: (8) implies:
% 158.68/25.12  | |   (9)  all_57_8 = e0
% 158.68/25.12  | | 
% 158.68/25.12  | | REF_CLOSE: (1), (2), (4), (5), (9) are inconsistent by sub-proof #430.
% 158.68/25.12  | | 
% 158.68/25.12  | End of split
% 158.68/25.12  | 
% 158.68/25.12  End of proof
% 158.68/25.12  
% 158.68/25.12  Sub-proof #206 shows that the following formulas are inconsistent:
% 158.68/25.12  ----------------------------------------------------------------
% 158.68/25.12    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.68/25.12         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.68/25.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.13    (3)  op(e0, e0) = e3
% 158.68/25.13    (4)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 158.68/25.13         (all_56_11 = e0 & op(e1, e0) = e0)
% 158.68/25.13    (5)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.68/25.13    (6)  all_56_11 = e2
% 158.68/25.13    (7)   ~ (e1 = e0)
% 158.68/25.13    (8)  op(e2, e1) = all_52_9
% 158.68/25.13    (9)   ~ (all_52_9 = e3)
% 158.68/25.13    (10)   ~ (e2 = e1)
% 158.68/25.13    (11)   ~ (e3 = e1)
% 158.68/25.13    (12)   ~ (e2 = e0)
% 158.68/25.13    (13)   ~ (e3 = e0)
% 158.68/25.13  
% 158.68/25.13  Begin of proof
% 158.68/25.13  | 
% 158.68/25.13  | BETA: splitting (5) gives:
% 158.68/25.13  | 
% 158.68/25.13  | Case 1:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (14)  all_56_5 = e3 & op(e2, e1) = e3
% 158.68/25.13  | | 
% 158.68/25.13  | | ALPHA: (14) implies:
% 158.68/25.13  | |   (15)  op(e2, e1) = e3
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (2), (8), (9), (15) are inconsistent by sub-proof #763.
% 158.68/25.13  | | 
% 158.68/25.13  | Case 2:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (16)  all_56_10 = e3 & op(e2, e0) = e3
% 158.68/25.13  | | 
% 158.68/25.13  | | ALPHA: (16) implies:
% 158.68/25.13  | |   (17)  all_56_10 = e3
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (10), (11), (12), (13), (17) are
% 158.68/25.13  | |            inconsistent by sub-proof #467.
% 158.68/25.13  | | 
% 158.68/25.13  | End of split
% 158.68/25.13  | 
% 158.68/25.13  End of proof
% 158.68/25.13  
% 158.68/25.13  Sub-proof #207 shows that the following formulas are inconsistent:
% 158.68/25.13  ----------------------------------------------------------------
% 158.68/25.13    (1)   ~ (all_52_7 = e0)
% 158.68/25.13    (2)  all_54_13 = all_52_7
% 158.68/25.13    (3)   ~ (all_52_7 = e2)
% 158.68/25.13    (4)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.68/25.13    (5)   ~ (all_52_7 = e3)
% 158.68/25.13    (6)   ~ (all_52_7 = e1)
% 158.68/25.13  
% 158.68/25.13  Begin of proof
% 158.68/25.13  | 
% 158.68/25.13  | BETA: splitting (4) gives:
% 158.68/25.13  | 
% 158.68/25.13  | Case 1:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (7)  all_54_13 = e3
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #385.
% 158.68/25.13  | | 
% 158.68/25.13  | Case 2:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (8)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (1), (2), (3), (6), (8) are inconsistent by sub-proof #502.
% 158.68/25.13  | | 
% 158.68/25.13  | End of split
% 158.68/25.13  | 
% 158.68/25.13  End of proof
% 158.68/25.13  
% 158.68/25.13  Sub-proof #208 shows that the following formulas are inconsistent:
% 158.68/25.13  ----------------------------------------------------------------
% 158.68/25.13    (1)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 158.68/25.13    (2)  all_56_2 = e3
% 158.68/25.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.13    (4)  op(e3, e3) = e2
% 158.68/25.13    (5)   ~ (e2 = e1)
% 158.68/25.13    (6)   ~ (e3 = e1)
% 158.68/25.13  
% 158.68/25.13  Begin of proof
% 158.68/25.13  | 
% 158.68/25.13  | BETA: splitting (1) gives:
% 158.68/25.13  | 
% 158.68/25.13  | Case 1:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | ALPHA: (7) implies:
% 158.68/25.13  | |   (8)  op(e3, e3) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #828.
% 158.68/25.13  | | 
% 158.68/25.13  | Case 2:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (9)  all_56_2 = e1 & op(e2, e3) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #774.
% 158.68/25.13  | | 
% 158.68/25.13  | End of split
% 158.68/25.13  | 
% 158.68/25.13  End of proof
% 158.68/25.13  
% 158.68/25.13  Sub-proof #209 shows that the following formulas are inconsistent:
% 158.68/25.13  ----------------------------------------------------------------
% 158.68/25.13    (1)   ~ (all_52_13 = e1)
% 158.68/25.13    (2)   ~ (all_52_12 = e1)
% 158.68/25.13    (3)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.68/25.13         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.68/25.13    (4)  op(e1, e1) = e3
% 158.68/25.13    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.13    (6)  op(e1, e0) = all_52_14
% 158.68/25.13    (7)  op(e0, e0) = all_14_2
% 158.68/25.13    (8)   ~ (e1 = e0)
% 158.68/25.13    (9)  op(e2, e0) = all_52_13
% 158.68/25.13    (10)  op(e3, e0) = all_52_12
% 158.68/25.13    (11)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 158.68/25.13              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.68/25.13            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.68/25.13                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 158.68/25.13              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.68/25.13          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 158.68/25.13              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.68/25.13            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 158.68/25.13                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 158.68/25.13                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.68/25.13                $i(all_57_13))))
% 158.68/25.13    (12)   ~ (e3 = e1)
% 158.68/25.13    (13)   ~ (e3 = e0)
% 158.68/25.13  
% 158.68/25.13  Begin of proof
% 158.68/25.13  | 
% 158.68/25.13  | BETA: splitting (11) gives:
% 158.68/25.13  | 
% 158.68/25.13  | Case 1:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (14)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 158.68/25.13  | |             e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 158.68/25.13  | |             $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 158.68/25.13  | |             (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 158.68/25.13  | |         ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 158.68/25.13  | |               e1) = all_57_8 & $i(all_57_8)))
% 158.68/25.13  | | 
% 158.68/25.13  | | ALPHA: (14) implies:
% 158.68/25.13  | |   (15)  op(e1, e1) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (4), (5), (12), (15) are inconsistent by sub-proof #1003.
% 158.68/25.13  | | 
% 158.68/25.13  | Case 2:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (16)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 158.68/25.13  | |             e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 158.68/25.13  | |             $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 158.68/25.13  | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 158.68/25.13  | |         ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 158.68/25.13  | |               e0) = all_57_13 & $i(all_57_13)))
% 158.68/25.13  | | 
% 158.68/25.13  | | ALPHA: (16) implies:
% 158.68/25.13  | |   (17)  op(e0, e0) = e0
% 158.68/25.13  | |   (18)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 158.68/25.13  | |             e0) = all_57_13 & $i(all_57_13))
% 158.68/25.13  | | 
% 158.68/25.13  | | BETA: splitting (3) gives:
% 158.68/25.13  | | 
% 158.68/25.13  | | Case 1:
% 158.68/25.13  | | | 
% 158.68/25.13  | | |   (19)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 158.68/25.13  | | |           e1)
% 158.68/25.13  | | | 
% 158.68/25.13  | | | BETA: splitting (19) gives:
% 158.68/25.13  | | | 
% 158.68/25.13  | | | Case 1:
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | |   (20)  all_56_9 = e1 & op(e3, e0) = e1
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | | REF_CLOSE: (2), (5), (10), (20) are inconsistent by sub-proof #851.
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | Case 2:
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | |   (21)  all_56_10 = e1 & op(e2, e0) = e1
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | | REF_CLOSE: (1), (5), (9), (21) are inconsistent by sub-proof #713.
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | End of split
% 158.68/25.13  | | | 
% 158.68/25.13  | | Case 2:
% 158.68/25.13  | | | 
% 158.68/25.13  | | |   (22)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0)
% 158.68/25.13  | | |           = e1)
% 158.68/25.13  | | | 
% 158.68/25.13  | | | BETA: splitting (22) gives:
% 158.68/25.13  | | | 
% 158.68/25.13  | | | Case 1:
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | |   (23)  all_56_11 = e1 & op(e1, e0) = e1
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | | ALPHA: (23) implies:
% 158.68/25.13  | | | |   (24)  op(e1, e0) = e1
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | | REF_CLOSE: (4), (5), (6), (13), (18), (24) are inconsistent by sub-proof
% 158.68/25.13  | | | |            #493.
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | Case 2:
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | |   (25)  all_56_15 = e1 & op(e0, e0) = e1
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | | ALPHA: (25) implies:
% 158.68/25.13  | | | |   (26)  op(e0, e0) = e1
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | | REF_CLOSE: (5), (7), (8), (17), (26) are inconsistent by sub-proof #991.
% 158.68/25.13  | | | | 
% 158.68/25.13  | | | End of split
% 158.68/25.13  | | | 
% 158.68/25.13  | | End of split
% 158.68/25.13  | | 
% 158.68/25.13  | End of split
% 158.68/25.13  | 
% 158.68/25.13  End of proof
% 158.68/25.13  
% 158.68/25.13  Sub-proof #210 shows that the following formulas are inconsistent:
% 158.68/25.13  ----------------------------------------------------------------
% 158.68/25.13    (1)  op(e1, e1) = e3
% 158.68/25.13    (2)  op(e0, e1) = all_52_11
% 158.68/25.13    (3)   ~ (e3 = e2)
% 158.68/25.13    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.13    (5)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 158.68/25.13    (6)   ~ (all_52_11 = e2)
% 158.68/25.13  
% 158.68/25.13  Begin of proof
% 158.68/25.13  | 
% 158.68/25.13  | BETA: splitting (5) gives:
% 158.68/25.13  | 
% 158.68/25.13  | Case 1:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (7)  all_56_8 = e2 & op(e1, e1) = e2
% 158.68/25.13  | | 
% 158.68/25.13  | | ALPHA: (7) implies:
% 158.68/25.13  | |   (8)  op(e1, e1) = e2
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #646.
% 158.68/25.13  | | 
% 158.68/25.13  | Case 2:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (9)  all_56_14 = e2 & op(e0, e1) = e2
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #263.
% 158.68/25.13  | | 
% 158.68/25.13  | End of split
% 158.68/25.13  | 
% 158.68/25.13  End of proof
% 158.68/25.13  
% 158.68/25.13  Sub-proof #211 shows that the following formulas are inconsistent:
% 158.68/25.13  ----------------------------------------------------------------
% 158.68/25.13    (1)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.68/25.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.13    (3)  all_56_13 = e1
% 158.68/25.13    (4)   ~ (all_52_6 = e3)
% 158.68/25.13    (5)  op(e1, e2) = all_52_6
% 158.68/25.13    (6)   ~ (e3 = e1)
% 158.68/25.13  
% 158.68/25.13  Begin of proof
% 158.68/25.13  | 
% 158.68/25.13  | BETA: splitting (1) gives:
% 158.68/25.13  | 
% 158.68/25.13  | Case 1:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (7)  all_56_7 = e3 & op(e1, e2) = e3
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #388.
% 158.68/25.13  | | 
% 158.68/25.13  | Case 2:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (8)  all_56_13 = e3 & op(e0, e2) = e3
% 158.68/25.13  | | 
% 158.68/25.13  | | ALPHA: (8) implies:
% 158.68/25.13  | |   (9)  all_56_13 = e3
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #936.
% 158.68/25.13  | | 
% 158.68/25.13  | End of split
% 158.68/25.13  | 
% 158.68/25.13  End of proof
% 158.68/25.13  
% 158.68/25.13  Sub-proof #212 shows that the following formulas are inconsistent:
% 158.68/25.13  ----------------------------------------------------------------
% 158.68/25.13    (1)   ~ (e3 = e2)
% 158.68/25.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.13    (3)  op(e3, e1) = all_52_8
% 158.68/25.13    (4)   ~ (all_52_12 = e3)
% 158.68/25.13    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.68/25.13         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.68/25.13    (6)  all_56_1 = e0
% 158.68/25.13    (7)  op(e3, e3) = e2
% 158.68/25.13    (8)  op(e3, e0) = all_52_12
% 158.68/25.13    (9)   ~ (all_52_8 = e3)
% 158.68/25.13    (10)   ~ (e3 = e0)
% 158.68/25.13  
% 158.68/25.13  Begin of proof
% 158.68/25.13  | 
% 158.68/25.13  | BETA: splitting (5) gives:
% 158.68/25.13  | 
% 158.68/25.13  | Case 1:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 158.68/25.13  | |           e3)
% 158.68/25.13  | | 
% 158.68/25.13  | | BETA: splitting (11) gives:
% 158.68/25.13  | | 
% 158.68/25.13  | | Case 1:
% 158.68/25.13  | | | 
% 158.68/25.13  | | |   (12)  all_56_0 = e3 & op(e3, e3) = e3
% 158.68/25.13  | | | 
% 158.68/25.13  | | | ALPHA: (12) implies:
% 158.68/25.13  | | |   (13)  op(e3, e3) = e3
% 158.68/25.13  | | | 
% 158.68/25.13  | | | REF_CLOSE: (1), (2), (7), (13) are inconsistent by sub-proof #958.
% 158.68/25.13  | | | 
% 158.68/25.13  | | Case 2:
% 158.68/25.13  | | | 
% 158.68/25.13  | | |   (14)  all_56_1 = e3 & op(e3, e2) = e3
% 158.68/25.13  | | | 
% 158.68/25.13  | | | REF_CLOSE: (6), (10), (14) are inconsistent by sub-proof #664.
% 158.68/25.13  | | | 
% 158.68/25.13  | | End of split
% 158.68/25.13  | | 
% 158.68/25.13  | Case 2:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (15)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 158.68/25.13  | |           e3)
% 158.68/25.13  | | 
% 158.68/25.13  | | BETA: splitting (15) gives:
% 158.68/25.13  | | 
% 158.68/25.13  | | Case 1:
% 158.68/25.13  | | | 
% 158.68/25.13  | | |   (16)  all_56_4 = e3 & op(e3, e1) = e3
% 158.68/25.13  | | | 
% 158.68/25.13  | | | ALPHA: (16) implies:
% 158.68/25.13  | | |   (17)  op(e3, e1) = e3
% 158.68/25.13  | | | 
% 158.68/25.13  | | | REF_CLOSE: (2), (3), (9), (17) are inconsistent by sub-proof #982.
% 158.68/25.13  | | | 
% 158.68/25.13  | | Case 2:
% 158.68/25.13  | | | 
% 158.68/25.13  | | |   (18)  all_56_9 = e3 & op(e3, e0) = e3
% 158.68/25.13  | | | 
% 158.68/25.13  | | | ALPHA: (18) implies:
% 158.68/25.13  | | |   (19)  op(e3, e0) = e3
% 158.68/25.13  | | | 
% 158.68/25.13  | | | REF_CLOSE: (2), (4), (8), (19) are inconsistent by sub-proof #976.
% 158.68/25.13  | | | 
% 158.68/25.13  | | End of split
% 158.68/25.13  | | 
% 158.68/25.13  | End of split
% 158.68/25.13  | 
% 158.68/25.13  End of proof
% 158.68/25.13  
% 158.68/25.13  Sub-proof #213 shows that the following formulas are inconsistent:
% 158.68/25.13  ----------------------------------------------------------------
% 158.68/25.13    (1)  op(e1, e0) = all_57_13
% 158.68/25.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.13    (3)   ~ (all_57_13 = e1)
% 158.68/25.13    (4)  op(e0, e0) = e0
% 158.68/25.13    (5)  op(e1, e0) = all_52_14
% 158.68/25.13    (6)  op(e0, e0) = all_14_2
% 158.68/25.13    (7)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.68/25.13    (8)   ~ (e1 = e0)
% 158.68/25.13  
% 158.68/25.13  Begin of proof
% 158.68/25.13  | 
% 158.68/25.13  | BETA: splitting (7) gives:
% 158.68/25.13  | 
% 158.68/25.13  | Case 1:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (9)  all_56_11 = e1 & op(e1, e0) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | ALPHA: (9) implies:
% 158.68/25.13  | |   (10)  op(e1, e0) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (1), (2), (3), (5), (10) are inconsistent by sub-proof #637.
% 158.68/25.13  | | 
% 158.68/25.13  | Case 2:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (11)  all_56_15 = e1 & op(e0, e0) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | ALPHA: (11) implies:
% 158.68/25.13  | |   (12)  op(e0, e0) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (2), (4), (6), (8), (12) are inconsistent by sub-proof #991.
% 158.68/25.13  | | 
% 158.68/25.13  | End of split
% 158.68/25.13  | 
% 158.68/25.13  End of proof
% 158.68/25.13  
% 158.68/25.13  Sub-proof #214 shows that the following formulas are inconsistent:
% 158.68/25.13  ----------------------------------------------------------------
% 158.68/25.13    (1)  all_56_14 = e2
% 158.68/25.13    (2)  all_56_14 = e0
% 158.68/25.13    (3)   ~ (e2 = e0)
% 158.68/25.13  
% 158.68/25.13  Begin of proof
% 158.68/25.13  | 
% 158.68/25.13  | COMBINE_EQS: (1), (2) imply:
% 158.68/25.13  |   (4)  e2 = e0
% 158.68/25.13  | 
% 158.68/25.13  | SIMP: (4) implies:
% 158.68/25.13  |   (5)  e2 = e0
% 158.68/25.13  | 
% 158.68/25.13  | REDUCE: (3), (5) imply:
% 158.68/25.13  |   (6)  $false
% 158.68/25.13  | 
% 158.68/25.13  | CLOSE: (6) is inconsistent.
% 158.68/25.13  | 
% 158.68/25.13  End of proof
% 158.68/25.13  
% 158.68/25.13  Sub-proof #215 shows that the following formulas are inconsistent:
% 158.68/25.13  ----------------------------------------------------------------
% 158.68/25.13    (1)  op(e0, e1) = all_52_11
% 158.68/25.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.13    (3)   ~ (all_52_11 = e1)
% 158.68/25.13    (4)  op(e0, e0) = e0
% 158.68/25.13    (5)  op(e0, e0) = all_14_2
% 158.68/25.13    (6)   ~ (e1 = e0)
% 158.68/25.13    (7)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.68/25.13  
% 158.68/25.13  Begin of proof
% 158.68/25.13  | 
% 158.68/25.13  | BETA: splitting (7) gives:
% 158.68/25.13  | 
% 158.68/25.13  | Case 1:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (8)  all_56_14 = e1 & op(e0, e1) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #803.
% 158.68/25.13  | | 
% 158.68/25.13  | Case 2:
% 158.68/25.13  | | 
% 158.68/25.13  | |   (9)  all_56_15 = e1 & op(e0, e0) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | ALPHA: (9) implies:
% 158.68/25.13  | |   (10)  op(e0, e0) = e1
% 158.68/25.13  | | 
% 158.68/25.13  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #991.
% 158.68/25.13  | | 
% 158.68/25.13  | End of split
% 158.68/25.13  | 
% 158.68/25.13  End of proof
% 158.68/25.13  
% 158.68/25.13  Sub-proof #216 shows that the following formulas are inconsistent:
% 158.68/25.13  ----------------------------------------------------------------
% 158.68/25.13    (1)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 158.68/25.13    (2)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.68/25.13         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.68/25.13    (3)  op(e1, e1) = e3
% 158.68/25.13    (4)   ~ (e3 = e2)
% 158.68/25.13    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.13    (6)  op(e0, e0) = e0
% 158.68/25.14    (7)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.68/25.14         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.68/25.14    (8)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.68/25.14         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.68/25.14    (9)   ~ (e1 = e0)
% 158.68/25.14    (10)   ~ (e2 = e1)
% 158.68/25.14    (11)  all_56_15 = e0
% 158.68/25.14    (12)   ~ (e3 = e1)
% 158.68/25.14    (13)   ~ (e2 = e0)
% 158.68/25.14    (14)   ~ (e3 = e0)
% 158.68/25.14  
% 158.68/25.14  Begin of proof
% 158.68/25.14  | 
% 158.68/25.14  | BETA: splitting (1) gives:
% 158.68/25.14  | 
% 158.68/25.14  | Case 1:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (15)  all_56_8 = e0 & op(e1, e1) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (15) implies:
% 158.68/25.14  | |   (16)  op(e1, e1) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (3), (5), (14), (16) are inconsistent by sub-proof #912.
% 158.68/25.14  | | 
% 158.68/25.14  | Case 2:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (17)  all_56_11 = e0 & op(e1, e0) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (17) implies:
% 158.68/25.14  | |   (18)  all_56_11 = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 158.68/25.14  | |            (18) are inconsistent by sub-proof #883.
% 158.68/25.14  | | 
% 158.68/25.14  | End of split
% 158.68/25.14  | 
% 158.68/25.14  End of proof
% 158.68/25.14  
% 158.68/25.14  Sub-proof #217 shows that the following formulas are inconsistent:
% 158.68/25.14  ----------------------------------------------------------------
% 158.68/25.14    (1)  op(e1, e1) = e3
% 158.68/25.14    (2)  op(e0, e1) = all_52_11
% 158.68/25.14    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.14    (4)   ~ (all_52_11 = e0)
% 158.68/25.14    (5)   ~ (e2 = e1)
% 158.68/25.14    (6)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.68/25.14           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.68/25.14           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 158.68/25.14           & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 158.68/25.14           & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.68/25.14           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.68/25.14           all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.68/25.14    (7)   ~ (e3 = e0)
% 158.68/25.14    (8)  op(e2, e0) = e1
% 158.68/25.14  
% 158.68/25.14  Begin of proof
% 158.68/25.14  | 
% 158.68/25.14  | BETA: splitting (6) gives:
% 158.68/25.14  | 
% 158.68/25.14  | Case 1:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (9)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.68/25.14  | |            e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.68/25.14  | |        (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.68/25.14  | |            e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0)
% 158.68/25.14  | | 
% 158.68/25.14  | | BETA: splitting (9) gives:
% 158.68/25.14  | | 
% 158.68/25.14  | | Case 1:
% 158.68/25.14  | | | 
% 158.68/25.14  | | |   (10)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.68/25.14  | | |           e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 158.68/25.14  | | | 
% 158.68/25.14  | | | ALPHA: (10) implies:
% 158.68/25.14  | | |   (11)  op(e2, e0) = e2
% 158.68/25.14  | | | 
% 158.68/25.14  | | | REF_CLOSE: (3), (5), (8), (11) are inconsistent by sub-proof #813.
% 158.68/25.14  | | | 
% 158.68/25.14  | | Case 2:
% 158.68/25.14  | | | 
% 158.68/25.14  | | |   (12)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.68/25.14  | | |           e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 158.68/25.14  | | | 
% 158.68/25.14  | | | ALPHA: (12) implies:
% 158.68/25.14  | | |   (13)  op(e1, e1) = e0
% 158.68/25.14  | | | 
% 158.68/25.14  | | | REF_CLOSE: (1), (3), (7), (13) are inconsistent by sub-proof #912.
% 158.68/25.14  | | | 
% 158.68/25.14  | | End of split
% 158.68/25.14  | | 
% 158.68/25.14  | Case 2:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (14)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.68/25.14  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 158.68/25.14  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 158.68/25.14  | |           & op(e0, e1) = e0)
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (2), (3), (4), (14) are inconsistent by sub-proof #965.
% 158.68/25.14  | | 
% 158.68/25.14  | End of split
% 158.68/25.14  | 
% 158.68/25.14  End of proof
% 158.68/25.14  
% 158.68/25.14  Sub-proof #218 shows that the following formulas are inconsistent:
% 158.68/25.14  ----------------------------------------------------------------
% 158.68/25.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.14    (2)  op(e0, e3) = e1
% 158.68/25.14    (3)   ~ (e1 = e0)
% 158.68/25.14    (4)  op(e3, e3) = e2
% 158.68/25.14    (5)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.68/25.14         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.68/25.14           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.68/25.14           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 158.68/25.14           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.68/25.14    (6)   ~ (e2 = e1)
% 158.68/25.14    (7)   ~ (e2 = e0)
% 158.68/25.14    (8)  op(e2, e0) = e1
% 158.68/25.14  
% 158.68/25.14  Begin of proof
% 158.68/25.14  | 
% 158.68/25.14  | BETA: splitting (5) gives:
% 158.68/25.14  | 
% 158.68/25.14  | Case 1:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (9)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (9) implies:
% 158.68/25.14  | |   (10)  op(e0, e3) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #786.
% 158.68/25.14  | | 
% 158.68/25.14  | Case 2:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (11)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.68/25.14  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.68/25.14  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.68/25.14  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (1), (4), (6), (7), (8), (11) are inconsistent by sub-proof #219.
% 158.68/25.14  | | 
% 158.68/25.14  | End of split
% 158.68/25.14  | 
% 158.68/25.14  End of proof
% 158.68/25.14  
% 158.68/25.14  Sub-proof #219 shows that the following formulas are inconsistent:
% 158.68/25.14  ----------------------------------------------------------------
% 158.68/25.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.14    (2)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.68/25.14           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.68/25.14           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 158.68/25.14           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.68/25.14    (3)  op(e3, e3) = e2
% 158.68/25.14    (4)   ~ (e2 = e1)
% 158.68/25.14    (5)   ~ (e2 = e0)
% 158.68/25.14    (6)  op(e2, e0) = e1
% 158.68/25.14  
% 158.68/25.14  Begin of proof
% 158.68/25.14  | 
% 158.68/25.14  | BETA: splitting (2) gives:
% 158.68/25.14  | 
% 158.68/25.14  | Case 1:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (7)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 158.68/25.14  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (7) implies:
% 158.68/25.14  | |   (8)  op(e3, e3) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #281.
% 158.68/25.14  | | 
% 158.68/25.14  | Case 2:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (9)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2)
% 158.68/25.14  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (9) implies:
% 158.68/25.14  | |   (10)  op(e2, e0) = e2
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #813.
% 158.68/25.14  | | 
% 158.68/25.14  | End of split
% 158.68/25.14  | 
% 158.68/25.14  End of proof
% 158.68/25.14  
% 158.68/25.14  Sub-proof #220 shows that the following formulas are inconsistent:
% 158.68/25.14  ----------------------------------------------------------------
% 158.68/25.14    (1)  op(e1, e1) = e3
% 158.68/25.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.14    (3)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.68/25.14           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.68/25.14           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 158.68/25.14           & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.68/25.14    (4)   ~ (e2 = e1)
% 158.68/25.14    (5)   ~ (e3 = e0)
% 158.68/25.14    (6)  op(e2, e0) = e1
% 158.68/25.14  
% 158.68/25.14  Begin of proof
% 158.68/25.14  | 
% 158.68/25.14  | BETA: splitting (3) gives:
% 158.68/25.14  | 
% 158.68/25.14  | Case 1:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (7)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3)
% 158.68/25.14  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (7) implies:
% 158.68/25.14  | |   (8)  op(e2, e0) = e2
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #813.
% 158.68/25.14  | | 
% 158.68/25.14  | Case 2:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (9)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3)
% 158.68/25.14  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (9) implies:
% 158.68/25.14  | |   (10)  op(e1, e1) = e0
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #912.
% 158.68/25.14  | | 
% 158.68/25.14  | End of split
% 158.68/25.14  | 
% 158.68/25.14  End of proof
% 158.68/25.14  
% 158.68/25.14  Sub-proof #221 shows that the following formulas are inconsistent:
% 158.68/25.14  ----------------------------------------------------------------
% 158.68/25.14    (1)  all_54_5 = all_4_2
% 158.68/25.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.14    (3)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.68/25.14           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.68/25.14           = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3
% 158.68/25.14           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.68/25.14           op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 158.68/25.14    (4)  op(e0, e0) = e0
% 158.68/25.14    (5)  op(e2, e2) = all_4_2
% 158.68/25.14    (6)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.68/25.14    (7)   ~ (all_4_2 = e1)
% 158.68/25.14    (8)   ~ (e3 = e0)
% 158.68/25.14  
% 158.68/25.14  Begin of proof
% 158.68/25.14  | 
% 158.68/25.14  | BETA: splitting (3) gives:
% 158.68/25.14  | 
% 158.68/25.14  | Case 1:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (9)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 158.68/25.14  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.68/25.14  | |          e0) = e1 & $i(all_57_14)
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (9) implies:
% 158.68/25.14  | |   (10)  op(e2, e2) = e1
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (1), (2), (5), (6), (7), (10) are inconsistent by sub-proof #691.
% 158.68/25.14  | | 
% 158.68/25.14  | Case 2:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (11)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0)
% 158.68/25.14  | |         & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 158.68/25.14  | |         op(e0, e0) = e3 & $i(all_57_10)
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (11) implies:
% 158.68/25.14  | |   (12)  op(e0, e0) = e3
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (2), (4), (8), (12) are inconsistent by sub-proof #999.
% 158.68/25.14  | | 
% 158.68/25.14  | End of split
% 158.68/25.14  | 
% 158.68/25.14  End of proof
% 158.68/25.14  
% 158.68/25.14  Sub-proof #222 shows that the following formulas are inconsistent:
% 158.68/25.14  ----------------------------------------------------------------
% 158.68/25.14    (1)  all_54_5 = all_4_2
% 158.68/25.14    (2)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.68/25.14           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.68/25.14           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 158.68/25.14           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 158.68/25.14           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.68/25.14    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.14    (4)  op(e3, e1) = all_52_8
% 158.68/25.14    (5)  op(e2, e2) = all_4_2
% 158.68/25.14    (6)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.68/25.14    (7)   ~ (all_4_2 = e1)
% 158.68/25.14    (8)   ~ (all_52_8 = e3)
% 158.68/25.14  
% 158.68/25.14  Begin of proof
% 158.68/25.14  | 
% 158.68/25.14  | BETA: splitting (2) gives:
% 158.68/25.14  | 
% 158.68/25.14  | Case 1:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (9)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 158.68/25.14  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.68/25.14  | |          e1) = e3 & $i(all_57_10)
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (9) implies:
% 158.68/25.14  | |   (10)  op(e3, e1) = e3
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (3), (4), (8), (10) are inconsistent by sub-proof #982.
% 158.68/25.14  | | 
% 158.68/25.14  | Case 2:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (11)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 158.68/25.14  | |         & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 158.68/25.14  | |         all_57_14 & $i(all_57_14)
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (11) implies:
% 158.68/25.14  | |   (12)  op(e2, e2) = e1
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (1), (3), (5), (6), (7), (12) are inconsistent by sub-proof #691.
% 158.68/25.14  | | 
% 158.68/25.14  | End of split
% 158.68/25.14  | 
% 158.68/25.14  End of proof
% 158.68/25.14  
% 158.68/25.14  Sub-proof #223 shows that the following formulas are inconsistent:
% 158.68/25.14  ----------------------------------------------------------------
% 158.68/25.14    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.68/25.14         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.68/25.14    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 158.68/25.14         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 158.68/25.14    (3)  all_56_12 = e1
% 158.68/25.14    (4)   ~ (e3 = e2)
% 158.68/25.14    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.14    (6)  op(e1, e3) = all_52_2
% 158.68/25.14    (7)   ~ (all_52_2 = e2)
% 158.68/25.14    (8)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.68/25.14           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.68/25.14           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 158.68/25.14           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 158.68/25.14           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.68/25.14    (9)   ~ (e1 = e0)
% 158.68/25.14    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.68/25.14          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.68/25.14    (11)   ~ (e2 = e1)
% 158.68/25.14    (12)   ~ (e3 = e1)
% 158.68/25.14    (13)   ~ (e2 = e0)
% 158.68/25.14    (14)   ~ (e3 = e0)
% 158.68/25.14    (15)  op(e2, e0) = e1
% 158.68/25.14  
% 158.68/25.14  Begin of proof
% 158.68/25.14  | 
% 158.68/25.14  | BETA: splitting (8) gives:
% 158.68/25.14  | 
% 158.68/25.14  | Case 1:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (16)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 =
% 158.68/25.14  | |           e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.68/25.14  | |         op(e2, e0) = e2 & $i(all_57_12)
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (16) implies:
% 158.68/25.14  | |   (17)  op(e2, e0) = e2
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (5), (11), (15), (17) are inconsistent by sub-proof #813.
% 158.68/25.14  | | 
% 158.68/25.14  | Case 2:
% 158.68/25.14  | | 
% 158.68/25.14  | |   (18)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 158.68/25.14  | |         & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.68/25.14  | |         all_57_14 & $i(all_57_14)
% 158.68/25.14  | | 
% 158.68/25.14  | | ALPHA: (18) implies:
% 158.68/25.14  | |   (19)  op(e3, e3) = e1
% 158.68/25.14  | | 
% 158.68/25.14  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 158.68/25.14  | |            (14), (19) are inconsistent by sub-proof #495.
% 158.68/25.14  | | 
% 158.68/25.14  | End of split
% 158.68/25.14  | 
% 158.68/25.14  End of proof
% 158.68/25.14  
% 158.68/25.14  Sub-proof #224 shows that the following formulas are inconsistent:
% 158.68/25.14  ----------------------------------------------------------------
% 158.68/25.14    (1)  all_56_1 = e2 & op(e3, e2) = e2
% 158.68/25.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.15    (3)  op(e3, e2) = all_52_4
% 158.68/25.15    (4)   ~ (all_52_4 = e2)
% 158.68/25.15  
% 158.68/25.15  Begin of proof
% 158.68/25.15  | 
% 158.68/25.15  | ALPHA: (1) implies:
% 158.68/25.15  |   (5)  op(e3, e2) = e2
% 158.68/25.15  | 
% 158.68/25.15  | GROUND_INST: instantiating (2) with all_52_4, e2, e2, e3, simplifying with
% 158.68/25.15  |              (3), (5) gives:
% 158.68/25.15  |   (6)  all_52_4 = e2
% 158.68/25.15  | 
% 158.68/25.15  | REDUCE: (4), (6) imply:
% 158.68/25.15  |   (7)  $false
% 158.68/25.15  | 
% 158.68/25.15  | CLOSE: (7) is inconsistent.
% 158.68/25.15  | 
% 158.68/25.15  End of proof
% 158.68/25.15  
% 158.68/25.15  Sub-proof #225 shows that the following formulas are inconsistent:
% 158.68/25.15  ----------------------------------------------------------------
% 158.68/25.15    (1)   ~ (all_52_12 = e2)
% 158.68/25.15    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.15    (3)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.68/25.15    (4)   ~ (e2 = e1)
% 158.68/25.15    (5)  op(e3, e0) = all_52_12
% 158.68/25.15    (6)  op(e2, e0) = e1
% 158.68/25.15  
% 158.68/25.15  Begin of proof
% 158.68/25.15  | 
% 158.68/25.15  | BETA: splitting (3) gives:
% 158.68/25.15  | 
% 158.68/25.15  | Case 1:
% 158.68/25.15  | | 
% 158.68/25.15  | |   (7)  all_56_9 = e2 & op(e3, e0) = e2
% 158.68/25.15  | | 
% 158.68/25.15  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #880.
% 158.68/25.15  | | 
% 158.68/25.15  | Case 2:
% 158.68/25.15  | | 
% 158.68/25.15  | |   (8)  all_56_10 = e2 & op(e2, e0) = e2
% 158.68/25.15  | | 
% 158.68/25.15  | | ALPHA: (8) implies:
% 158.68/25.15  | |   (9)  op(e2, e0) = e2
% 158.68/25.15  | | 
% 158.68/25.15  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #813.
% 158.68/25.15  | | 
% 158.68/25.15  | End of split
% 158.68/25.15  | 
% 158.68/25.15  End of proof
% 158.68/25.15  
% 158.68/25.15  Sub-proof #226 shows that the following formulas are inconsistent:
% 158.68/25.15  ----------------------------------------------------------------
% 158.68/25.15    (1)  all_54_5 = all_4_2
% 158.68/25.15    (2)  op(e1, e1) = e3
% 158.68/25.15    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.68/25.15         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.68/25.15    (4)  op(e0, e1) = all_52_11
% 158.68/25.15    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.68/25.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.68/25.15    (6)   ~ (all_52_9 = e1)
% 158.68/25.15    (7)   ~ (all_52_11 = e1)
% 158.68/25.15    (8)  op(e2, e2) = all_4_2
% 158.68/25.15    (9)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.68/25.15    (10)   ~ (all_4_2 = e1)
% 158.68/25.15    (11)   ~ (e1 = e0)
% 158.68/25.15    (12)  op(e2, e1) = all_52_9
% 158.68/25.15    (13)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.68/25.15          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.68/25.15    (14)  op(e3, e3) = e2
% 158.68/25.15    (15)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 158.68/25.15    (16)  all_56_9 = e3
% 158.68/25.15    (17)   ~ (e3 = e1)
% 158.68/25.15    (18)   ~ (e2 = e0)
% 158.68/25.15    (19)   ~ (e3 = e0)
% 158.68/25.15  
% 158.78/25.15  Begin of proof
% 158.78/25.15  | 
% 158.78/25.15  | BETA: splitting (15) gives:
% 158.78/25.15  | 
% 158.78/25.15  | Case 1:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (20)  all_56_1 = e1 & op(e3, e2) = e1
% 158.78/25.15  | | 
% 158.78/25.15  | | ALPHA: (20) implies:
% 158.78/25.15  | |   (21)  all_56_1 = e1
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (11), (12), (13), (14), (16), (17),
% 158.78/25.15  | |            (18), (19), (21) are inconsistent by sub-proof #229.
% 158.78/25.15  | | 
% 158.78/25.15  | Case 2:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (22)  all_56_3 = e1 & op(e2, e2) = e1
% 158.78/25.15  | | 
% 158.78/25.15  | | ALPHA: (22) implies:
% 158.78/25.15  | |   (23)  op(e2, e2) = e1
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (1), (5), (8), (9), (10), (23) are inconsistent by sub-proof
% 158.78/25.15  | |            #691.
% 158.78/25.15  | | 
% 158.78/25.15  | End of split
% 158.78/25.15  | 
% 158.78/25.15  End of proof
% 158.78/25.15  
% 158.78/25.15  Sub-proof #227 shows that the following formulas are inconsistent:
% 158.78/25.15  ----------------------------------------------------------------
% 158.78/25.15    (1)   ~ (all_52_4 = e3)
% 158.78/25.15    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.78/25.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.78/25.15    (3)   ~ (all_4_2 = e3)
% 158.78/25.15    (4)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 158.78/25.15    (5)  op(e2, e2) = all_4_2
% 158.78/25.15    (6)  op(e3, e2) = all_52_4
% 158.78/25.15  
% 158.78/25.15  Begin of proof
% 158.78/25.15  | 
% 158.78/25.15  | BETA: splitting (4) gives:
% 158.78/25.15  | 
% 158.78/25.15  | Case 1:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (7)  all_56_1 = e3 & op(e3, e2) = e3
% 158.78/25.15  | | 
% 158.78/25.15  | | ALPHA: (7) implies:
% 158.78/25.15  | |   (8)  op(e3, e2) = e3
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #998.
% 158.78/25.15  | | 
% 158.78/25.15  | Case 2:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (9)  all_56_3 = e3 & op(e2, e2) = e3
% 158.78/25.15  | | 
% 158.78/25.15  | | ALPHA: (9) implies:
% 158.78/25.15  | |   (10)  op(e2, e2) = e3
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #711.
% 158.78/25.15  | | 
% 158.78/25.15  | End of split
% 158.78/25.15  | 
% 158.78/25.15  End of proof
% 158.78/25.15  
% 158.78/25.15  Sub-proof #228 shows that the following formulas are inconsistent:
% 158.78/25.15  ----------------------------------------------------------------
% 158.78/25.15    (1)  op(e3, e2) = e1
% 158.78/25.15    (2)  op(e1, e1) = e3
% 158.78/25.15    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.78/25.15         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.78/25.15    (4)  op(e0, e1) = all_52_11
% 158.78/25.15    (5)   ~ (e3 = e2)
% 158.78/25.15    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.78/25.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.78/25.15    (7)  op(e3, e1) = all_52_8
% 158.78/25.15    (8)   ~ (all_52_9 = e1)
% 158.78/25.15    (9)   ~ (all_52_11 = e1)
% 158.78/25.15    (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 158.78/25.15          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 158.78/25.15    (11)  all_56_1 = e1
% 158.78/25.15    (12)   ~ (e1 = e0)
% 158.78/25.15    (13)  op(e2, e1) = all_52_9
% 158.78/25.15    (14)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.78/25.15          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.78/25.15    (15)  op(e3, e3) = e2
% 158.78/25.15    (16)   ~ (e3 = e1)
% 158.78/25.15    (17)   ~ (e2 = e0)
% 158.78/25.15    (18)   ~ (all_52_8 = e3)
% 158.78/25.15    (19)   ~ (e3 = e0)
% 158.78/25.15  
% 158.78/25.15  Begin of proof
% 158.78/25.15  | 
% 158.78/25.15  | BETA: splitting (10) gives:
% 158.78/25.15  | 
% 158.78/25.15  | Case 1:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (20)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 158.78/25.15  | |           e3)
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (1), (5), (6), (15), (16), (20) are inconsistent by sub-proof
% 158.78/25.15  | |            #233.
% 158.78/25.15  | | 
% 158.78/25.15  | Case 2:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (21)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 158.78/25.15  | |           e3)
% 158.78/25.15  | | 
% 158.78/25.15  | | BETA: splitting (21) gives:
% 158.78/25.15  | | 
% 158.78/25.15  | | Case 1:
% 158.78/25.15  | | | 
% 158.78/25.15  | | |   (22)  all_56_4 = e3 & op(e3, e1) = e3
% 158.78/25.15  | | | 
% 158.78/25.15  | | | ALPHA: (22) implies:
% 158.78/25.15  | | |   (23)  op(e3, e1) = e3
% 158.78/25.15  | | | 
% 158.78/25.15  | | | REF_CLOSE: (6), (7), (18), (23) are inconsistent by sub-proof #982.
% 158.78/25.15  | | | 
% 158.78/25.15  | | Case 2:
% 158.78/25.15  | | | 
% 158.78/25.15  | | |   (24)  all_56_9 = e3 & op(e3, e0) = e3
% 158.78/25.15  | | | 
% 158.78/25.15  | | | ALPHA: (24) implies:
% 158.78/25.15  | | |   (25)  all_56_9 = e3
% 158.78/25.15  | | | 
% 158.78/25.15  | | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (11), (12), (13), (14), (15),
% 158.78/25.15  | | |            (16), (17), (19), (25) are inconsistent by sub-proof #229.
% 158.78/25.15  | | | 
% 158.78/25.15  | | End of split
% 158.78/25.15  | | 
% 158.78/25.15  | End of split
% 158.78/25.15  | 
% 158.78/25.15  End of proof
% 158.78/25.15  
% 158.78/25.15  Sub-proof #229 shows that the following formulas are inconsistent:
% 158.78/25.15  ----------------------------------------------------------------
% 158.78/25.15    (1)  op(e1, e1) = e3
% 158.78/25.15    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.78/25.15         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.78/25.15    (3)  op(e0, e1) = all_52_11
% 158.78/25.15    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.78/25.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.78/25.15    (5)   ~ (all_52_9 = e1)
% 158.78/25.15    (6)   ~ (all_52_11 = e1)
% 158.78/25.15    (7)  all_56_1 = e1
% 158.78/25.15    (8)   ~ (e1 = e0)
% 158.78/25.15    (9)  op(e2, e1) = all_52_9
% 158.78/25.15    (10)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.78/25.15          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.78/25.15    (11)  op(e3, e3) = e2
% 158.78/25.15    (12)  all_56_9 = e3
% 158.78/25.15    (13)   ~ (e3 = e1)
% 158.78/25.15    (14)   ~ (e2 = e0)
% 158.78/25.15    (15)   ~ (e3 = e0)
% 158.78/25.15  
% 158.78/25.15  Begin of proof
% 158.78/25.15  | 
% 158.78/25.15  | BETA: splitting (2) gives:
% 158.78/25.15  | 
% 158.78/25.15  | Case 1:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (16)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 158.78/25.15  | |           e0)
% 158.78/25.15  | | 
% 158.78/25.15  | | BETA: splitting (16) gives:
% 158.78/25.15  | | 
% 158.78/25.15  | | Case 1:
% 158.78/25.15  | | | 
% 158.78/25.15  | | |   (17)  all_56_0 = e0 & op(e3, e3) = e0
% 158.78/25.15  | | | 
% 158.78/25.15  | | | ALPHA: (17) implies:
% 158.78/25.15  | | |   (18)  op(e3, e3) = e0
% 158.78/25.15  | | | 
% 158.78/25.15  | | | REF_CLOSE: (4), (11), (14), (18) are inconsistent by sub-proof #281.
% 158.78/25.15  | | | 
% 158.78/25.15  | | Case 2:
% 158.78/25.15  | | | 
% 158.78/25.15  | | |   (19)  all_56_1 = e0 & op(e3, e2) = e0
% 158.78/25.15  | | | 
% 158.78/25.15  | | | REF_CLOSE: (7), (8), (19) are inconsistent by sub-proof #760.
% 158.78/25.15  | | | 
% 158.78/25.15  | | End of split
% 158.78/25.15  | | 
% 158.78/25.15  | Case 2:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (20)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 158.78/25.15  | |           e0)
% 158.78/25.15  | | 
% 158.78/25.15  | | BETA: splitting (20) gives:
% 158.78/25.15  | | 
% 158.78/25.15  | | Case 1:
% 158.78/25.15  | | | 
% 158.78/25.15  | | |   (21)  all_56_4 = e0 & op(e3, e1) = e0
% 158.78/25.15  | | | 
% 158.78/25.15  | | | ALPHA: (21) implies:
% 158.78/25.15  | | |   (22)  all_56_4 = e0
% 158.78/25.15  | | | 
% 158.78/25.15  | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (13), (22) are
% 158.78/25.15  | | |            inconsistent by sub-proof #230.
% 158.78/25.15  | | | 
% 158.78/25.15  | | Case 2:
% 158.78/25.15  | | | 
% 158.78/25.15  | | |   (23)  all_56_9 = e0 & op(e3, e0) = e0
% 158.78/25.15  | | | 
% 158.78/25.15  | | | REF_CLOSE: (12), (15), (23) are inconsistent by sub-proof #759.
% 158.78/25.15  | | | 
% 158.78/25.15  | | End of split
% 158.78/25.15  | | 
% 158.78/25.15  | End of split
% 158.78/25.15  | 
% 158.78/25.15  End of proof
% 158.78/25.15  
% 158.78/25.15  Sub-proof #230 shows that the following formulas are inconsistent:
% 158.78/25.15  ----------------------------------------------------------------
% 158.78/25.15    (1)  op(e1, e1) = e3
% 158.78/25.15    (2)  op(e0, e1) = all_52_11
% 158.78/25.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.78/25.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.78/25.15    (4)   ~ (all_52_9 = e1)
% 158.78/25.15    (5)   ~ (all_52_11 = e1)
% 158.78/25.15    (6)   ~ (e1 = e0)
% 158.78/25.15    (7)  op(e2, e1) = all_52_9
% 158.78/25.15    (8)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.78/25.15         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.78/25.15    (9)   ~ (e3 = e1)
% 158.78/25.15    (10)  all_56_4 = e0
% 158.78/25.15  
% 158.78/25.15  Begin of proof
% 158.78/25.15  | 
% 158.78/25.15  | BETA: splitting (8) gives:
% 158.78/25.15  | 
% 158.78/25.15  | Case 1:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (11)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) =
% 158.78/25.15  | |           e1)
% 158.78/25.15  | | 
% 158.78/25.15  | | BETA: splitting (11) gives:
% 158.78/25.15  | | 
% 158.78/25.15  | | Case 1:
% 158.78/25.15  | | | 
% 158.78/25.15  | | |   (12)  all_56_4 = e1 & op(e3, e1) = e1
% 158.78/25.15  | | | 
% 158.78/25.15  | | | REF_CLOSE: (6), (10), (12) are inconsistent by sub-proof #232.
% 158.78/25.15  | | | 
% 158.78/25.15  | | Case 2:
% 158.78/25.15  | | | 
% 158.78/25.15  | | |   (13)  all_56_5 = e1 & op(e2, e1) = e1
% 158.78/25.15  | | | 
% 158.78/25.15  | | | REF_CLOSE: (3), (4), (7), (13) are inconsistent by sub-proof #423.
% 158.78/25.15  | | | 
% 158.78/25.15  | | End of split
% 158.78/25.15  | | 
% 158.78/25.15  | Case 2:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (14)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) =
% 158.78/25.15  | |           e1)
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (1), (2), (3), (5), (9), (14) are inconsistent by sub-proof #231.
% 158.78/25.15  | | 
% 158.78/25.15  | End of split
% 158.78/25.15  | 
% 158.78/25.15  End of proof
% 158.78/25.15  
% 158.78/25.15  Sub-proof #231 shows that the following formulas are inconsistent:
% 158.78/25.15  ----------------------------------------------------------------
% 158.78/25.15    (1)  op(e1, e1) = e3
% 158.78/25.15    (2)  op(e0, e1) = all_52_11
% 158.78/25.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.78/25.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.78/25.15    (4)   ~ (all_52_11 = e1)
% 158.78/25.15    (5)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.78/25.15    (6)   ~ (e3 = e1)
% 158.78/25.15  
% 158.78/25.15  Begin of proof
% 158.78/25.15  | 
% 158.78/25.15  | BETA: splitting (5) gives:
% 158.78/25.15  | 
% 158.78/25.15  | Case 1:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (7)  all_56_8 = e1 & op(e1, e1) = e1
% 158.78/25.15  | | 
% 158.78/25.15  | | ALPHA: (7) implies:
% 158.78/25.15  | |   (8)  op(e1, e1) = e1
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #1003.
% 158.78/25.15  | | 
% 158.78/25.15  | Case 2:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (9)  all_56_14 = e1 & op(e0, e1) = e1
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #803.
% 158.78/25.15  | | 
% 158.78/25.15  | End of split
% 158.78/25.15  | 
% 158.78/25.15  End of proof
% 158.78/25.15  
% 158.78/25.15  Sub-proof #232 shows that the following formulas are inconsistent:
% 158.78/25.15  ----------------------------------------------------------------
% 158.78/25.15    (1)  all_56_4 = e1 & op(e3, e1) = e1
% 158.78/25.15    (2)  all_56_4 = e0
% 158.78/25.15    (3)   ~ (e1 = e0)
% 158.78/25.15  
% 158.78/25.15  Begin of proof
% 158.78/25.15  | 
% 158.78/25.15  | ALPHA: (1) implies:
% 158.78/25.15  |   (4)  all_56_4 = e1
% 158.78/25.15  | 
% 158.78/25.15  | COMBINE_EQS: (2), (4) imply:
% 158.78/25.15  |   (5)  e1 = e0
% 158.78/25.15  | 
% 158.78/25.15  | REDUCE: (3), (5) imply:
% 158.78/25.15  |   (6)  $false
% 158.78/25.15  | 
% 158.78/25.15  | CLOSE: (6) is inconsistent.
% 158.78/25.15  | 
% 158.78/25.15  End of proof
% 158.78/25.15  
% 158.78/25.15  Sub-proof #233 shows that the following formulas are inconsistent:
% 158.78/25.15  ----------------------------------------------------------------
% 158.78/25.15    (1)  op(e3, e2) = e1
% 158.78/25.15    (2)   ~ (e3 = e2)
% 158.78/25.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.78/25.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.78/25.15    (4)  op(e3, e3) = e2
% 158.78/25.15    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 158.78/25.15    (6)   ~ (e3 = e1)
% 158.78/25.15  
% 158.78/25.15  Begin of proof
% 158.78/25.15  | 
% 158.78/25.15  | BETA: splitting (5) gives:
% 158.78/25.15  | 
% 158.78/25.15  | Case 1:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (7)  all_56_0 = e3 & op(e3, e3) = e3
% 158.78/25.15  | | 
% 158.78/25.15  | | ALPHA: (7) implies:
% 158.78/25.15  | |   (8)  op(e3, e3) = e3
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #958.
% 158.78/25.15  | | 
% 158.78/25.15  | Case 2:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (9)  all_56_1 = e3 & op(e3, e2) = e3
% 158.78/25.15  | | 
% 158.78/25.15  | | ALPHA: (9) implies:
% 158.78/25.15  | |   (10)  op(e3, e2) = e3
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #345.
% 158.78/25.15  | | 
% 158.78/25.15  | End of split
% 158.78/25.15  | 
% 158.78/25.15  End of proof
% 158.78/25.15  
% 158.78/25.15  Sub-proof #234 shows that the following formulas are inconsistent:
% 158.78/25.15  ----------------------------------------------------------------
% 158.78/25.15    (1)   ~ (all_52_13 = e1)
% 158.78/25.15    (2)   ~ (all_52_13 = e3)
% 158.78/25.15    (3)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.78/25.15    (4)   ~ (all_52_13 = e0)
% 158.78/25.15    (5)  all_54_7 = all_52_13
% 158.78/25.15    (6)   ~ (all_52_13 = e2)
% 158.78/25.15  
% 158.78/25.15  Begin of proof
% 158.78/25.15  | 
% 158.78/25.15  | BETA: splitting (3) gives:
% 158.78/25.15  | 
% 158.78/25.15  | Case 1:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (7)  all_54_7 = e3
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #383.
% 158.78/25.15  | | 
% 158.78/25.15  | Case 2:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (8)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (1), (4), (5), (6), (8) are inconsistent by sub-proof #235.
% 158.78/25.15  | | 
% 158.78/25.15  | End of split
% 158.78/25.15  | 
% 158.78/25.15  End of proof
% 158.78/25.15  
% 158.78/25.15  Sub-proof #235 shows that the following formulas are inconsistent:
% 158.78/25.15  ----------------------------------------------------------------
% 158.78/25.15    (1)   ~ (all_52_13 = e1)
% 158.78/25.15    (2)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.78/25.15    (3)   ~ (all_52_13 = e0)
% 158.78/25.15    (4)  all_54_7 = all_52_13
% 158.78/25.15    (5)   ~ (all_52_13 = e2)
% 158.78/25.15  
% 158.78/25.15  Begin of proof
% 158.78/25.15  | 
% 158.78/25.15  | BETA: splitting (2) gives:
% 158.78/25.15  | 
% 158.78/25.15  | Case 1:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (6)  all_54_7 = e2
% 158.78/25.15  | | 
% 158.78/25.15  | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #382.
% 158.78/25.15  | | 
% 158.78/25.15  | Case 2:
% 158.78/25.15  | | 
% 158.78/25.15  | |   (7)  all_54_7 = e1 | all_54_7 = e0
% 158.78/25.15  | | 
% 158.78/25.15  | | BETA: splitting (7) gives:
% 158.78/25.15  | | 
% 158.78/25.15  | | Case 1:
% 158.78/25.15  | | | 
% 158.78/25.15  | | |   (8)  all_54_7 = e1
% 158.78/25.15  | | | 
% 158.78/25.15  | | | COMBINE_EQS: (4), (8) imply:
% 158.78/25.16  | | |   (9)  all_52_13 = e1
% 158.78/25.16  | | | 
% 158.78/25.16  | | | SIMP: (9) implies:
% 158.78/25.16  | | |   (10)  all_52_13 = e1
% 158.78/25.16  | | | 
% 158.78/25.16  | | | REDUCE: (1), (10) imply:
% 158.78/25.16  | | |   (11)  $false
% 158.78/25.16  | | | 
% 158.78/25.16  | | | CLOSE: (11) is inconsistent.
% 158.78/25.16  | | | 
% 158.78/25.16  | | Case 2:
% 158.78/25.16  | | | 
% 158.78/25.16  | | |   (12)  all_54_7 = e0
% 158.78/25.16  | | | 
% 158.78/25.16  | | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #368.
% 158.78/25.16  | | | 
% 158.78/25.16  | | End of split
% 158.78/25.16  | | 
% 158.78/25.16  | End of split
% 158.78/25.16  | 
% 158.78/25.16  End of proof
% 158.78/25.16  
% 158.78/25.16  Sub-proof #236 shows that the following formulas are inconsistent:
% 158.78/25.16  ----------------------------------------------------------------
% 158.78/25.16    (1)   ~ (e3 = e2)
% 158.78/25.16    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.78/25.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.78/25.16    (3)   ~ (all_52_9 = all_4_2)
% 158.78/25.16    (4)  op(e2, e2) = all_4_2
% 158.78/25.16    (5)  op(e2, e1) = all_52_9
% 158.78/25.16    (6)  op(e2, e1) = e2
% 158.78/25.16    (7)  op(e3, e3) = e2
% 158.78/25.16    (8)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.78/25.16             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.78/25.16           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.78/25.16               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.78/25.16             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.78/25.16         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.78/25.16             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.78/25.16           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.78/25.16               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.78/25.16             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 158.78/25.16  
% 158.78/25.16  Begin of proof
% 158.78/25.16  | 
% 158.78/25.16  | BETA: splitting (8) gives:
% 158.78/25.16  | 
% 158.78/25.16  | Case 1:
% 158.78/25.16  | | 
% 158.78/25.16  | |   (9)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.78/25.16  | |            e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.78/25.16  | |            $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.78/25.16  | |            (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.78/25.16  | |        ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.78/25.16  | |              e3) = all_57_6 & $i(all_57_6)))
% 158.78/25.16  | | 
% 158.78/25.16  | | ALPHA: (9) implies:
% 158.78/25.16  | |   (10)  op(e3, e3) = e3
% 158.78/25.16  | | 
% 158.78/25.16  | | REF_CLOSE: (1), (2), (7), (10) are inconsistent by sub-proof #958.
% 158.78/25.16  | | 
% 158.78/25.16  | Case 2:
% 158.78/25.16  | | 
% 158.78/25.16  | |   (11)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 158.78/25.16  | |             e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.78/25.16  | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 158.78/25.16  | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 158.78/25.16  | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 158.78/25.16  | |               e2) = all_57_7 & $i(all_57_7)))
% 158.78/25.16  | | 
% 158.78/25.16  | | ALPHA: (11) implies:
% 158.78/25.16  | |   (12)  op(e2, e2) = e2
% 158.78/25.16  | | 
% 158.78/25.16  | | REF_CLOSE: (2), (3), (4), (5), (6), (12) are inconsistent by sub-proof #237.
% 158.78/25.16  | | 
% 158.78/25.16  | End of split
% 158.78/25.16  | 
% 158.78/25.16  End of proof
% 158.78/25.16  
% 158.78/25.16  Sub-proof #237 shows that the following formulas are inconsistent:
% 158.78/25.16  ----------------------------------------------------------------
% 158.78/25.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.78/25.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.78/25.16    (2)   ~ (all_52_9 = all_4_2)
% 158.78/25.16    (3)  op(e2, e2) = e2
% 158.78/25.16    (4)  op(e2, e2) = all_4_2
% 158.78/25.16    (5)  op(e2, e1) = all_52_9
% 158.78/25.16    (6)  op(e2, e1) = e2
% 158.78/25.16  
% 158.78/25.16  Begin of proof
% 158.78/25.16  | 
% 158.78/25.16  | GROUND_INST: instantiating (1) with all_52_9, e2, e1, e2, simplifying with
% 158.78/25.16  |              (5), (6) gives:
% 158.78/25.16  |   (7)  all_52_9 = e2
% 158.78/25.16  | 
% 158.78/25.16  | GROUND_INST: instantiating (1) with all_4_2, e2, e2, e2, simplifying with (3),
% 158.78/25.16  |              (4) gives:
% 158.78/25.16  |   (8)  all_4_2 = e2
% 158.78/25.16  | 
% 158.78/25.16  | REDUCE: (2), (7), (8) imply:
% 158.78/25.16  |   (9)  $false
% 158.78/25.16  | 
% 158.78/25.16  | CLOSE: (9) is inconsistent.
% 158.78/25.16  | 
% 158.78/25.16  End of proof
% 158.78/25.16  
% 158.78/25.16  Sub-proof #238 shows that the following formulas are inconsistent:
% 158.78/25.16  ----------------------------------------------------------------
% 158.78/25.16    (1)   ~ (all_52_1 = all_52_3)
% 158.78/25.16    (2)  all_54_5 = all_4_2
% 158.78/25.16    (3)  op(e1, e1) = e0
% 158.78/25.16    (4)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.78/25.16    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.78/25.16         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.78/25.16    (6)  op(e0, e1) = all_52_11
% 158.78/25.16    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.78/25.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.78/25.16    (8)  op(e0, e3) = all_52_3
% 158.78/25.16    (9)  op(e3, e1) = all_52_8
% 158.78/25.16    (10)   ~ (all_52_9 = all_4_2)
% 158.78/25.16    (11)   ~ (all_4_2 = e3)
% 158.78/25.16    (12)   ~ (all_52_3 = e0)
% 158.78/25.16    (13)  op(e1, e3) = all_52_2
% 158.78/25.16    (14)  op(e0, e2) = all_52_7
% 158.78/25.16    (15)   ~ (all_52_8 = e0)
% 158.78/25.16    (16)   ~ (all_52_13 = all_4_2)
% 158.78/25.16    (17)  op(e0, e0) = e0
% 158.78/25.16    (18)  op(e2, e2) = all_4_2
% 158.78/25.16    (19)   ~ (all_52_4 = all_4_2)
% 158.78/25.16    (20)   ~ (all_52_4 = all_52_7)
% 158.78/25.16    (21)  op(e0, e0) = all_14_2
% 158.78/25.16    (22)  op(e2, e3) = all_52_1
% 158.78/25.16    (23)   ~ (all_4_2 = e1)
% 158.78/25.16    (24)  op(e3, e2) = all_52_4
% 158.78/25.16    (25)   ~ (e1 = e0)
% 158.78/25.16    (26)  op(e2, e1) = all_52_9
% 158.78/25.16    (27)   ~ (all_52_12 = e0)
% 158.78/25.16    (28)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.78/25.16          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.78/25.16    (29)  op(e2, e0) = all_52_13
% 158.78/25.16    (30)  op(e3, e3) = e2
% 158.78/25.16    (31)   ~ (all_52_11 = e0)
% 158.78/25.16    (32)  op(e3, e0) = all_52_12
% 158.78/25.16    (33)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.78/25.16            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.78/25.16            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.78/25.16            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.78/25.16              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.78/25.16          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.78/25.16            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.78/25.16              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.78/25.16            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.78/25.16              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.78/25.16          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.78/25.16            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.78/25.16              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.78/25.16            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.78/25.16              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.78/25.16          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.78/25.16            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.78/25.16            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.78/25.16              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.78/25.16            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.78/25.16            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.78/25.16            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.78/25.16            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.78/25.16              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.78/25.16            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.78/25.16          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.78/25.16            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.78/25.16              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.78/25.16            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.78/25.16            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.78/25.16          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.78/25.16            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.78/25.16              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.78/25.16            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.78/25.16            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.78/25.16          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.78/25.16            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.78/25.16              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.78/25.16            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.78/25.16              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.78/25.16          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.78/25.16            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.78/25.16            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.78/25.16            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.78/25.16            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.78/25.16            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.78/25.16            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.78/25.16            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.78/25.16              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.78/25.16            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.78/25.16            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.78/25.16            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.78/25.16            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.78/25.16              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.78/25.16            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.78/25.16          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.78/25.16            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.78/25.16              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.78/25.16              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.78/25.16            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.78/25.16            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.78/25.16            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.78/25.16            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.78/25.16              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.78/25.16            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.78/25.16          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.78/25.16            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.78/25.16              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.78/25.16            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.78/25.16              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.78/25.16          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.78/25.16            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.78/25.16              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.78/25.16              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.78/25.16            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.78/25.16          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.78/25.16            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.78/25.16            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.78/25.16                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.78/25.16                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.78/25.16                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.78/25.16                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.78/25.16                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.78/25.16                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.78/25.16                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.78/25.16                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.78/25.16                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.78/25.16                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.78/25.16                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.78/25.16                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.78/25.16                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.78/25.16                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.78/25.16                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.78/25.16                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.78/25.16                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.78/25.16                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.78/25.16                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.78/25.16                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.78/25.16                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.78/25.16                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.78/25.16                op(e0, e1) = e0)))
% 158.78/25.16    (34)   ~ (all_52_2 = e0)
% 158.78/25.16    (35)   ~ (e2 = e0)
% 158.78/25.16    (36)   ~ (e3 = e0)
% 158.78/25.16  
% 158.78/25.16  Begin of proof
% 158.78/25.16  | 
% 158.78/25.16  | BETA: splitting (5) gives:
% 158.78/25.16  | 
% 158.78/25.16  | Case 1:
% 158.78/25.16  | | 
% 158.78/25.16  | |   (37)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 158.78/25.16  | |           e0)
% 158.78/25.16  | | 
% 158.78/25.16  | | BETA: splitting (37) gives:
% 158.78/25.16  | | 
% 158.78/25.16  | | Case 1:
% 158.78/25.16  | | | 
% 158.78/25.16  | | |   (38)  all_56_0 = e0 & op(e3, e3) = e0
% 158.78/25.16  | | | 
% 158.78/25.16  | | | ALPHA: (38) implies:
% 158.78/25.16  | | |   (39)  op(e3, e3) = e0
% 158.78/25.16  | | | 
% 158.78/25.16  | | | REF_CLOSE: (7), (30), (35), (39) are inconsistent by sub-proof #281.
% 158.78/25.16  | | | 
% 158.78/25.16  | | Case 2:
% 158.78/25.16  | | | 
% 158.78/25.16  | | |   (40)  all_56_1 = e0 & op(e3, e2) = e0
% 158.78/25.16  | | | 
% 158.78/25.16  | | | ALPHA: (40) implies:
% 158.78/25.16  | | |   (41)  op(e3, e2) = e0
% 158.78/25.16  | | | 
% 158.78/25.16  | | | BETA: splitting (28) gives:
% 158.78/25.16  | | | 
% 158.78/25.16  | | | Case 1:
% 158.78/25.16  | | | | 
% 158.78/25.16  | | | |   (42)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3)
% 158.78/25.16  | | | |           = e0)
% 158.78/25.16  | | | | 
% 158.78/25.16  | | | | BETA: splitting (42) gives:
% 158.78/25.16  | | | | 
% 158.78/25.16  | | | | Case 1:
% 158.78/25.16  | | | | | 
% 158.78/25.16  | | | | |   (43)  all_56_0 = e0 & op(e3, e3) = e0
% 158.78/25.16  | | | | | 
% 158.78/25.16  | | | | | ALPHA: (43) implies:
% 158.78/25.16  | | | | |   (44)  op(e3, e3) = e0
% 158.78/25.16  | | | | | 
% 158.78/25.16  | | | | | REF_CLOSE: (7), (30), (35), (44) are inconsistent by sub-proof #281.
% 158.78/25.16  | | | | | 
% 158.78/25.16  | | | | Case 2:
% 158.78/25.16  | | | | | 
% 158.78/25.16  | | | | |   (45)  all_56_2 = e0 & op(e2, e3) = e0
% 158.78/25.16  | | | | | 
% 158.78/25.16  | | | | | ALPHA: (45) implies:
% 158.78/25.16  | | | | |   (46)  op(e2, e3) = e0
% 158.78/25.16  | | | | | 
% 158.78/25.16  | | | | | GROUND_INST: instantiating (7) with all_52_1, e0, e3, e2, simplifying
% 158.78/25.16  | | | | |              with (22), (46) gives:
% 158.78/25.16  | | | | |   (47)  all_52_1 = e0
% 158.78/25.16  | | | | | 
% 158.78/25.16  | | | | | GROUND_INST: instantiating (7) with all_52_4, e0, e2, e3, simplifying
% 158.78/25.16  | | | | |              with (24), (41) gives:
% 158.78/25.16  | | | | |   (48)  all_52_4 = e0
% 158.78/25.16  | | | | | 
% 158.78/25.16  | | | | | REDUCE: (1), (47) imply:
% 158.78/25.17  | | | | |   (49)   ~ (all_52_3 = e0)
% 158.78/25.17  | | | | | 
% 158.78/25.17  | | | | | REDUCE: (20), (48) imply:
% 158.78/25.17  | | | | |   (50)   ~ (all_52_7 = e0)
% 158.78/25.17  | | | | | 
% 158.78/25.17  | | | | | SIMP: (50) implies:
% 158.78/25.17  | | | | |   (51)   ~ (all_52_7 = e0)
% 158.78/25.17  | | | | | 
% 158.78/25.17  | | | | | REDUCE: (19), (48) imply:
% 158.78/25.17  | | | | |   (52)   ~ (all_4_2 = e0)
% 158.78/25.17  | | | | | 
% 158.78/25.17  | | | | | SIMP: (52) implies:
% 158.78/25.17  | | | | |   (53)   ~ (all_4_2 = e0)
% 158.78/25.17  | | | | | 
% 158.78/25.17  | | | | | BETA: splitting (4) gives:
% 158.78/25.17  | | | | | 
% 158.78/25.17  | | | | | Case 1:
% 158.78/25.17  | | | | | | 
% 158.78/25.17  | | | | | |   (54)  all_54_5 = e3
% 158.78/25.17  | | | | | | 
% 158.78/25.17  | | | | | | COMBINE_EQS: (2), (54) imply:
% 158.78/25.17  | | | | | |   (55)  all_4_2 = e3
% 158.78/25.17  | | | | | | 
% 158.78/25.17  | | | | | | REDUCE: (11), (55) imply:
% 158.78/25.17  | | | | | |   (56)  $false
% 158.78/25.17  | | | | | | 
% 158.78/25.17  | | | | | | CLOSE: (56) is inconsistent.
% 158.78/25.17  | | | | | | 
% 158.78/25.17  | | | | | Case 2:
% 158.78/25.17  | | | | | | 
% 158.78/25.17  | | | | | |   (57)   ~ (all_54_5 = e3)
% 158.78/25.17  | | | | | |   (58)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.78/25.17  | | | | | | 
% 158.78/25.17  | | | | | | BETA: splitting (58) gives:
% 158.78/25.17  | | | | | | 
% 158.78/25.17  | | | | | | Case 1:
% 158.78/25.17  | | | | | | | 
% 158.78/25.17  | | | | | | |   (59)  all_54_5 = e2
% 158.78/25.17  | | | | | | | 
% 158.78/25.17  | | | | | | | COMBINE_EQS: (2), (59) imply:
% 158.78/25.17  | | | | | | |   (60)  all_4_2 = e2
% 158.78/25.17  | | | | | | | 
% 158.78/25.17  | | | | | | | REDUCE: (10), (60) imply:
% 158.78/25.17  | | | | | | |   (61)   ~ (all_52_9 = e2)
% 158.78/25.17  | | | | | | | 
% 158.78/25.17  | | | | | | | REDUCE: (16), (60) imply:
% 158.78/25.17  | | | | | | |   (62)   ~ (all_52_13 = e2)
% 158.78/25.17  | | | | | | | 
% 158.78/25.17  | | | | | | | REDUCE: (11), (60) imply:
% 158.78/25.17  | | | | | | |   (63)   ~ (e3 = e2)
% 158.78/25.17  | | | | | | | 
% 158.78/25.17  | | | | | | | SIMP: (63) implies:
% 158.78/25.17  | | | | | | |   (64)   ~ (e3 = e2)
% 158.78/25.17  | | | | | | | 
% 158.78/25.17  | | | | | | | REDUCE: (23), (60) imply:
% 158.78/25.17  | | | | | | |   (65)   ~ (e2 = e1)
% 158.78/25.17  | | | | | | | 
% 158.78/25.17  | | | | | | | REDUCE: (18), (60) imply:
% 158.78/25.17  | | | | | | |   (66)  op(e2, e2) = e2
% 158.78/25.17  | | | | | | | 
% 158.78/25.17  | | | | | | | BETA: splitting (33) gives:
% 158.78/25.17  | | | | | | | 
% 158.78/25.17  | | | | | | | Case 1:
% 158.78/25.17  | | | | | | | | 
% 158.78/25.17  | | | | | | | |   (67)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.78/25.17  | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.78/25.17  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.78/25.17  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.78/25.17  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.78/25.17  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 158.78/25.17  | | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.78/25.17  | | | | | | | |           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.78/25.17  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 158.78/25.17  | | | | | | | |           = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 =
% 158.78/25.17  | | | | | | | |           e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.78/25.17  | | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 158.78/25.17  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.78/25.17  | | | | | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.78/25.17  | | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.78/25.17  | | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.78/25.17  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.78/25.17  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.78/25.17  | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.78/25.17  | | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.78/25.17  | | | | | | | |           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.78/25.17  | | | | | | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 158.78/25.17  | | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.78/25.17  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 158.78/25.17  | | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.78/25.17  | | | | | | | |           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.78/25.17  | | | | | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.78/25.17  | | | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 158.78/25.17  | | | | | | | |         (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.78/25.17  | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2)
% 158.78/25.17  | | | | | | | |           = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.78/25.17  | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~
% 158.78/25.17  | | | | | | | |           (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.78/25.17  | | | | | | | |         (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.78/25.17  | | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.78/25.17  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.78/25.17  | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.78/25.17  | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1
% 158.78/25.17  | | | | | | | |           & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.78/25.17  | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_4
% 158.78/25.17  | | | | | | | |           = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 158.78/25.17  | | | | | | | |             e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1
% 158.78/25.17  | | | | | | | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 158.78/25.17  | | | | | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.78/25.17  | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 158.78/25.17  | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2 =
% 158.78/25.17  | | | | | | | |           e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.78/25.17  | | | | | | | |             e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.78/25.17  | | | | | | | |           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 158.78/25.17  | | | | | | | |         (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~
% 158.78/25.17  | | | | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0)
% 158.78/25.17  | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.78/25.17  | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~
% 158.78/25.17  | | | | | | | |           (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.78/25.17  | | | | | | | | 
% 158.78/25.17  | | | | | | | | BETA: splitting (67) gives:
% 158.78/25.17  | | | | | | | | 
% 158.78/25.17  | | | | | | | | Case 1:
% 158.78/25.17  | | | | | | | | | 
% 158.78/25.17  | | | | | | | | |   (68)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.78/25.17  | | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.78/25.17  | | | | | | | | |           & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.78/25.17  | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.78/25.17  | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.78/25.17  | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.78/25.17  | | | | | | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.78/25.17  | | | | | | | | |           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 158.78/25.17  | | | | | | | | |           & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1,
% 158.78/25.17  | | | | | | | | |             e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.78/25.17  | | | | | | | | |         (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.78/25.17  | | | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.78/25.17  | | | | | | | | |             e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.78/25.17  | | | | | | | | |           $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 158.78/25.17  | | | | | | | | |           all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 158.78/25.17  | | | | | | | | |           e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 158.78/25.17  | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.78/25.17  | | | | | | | | |           all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 158.78/25.17  | | | | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 158.78/25.17  | | | | | | | | |             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.78/25.17  | | | | | | | | |         (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.78/25.17  | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3
% 158.78/25.17  | | | | | | | | |           & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.78/25.17  | | | | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 158.78/25.17  | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.78/25.17  | | | | | | | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 158.78/25.17  | | | | | | | | |           (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.78/25.17  | | | | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.78/25.17  | | | | | | | | |           $i(all_57_12))
% 158.78/25.17  | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | BETA: splitting (68) gives:
% 158.78/25.17  | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | Case 1:
% 158.78/25.17  | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | |   (69)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.78/25.17  | | | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) =
% 158.78/25.17  | | | | | | | | | |           e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.78/25.17  | | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.78/25.17  | | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 158.78/25.17  | | | | | | | | | |           = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.78/25.17  | | | | | | | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 158.78/25.17  | | | | | | | | | |           & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 158.78/25.17  | | | | | | | | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.78/25.17  | | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 158.78/25.17  | | | | | | | | | |         | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 158.78/25.17  | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.78/25.17  | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.78/25.17  | | | | | | | | | |           e3 & $i(all_57_10))
% 158.78/25.17  | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | | REF_CLOSE: (7), (35), (46), (69) are inconsistent by
% 158.78/25.17  | | | | | | | | | |            sub-proof #242.
% 158.78/25.17  | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | Case 2:
% 158.78/25.17  | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | |   (70)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.78/25.17  | | | | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.78/25.17  | | | | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.78/25.17  | | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.78/25.17  | | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.78/25.17  | | | | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 158.78/25.17  | | | | | | | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 158.78/25.17  | | | | | | | | | |           & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 158.78/25.17  | | | | | | | | | |           & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 158.78/25.17  | | | | | | | | | |           e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3,
% 158.78/25.17  | | | | | | | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) =
% 158.78/25.17  | | | | | | | | | |           e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1
% 158.78/25.17  | | | | | | | | | |           = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 158.78/25.17  | | | | | | | | | |           (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) =
% 158.78/25.17  | | | | | | | | | |           e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.78/25.17  | | | | | | | | | |           $i(all_57_12))
% 158.78/25.17  | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | | BETA: splitting (70) gives:
% 158.78/25.17  | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | | Case 1:
% 158.78/25.17  | | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | | |   (71)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.78/25.17  | | | | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 158.78/25.17  | | | | | | | | | | |             e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 158.78/25.17  | | | | | | | | | | |           = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.78/25.17  | | | | | | | | | | |           all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.78/25.17  | | | | | | | | | | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.78/25.17  | | | | | | | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.78/25.17  | | | | | | | | | | |           $i(all_57_10))
% 158.78/25.17  | | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | | | REF_CLOSE: (7), (35), (46), (71) are inconsistent by
% 158.78/25.17  | | | | | | | | | | |            sub-proof #241.
% 158.78/25.17  | | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | | Case 2:
% 158.78/25.17  | | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | | |   (72)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.78/25.17  | | | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 158.78/25.17  | | | | | | | | | | |           e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.78/25.17  | | | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.78/25.17  | | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.78/25.17  | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 158.78/25.17  | | | | | | | | | | |           = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.78/25.17  | | | | | | | | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.78/25.17  | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.78/25.17  | | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | | | REF_CLOSE: (3), (7), (26), (35), (36), (46), (61), (72) are
% 158.78/25.17  | | | | | | | | | | |            inconsistent by sub-proof #707.
% 158.78/25.17  | | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | | End of split
% 158.78/25.17  | | | | | | | | | | 
% 158.78/25.17  | | | | | | | | | End of split
% 158.78/25.17  | | | | | | | | | 
% 158.78/25.17  | | | | | | | | Case 2:
% 158.78/25.17  | | | | | | | | | 
% 158.80/25.17  | | | | | | | | |   (73)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.80/25.17  | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.80/25.17  | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.80/25.17  | | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 & 
% 158.80/25.17  | | | | | | | | |           ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.80/25.17  | | | | | | | | |         (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.80/25.17  | | | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3
% 158.80/25.17  | | | | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.80/25.17  | | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.80/25.17  | | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) =
% 158.80/25.17  | | | | | | | | |           e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.80/25.17  | | | | | | | | |           = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.80/25.17  | | | | | | | | |           all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 158.80/25.17  | | | | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1,
% 158.80/25.17  | | | | | | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.80/25.17  | | | | | | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.80/25.17  | | | | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2
% 158.80/25.17  | | | | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.80/25.17  | | | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 158.80/25.17  | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 158.80/25.17  | | | | | | | | |           e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.80/25.17  | | | | | | | | |           op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.80/25.17  | | | | | | | | |           all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 158.80/25.17  | | | | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1,
% 158.80/25.17  | | | | | | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.80/25.17  | | | | | | | | |         (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 158.80/25.17  | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.80/25.17  | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | BETA: splitting (73) gives:
% 158.80/25.17  | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | Case 1:
% 158.80/25.17  | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | |   (74)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.80/25.17  | | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.80/25.17  | | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.80/25.17  | | | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &
% 158.80/25.17  | | | | | | | | | |            ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 158.80/25.17  | | | | | | | | | |         | (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 158.80/25.17  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 158.80/25.17  | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.80/25.17  | | | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.80/25.17  | | | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3)
% 158.80/25.17  | | | | | | | | | |           = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.80/25.17  | | | | | | | | | |             e1) = all_57_14 & $i(all_57_14))
% 158.80/25.17  | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | BETA: splitting (74) gives:
% 158.80/25.17  | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | Case 1:
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | |   (75)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.80/25.17  | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.80/25.17  | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.80/25.17  | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 158.80/25.17  | | | | | | | | | | |           = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 158.80/25.17  | | | | | | | | | | |             e2) = e3)
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | | REF_CLOSE: (7), (17), (30), (36), (75) are inconsistent by
% 158.80/25.17  | | | | | | | | | | |            sub-proof #287.
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | Case 2:
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | |   (76)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 158.80/25.17  | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 158.80/25.17  | | | | | | | | | | |             e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.80/25.17  | | | | | | | | | | |           = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 158.80/25.17  | | | | | | | | | | |           all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 158.80/25.17  | | | | | | | | | | |             e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.80/25.17  | | | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.80/25.17  | | | | | | | | | | |           $i(all_57_14))
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | | REF_CLOSE: (7), (29), (30), (62), (65), (76) are inconsistent
% 158.80/25.17  | | | | | | | | | | |            by sub-proof #286.
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | End of split
% 158.80/25.17  | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | Case 2:
% 158.80/25.17  | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | |   (77)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.80/25.17  | | | | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.80/25.17  | | | | | | | | | |             e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.80/25.17  | | | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.80/25.17  | | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2)
% 158.80/25.17  | | | | | | | | | |           = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1,
% 158.80/25.17  | | | | | | | | | |             e1) = all_57_14 & $i(all_57_14)) | (all_57_2 =
% 158.80/25.17  | | | | | | | | | |           e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.80/25.17  | | | | | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 158.80/25.17  | | | | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.80/25.17  | | | | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.80/25.17  | | | | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.80/25.17  | | | | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 158.80/25.17  | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 158.80/25.17  | | | | | | | | | |           & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1
% 158.80/25.17  | | | | | | | | | |           & op(e1, e1) = e1)
% 158.80/25.17  | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | BETA: splitting (77) gives:
% 158.80/25.17  | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | Case 1:
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | |   (78)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 158.80/25.17  | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.80/25.17  | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.80/25.17  | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 158.80/25.17  | | | | | | | | | | |           = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 158.80/25.17  | | | | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 158.80/25.17  | | | | | | | | | | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | | REF_CLOSE: (3), (7), (36), (65), (66), (78) are inconsistent
% 158.80/25.17  | | | | | | | | | | |            by sub-proof #705.
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | Case 2:
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | |   (79)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 158.80/25.17  | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 158.80/25.17  | | | | | | | | | | |             e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.80/25.17  | | | | | | | | | | |           = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.80/25.17  | | | | | | | | | | |           all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.80/25.17  | | | | | | | | | | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.80/25.17  | | | | | | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.80/25.17  | | | | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 158.80/25.17  | | | | | | | | | | |           &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 158.80/25.17  | | | | | | | | | | |           e1)
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | | REF_CLOSE: (3), (7), (17), (21), (25), (36), (79) are
% 158.80/25.17  | | | | | | | | | | |            inconsistent by sub-proof #240.
% 158.80/25.17  | | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | | End of split
% 158.80/25.17  | | | | | | | | | | 
% 158.80/25.17  | | | | | | | | | End of split
% 158.80/25.17  | | | | | | | | | 
% 158.80/25.17  | | | | | | | | End of split
% 158.80/25.17  | | | | | | | | 
% 158.80/25.17  | | | | | | | Case 2:
% 158.80/25.17  | | | | | | | | 
% 158.80/25.18  | | | | | | | |   (80)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.80/25.18  | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.80/25.18  | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.80/25.18  | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.80/25.18  | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.80/25.18  | | | | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.80/25.18  | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5
% 158.80/25.18  | | | | | | | |           = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 158.80/25.18  | | | | | | | |             e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1
% 158.80/25.18  | | | | | | | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.80/25.18  | | | | | | | |           all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.80/25.18  | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1)
% 158.80/25.18  | | | | | | | |           = e0 & op(e0, e0) = e1 & $i(all_57_14)) | (all_57_3 =
% 158.80/25.18  | | | | | | | |           e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 158.80/25.18  | | | | | | | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.80/25.18  | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.80/25.18  | | | | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1,
% 158.80/25.18  | | | | | | | |             e2) = e1 & op(e1, e1) = e1) | (all_57_4 = e3 &
% 158.80/25.18  | | | | | | | |           all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.80/25.18  | | | | | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 158.80/25.18  | | | | | | | |           = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 158.80/25.18  | | | | | | | |           e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.80/25.18  | | | | | | | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.80/25.18  | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1
% 158.80/25.18  | | | | | | | |           & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 158.80/25.18  | | | | | | | |             e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 &
% 158.80/25.18  | | | | | | | |           all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 158.80/25.18  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 158.80/25.18  | | | | | | | |           = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 =
% 158.80/25.18  | | | | | | | |           e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 158.80/25.18  | | | | | | | |           op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.80/25.18  | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1
% 158.80/25.18  | | | | | | | |           & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.80/25.18  | | | | | | | |             e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 158.80/25.18  | | | | | | | |           all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 158.80/25.18  | | | | | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3)
% 158.80/25.18  | | | | | | | |           = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 =
% 158.80/25.18  | | | | | | | |           e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 158.80/25.18  | | | | | | | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.80/25.18  | | | | | | | |           op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.80/25.18  | | | | | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3,
% 158.80/25.18  | | | | | | | |             e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.80/25.18  | | | | | | | |           all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 &
% 158.80/25.18  | | | | | | | |           op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1 & 
% 158.80/25.18  | | | | | | | |           ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 158.80/25.18  | | | | | | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 =
% 158.80/25.18  | | | | | | | |               e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.80/25.18  | | | | | | | |               (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 158.80/25.18  | | | | | | | |               e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 158.80/25.18  | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.80/25.18  | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 158.80/25.18  | | | | | | | |               e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 158.80/25.18  | | | | | | | |               = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 158.80/25.18  | | | | | | | |               op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.80/25.18  | | | | | | | |               e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.80/25.18  | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 158.80/25.18  | | | | | | | |               e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 158.80/25.18  | | | | | | | |               op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.80/25.18  | | | | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.80/25.18  | | | | | | | |               (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 158.80/25.18  | | | | | | | |               e2 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_13
% 158.80/25.18  | | | | | | | |               = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.18  | | | | | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.80/25.18  | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 =
% 158.80/25.18  | | | | | | | |                 e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.80/25.18  | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.80/25.18  | | | | | | | |                 e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.80/25.18  | | | | | | | |                 e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.80/25.18  | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2)
% 158.80/25.18  | | | | | | | |               = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.80/25.18  | | | | | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 158.80/25.18  | | | | | | | |               ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 158.80/25.18  | | | | | | | |               = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.80/25.18  | | | | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.80/25.18  | | | | | | | |                 e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.80/25.18  | | | | | | | |               op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0
% 158.80/25.18  | | | | | | | |               & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.80/25.18  | | | | | | | |               e0)))
% 158.80/25.18  | | | | | | | | 
% 158.80/25.18  | | | | | | | | BETA: splitting (80) gives:
% 158.80/25.18  | | | | | | | | 
% 158.80/25.18  | | | | | | | | Case 1:
% 158.80/25.18  | | | | | | | | | 
% 158.80/25.18  | | | | | | | | |   (81)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.80/25.18  | | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3
% 158.80/25.18  | | | | | | | | |           & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.80/25.18  | | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.80/25.18  | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 158.80/25.18  | | | | | | | | |           e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.80/25.18  | | | | | | | | |           = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.80/25.18  | | | | | | | | |           all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 158.80/25.18  | | | | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.80/25.18  | | | | | | | | |             e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.80/25.18  | | | | | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.80/25.18  | | | | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.80/25.18  | | | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.80/25.18  | | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 158.80/25.18  | | | | | | | | |           all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 158.80/25.18  | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 158.80/25.18  | | | | | | | | |           op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.80/25.18  | | | | | | | | |           all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.80/25.18  | | | | | | | | |           op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.80/25.18  | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.80/25.18  | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 158.80/25.18  | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 158.80/25.18  | | | | | | | | |           all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.80/25.18  | | | | | | | | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.80/25.18  | | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.80/25.18  | | | | | | | | |           e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.80/25.18  | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_14))
% 158.80/25.18  | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | BETA: splitting (81) gives:
% 158.80/25.18  | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | Case 1:
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | |   (82)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.80/25.18  | | | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) =
% 158.80/25.18  | | | | | | | | | |           e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.80/25.18  | | | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.80/25.18  | | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 158.80/25.18  | | | | | | | | | |           = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 158.80/25.18  | | | | | | | | | |             e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 158.80/25.18  | | | | | | | | | |           e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.80/25.18  | | | | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.80/25.18  | | | | | | | | | |             e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.80/25.18  | | | | | | | | | |           $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 &
% 158.80/25.18  | | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2)
% 158.80/25.18  | | | | | | | | | |           = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.80/25.18  | | | | | | | | | |           op(e0, e0) = e1 & $i(all_57_14))
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | BETA: splitting (82) gives:
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | Case 1:
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | |   (83)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.80/25.18  | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 158.80/25.18  | | | | | | | | | | |             e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.80/25.18  | | | | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.80/25.18  | | | | | | | | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 158.80/25.18  | | | | | | | | | | |             e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.80/25.18  | | | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.80/25.18  | | | | | | | | | | |           $i(all_57_14))
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | | REF_CLOSE: (7), (30), (65), (66), (83) are inconsistent by
% 158.80/25.18  | | | | | | | | | | |            sub-proof #285.
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | Case 2:
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | |   (84)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 158.80/25.18  | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.80/25.18  | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.80/25.18  | | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 158.80/25.18  | | | | | | | | | | |           = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 158.80/25.18  | | | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.80/25.18  | | | | | | | | | | |           op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.80/25.18  | | | | | | | | | | |           $i(all_57_14))
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | | REF_CLOSE: (3), (7), (17), (21), (25), (35), (84) are
% 158.80/25.18  | | | | | | | | | | |            inconsistent by sub-proof #491.
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | End of split
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | Case 2:
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | |   (85)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 158.80/25.18  | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.80/25.18  | | | | | | | | | |           op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.80/25.18  | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 =
% 158.80/25.18  | | | | | | | | | |           e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 158.80/25.18  | | | | | | | | | |           e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15 =
% 158.80/25.18  | | | | | | | | | |           e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 158.80/25.18  | | | | | | | | | |           & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.80/25.18  | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 =
% 158.80/25.18  | | | | | | | | | |           e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) =
% 158.80/25.18  | | | | | | | | | |           e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13
% 158.80/25.18  | | | | | | | | | |           = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 &
% 158.80/25.18  | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 158.80/25.18  | | | | | | | | | |             e0) = e1 & $i(all_57_14))
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | BETA: splitting (85) gives:
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | Case 1:
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | |   (86)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 158.80/25.18  | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.80/25.18  | | | | | | | | | | |           op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.80/25.18  | | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 158.80/25.18  | | | | | | | | | | |           = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 158.80/25.18  | | | | | | | | | | |             e1) = e1)
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | | REF_CLOSE: (3), (7), (25), (35), (86) are inconsistent by
% 158.80/25.18  | | | | | | | | | | |            sub-proof #701.
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | Case 2:
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | |   (87)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 158.80/25.18  | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 158.80/25.18  | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.80/25.18  | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 158.80/25.18  | | | | | | | | | | |           = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 158.80/25.18  | | | | | | | | | | |             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 158.80/25.18  | | | | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 158.80/25.18  | | | | | | | | | | |             e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.80/25.18  | | | | | | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | | REF_CLOSE: (7), (17), (30), (36), (64), (65), (87) are
% 158.80/25.18  | | | | | | | | | | |            inconsistent by sub-proof #283.
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | End of split
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | End of split
% 158.80/25.18  | | | | | | | | | 
% 158.80/25.18  | | | | | | | | Case 2:
% 158.80/25.18  | | | | | | | | | 
% 158.80/25.18  | | | | | | | | |   (88)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.80/25.18  | | | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.80/25.18  | | | | | | | | |             e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.80/25.18  | | | | | | | | |           $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 & 
% 158.80/25.18  | | | | | | | | |           ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.80/25.18  | | | | | | | | |         (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 158.80/25.18  | | | | | | | | |           (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2
% 158.80/25.18  | | | | | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.80/25.18  | | | | | | | | |           $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.80/25.18  | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.80/25.18  | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 158.80/25.18  | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 &
% 158.80/25.18  | | | | | | | | |           all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 158.80/25.18  | | | | | | | | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.80/25.18  | | | | | | | | |           op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.80/25.18  | | | | | | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 158.80/25.18  | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2
% 158.80/25.18  | | | | | | | | |           & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 &
% 158.80/25.18  | | | | | | | | |           op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1
% 158.80/25.18  | | | | | | | | |           &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0) = e1)
% 158.80/25.18  | | | | | | | | |         | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6
% 158.80/25.18  | | | | | | | | |               = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.80/25.18  | | | | | | | | |               (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 158.80/25.18  | | | | | | | | |               = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.80/25.18  | | | | | | | | |               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.80/25.18  | | | | | | | | |                 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.80/25.18  | | | | | | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.80/25.18  | | | | | | | | |               e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.80/25.18  | | | | | | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.80/25.18  | | | | | | | | |               e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.80/25.18  | | | | | | | | |                 e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.80/25.18  | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.80/25.18  | | | | | | | | |                 e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.18  | | | | | | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.80/25.18  | | | | | | | | |               e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.18  | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.80/25.18  | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.80/25.18  | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.80/25.18  | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 158.80/25.18  | | | | | | | | |             | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.80/25.18  | | | | | | | | |               op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.80/25.18  | | | | | | | | |               e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.80/25.18  | | | | | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.80/25.18  | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.80/25.18  | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 158.80/25.18  | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 158.80/25.18  | | | | | | | | |             | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 158.80/25.18  | | | | | | | | |               &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.80/25.18  | | | | | | | | |                 e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.80/25.18  | | | | | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.80/25.18  | | | | | | | | |                 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.80/25.18  | | | | | | | | |               e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.80/25.18  | | | | | | | | |             (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.80/25.18  | | | | | | | | |               op(e0, e1) = e0)))
% 158.80/25.18  | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | BETA: splitting (88) gives:
% 158.80/25.18  | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | Case 1:
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | |   (89)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.80/25.18  | | | | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 158.80/25.18  | | | | | | | | | |             e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.80/25.18  | | | | | | | | | |           $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &
% 158.80/25.18  | | | | | | | | | |            ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 158.80/25.18  | | | | | | | | | |         | (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 158.80/25.18  | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 158.80/25.18  | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.80/25.18  | | | | | | | | | |           $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.80/25.18  | | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 158.80/25.18  | | | | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 158.80/25.18  | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_10))
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | BETA: splitting (89) gives:
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | Case 1:
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | |   (90)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 158.80/25.18  | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 158.80/25.18  | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.80/25.18  | | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 158.80/25.18  | | | | | | | | | | |           = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 158.80/25.18  | | | | | | | | | | |             e1) = e2)
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | | REF_CLOSE: (7), (17), (26), (35), (61), (90) are inconsistent
% 158.80/25.18  | | | | | | | | | | |            by sub-proof #978.
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | Case 2:
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | |   (91)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 158.80/25.18  | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 158.80/25.18  | | | | | | | | | | |             e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 158.80/25.18  | | | | | | | | | | |           = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 158.80/25.18  | | | | | | | | | | |           all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 158.80/25.18  | | | | | | | | | | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.80/25.18  | | | | | | | | | | |           & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.80/25.18  | | | | | | | | | | |           $i(all_57_10))
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | | REF_CLOSE: (7), (17), (36), (65), (66), (91) are inconsistent
% 158.80/25.18  | | | | | | | | | | |            by sub-proof #977.
% 158.80/25.18  | | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | | End of split
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.18  | | | | | | | | | Case 2:
% 158.80/25.18  | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | |   (92)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 158.80/25.19  | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.80/25.19  | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.80/25.19  | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 =
% 158.80/25.19  | | | | | | | | | |           e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 158.80/25.19  | | | | | | | | | |           e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 =
% 158.80/25.19  | | | | | | | | | |             e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.80/25.19  | | | | | | | | | |         (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.80/25.19  | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.80/25.19  | | | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.80/25.19  | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.80/25.19  | | | | | | | | | |                 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.19  | | | | | | | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 158.80/25.19  | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.80/25.19  | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3)
% 158.80/25.19  | | | | | | | | | |               = e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 158.80/25.19  | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 158.80/25.19  | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.80/25.19  | | | | | | | | | |               e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3
% 158.80/25.19  | | | | | | | | | |                 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.80/25.19  | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.80/25.19  | | | | | | | | | |                 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.19  | | | | | | | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11
% 158.80/25.19  | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.19  | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2)
% 158.80/25.19  | | | | | | | | | |               = e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.80/25.19  | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.80/25.19  | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.80/25.19  | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 158.80/25.19  | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.80/25.19  | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.80/25.19  | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.19  | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.80/25.19  | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.80/25.19  | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 158.80/25.19  | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.80/25.19  | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 158.80/25.19  | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.80/25.19  | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.80/25.19  | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.80/25.19  | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.80/25.19  | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.80/25.19  | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.80/25.19  | | | | | | | | | |               e0)))
% 158.80/25.19  | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | BETA: splitting (92) gives:
% 158.80/25.19  | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | Case 1:
% 158.80/25.19  | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | |   (93)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 158.80/25.19  | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 158.80/25.19  | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 158.80/25.19  | | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 158.80/25.19  | | | | | | | | | | |           = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 158.80/25.19  | | | | | | | | | | |             e0) = e3)
% 158.80/25.19  | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | REF_CLOSE: (7), (17), (30), (35), (64), (93) are inconsistent
% 158.80/25.19  | | | | | | | | | | |            by sub-proof #282.
% 158.80/25.19  | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | Case 2:
% 158.80/25.19  | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | |   (94)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.80/25.19  | | | | | | | | | | |           op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 158.80/25.19  | | | | | | | | | | |           = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 158.80/25.19  | | | | | | | | | | |             e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.80/25.19  | | | | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.80/25.19  | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.80/25.19  | | | | | | | | | | |               (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.80/25.19  | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.80/25.19  | | | | | | | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.80/25.19  | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.80/25.19  | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.80/25.19  | | | | | | | | | | |               e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.80/25.19  | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.80/25.19  | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.80/25.19  | | | | | | | | | | |               e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.80/25.19  | | | | | | | | | | |                 e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.80/25.19  | | | | | | | | | | |               & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.19  | | | | | | | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.80/25.19  | | | | | | | | | | |                 e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.80/25.19  | | | | | | | | | | |               e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.19  | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.80/25.19  | | | | | | | | | | |                 e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.80/25.19  | | | | | | | | | | |               e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.19  | | | | | | | | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.80/25.19  | | | | | | | | | | |                 e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.80/25.19  | | | | | | | | | | |               e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.80/25.19  | | | | | | | | | | |             (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.80/25.19  | | | | | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.80/25.19  | | | | | | | | | | |               op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.80/25.19  | | | | | | | | | | |             (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.80/25.19  | | | | | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.80/25.19  | | | | | | | | | | |               op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.80/25.19  | | | | | | | | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.80/25.19  | | | | | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.80/25.19  | | | | | | | | | | |               op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.80/25.19  | | | | | | | | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.80/25.19  | | | | | | | | | | |               e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.80/25.19  | | | | | | | | | | |               all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.80/25.19  | | | | | | | | | | |               e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.80/25.19  | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.80/25.19  | | | | | | | | | | |               e0)))
% 158.80/25.19  | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | BETA: splitting (94) gives:
% 158.80/25.19  | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | Case 1:
% 158.80/25.19  | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | |   (95)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 158.80/25.19  | | | | | | | | | | | |         op(e2, e2) = e2 & op(e2, e0) = e2
% 158.80/25.19  | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | ALPHA: (95) implies:
% 158.80/25.19  | | | | | | | | | | | |   (96)  op(e2, e0) = e2
% 158.80/25.19  | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | REF_CLOSE: (7), (29), (62), (96) are inconsistent by
% 158.80/25.19  | | | | | | | | | | | |            sub-proof #996.
% 158.80/25.19  | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | Case 2:
% 158.80/25.19  | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | |   (97)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.80/25.19  | | | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 158.80/25.19  | | | | | | | | | | | |           = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 158.80/25.19  | | | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.80/25.19  | | | | | | | | | | | |               (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.80/25.19  | | | | | | | | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 158.80/25.19  | | | | | | | | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.80/25.19  | | | | | | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.80/25.19  | | | | | | | | | | | |                 e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.80/25.19  | | | | | | | | | | | |               e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.80/25.19  | | | | | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.80/25.19  | | | | | | | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.80/25.19  | | | | | | | | | | | |               e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 158.80/25.19  | | | | | | | | | | | |                 e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 158.80/25.19  | | | | | | | | | | | |               & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.19  | | | | | | | | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.80/25.19  | | | | | | | | | | | |                 e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.80/25.19  | | | | | | | | | | | |               e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.19  | | | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.80/25.19  | | | | | | | | | | | |                 e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 158.80/25.19  | | | | | | | | | | | |               e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.19  | | | | | | | | | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.80/25.19  | | | | | | | | | | | |                 e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 158.80/25.19  | | | | | | | | | | | |               e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.80/25.19  | | | | | | | | | | | |             (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.80/25.19  | | | | | | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.80/25.19  | | | | | | | | | | | |               op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.80/25.19  | | | | | | | | | | | |             (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.80/25.19  | | | | | | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.80/25.19  | | | | | | | | | | | |               op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.80/25.19  | | | | | | | | | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.80/25.19  | | | | | | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.80/25.19  | | | | | | | | | | | |               op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.80/25.19  | | | | | | | | | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 158.80/25.19  | | | | | | | | | | | |               e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.80/25.19  | | | | | | | | | | | |               all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.80/25.19  | | | | | | | | | | | |               e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.80/25.19  | | | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.80/25.19  | | | | | | | | | | | |               e0)))
% 158.80/25.19  | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | BETA: splitting (97) gives:
% 158.80/25.19  | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | Case 1:
% 158.80/25.19  | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | |   (98)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.80/25.19  | | | | | | | | | | | | |         op(e1, e1) = e1 & op(e1, e0) = e1
% 158.80/25.19  | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | ALPHA: (98) implies:
% 158.80/25.19  | | | | | | | | | | | | |   (99)  op(e1, e1) = e1
% 158.80/25.19  | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | REF_CLOSE: (3), (7), (25), (99) are inconsistent by sub-proof
% 158.80/25.19  | | | | | | | | | | | | |            #903.
% 158.80/25.19  | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | Case 2:
% 158.80/25.19  | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | |   (100)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.80/25.19  | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.80/25.19  | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.80/25.19  | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.80/25.19  | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.80/25.19  | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 158.80/25.19  | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.80/25.19  | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.80/25.19  | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.80/25.19  | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.80/25.19  | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.80/25.19  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.80/25.19  | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 158.80/25.19  | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.80/25.19  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.80/25.19  | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.80/25.19  | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.80/25.19  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.80/25.19  | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.80/25.19  | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.80/25.19  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 158.80/25.19  | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.80/25.19  | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.80/25.19  | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.19  | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.80/25.19  | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.80/25.19  | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 158.80/25.19  | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.80/25.19  | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 158.80/25.19  | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.80/25.19  | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.80/25.19  | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.80/25.19  | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.80/25.19  | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.80/25.19  | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.80/25.19  | | | | | | | | | | | | |              e0))
% 158.80/25.19  | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | ALPHA: (100) implies:
% 158.80/25.19  | | | | | | | | | | | | |   (101)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.80/25.19  | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.80/25.19  | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.80/25.19  | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.80/25.19  | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.80/25.19  | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.80/25.19  | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.80/25.19  | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.80/25.19  | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.80/25.19  | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.80/25.19  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.80/25.19  | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.19  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.80/25.19  | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.19  | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.80/25.19  | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 158.80/25.19  | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.80/25.19  | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 158.80/25.19  | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.80/25.19  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.80/25.19  | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.80/25.19  | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.80/25.19  | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.80/25.19  | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 158.80/25.19  | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 158.80/25.19  | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 158.80/25.19  | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.80/25.19  | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.80/25.19  | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 158.80/25.19  | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.80/25.19  | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.80/25.19  | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.80/25.19  | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.80/25.19  | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | BETA: splitting (101) gives:
% 158.80/25.19  | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | Case 1:
% 158.80/25.19  | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | |   (102)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.80/25.19  | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.80/25.19  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.80/25.19  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.80/25.19  | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.80/25.19  | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.80/25.19  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.80/25.19  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.80/25.19  | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.80/25.19  | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.80/25.19  | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.80/25.19  | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.19  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.80/25.19  | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.19  | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.80/25.19  | | | | | | | | | | | | | |            e0)
% 158.80/25.19  | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 158.80/25.19  | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | Case 1:
% 158.80/25.19  | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | |   (103)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.80/25.19  | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.80/25.19  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.80/25.19  | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.80/25.19  | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.80/25.19  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.80/25.19  | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.80/25.19  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.80/25.19  | | | | | | | | | | | | | | |            e0)
% 158.80/25.19  | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (12), (29), (62), (103) are inconsistent
% 158.80/25.19  | | | | | | | | | | | | | | |            by sub-proof #239.
% 158.80/25.19  | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | Case 2:
% 158.80/25.19  | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | |   (104)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.80/25.19  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 158.80/25.19  | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.80/25.19  | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.80/25.19  | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.80/25.19  | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.80/25.19  | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.80/25.19  | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 158.80/25.19  | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | Case 1:
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | |   (105)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.80/25.19  | | | | | | | | | | | | | | | |          op(e0, e3) = e0
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 158.80/25.19  | | | | | | | | | | | | | | | |   (106)  op(e0, e3) = e0
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (12), (106) are inconsistent by
% 158.80/25.19  | | | | | | | | | | | | | | | |            sub-proof #973.
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | Case 2:
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | |   (107)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.80/25.19  | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.80/25.19  | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.80/25.19  | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.80/25.19  | | | | | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.80/25.19  | | | | | | | | | | | | | | | |            op(e0, e2) = e0)
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (29), (30), (35), (62), (107) are
% 158.80/25.19  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #264.
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | End of split
% 158.80/25.19  | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | End of split
% 158.80/25.19  | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | Case 2:
% 158.80/25.19  | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | |   (108)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.80/25.19  | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.80/25.19  | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.80/25.19  | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.80/25.19  | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.80/25.19  | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.80/25.19  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.80/25.19  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.80/25.19  | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.80/25.19  | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.80/25.19  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.80/25.19  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.80/25.19  | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.80/25.19  | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 158.80/25.19  | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 158.80/25.19  | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.80/25.19  | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.80/25.19  | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 158.80/25.19  | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | Case 1:
% 158.80/25.19  | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | |   (109)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.80/25.19  | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.80/25.19  | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.80/25.19  | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.80/25.19  | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.80/25.19  | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.80/25.19  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 158.80/25.19  | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 158.80/25.19  | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | Case 1:
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | |   (110)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 158.80/25.19  | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 158.80/25.19  | | | | | | | | | | | | | | | |          = e1 & op(e0, e2) = e0
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 158.80/25.19  | | | | | | | | | | | | | | | |   (111)  op(e0, e2) = e0
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14), (51), (111) are inconsistent by
% 158.80/25.19  | | | | | | | | | | | | | | | |            sub-proof #969.
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.19  | | | | | | | | | | | | | | | Case 2:
% 158.80/25.19  | | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | |   (112)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.80/25.20  | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.80/25.20  | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.80/25.20  | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.80/25.20  | | | | | | | | | | | | | | | |            e0)
% 158.80/25.20  | | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14), (30), (35), (51), (112) are
% 158.80/25.20  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #279.
% 158.80/25.20  | | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | End of split
% 158.80/25.20  | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | Case 2:
% 158.80/25.20  | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | |   (113)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.80/25.20  | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.80/25.20  | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.80/25.20  | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.80/25.20  | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.80/25.20  | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.80/25.20  | | | | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.80/25.20  | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.80/25.20  | | | | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 158.80/25.20  | | | | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 158.80/25.20  | | | | | | | | | | | | | | |            = e0)
% 158.80/25.20  | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 158.80/25.20  | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | Case 1:
% 158.80/25.20  | | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | |   (114)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.80/25.20  | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.80/25.20  | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.80/25.20  | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.80/25.20  | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.80/25.20  | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 158.80/25.20  | | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (29), (31), (62), (114) are inconsistent
% 158.80/25.20  | | | | | | | | | | | | | | | |            by sub-proof #682.
% 158.80/25.20  | | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | Case 2:
% 158.80/25.20  | | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | |   (115)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 158.80/25.20  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.80/25.20  | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.80/25.20  | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 158.80/25.20  | | | | | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.80/25.20  | | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (31), (115) are inconsistent by
% 158.80/25.20  | | | | | | | | | | | | | | | |            sub-proof #965.
% 158.80/25.20  | | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | | End of split
% 158.80/25.20  | | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | | End of split
% 158.80/25.20  | | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | | End of split
% 158.80/25.20  | | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | | End of split
% 158.80/25.20  | | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | | End of split
% 158.80/25.20  | | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | | End of split
% 158.80/25.20  | | | | | | | | | | 
% 158.80/25.20  | | | | | | | | | End of split
% 158.80/25.20  | | | | | | | | | 
% 158.80/25.20  | | | | | | | | End of split
% 158.80/25.20  | | | | | | | | 
% 158.80/25.20  | | | | | | | End of split
% 158.80/25.20  | | | | | | | 
% 158.80/25.20  | | | | | | Case 2:
% 158.80/25.20  | | | | | | | 
% 158.80/25.20  | | | | | | |   (116)  all_54_5 = e1 | all_54_5 = e0
% 158.80/25.20  | | | | | | | 
% 158.80/25.20  | | | | | | | REF_CLOSE: (2), (23), (53), (116) are inconsistent by sub-proof
% 158.80/25.20  | | | | | | |            #962.
% 158.80/25.20  | | | | | | | 
% 158.80/25.20  | | | | | | End of split
% 158.80/25.20  | | | | | | 
% 158.80/25.20  | | | | | End of split
% 158.80/25.20  | | | | | 
% 158.80/25.20  | | | | End of split
% 158.80/25.20  | | | | 
% 158.80/25.20  | | | Case 2:
% 158.80/25.20  | | | | 
% 158.80/25.20  | | | |   (117)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0,
% 158.80/25.20  | | | |              e3) = e0)
% 158.80/25.20  | | | | 
% 158.80/25.20  | | | | REF_CLOSE: (7), (8), (12), (13), (34), (117) are inconsistent by
% 158.80/25.20  | | | |            sub-proof #698.
% 158.80/25.20  | | | | 
% 158.80/25.20  | | | End of split
% 158.80/25.20  | | | 
% 158.80/25.20  | | End of split
% 158.80/25.20  | | 
% 158.80/25.20  | Case 2:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (118)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 158.80/25.20  | |            e0)
% 158.80/25.20  | | 
% 158.80/25.20  | | BETA: splitting (118) gives:
% 158.80/25.20  | | 
% 158.80/25.20  | | Case 1:
% 158.80/25.20  | | | 
% 158.80/25.20  | | |   (119)  all_56_4 = e0 & op(e3, e1) = e0
% 158.80/25.20  | | | 
% 158.80/25.20  | | | REF_CLOSE: (7), (9), (15), (119) are inconsistent by sub-proof #700.
% 158.80/25.20  | | | 
% 158.80/25.20  | | Case 2:
% 158.80/25.20  | | | 
% 158.80/25.20  | | |   (120)  all_56_9 = e0 & op(e3, e0) = e0
% 158.80/25.20  | | | 
% 158.80/25.20  | | | REF_CLOSE: (7), (27), (32), (120) are inconsistent by sub-proof #620.
% 158.80/25.20  | | | 
% 158.80/25.20  | | End of split
% 158.80/25.20  | | 
% 158.80/25.20  | End of split
% 158.80/25.20  | 
% 158.80/25.20  End of proof
% 158.80/25.20  
% 158.80/25.20  Sub-proof #239 shows that the following formulas are inconsistent:
% 158.80/25.20  ----------------------------------------------------------------
% 158.80/25.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.20    (2)  op(e0, e3) = all_52_3
% 158.80/25.20    (3)   ~ (all_52_3 = e0)
% 158.80/25.20    (4)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.80/25.20           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.80/25.20           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 158.80/25.20           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 158.80/25.20           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 158.80/25.20           e1 & op(e0, e3) = e0)
% 158.80/25.20    (5)  op(e2, e0) = all_52_13
% 158.80/25.20    (6)   ~ (all_52_13 = e2)
% 158.80/25.20  
% 158.80/25.20  Begin of proof
% 158.80/25.20  | 
% 158.80/25.20  | BETA: splitting (4) gives:
% 158.80/25.20  | 
% 158.80/25.20  | Case 1:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (7)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.80/25.20  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 158.80/25.20  | | 
% 158.80/25.20  | | ALPHA: (7) implies:
% 158.80/25.20  | |   (8)  op(e0, e3) = e0
% 158.80/25.20  | | 
% 158.80/25.20  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #973.
% 158.80/25.20  | | 
% 158.80/25.20  | Case 2:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (9)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.80/25.20  | |            e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.80/25.20  | |        (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.80/25.20  | |            e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.80/25.20  | | 
% 158.80/25.20  | | BETA: splitting (9) gives:
% 158.80/25.20  | | 
% 158.80/25.20  | | Case 1:
% 158.80/25.20  | | | 
% 158.80/25.20  | | |   (10)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.80/25.20  | | |           e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 158.80/25.20  | | | 
% 158.80/25.20  | | | ALPHA: (10) implies:
% 158.80/25.20  | | |   (11)  op(e2, e0) = e2
% 158.80/25.20  | | | 
% 158.80/25.20  | | | REF_CLOSE: (1), (5), (6), (11) are inconsistent by sub-proof #996.
% 158.80/25.20  | | | 
% 158.80/25.20  | | Case 2:
% 158.80/25.20  | | | 
% 158.80/25.20  | | |   (12)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.80/25.20  | | |           e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 158.80/25.20  | | | 
% 158.80/25.20  | | | ALPHA: (12) implies:
% 158.80/25.20  | | |   (13)  op(e0, e3) = e0
% 158.80/25.20  | | | 
% 158.80/25.20  | | | REF_CLOSE: (1), (2), (3), (13) are inconsistent by sub-proof #973.
% 158.80/25.20  | | | 
% 158.80/25.20  | | End of split
% 158.80/25.20  | | 
% 158.80/25.20  | End of split
% 158.80/25.20  | 
% 158.80/25.20  End of proof
% 158.80/25.20  
% 158.80/25.20  Sub-proof #240 shows that the following formulas are inconsistent:
% 158.80/25.20  ----------------------------------------------------------------
% 158.80/25.20    (1)  op(e1, e1) = e0
% 158.80/25.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.20    (3)  op(e0, e0) = e0
% 158.80/25.20    (4)  op(e0, e0) = all_14_2
% 158.80/25.20    (5)   ~ (e1 = e0)
% 158.80/25.20    (6)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.80/25.20           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.80/25.20           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 158.80/25.20           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.80/25.20           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 158.80/25.20           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.80/25.20    (7)   ~ (e3 = e0)
% 158.80/25.20  
% 158.80/25.20  Begin of proof
% 158.80/25.20  | 
% 158.80/25.20  | BETA: splitting (6) gives:
% 158.80/25.20  | 
% 158.80/25.20  | Case 1:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (8)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 158.80/25.20  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.80/25.20  | |          e0) = e1 & $i(all_57_14)
% 158.80/25.20  | | 
% 158.80/25.20  | | ALPHA: (8) implies:
% 158.80/25.20  | |   (9)  op(e0, e0) = e1
% 158.80/25.20  | | 
% 158.80/25.20  | | REF_CLOSE: (2), (3), (4), (5), (9) are inconsistent by sub-proof #991.
% 158.80/25.20  | | 
% 158.80/25.20  | Case 2:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (10)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.80/25.20  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 158.80/25.20  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 158.80/25.20  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.80/25.20  | | 
% 158.80/25.20  | | REF_CLOSE: (1), (2), (5), (7), (10) are inconsistent by sub-proof #704.
% 158.80/25.20  | | 
% 158.80/25.20  | End of split
% 158.80/25.20  | 
% 158.80/25.20  End of proof
% 158.80/25.20  
% 158.80/25.20  Sub-proof #241 shows that the following formulas are inconsistent:
% 158.80/25.20  ----------------------------------------------------------------
% 158.80/25.20    (1)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.80/25.20           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 158.80/25.20           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 158.80/25.20           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.80/25.20           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 158.80/25.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.20    (3)  op(e2, e3) = e0
% 158.80/25.20    (4)   ~ (e2 = e0)
% 158.80/25.20  
% 158.80/25.20  Begin of proof
% 158.80/25.20  | 
% 158.80/25.20  | BETA: splitting (1) gives:
% 158.80/25.20  | 
% 158.80/25.20  | Case 1:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (5)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 158.80/25.20  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.80/25.20  | |          e0) = e2 & $i(all_57_12)
% 158.80/25.20  | | 
% 158.80/25.20  | | ALPHA: (5) implies:
% 158.80/25.20  | |   (6)  op(e2, e3) = e2
% 158.80/25.20  | | 
% 158.80/25.20  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #709.
% 158.80/25.20  | | 
% 158.80/25.20  | Case 2:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (7)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 158.80/25.20  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.80/25.20  | |          e2) = e3 & $i(all_57_10)
% 158.80/25.20  | | 
% 158.80/25.20  | | ALPHA: (7) implies:
% 158.80/25.20  | |   (8)  op(e2, e3) = e2
% 158.80/25.20  | | 
% 158.80/25.20  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #709.
% 158.80/25.20  | | 
% 158.80/25.20  | End of split
% 158.80/25.20  | 
% 158.80/25.20  End of proof
% 158.80/25.20  
% 158.80/25.20  Sub-proof #242 shows that the following formulas are inconsistent:
% 158.80/25.20  ----------------------------------------------------------------
% 158.80/25.20    (1)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.80/25.20           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.80/25.20           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 158.80/25.20           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 158.80/25.20           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.80/25.20           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 158.80/25.20           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.80/25.20           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.80/25.20           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 158.80/25.20             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 158.80/25.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.20    (3)  op(e2, e3) = e0
% 158.80/25.20    (4)   ~ (e2 = e0)
% 158.80/25.20  
% 158.80/25.20  Begin of proof
% 158.80/25.20  | 
% 158.80/25.20  | BETA: splitting (1) gives:
% 158.80/25.20  | 
% 158.80/25.20  | Case 1:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (5)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 158.80/25.20  | |          & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 158.80/25.20  | |          = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.80/25.20  | |          all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.80/25.20  | |          op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.80/25.20  | |          $i(all_57_10))
% 158.80/25.20  | | 
% 158.80/25.20  | | BETA: splitting (5) gives:
% 158.80/25.20  | | 
% 158.80/25.20  | | Case 1:
% 158.80/25.20  | | | 
% 158.80/25.20  | | |   (6)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 =
% 158.80/25.20  | | |          e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 158.80/25.20  | | |        op(e2, e2) = all_57_12 & $i(all_57_12)
% 158.80/25.20  | | | 
% 158.80/25.20  | | | ALPHA: (6) implies:
% 158.80/25.20  | | |   (7)  op(e2, e3) = e2
% 158.80/25.20  | | | 
% 158.80/25.20  | | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #709.
% 158.80/25.20  | | | 
% 158.80/25.20  | | Case 2:
% 158.80/25.20  | | | 
% 158.80/25.20  | | |   (8)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.80/25.20  | | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2
% 158.80/25.20  | | |        & op(e2, e2) = e3 & $i(all_57_10)
% 158.80/25.20  | | | 
% 158.80/25.20  | | | ALPHA: (8) implies:
% 158.80/25.20  | | |   (9)  op(e2, e3) = e2
% 158.80/25.20  | | | 
% 158.80/25.20  | | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #709.
% 158.80/25.20  | | | 
% 158.80/25.20  | | End of split
% 158.80/25.20  | | 
% 158.80/25.20  | Case 2:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (10)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 158.80/25.20  | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 158.80/25.20  | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 =
% 158.80/25.20  | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 158.80/25.20  | |           & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.80/25.20  | |           $i(all_57_10))
% 158.80/25.20  | | 
% 158.80/25.20  | | BETA: splitting (10) gives:
% 158.80/25.20  | | 
% 158.80/25.20  | | Case 1:
% 158.80/25.20  | | | 
% 158.80/25.20  | | |   (11)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 158.80/25.20  | | |           e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 158.80/25.20  | | |         & op(e1, e1) = e2 & $i(all_57_12)
% 158.80/25.20  | | | 
% 158.80/25.20  | | | ALPHA: (11) implies:
% 158.80/25.20  | | |   (12)  op(e2, e3) = e2
% 158.80/25.20  | | | 
% 158.80/25.20  | | | REF_CLOSE: (2), (3), (4), (12) are inconsistent by sub-proof #709.
% 158.80/25.20  | | | 
% 158.80/25.20  | | Case 2:
% 158.80/25.20  | | | 
% 158.80/25.20  | | |   (13)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 158.80/25.20  | | |           e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2
% 158.80/25.20  | | |         & op(e2, e2) = e3 & $i(all_57_10)
% 158.80/25.20  | | | 
% 158.80/25.20  | | | ALPHA: (13) implies:
% 158.80/25.20  | | |   (14)  op(e2, e3) = e2
% 158.80/25.20  | | | 
% 158.80/25.20  | | | REF_CLOSE: (2), (3), (4), (14) are inconsistent by sub-proof #709.
% 158.80/25.20  | | | 
% 158.80/25.20  | | End of split
% 158.80/25.20  | | 
% 158.80/25.20  | End of split
% 158.80/25.20  | 
% 158.80/25.20  End of proof
% 158.80/25.20  
% 158.80/25.20  Sub-proof #243 shows that the following formulas are inconsistent:
% 158.80/25.20  ----------------------------------------------------------------
% 158.80/25.20    (1)   ~ (all_12_1 = e1) & op(e2, e2) = all_12_1 & $i(all_12_1)
% 158.80/25.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.20    (3)  op(e2, e2) = e1
% 158.80/25.20  
% 158.80/25.20  Begin of proof
% 158.80/25.20  | 
% 158.80/25.20  | ALPHA: (1) implies:
% 158.80/25.20  |   (4)   ~ (all_12_1 = e1)
% 158.80/25.20  |   (5)  op(e2, e2) = all_12_1
% 158.80/25.20  | 
% 158.80/25.20  | GROUND_INST: instantiating (2) with e1, all_12_1, e2, e2, simplifying with
% 158.80/25.20  |              (3), (5) gives:
% 158.80/25.20  |   (6)  all_12_1 = e1
% 158.80/25.20  | 
% 158.80/25.20  | REDUCE: (4), (6) imply:
% 158.80/25.20  |   (7)  $false
% 158.80/25.20  | 
% 158.80/25.20  | CLOSE: (7) is inconsistent.
% 158.80/25.20  | 
% 158.80/25.20  End of proof
% 158.80/25.20  
% 158.80/25.20  Sub-proof #244 shows that the following formulas are inconsistent:
% 158.80/25.20  ----------------------------------------------------------------
% 158.80/25.20    (1)   ~ (all_12_0 = e1)
% 158.80/25.20    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 158.80/25.20    (3)  all_54_4 = all_12_0
% 158.80/25.20    (4)   ~ (all_12_0 = e0)
% 158.80/25.20    (5)   ~ (all_12_0 = e2)
% 158.80/25.20  
% 158.80/25.20  Begin of proof
% 158.80/25.20  | 
% 158.80/25.20  | BETA: splitting (2) gives:
% 158.80/25.20  | 
% 158.80/25.20  | Case 1:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (6)  all_54_4 = e2
% 158.80/25.20  | | 
% 158.80/25.20  | | COMBINE_EQS: (3), (6) imply:
% 158.80/25.20  | |   (7)  all_12_0 = e2
% 158.80/25.20  | | 
% 158.80/25.20  | | SIMP: (7) implies:
% 158.80/25.20  | |   (8)  all_12_0 = e2
% 158.80/25.20  | | 
% 158.80/25.20  | | REDUCE: (5), (8) imply:
% 158.80/25.20  | |   (9)  $false
% 158.80/25.20  | | 
% 158.80/25.20  | | CLOSE: (9) is inconsistent.
% 158.80/25.20  | | 
% 158.80/25.20  | Case 2:
% 158.80/25.20  | | 
% 158.80/25.20  | |   (10)  all_54_4 = e1 | all_54_4 = e0
% 158.80/25.20  | | 
% 158.80/25.20  | | BETA: splitting (10) gives:
% 158.80/25.20  | | 
% 158.80/25.20  | | Case 1:
% 158.80/25.20  | | | 
% 158.80/25.20  | | |   (11)  all_54_4 = e1
% 158.80/25.20  | | | 
% 158.80/25.20  | | | COMBINE_EQS: (3), (11) imply:
% 158.80/25.20  | | |   (12)  all_12_0 = e1
% 158.80/25.20  | | | 
% 158.80/25.20  | | | SIMP: (12) implies:
% 158.80/25.20  | | |   (13)  all_12_0 = e1
% 158.80/25.20  | | | 
% 158.80/25.20  | | | REDUCE: (1), (13) imply:
% 158.80/25.20  | | |   (14)  $false
% 158.80/25.20  | | | 
% 158.80/25.20  | | | CLOSE: (14) is inconsistent.
% 158.80/25.20  | | | 
% 158.80/25.20  | | Case 2:
% 158.80/25.20  | | | 
% 158.80/25.20  | | |   (15)  all_54_4 = e0
% 158.80/25.20  | | | 
% 158.80/25.20  | | | COMBINE_EQS: (3), (15) imply:
% 158.80/25.20  | | |   (16)  all_12_0 = e0
% 158.80/25.20  | | | 
% 158.80/25.20  | | | SIMP: (16) implies:
% 158.80/25.20  | | |   (17)  all_12_0 = e0
% 158.80/25.20  | | | 
% 158.80/25.20  | | | REDUCE: (4), (17) imply:
% 158.80/25.20  | | |   (18)  $false
% 158.80/25.20  | | | 
% 158.80/25.20  | | | CLOSE: (18) is inconsistent.
% 158.80/25.20  | | | 
% 158.80/25.20  | | End of split
% 158.80/25.20  | | 
% 158.80/25.20  | End of split
% 158.80/25.20  | 
% 158.80/25.20  End of proof
% 158.80/25.20  
% 158.80/25.20  Sub-proof #245 shows that the following formulas are inconsistent:
% 158.80/25.20  ----------------------------------------------------------------
% 158.80/25.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.20    (2)  op(e0, e0) = all_14_2
% 158.80/25.20    (3)  op(e0, e0) = e3
% 158.80/25.20    (4)   ~ (all_14_2 = e3)
% 158.80/25.20  
% 158.80/25.20  Begin of proof
% 158.80/25.20  | 
% 158.80/25.21  | GROUND_INST: instantiating (1) with all_14_2, e3, e0, e0, simplifying with
% 158.80/25.21  |              (2), (3) gives:
% 158.80/25.21  |   (5)  all_14_2 = e3
% 158.80/25.21  | 
% 158.80/25.21  | REDUCE: (4), (5) imply:
% 158.80/25.21  |   (6)  $false
% 158.80/25.21  | 
% 158.80/25.21  | CLOSE: (6) is inconsistent.
% 158.80/25.21  | 
% 158.80/25.21  End of proof
% 158.80/25.21  
% 158.80/25.21  Sub-proof #246 shows that the following formulas are inconsistent:
% 158.80/25.21  ----------------------------------------------------------------
% 158.80/25.21    (1)  op(e0, e0) = e1
% 158.80/25.21    (2)   ~ (all_52_12 = e2)
% 158.80/25.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.21    (4)  op(e1, e1) = e1
% 158.80/25.21    (5)  op(e1, e0) = all_52_14
% 158.80/25.21    (6)  op(e0, e0) = all_57_15
% 158.80/25.21    (7)   ~ (all_52_13 = all_52_14)
% 158.80/25.21    (8)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.80/25.21         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.80/25.21    (9)   ~ (e1 = e0)
% 158.80/25.21    (10)  op(e2, e0) = all_52_13
% 158.80/25.21    (11)  op(e3, e3) = e2
% 158.80/25.21    (12)   ~ (e2 = e1)
% 158.80/25.21    (13)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.80/25.21            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.80/25.21            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 158.80/25.21            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.80/25.21            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.80/25.21              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.80/25.21            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.80/25.21            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 158.80/25.21            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 158.80/25.21            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.80/25.21              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.80/25.21            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.80/25.21            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.80/25.21            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.80/25.21              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.80/25.21          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.80/25.21            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 158.80/25.21            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 158.80/25.21            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.80/25.21            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.80/25.21            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.80/25.21            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.80/25.21    (14)  op(e3, e0) = all_52_12
% 158.80/25.21    (15)   ~ (all_52_14 = e1)
% 158.80/25.21    (16)   ~ (e2 = e0)
% 158.80/25.21    (17)   ~ (all_52_13 = e2)
% 158.80/25.21  
% 158.80/25.21  Begin of proof
% 158.80/25.21  | 
% 158.80/25.21  | BETA: splitting (8) gives:
% 158.80/25.21  | 
% 158.80/25.21  | Case 1:
% 158.80/25.21  | | 
% 158.80/25.21  | |   (18)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 158.80/25.21  | |           e2)
% 158.80/25.21  | | 
% 158.80/25.21  | | REF_CLOSE: (2), (3), (10), (14), (17), (18) are inconsistent by sub-proof
% 158.80/25.21  | |            #384.
% 158.80/25.21  | | 
% 158.80/25.21  | Case 2:
% 158.80/25.21  | | 
% 158.80/25.21  | |   (19)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 158.80/25.21  | |           e2)
% 158.80/25.21  | | 
% 158.80/25.21  | | BETA: splitting (19) gives:
% 158.80/25.21  | | 
% 158.80/25.21  | | Case 1:
% 158.80/25.21  | | | 
% 158.80/25.21  | | |   (20)  all_56_11 = e2 & op(e1, e0) = e2
% 158.80/25.21  | | | 
% 158.80/25.21  | | | ALPHA: (20) implies:
% 158.80/25.21  | | |   (21)  op(e1, e0) = e2
% 158.80/25.21  | | | 
% 158.80/25.21  | | | GROUND_INST: instantiating (3) with e1, all_57_15, e0, e0, simplifying
% 158.80/25.21  | | |              with (1), (6) gives:
% 158.80/25.21  | | |   (22)  all_57_15 = e1
% 158.80/25.21  | | | 
% 158.80/25.21  | | | GROUND_INST: instantiating (3) with all_52_14, e2, e0, e1, simplifying
% 158.80/25.21  | | |              with (5), (21) gives:
% 158.80/25.21  | | |   (23)  all_52_14 = e2
% 158.80/25.21  | | | 
% 158.80/25.21  | | | BETA: splitting (13) gives:
% 158.80/25.21  | | | 
% 158.80/25.21  | | | Case 1:
% 158.80/25.21  | | | | 
% 158.80/25.21  | | | |   (24)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.80/25.21  | | | |             = e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0)
% 158.80/25.21  | | | |         | (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.80/25.21  | | | |           (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.80/25.21  | | | |             e3) = e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0
% 158.80/25.21  | | | |           &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.80/25.21  | | | |           op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.80/25.21  | | | |             e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.80/25.21  | | | |           all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 158.80/25.21  | | | |           op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.80/25.21  | | | |           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.80/25.21  | | | |             e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.80/25.21  | | | | 
% 158.80/25.21  | | | | BETA: splitting (24) gives:
% 158.80/25.21  | | | | 
% 158.80/25.21  | | | | Case 1:
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | |   (25)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.80/25.21  | | | | |           (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.21  | | | | |           op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2 &
% 158.80/25.21  | | | | |           all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 158.80/25.21  | | | | |           op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.80/25.21  | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.80/25.21  | | | | |           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | | REF_CLOSE: (3), (4), (9), (10), (11), (16), (17), (25) are
% 158.80/25.21  | | | | |            inconsistent by sub-proof #265.
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | Case 2:
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | |   (26)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.80/25.21  | | | | |           e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.80/25.21  | | | | |           (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.21  | | | | |           op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.80/25.21  | | | | |           all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 158.80/25.21  | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | | BETA: splitting (26) gives:
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | | Case 1:
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | |   (27)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 158.80/25.21  | | | | | |         e0
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | | REF_CLOSE: (9), (22), (27) are inconsistent by sub-proof #372.
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | Case 2:
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | |   (28)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.80/25.21  | | | | | |           (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.21  | | | | | |           op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.80/25.21  | | | | | |           all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 158.80/25.21  | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | | REF_CLOSE: (3), (10), (11), (16), (17), (28) are inconsistent by
% 158.80/25.21  | | | | | |            sub-proof #264.
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | End of split
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | End of split
% 158.80/25.21  | | | | 
% 158.80/25.21  | | | Case 2:
% 158.80/25.21  | | | | 
% 158.80/25.21  | | | |   (29)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.80/25.21  | | | |             = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 158.80/25.21  | | | |         | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.80/25.21  | | | |           e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.80/25.21  | | | |           (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 158.80/25.21  | | | |             e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0
% 158.80/25.21  | | | |           &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.80/25.21  | | | |           op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14
% 158.80/25.21  | | | |           = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1
% 158.80/25.21  | | | |           & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.80/25.21  | | | |           all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14
% 158.80/25.21  | | | |           & op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 158.80/25.21  | | | |         (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 158.80/25.21  | | | |           e0)
% 158.80/25.21  | | | | 
% 158.80/25.21  | | | | BETA: splitting (29) gives:
% 158.80/25.21  | | | | 
% 158.80/25.21  | | | | Case 1:
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | |   (30)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.80/25.21  | | | | |           (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.80/25.21  | | | | |           op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 158.80/25.21  | | | | |             = e0) & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 158.80/25.21  | | | | |           & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.80/25.21  | | | | |           op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | | BETA: splitting (30) gives:
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | | Case 1:
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | |   (31)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.80/25.21  | | | | | |         (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.80/25.21  | | | | | |         op(e0, e2) = e0
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | | ALPHA: (31) implies:
% 158.80/25.21  | | | | | |   (32)  op(e1, e1) = e0
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | | REF_CLOSE: (3), (4), (9), (32) are inconsistent by sub-proof #903.
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | Case 2:
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | |   (33)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2)
% 158.80/25.21  | | | | | |           = e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.80/25.21  | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.21  | | | | | |           op(e0, e1) = e0)
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | | BETA: splitting (33) gives:
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | | Case 1:
% 158.80/25.21  | | | | | | | 
% 158.80/25.21  | | | | | | |   (34)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2)
% 158.80/25.21  | | | | | | |         = e0
% 158.80/25.21  | | | | | | | 
% 158.80/25.21  | | | | | | | REF_CLOSE: (9), (22), (34) are inconsistent by sub-proof #371.
% 158.80/25.21  | | | | | | | 
% 158.80/25.21  | | | | | | Case 2:
% 158.80/25.21  | | | | | | | 
% 158.80/25.21  | | | | | | |   (35)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.80/25.21  | | | | | | |         (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.80/25.21  | | | | | | |         op(e0, e1) = e0
% 158.80/25.21  | | | | | | | 
% 158.80/25.21  | | | | | | | ALPHA: (35) implies:
% 158.80/25.21  | | | | | | |   (36)  op(e3, e3) = e0
% 158.80/25.21  | | | | | | | 
% 158.80/25.21  | | | | | | | REF_CLOSE: (3), (11), (16), (36) are inconsistent by sub-proof
% 158.80/25.21  | | | | | | |            #281.
% 158.80/25.21  | | | | | | | 
% 158.80/25.21  | | | | | | End of split
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | End of split
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | Case 2:
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | |   (37)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.80/25.21  | | | | |           (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.80/25.21  | | | | |           op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.80/25.21  | | | | |           all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.80/25.21  | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.80/25.21  | | | | |           all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.80/25.21  | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.80/25.21  | | | | |           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 158.80/25.21  | | | | |             e0) & op(e0, e1) = e0)
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | | BETA: splitting (37) gives:
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | | Case 1:
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | |   (38)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.80/25.21  | | | | | |           (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.80/25.21  | | | | | |           op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.80/25.21  | | | | | |           all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.80/25.21  | | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0)
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | | REF_CLOSE: (3), (4), (9), (10), (17), (38) are inconsistent by
% 158.80/25.21  | | | | | |            sub-proof #862.
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | Case 2:
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | |   (39)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 158.80/25.21  | | | | | |           (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.80/25.21  | | | | | |           e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.80/25.21  | | | | | |           all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | | REF_CLOSE: (3), (5), (15), (22), (39) are inconsistent by sub-proof
% 158.80/25.21  | | | | | |            #349.
% 158.80/25.21  | | | | | | 
% 158.80/25.21  | | | | | End of split
% 158.80/25.21  | | | | | 
% 158.80/25.21  | | | | End of split
% 158.80/25.21  | | | | 
% 158.80/25.21  | | | End of split
% 158.80/25.21  | | | 
% 158.80/25.21  | | Case 2:
% 158.80/25.21  | | | 
% 158.80/25.21  | | |   (40)  all_56_15 = e2 & op(e0, e0) = e2
% 158.80/25.21  | | | 
% 158.80/25.21  | | | ALPHA: (40) implies:
% 158.80/25.21  | | |   (41)  op(e0, e0) = e2
% 158.80/25.21  | | | 
% 158.80/25.21  | | | REF_CLOSE: (1), (3), (12), (41) are inconsistent by sub-proof #875.
% 158.80/25.21  | | | 
% 158.80/25.21  | | End of split
% 158.80/25.21  | | 
% 158.80/25.21  | End of split
% 158.80/25.21  | 
% 158.80/25.21  End of proof
% 158.80/25.21  
% 158.80/25.21  Sub-proof #247 shows that the following formulas are inconsistent:
% 158.80/25.21  ----------------------------------------------------------------
% 158.80/25.21    (1)   ~ (e3 = e2)
% 158.80/25.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.21    (3)  op(e1, e1) = e1
% 158.80/25.21    (4)  all_56_14 = e2
% 158.80/25.21    (5)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.80/25.21    (6)   ~ (e3 = e1)
% 158.80/25.21  
% 158.80/25.21  Begin of proof
% 158.80/25.21  | 
% 158.80/25.21  | BETA: splitting (5) gives:
% 158.80/25.21  | 
% 158.80/25.21  | Case 1:
% 158.80/25.21  | | 
% 158.80/25.21  | |   (7)  all_56_8 = e3 & op(e1, e1) = e3
% 158.80/25.21  | | 
% 158.80/25.21  | | ALPHA: (7) implies:
% 158.80/25.21  | |   (8)  op(e1, e1) = e3
% 158.80/25.21  | | 
% 158.80/25.21  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1003.
% 158.80/25.21  | | 
% 158.80/25.21  | Case 2:
% 158.80/25.21  | | 
% 158.80/25.21  | |   (9)  all_56_14 = e3 & op(e0, e1) = e3
% 158.80/25.21  | | 
% 158.80/25.21  | | ALPHA: (9) implies:
% 158.80/25.21  | |   (10)  all_56_14 = e3
% 158.80/25.21  | | 
% 158.80/25.21  | | REF_CLOSE: (1), (4), (10) are inconsistent by sub-proof #723.
% 158.80/25.21  | | 
% 158.80/25.21  | End of split
% 158.80/25.21  | 
% 158.80/25.21  End of proof
% 158.80/25.21  
% 158.80/25.21  Sub-proof #248 shows that the following formulas are inconsistent:
% 158.80/25.21  ----------------------------------------------------------------
% 158.80/25.21    (1)  all_56_4 = e0 & op(e3, e1) = e0
% 158.80/25.21    (2)  all_56_4 = e3
% 158.80/25.21    (3)   ~ (e3 = e0)
% 158.80/25.21  
% 158.80/25.21  Begin of proof
% 158.80/25.21  | 
% 158.80/25.21  | ALPHA: (1) implies:
% 158.80/25.21  |   (4)  all_56_4 = e0
% 158.80/25.21  | 
% 158.80/25.21  | COMBINE_EQS: (2), (4) imply:
% 158.80/25.21  |   (5)  e3 = e0
% 158.80/25.21  | 
% 158.80/25.21  | REDUCE: (3), (5) imply:
% 158.80/25.21  |   (6)  $false
% 158.80/25.21  | 
% 158.80/25.21  | CLOSE: (6) is inconsistent.
% 158.80/25.21  | 
% 158.80/25.21  End of proof
% 158.80/25.21  
% 158.80/25.21  Sub-proof #249 shows that the following formulas are inconsistent:
% 158.80/25.21  ----------------------------------------------------------------
% 158.80/25.21    (1)  all_56_11 = e2 & op(e1, e0) = e2
% 158.80/25.21    (2)  all_56_11 = e3
% 158.80/25.21    (3)   ~ (e3 = e2)
% 158.80/25.21  
% 158.80/25.21  Begin of proof
% 158.80/25.21  | 
% 158.80/25.21  | ALPHA: (1) implies:
% 158.80/25.21  |   (4)  all_56_11 = e2
% 158.80/25.21  | 
% 158.80/25.21  | COMBINE_EQS: (2), (4) imply:
% 158.80/25.21  |   (5)  e3 = e2
% 158.80/25.21  | 
% 158.80/25.21  | REDUCE: (3), (5) imply:
% 158.80/25.21  |   (6)  $false
% 158.80/25.21  | 
% 158.80/25.21  | CLOSE: (6) is inconsistent.
% 158.80/25.21  | 
% 158.80/25.21  End of proof
% 158.80/25.21  
% 158.80/25.21  Sub-proof #250 shows that the following formulas are inconsistent:
% 158.80/25.21  ----------------------------------------------------------------
% 158.80/25.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.21    (2)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.80/25.21         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.80/25.21           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.80/25.21    (3)  op(e3, e3) = e2
% 158.80/25.21    (4)  op(e0, e2) = e3
% 158.80/25.21    (5)   ~ (e2 = e0)
% 158.80/25.21    (6)   ~ (e3 = e0)
% 158.80/25.21  
% 158.80/25.21  Begin of proof
% 158.80/25.21  | 
% 158.80/25.21  | BETA: splitting (2) gives:
% 158.80/25.21  | 
% 158.80/25.21  | Case 1:
% 158.80/25.21  | | 
% 158.80/25.21  | |   (7)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 158.80/25.21  | | 
% 158.80/25.21  | | ALPHA: (7) implies:
% 158.80/25.21  | |   (8)  op(e0, e2) = e0
% 158.80/25.21  | | 
% 158.80/25.21  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #726.
% 158.80/25.21  | | 
% 158.80/25.21  | Case 2:
% 158.80/25.21  | | 
% 158.80/25.21  | |   (9)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 158.80/25.21  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 158.80/25.21  | | 
% 158.80/25.21  | | ALPHA: (9) implies:
% 158.80/25.21  | |   (10)  op(e3, e3) = e0
% 158.80/25.21  | | 
% 158.80/25.21  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #281.
% 158.80/25.21  | | 
% 158.80/25.21  | End of split
% 158.80/25.21  | 
% 158.80/25.21  End of proof
% 158.80/25.21  
% 158.80/25.21  Sub-proof #251 shows that the following formulas are inconsistent:
% 158.80/25.21  ----------------------------------------------------------------
% 158.80/25.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.21    (2)  op(e1, e1) = e1
% 158.80/25.21    (3)  op(e0, e3) = e1
% 158.80/25.21    (4)   ~ (e1 = e0)
% 158.80/25.21    (5)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.80/25.21           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.80/25.22           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 158.80/25.22           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 158.80/25.22           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 158.80/25.22           e1 & op(e0, e3) = e0)
% 158.80/25.22  
% 158.80/25.22  Begin of proof
% 158.80/25.22  | 
% 158.80/25.22  | BETA: splitting (5) gives:
% 158.80/25.22  | 
% 158.80/25.22  | Case 1:
% 158.80/25.22  | | 
% 158.80/25.22  | |   (6)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.80/25.22  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 158.80/25.22  | | 
% 158.80/25.22  | | ALPHA: (6) implies:
% 158.80/25.22  | |   (7)  op(e0, e3) = e0
% 158.80/25.22  | | 
% 158.80/25.22  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #786.
% 158.80/25.22  | | 
% 158.80/25.22  | Case 2:
% 158.80/25.22  | | 
% 158.80/25.22  | |   (8)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.80/25.22  | |            e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.80/25.22  | |        (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.80/25.22  | |            e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.80/25.22  | | 
% 158.80/25.22  | | BETA: splitting (8) gives:
% 158.80/25.22  | | 
% 158.80/25.22  | | Case 1:
% 158.80/25.22  | | | 
% 158.80/25.22  | | |   (9)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.80/25.22  | | |          e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 158.80/25.22  | | | 
% 158.80/25.22  | | | ALPHA: (9) implies:
% 158.80/25.22  | | |   (10)  op(e0, e3) = e0
% 158.80/25.22  | | | 
% 158.80/25.22  | | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #786.
% 158.80/25.22  | | | 
% 158.80/25.22  | | Case 2:
% 158.80/25.22  | | | 
% 158.80/25.22  | | |   (11)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.80/25.22  | | |           e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 158.80/25.22  | | | 
% 158.80/25.22  | | | ALPHA: (11) implies:
% 158.80/25.22  | | |   (12)  op(e1, e1) = e0
% 158.80/25.22  | | | 
% 158.80/25.22  | | | REF_CLOSE: (1), (2), (4), (12) are inconsistent by sub-proof #903.
% 158.80/25.22  | | | 
% 158.80/25.22  | | End of split
% 158.80/25.22  | | 
% 158.80/25.22  | End of split
% 158.80/25.22  | 
% 158.80/25.22  End of proof
% 158.80/25.22  
% 158.80/25.22  Sub-proof #252 shows that the following formulas are inconsistent:
% 158.80/25.22  ----------------------------------------------------------------
% 158.80/25.22    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.80/25.22         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.80/25.22    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 158.80/25.22         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 158.80/25.22    (3)  all_56_12 = e1
% 158.80/25.22    (4)   ~ (e3 = e2)
% 158.80/25.22    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.22    (6)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 158.80/25.22             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.80/25.22           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.80/25.22           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.80/25.22    (7)  op(e1, e3) = all_52_2
% 158.80/25.22    (8)   ~ (all_52_2 = e2)
% 158.80/25.22    (9)   ~ (e1 = e0)
% 158.80/25.22    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.80/25.22          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.80/25.22    (11)  op(e3, e3) = e2
% 158.80/25.22    (12)   ~ (e2 = e1)
% 158.80/25.22    (13)   ~ (e3 = e1)
% 158.80/25.22    (14)   ~ (e2 = e0)
% 158.80/25.22    (15)   ~ (e3 = e0)
% 158.80/25.22  
% 158.80/25.22  Begin of proof
% 158.80/25.22  | 
% 158.80/25.22  | BETA: splitting (6) gives:
% 158.80/25.22  | 
% 158.80/25.22  | Case 1:
% 158.80/25.22  | | 
% 158.80/25.22  | |   (16)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.80/25.22  | |         op(e3, e1) = e3
% 158.80/25.22  | | 
% 158.80/25.22  | | ALPHA: (16) implies:
% 158.80/25.22  | |   (17)  op(e3, e3) = e3
% 158.80/25.22  | | 
% 158.80/25.22  | | REF_CLOSE: (4), (5), (11), (17) are inconsistent by sub-proof #958.
% 158.80/25.22  | | 
% 158.80/25.22  | Case 2:
% 158.80/25.22  | | 
% 158.80/25.22  | |   (18)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 158.80/25.22  | |           e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.80/25.22  | |         op(e1, e0) = e1 & $i(all_57_14)
% 158.80/25.22  | | 
% 158.80/25.22  | | ALPHA: (18) implies:
% 158.80/25.22  | |   (19)  op(e3, e3) = e1
% 158.80/25.22  | | 
% 158.80/25.22  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 158.80/25.22  | |            (15), (19) are inconsistent by sub-proof #495.
% 158.80/25.22  | | 
% 158.80/25.22  | End of split
% 158.80/25.22  | 
% 158.80/25.22  End of proof
% 158.80/25.22  
% 158.80/25.22  Sub-proof #253 shows that the following formulas are inconsistent:
% 158.80/25.22  ----------------------------------------------------------------
% 158.80/25.22    (1)   ~ (all_52_1 = e2)
% 158.80/25.22    (2)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.80/25.22             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.80/25.22           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.80/25.22               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.80/25.22             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.80/25.22         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.80/25.22             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.80/25.22           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.80/25.22               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.80/25.22             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.80/25.22         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.80/25.22             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.80/25.22           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.80/25.22               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.80/25.22             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.80/25.22         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.80/25.22             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.80/25.22           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.80/25.22               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.80/25.22             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.80/25.22    (3)   ~ (e3 = e2)
% 158.80/25.22    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.80/25.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.80/25.22    (5)  op(e1, e1) = e2
% 158.80/25.22    (6)  op(e2, e3) = all_52_1
% 158.80/25.22    (7)  op(e2, e2) = e1
% 158.80/25.22    (8)   ~ (e1 = e0)
% 158.80/25.22    (9)  op(e2, e1) = all_52_9
% 158.80/25.22    (10)  op(e2, e0) = all_52_13
% 158.80/25.22    (11)  op(e3, e3) = e2
% 158.80/25.22    (12)   ~ (e2 = e1)
% 158.80/25.22    (13)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.80/25.22          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.80/25.22    (14)   ~ (all_52_9 = e2)
% 158.80/25.22  
% 158.80/25.22  Begin of proof
% 158.80/25.22  | 
% 158.80/25.22  | BETA: splitting (13) gives:
% 158.80/25.22  | 
% 158.80/25.22  | Case 1:
% 158.80/25.22  | | 
% 158.80/25.22  | |   (15)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 158.80/25.22  | |           e2)
% 158.80/25.22  | | 
% 158.80/25.22  | | REF_CLOSE: (1), (4), (6), (7), (12), (15) are inconsistent by sub-proof
% 158.80/25.22  | |            #258.
% 158.80/25.22  | | 
% 158.80/25.22  | Case 2:
% 158.80/25.22  | | 
% 158.80/25.22  | |   (16)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 158.80/25.22  | |           e2)
% 158.80/25.22  | | 
% 158.80/25.22  | | BETA: splitting (16) gives:
% 158.80/25.22  | | 
% 158.80/25.22  | | Case 1:
% 158.80/25.22  | | | 
% 158.80/25.22  | | |   (17)  all_56_5 = e2 & op(e2, e1) = e2
% 158.80/25.22  | | | 
% 158.80/25.22  | | | ALPHA: (17) implies:
% 158.80/25.22  | | |   (18)  op(e2, e1) = e2
% 158.80/25.22  | | | 
% 158.80/25.22  | | | REF_CLOSE: (4), (9), (14), (18) are inconsistent by sub-proof #1002.
% 158.80/25.22  | | | 
% 158.80/25.22  | | Case 2:
% 158.80/25.22  | | | 
% 158.80/25.22  | | |   (19)  all_56_10 = e2 & op(e2, e0) = e2
% 158.80/25.22  | | | 
% 158.80/25.22  | | | ALPHA: (19) implies:
% 158.80/25.22  | | |   (20)  op(e2, e0) = e2
% 158.80/25.22  | | | 
% 158.80/25.22  | | | BETA: splitting (2) gives:
% 158.80/25.22  | | | 
% 158.80/25.22  | | | Case 1:
% 158.80/25.22  | | | | 
% 158.80/25.22  | | | |   (21)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2,
% 158.80/25.22  | | | |                 e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0
% 158.80/25.22  | | | |               & $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | (
% 158.80/25.22  | | | |               ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)))
% 158.80/25.22  | | | |           & ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 158.80/25.22  | | | |               op(e0, e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2
% 158.80/25.22  | | | |           & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 158.80/25.22  | | | |               (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.80/25.22  | | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 158.80/25.22  | | | |               op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2
% 158.80/25.22  | | | |               & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 158.80/25.22  | | | |               all_57_7 & $i(all_57_7))))
% 158.80/25.22  | | | | 
% 158.80/25.22  | | | | REF_CLOSE: (3), (4), (7), (11), (12), (21) are inconsistent by sub-proof
% 158.80/25.22  | | | |            #254.
% 158.80/25.22  | | | | 
% 158.80/25.22  | | | Case 2:
% 158.80/25.22  | | | | 
% 158.80/25.22  | | | |   (22)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 158.80/25.22  | | | |                 e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4
% 158.80/25.22  | | | |               & $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | (
% 158.80/25.22  | | | |               ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)))
% 158.80/25.22  | | | |           & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.80/25.22  | | | |               op(e0, e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0
% 158.80/25.22  | | | |           & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 158.80/25.22  | | | |               (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.80/25.22  | | | |           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 158.80/25.22  | | | |               op(e2, e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 =
% 158.80/25.22  | | | |               e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0)
% 158.80/25.22  | | | |               = all_57_13 & $i(all_57_13))))
% 158.80/25.22  | | | | 
% 158.80/25.22  | | | | BETA: splitting (22) gives:
% 158.80/25.22  | | | | 
% 158.80/25.22  | | | | Case 1:
% 158.80/25.22  | | | | | 
% 158.86/25.22  | | | | |   (23)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 158.86/25.22  | | | | |               e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4
% 158.86/25.22  | | | | |             & $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | (
% 158.86/25.22  | | | | |             ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)))
% 158.86/25.22  | | | | |         & ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.86/25.22  | | | | |             op(e0, e1) = all_57_8 & $i(all_57_8)))
% 158.86/25.22  | | | | | 
% 158.86/25.22  | | | | | ALPHA: (23) implies:
% 158.86/25.22  | | | | |   (24)  op(e1, e1) = e1
% 158.86/25.22  | | | | | 
% 158.86/25.22  | | | | | REF_CLOSE: (4), (5), (12), (24) are inconsistent by sub-proof #986.
% 158.86/25.22  | | | | | 
% 158.86/25.22  | | | | Case 2:
% 158.86/25.22  | | | | | 
% 158.86/25.22  | | | | |   (25)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3,
% 158.86/25.22  | | | | |               e3) = e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9
% 158.86/25.22  | | | | |             & $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | (
% 158.86/25.22  | | | | |             ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 158.86/25.22  | | | | |             $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0) | (
% 158.86/25.22  | | | | |             ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 158.86/25.22  | | | | |             $i(all_57_13)))
% 158.86/25.22  | | | | | 
% 158.86/25.22  | | | | | ALPHA: (25) implies:
% 158.86/25.22  | | | | |   (26)  (all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 158.86/25.22  | | | | |           op(e2, e0) = all_57_11 & $i(all_57_11))
% 158.86/25.22  | | | | | 
% 158.86/25.22  | | | | | BETA: splitting (26) gives:
% 158.86/25.22  | | | | | 
% 158.86/25.22  | | | | | Case 1:
% 158.86/25.22  | | | | | | 
% 158.86/25.22  | | | | | |   (27)  all_57_12 = e0 & op(e2, e2) = e0
% 158.86/25.22  | | | | | | 
% 158.86/25.22  | | | | | | ALPHA: (27) implies:
% 158.86/25.22  | | | | | |   (28)  op(e2, e2) = e0
% 158.86/25.22  | | | | | | 
% 158.86/25.22  | | | | | | REF_CLOSE: (4), (7), (8), (28) are inconsistent by sub-proof #960.
% 158.86/25.22  | | | | | | 
% 158.86/25.22  | | | | | Case 2:
% 158.86/25.22  | | | | | | 
% 158.86/25.22  | | | | | |   (29)   ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11)
% 158.86/25.22  | | | | | | 
% 158.86/25.22  | | | | | | ALPHA: (29) implies:
% 158.86/25.22  | | | | | |   (30)   ~ (all_57_11 = e2)
% 158.86/25.22  | | | | | |   (31)  op(e2, e0) = all_57_11
% 158.86/25.22  | | | | | | 
% 158.86/25.22  | | | | | | REF_CLOSE: (4), (10), (20), (30), (31) are inconsistent by sub-proof
% 158.86/25.22  | | | | | |            #627.
% 158.86/25.22  | | | | | | 
% 158.86/25.22  | | | | | End of split
% 158.86/25.22  | | | | | 
% 158.86/25.22  | | | | End of split
% 158.86/25.22  | | | | 
% 158.86/25.22  | | | End of split
% 158.86/25.22  | | | 
% 158.86/25.22  | | End of split
% 158.86/25.22  | | 
% 158.86/25.22  | End of split
% 158.86/25.22  | 
% 158.86/25.22  End of proof
% 158.86/25.22  
% 158.86/25.22  Sub-proof #254 shows that the following formulas are inconsistent:
% 158.86/25.22  ----------------------------------------------------------------
% 158.86/25.22    (1)   ~ (e3 = e2)
% 158.86/25.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.22    (3)  op(e2, e2) = e1
% 158.86/25.22    (4)  op(e3, e3) = e2
% 158.86/25.22    (5)   ~ (e2 = e1)
% 158.86/25.22    (6)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.86/25.22             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.86/25.22           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.86/25.22               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.86/25.22             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.86/25.22         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.86/25.22             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.86/25.22           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.86/25.22               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.86/25.22             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 158.86/25.22  
% 158.86/25.22  Begin of proof
% 158.86/25.22  | 
% 158.86/25.22  | BETA: splitting (6) gives:
% 158.86/25.22  | 
% 158.86/25.22  | Case 1:
% 158.86/25.22  | | 
% 158.86/25.22  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 158.86/25.22  | |            e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.86/25.22  | |            $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.86/25.22  | |            (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.86/25.22  | |        ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 158.86/25.22  | |              e3) = all_57_6 & $i(all_57_6)))
% 158.86/25.22  | | 
% 158.86/25.22  | | ALPHA: (7) implies:
% 158.86/25.22  | |   (8)  op(e3, e3) = e3
% 158.86/25.22  | | 
% 158.86/25.22  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #958.
% 158.86/25.22  | | 
% 158.86/25.22  | Case 2:
% 158.86/25.22  | | 
% 158.86/25.22  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 158.86/25.22  | |            e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.86/25.22  | |            $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 158.86/25.22  | |            (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 158.86/25.22  | |        ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 158.86/25.22  | |              e2) = all_57_7 & $i(all_57_7)))
% 158.86/25.22  | | 
% 158.86/25.22  | | ALPHA: (9) implies:
% 158.86/25.22  | |   (10)  op(e2, e2) = e2
% 158.86/25.22  | | 
% 158.86/25.22  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #993.
% 158.86/25.22  | | 
% 158.86/25.22  | End of split
% 158.86/25.22  | 
% 158.86/25.22  End of proof
% 158.86/25.22  
% 158.86/25.22  Sub-proof #255 shows that the following formulas are inconsistent:
% 158.86/25.22  ----------------------------------------------------------------
% 158.86/25.22    (1)  all_54_15 = e1 | all_54_15 = e0
% 158.86/25.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.22    (3)  op(e1, e1) = e1
% 158.86/25.22    (4)  op(e1, e3) = all_52_2
% 158.86/25.22    (5)  all_54_15 = all_14_2
% 158.86/25.22    (6)   ~ (all_52_2 = e1)
% 158.86/25.22    (7)  op(e0, e0) = all_14_2
% 158.86/25.22    (8)   ~ (all_14_2 = e1)
% 158.86/25.22    (9)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.86/25.22           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 158.86/25.22           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 158.86/25.22           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 158.86/25.22           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 158.86/25.22           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.86/25.22    (10)   ~ (e3 = e1)
% 158.86/25.22  
% 158.86/25.22  Begin of proof
% 158.86/25.22  | 
% 158.86/25.22  | BETA: splitting (9) gives:
% 158.86/25.22  | 
% 158.86/25.22  | Case 1:
% 158.86/25.22  | | 
% 158.86/25.22  | |   (11)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 158.86/25.22  | |         & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 158.86/25.22  | |         op(e0, e0) = e1 & $i(all_57_14)
% 158.86/25.23  | | 
% 158.86/25.23  | | ALPHA: (11) implies:
% 158.86/25.23  | |   (12)  op(e0, e0) = e1
% 158.86/25.23  | | 
% 158.86/25.23  | | REF_CLOSE: (1), (2), (5), (7), (8), (12) are inconsistent by sub-proof #790.
% 158.86/25.23  | | 
% 158.86/25.23  | Case 2:
% 158.86/25.23  | | 
% 158.86/25.23  | |   (13)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 158.86/25.23  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 158.86/25.23  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 158.86/25.23  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.86/25.23  | | 
% 158.86/25.23  | | REF_CLOSE: (2), (3), (4), (6), (10), (13) are inconsistent by sub-proof
% 158.86/25.23  | |            #989.
% 158.86/25.23  | | 
% 158.86/25.23  | End of split
% 158.86/25.23  | 
% 158.86/25.23  End of proof
% 158.86/25.23  
% 158.86/25.23  Sub-proof #256 shows that the following formulas are inconsistent:
% 158.86/25.23  ----------------------------------------------------------------
% 158.86/25.23    (1)   ~ (all_52_1 = e2)
% 158.86/25.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.23    (3)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.86/25.23           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.86/25.23           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 158.86/25.23           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 158.86/25.23           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.86/25.23           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 158.86/25.23           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.86/25.23           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.86/25.23           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 158.86/25.23             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.86/25.23           all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 158.86/25.23           & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.86/25.23           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 158.86/25.23           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 158.86/25.23             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 158.86/25.23           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 158.86/25.23         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.86/25.23           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.86/25.23           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 158.86/25.23           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 158.86/25.23           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.86/25.23    (4)  op(e1, e1) = e1
% 158.86/25.23    (5)  op(e2, e3) = all_52_1
% 158.86/25.23    (6)  op(e2, e2) = e1
% 158.86/25.23    (7)   ~ (e3 = e1)
% 158.86/25.23  
% 158.86/25.23  Begin of proof
% 158.86/25.23  | 
% 158.86/25.23  | BETA: splitting (3) gives:
% 158.86/25.23  | 
% 158.86/25.23  | Case 1:
% 158.86/25.23  | | 
% 158.86/25.23  | |   (8)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 158.86/25.23  | |          & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 158.86/25.23  | |          = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.86/25.23  | |          all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.86/25.23  | |          op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.86/25.23  | |          $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 158.86/25.23  | |          ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.86/25.23  | |          op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 158.86/25.23  | |          & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 158.86/25.23  | |          = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.86/25.23  | |          $i(all_57_10))
% 158.86/25.23  | | 
% 158.86/25.23  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1005.
% 158.86/25.23  | | 
% 158.86/25.23  | Case 2:
% 158.86/25.23  | | 
% 158.86/25.23  | |   (9)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 158.86/25.23  | |          & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 158.86/25.23  | |          op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.86/25.23  | |          all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 158.86/25.23  | |          op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 158.86/25.23  | |          $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 158.86/25.23  | |          op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1
% 158.86/25.23  | |          & all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 158.86/25.23  | |          op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.86/25.23  | |          $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 158.86/25.23  | |          ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 158.86/25.23  | |          = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.86/25.23  | | 
% 158.86/25.23  | | BETA: splitting (9) gives:
% 158.86/25.23  | | 
% 158.86/25.23  | | Case 1:
% 158.86/25.23  | | | 
% 158.86/25.23  | | |   (10)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 158.86/25.23  | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) =
% 158.86/25.23  | | |           e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.86/25.23  | | |           all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 158.86/25.23  | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.86/25.23  | | |             e2) = e3 & $i(all_57_10))
% 158.86/25.23  | | | 
% 158.86/25.23  | | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1004.
% 158.86/25.23  | | | 
% 158.86/25.23  | | Case 2:
% 158.86/25.23  | | | 
% 158.86/25.23  | | |   (11)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.86/25.23  | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 =
% 158.86/25.23  | | |           e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.86/25.23  | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.86/25.23  | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 =
% 158.86/25.23  | | |             e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.86/25.23  | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.86/25.23  | | | 
% 158.86/25.23  | | | BETA: splitting (11) gives:
% 158.86/25.23  | | | 
% 158.86/25.23  | | | Case 1:
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | |   (12)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 158.86/25.23  | | | |         & op(e2, e2) = e2
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | | ALPHA: (12) implies:
% 158.86/25.23  | | | |   (13)  op(e2, e3) = e2
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | | REF_CLOSE: (1), (2), (5), (13) are inconsistent by sub-proof #1007.
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | Case 2:
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | |   (14)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 158.86/25.23  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.86/25.23  | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 158.86/25.23  | | | |           & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.86/25.23  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.86/25.23  | | | |           op(e2, e1) = e2 & $i(all_57_12))
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | | REF_CLOSE: (2), (4), (6), (7), (14) are inconsistent by sub-proof #794.
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | End of split
% 158.86/25.23  | | | 
% 158.86/25.23  | | End of split
% 158.86/25.23  | | 
% 158.86/25.23  | End of split
% 158.86/25.23  | 
% 158.86/25.23  End of proof
% 158.86/25.23  
% 158.86/25.23  Sub-proof #257 shows that the following formulas are inconsistent:
% 158.86/25.23  ----------------------------------------------------------------
% 158.86/25.23    (1)  all_56_5 = e0 & op(e2, e1) = e0
% 158.86/25.23    (2)  all_56_5 = e2
% 158.86/25.23    (3)   ~ (e2 = e0)
% 158.86/25.23  
% 158.86/25.23  Begin of proof
% 158.86/25.23  | 
% 158.86/25.23  | ALPHA: (1) implies:
% 158.86/25.23  |   (4)  all_56_5 = e0
% 158.86/25.23  | 
% 158.86/25.23  | COMBINE_EQS: (2), (4) imply:
% 158.86/25.23  |   (5)  e2 = e0
% 158.86/25.23  | 
% 158.86/25.23  | REDUCE: (3), (5) imply:
% 158.86/25.23  |   (6)  $false
% 158.86/25.23  | 
% 158.86/25.23  | CLOSE: (6) is inconsistent.
% 158.86/25.23  | 
% 158.86/25.23  End of proof
% 158.86/25.23  
% 158.86/25.23  Sub-proof #258 shows that the following formulas are inconsistent:
% 158.86/25.23  ----------------------------------------------------------------
% 158.86/25.23    (1)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 158.86/25.23    (2)   ~ (all_52_1 = e2)
% 158.86/25.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.23    (4)  op(e2, e3) = all_52_1
% 158.86/25.23    (5)  op(e2, e2) = e1
% 158.86/25.23    (6)   ~ (e2 = e1)
% 158.86/25.23  
% 158.86/25.23  Begin of proof
% 158.86/25.23  | 
% 158.86/25.23  | BETA: splitting (1) gives:
% 158.86/25.23  | 
% 158.86/25.23  | Case 1:
% 158.86/25.23  | | 
% 158.86/25.23  | |   (7)  all_56_2 = e2 & op(e2, e3) = e2
% 158.86/25.23  | | 
% 158.86/25.23  | | ALPHA: (7) implies:
% 158.86/25.23  | |   (8)  op(e2, e3) = e2
% 158.86/25.23  | | 
% 158.86/25.23  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1007.
% 158.86/25.23  | | 
% 158.86/25.23  | Case 2:
% 158.86/25.23  | | 
% 158.86/25.23  | |   (9)  all_56_3 = e2 & op(e2, e2) = e2
% 158.86/25.23  | | 
% 158.86/25.23  | | ALPHA: (9) implies:
% 158.86/25.23  | |   (10)  op(e2, e2) = e2
% 158.86/25.23  | | 
% 158.86/25.23  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #993.
% 158.86/25.23  | | 
% 158.86/25.23  | End of split
% 158.86/25.23  | 
% 158.86/25.23  End of proof
% 158.86/25.23  
% 158.86/25.23  Sub-proof #259 shows that the following formulas are inconsistent:
% 158.86/25.23  ----------------------------------------------------------------
% 158.86/25.23    (1)   ~ (e3 = e2)
% 158.86/25.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.23    (3)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.86/25.23         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.86/25.23    (4)  op(e2, e2) = e1
% 158.86/25.23    (5)   ~ (e1 = e0)
% 158.86/25.23    (6)  all_56_2 = e1
% 158.86/25.23    (7)  op(e2, e3) = e1
% 158.86/25.23    (8)   ~ (e2 = e1)
% 158.86/25.23    (9)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.86/25.23         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.86/25.23    (10)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.86/25.23          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.86/25.23    (11)   ~ (e3 = e1)
% 158.86/25.23    (12)   ~ (e2 = e0)
% 158.86/25.23    (13)   ~ (e3 = e0)
% 158.86/25.23  
% 158.86/25.23  Begin of proof
% 158.86/25.23  | 
% 158.86/25.23  | BETA: splitting (9) gives:
% 158.86/25.23  | 
% 158.86/25.23  | Case 1:
% 158.86/25.23  | | 
% 158.86/25.23  | |   (14)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 158.86/25.23  | |           e0)
% 158.86/25.23  | | 
% 158.86/25.23  | | REF_CLOSE: (2), (4), (5), (6), (14) are inconsistent by sub-proof #357.
% 158.86/25.23  | | 
% 158.86/25.23  | Case 2:
% 158.86/25.23  | | 
% 158.86/25.23  | |   (15)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 158.86/25.23  | |           e0)
% 158.86/25.23  | | 
% 158.86/25.23  | | BETA: splitting (15) gives:
% 158.86/25.23  | | 
% 158.86/25.23  | | Case 1:
% 158.86/25.23  | | | 
% 158.86/25.23  | | |   (16)  all_56_5 = e0 & op(e2, e1) = e0
% 158.86/25.23  | | | 
% 158.86/25.23  | | | ALPHA: (16) implies:
% 158.86/25.23  | | |   (17)  all_56_5 = e0
% 158.86/25.23  | | | 
% 158.86/25.23  | | | BETA: splitting (10) gives:
% 158.86/25.23  | | | 
% 158.86/25.23  | | | Case 1:
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | |   (18)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2)
% 158.86/25.23  | | | |           = e2)
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | | REF_CLOSE: (2), (4), (7), (8), (18) are inconsistent by sub-proof #262.
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | Case 2:
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | |   (19)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0)
% 158.86/25.23  | | | |           = e2)
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | | BETA: splitting (19) gives:
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | | Case 1:
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | |   (20)  all_56_5 = e2 & op(e2, e1) = e2
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | | REF_CLOSE: (12), (17), (20) are inconsistent by sub-proof #553.
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | Case 2:
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | |   (21)  all_56_10 = e2 & op(e2, e0) = e2
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | | ALPHA: (21) implies:
% 158.86/25.23  | | | | |   (22)  all_56_10 = e2
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (11), (12), (13), (22)
% 158.86/25.23  | | | | |            are inconsistent by sub-proof #356.
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | End of split
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | End of split
% 158.86/25.23  | | | 
% 158.86/25.23  | | Case 2:
% 158.86/25.23  | | | 
% 158.86/25.23  | | |   (23)  all_56_10 = e0 & op(e2, e0) = e0
% 158.86/25.23  | | | 
% 158.86/25.23  | | | ALPHA: (23) implies:
% 158.86/25.23  | | |   (24)  all_56_10 = e0
% 158.86/25.23  | | | 
% 158.86/25.23  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.86/25.23  | | |            (13), (24) are inconsistent by sub-proof #260.
% 158.86/25.23  | | | 
% 158.86/25.23  | | End of split
% 158.86/25.23  | | 
% 158.86/25.23  | End of split
% 158.86/25.23  | 
% 158.86/25.23  End of proof
% 158.86/25.23  
% 158.86/25.23  Sub-proof #260 shows that the following formulas are inconsistent:
% 158.86/25.23  ----------------------------------------------------------------
% 158.86/25.23    (1)   ~ (e3 = e2)
% 158.86/25.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.23    (3)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.86/25.23         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.86/25.23    (4)  op(e2, e2) = e1
% 158.86/25.23    (5)   ~ (e1 = e0)
% 158.86/25.23    (6)  all_56_2 = e1
% 158.86/25.23    (7)  op(e2, e3) = e1
% 158.86/25.23    (8)  all_56_10 = e0
% 158.86/25.23    (9)   ~ (e2 = e1)
% 158.86/25.23    (10)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.86/25.23          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 158.86/25.23    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.86/25.23          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.86/25.23    (12)   ~ (e3 = e1)
% 158.86/25.23    (13)   ~ (e2 = e0)
% 158.86/25.23    (14)   ~ (e3 = e0)
% 158.86/25.23  
% 158.86/25.23  Begin of proof
% 158.86/25.23  | 
% 158.86/25.23  | BETA: splitting (11) gives:
% 158.86/25.23  | 
% 158.86/25.23  | Case 1:
% 158.86/25.23  | | 
% 158.86/25.23  | |   (15)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 158.86/25.23  | |           e2)
% 158.86/25.23  | | 
% 158.86/25.23  | | REF_CLOSE: (2), (4), (7), (9), (15) are inconsistent by sub-proof #262.
% 158.86/25.23  | | 
% 158.86/25.23  | Case 2:
% 158.86/25.23  | | 
% 158.86/25.23  | |   (16)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 158.86/25.23  | |           e2)
% 158.86/25.23  | | 
% 158.86/25.23  | | BETA: splitting (16) gives:
% 158.86/25.23  | | 
% 158.86/25.23  | | Case 1:
% 158.86/25.23  | | | 
% 158.86/25.23  | | |   (17)  all_56_5 = e2 & op(e2, e1) = e2
% 158.86/25.23  | | | 
% 158.86/25.23  | | | ALPHA: (17) implies:
% 158.86/25.23  | | |   (18)  all_56_5 = e2
% 158.86/25.23  | | | 
% 158.86/25.23  | | | BETA: splitting (3) gives:
% 158.86/25.23  | | | 
% 158.86/25.23  | | | Case 1:
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | |   (19)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2)
% 158.86/25.23  | | | |           = e3)
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | | REF_CLOSE: (2), (4), (6), (12), (19) are inconsistent by sub-proof #358.
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | Case 2:
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | |   (20)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0)
% 158.86/25.23  | | | |           = e3)
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | | BETA: splitting (20) gives:
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | | Case 1:
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | |   (21)  all_56_5 = e3 & op(e2, e1) = e3
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | | ALPHA: (21) implies:
% 158.86/25.23  | | | | |   (22)  all_56_5 = e3
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | | REF_CLOSE: (1), (18), (22) are inconsistent by sub-proof #593.
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | Case 2:
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | |   (23)  all_56_10 = e3 & op(e2, e0) = e3
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | | REF_CLOSE: (8), (14), (23) are inconsistent by sub-proof #261.
% 158.86/25.23  | | | | | 
% 158.86/25.23  | | | | End of split
% 158.86/25.23  | | | | 
% 158.86/25.23  | | | End of split
% 158.86/25.23  | | | 
% 158.86/25.23  | | Case 2:
% 158.86/25.23  | | | 
% 158.86/25.23  | | |   (24)  all_56_10 = e2 & op(e2, e0) = e2
% 158.86/25.23  | | | 
% 158.86/25.23  | | | ALPHA: (24) implies:
% 158.86/25.23  | | |   (25)  all_56_10 = e2
% 158.86/25.23  | | | 
% 158.86/25.23  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (12), (13), (14), (25) are
% 158.86/25.23  | | |            inconsistent by sub-proof #356.
% 158.86/25.23  | | | 
% 158.86/25.23  | | End of split
% 158.86/25.23  | | 
% 158.86/25.23  | End of split
% 158.86/25.23  | 
% 158.86/25.23  End of proof
% 158.86/25.23  
% 158.86/25.23  Sub-proof #261 shows that the following formulas are inconsistent:
% 158.86/25.23  ----------------------------------------------------------------
% 158.86/25.23    (1)  all_56_10 = e3 & op(e2, e0) = e3
% 158.86/25.23    (2)  all_56_10 = e0
% 158.86/25.23    (3)   ~ (e3 = e0)
% 158.86/25.23  
% 158.86/25.23  Begin of proof
% 158.86/25.23  | 
% 158.86/25.23  | ALPHA: (1) implies:
% 158.86/25.23  |   (4)  all_56_10 = e3
% 158.86/25.23  | 
% 158.86/25.23  | COMBINE_EQS: (2), (4) imply:
% 158.86/25.24  |   (5)  e3 = e0
% 158.86/25.24  | 
% 158.86/25.24  | REDUCE: (3), (5) imply:
% 158.86/25.24  |   (6)  $false
% 158.86/25.24  | 
% 158.86/25.24  | CLOSE: (6) is inconsistent.
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #262 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 158.86/25.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.24    (3)  op(e2, e2) = e1
% 158.86/25.24    (4)  op(e2, e3) = e1
% 158.86/25.24    (5)   ~ (e2 = e1)
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | BETA: splitting (1) gives:
% 158.86/25.24  | 
% 158.86/25.24  | Case 1:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (6)  all_56_2 = e2 & op(e2, e3) = e2
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (6) implies:
% 158.86/25.24  | |   (7)  op(e2, e3) = e2
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #428.
% 158.86/25.24  | | 
% 158.86/25.24  | Case 2:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (8)  all_56_3 = e2 & op(e2, e2) = e2
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (8) implies:
% 158.86/25.24  | |   (9)  op(e2, e2) = e2
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #993.
% 158.86/25.24  | | 
% 158.86/25.24  | End of split
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #263 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)  all_56_14 = e2 & op(e0, e1) = e2
% 158.86/25.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.24    (3)  op(e0, e1) = all_52_11
% 158.86/25.24    (4)   ~ (all_52_11 = e2)
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | ALPHA: (1) implies:
% 158.86/25.24  |   (5)  op(e0, e1) = e2
% 158.86/25.24  | 
% 158.86/25.24  | GROUND_INST: instantiating (2) with all_52_11, e2, e1, e0, simplifying with
% 158.86/25.24  |              (3), (5) gives:
% 158.86/25.24  |   (6)  all_52_11 = e2
% 158.86/25.24  | 
% 158.86/25.24  | REDUCE: (4), (6) imply:
% 158.86/25.24  |   (7)  $false
% 158.86/25.24  | 
% 158.86/25.24  | CLOSE: (7) is inconsistent.
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #264 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.24    (2)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.86/25.24           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.86/25.24           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 158.86/25.24           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.86/25.24    (3)  op(e2, e0) = all_52_13
% 158.86/25.24    (4)  op(e3, e3) = e2
% 158.86/25.24    (5)   ~ (e2 = e0)
% 158.86/25.24    (6)   ~ (all_52_13 = e2)
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | BETA: splitting (2) gives:
% 158.86/25.24  | 
% 158.86/25.24  | Case 1:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (7)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 158.86/25.24  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (7) implies:
% 158.86/25.24  | |   (8)  op(e3, e3) = e0
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #281.
% 158.86/25.24  | | 
% 158.86/25.24  | Case 2:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (9)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2)
% 158.86/25.24  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (9) implies:
% 158.86/25.24  | |   (10)  op(e2, e0) = e2
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #996.
% 158.86/25.24  | | 
% 158.86/25.24  | End of split
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #265 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.24    (2)  op(e1, e1) = e1
% 158.86/25.24    (3)   ~ (e1 = e0)
% 158.86/25.24    (4)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.86/25.24           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.86/25.24           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 158.86/25.24           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 158.86/25.24           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 158.86/25.24           e1 & op(e0, e3) = e0)
% 158.86/25.24    (5)  op(e2, e0) = all_52_13
% 158.86/25.24    (6)  op(e3, e3) = e2
% 158.86/25.24    (7)   ~ (e2 = e0)
% 158.86/25.24    (8)   ~ (all_52_13 = e2)
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | BETA: splitting (4) gives:
% 158.86/25.24  | 
% 158.86/25.24  | Case 1:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.86/25.24  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (9) implies:
% 158.86/25.24  | |   (10)  op(e3, e3) = e0
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (6), (7), (10) are inconsistent by sub-proof #281.
% 158.86/25.24  | | 
% 158.86/25.24  | Case 2:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (11)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.24  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.86/25.24  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.24  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (2), (3), (5), (8), (11) are inconsistent by sub-proof #867.
% 158.86/25.24  | | 
% 158.86/25.24  | End of split
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #266 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)   ~ (e3 = e2)
% 158.86/25.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.24    (3)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.86/25.24           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 158.86/25.24           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 158.86/25.24           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 158.86/25.24    (4)  op(e2, e0) = all_52_13
% 158.86/25.24    (5)  op(e3, e3) = e2
% 158.86/25.24    (6)   ~ (all_52_13 = e2)
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | BETA: splitting (3) gives:
% 158.86/25.24  | 
% 158.86/25.24  | Case 1:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (7)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 158.86/25.24  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.86/25.24  | |          e0) = e2 & $i(all_57_12)
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (7) implies:
% 158.86/25.24  | |   (8)  op(e2, e0) = e2
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #996.
% 158.86/25.24  | | 
% 158.86/25.24  | Case 2:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (9)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 158.86/25.24  | |        op(e3, e0) = e3
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (9) implies:
% 158.86/25.24  | |   (10)  op(e3, e3) = e3
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #958.
% 158.86/25.24  | | 
% 158.86/25.24  | End of split
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #267 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)  all_54_5 = all_4_2
% 158.86/25.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.24    (3)  op(e2, e2) = all_4_2
% 158.86/25.24    (4)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 158.86/25.24    (5)   ~ (all_4_2 = e2)
% 158.86/25.24    (6)   ~ (all_4_2 = e1)
% 158.86/25.24    (7)  op(e2, e2) = e1
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | BETA: splitting (4) gives:
% 158.86/25.24  | 
% 158.86/25.24  | Case 1:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (8)  all_54_5 = e2
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #268.
% 158.86/25.24  | | 
% 158.86/25.24  | Case 2:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (9)  all_54_5 = e1 | all_54_5 = e0
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (2), (3), (6), (7), (9) are inconsistent by sub-proof #692.
% 158.86/25.24  | | 
% 158.86/25.24  | End of split
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #268 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)  all_54_5 = all_4_2
% 158.86/25.24    (2)  all_54_5 = e2
% 158.86/25.24    (3)   ~ (all_4_2 = e2)
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | COMBINE_EQS: (1), (2) imply:
% 158.86/25.24  |   (4)  all_4_2 = e2
% 158.86/25.24  | 
% 158.86/25.24  | SIMP: (4) implies:
% 158.86/25.24  |   (5)  all_4_2 = e2
% 158.86/25.24  | 
% 158.86/25.24  | REDUCE: (3), (5) imply:
% 158.86/25.24  |   (6)  $false
% 158.86/25.24  | 
% 158.86/25.24  | CLOSE: (6) is inconsistent.
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #269 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)  op(e0, e0) = e2
% 158.86/25.24    (2)   ~ (e3 = e2)
% 158.86/25.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.24    (4)  op(e3, e3) = e2
% 158.86/25.24    (5)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 158.86/25.24           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.86/25.24           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 158.86/25.24           & op(e3, e3) = e3 & op(e3, e2) = e3)
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | BETA: splitting (5) gives:
% 158.86/25.24  | 
% 158.86/25.24  | Case 1:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (6)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 158.86/25.24  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 158.86/25.24  | |          e0) = e3 & $i(all_57_10)
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (6) implies:
% 158.86/25.24  | |   (7)  op(e0, e0) = e3
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #878.
% 158.86/25.24  | | 
% 158.86/25.24  | Case 2:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (8)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 158.86/25.24  | |        op(e3, e2) = e3
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (8) implies:
% 158.86/25.24  | |   (9)  op(e3, e3) = e3
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #958.
% 158.86/25.24  | | 
% 158.86/25.24  | End of split
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #270 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.24    (2)  op(e1, e1) = e1
% 158.86/25.24    (3)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 158.86/25.24           all_57_5 & $i(all_57_5))
% 158.86/25.24    (4)   ~ (e3 = e1)
% 158.86/25.24    (5)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.86/25.24           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.86/25.24           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 158.86/25.24           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 158.86/25.24           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | BETA: splitting (5) gives:
% 158.86/25.24  | 
% 158.86/25.24  | Case 1:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (6)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 158.86/25.24  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 158.86/25.24  | |          e1) = e3 & $i(all_57_10)
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (6) implies:
% 158.86/25.24  | |   (7)  op(e1, e1) = e3
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #1003.
% 158.86/25.24  | | 
% 158.86/25.24  | Case 2:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (8)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 158.86/25.24  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.86/25.24  | |          e1) = e2 & $i(all_57_12)
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (8) implies:
% 158.86/25.24  | |   (9)  all_57_5 = e2
% 158.86/25.24  | |   (10)   ~ (all_57_12 = e1)
% 158.86/25.24  | |   (11)  op(e2, e2) = all_57_12
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (3), (9), (10), (11) are inconsistent by sub-proof #274.
% 158.86/25.24  | | 
% 158.86/25.24  | End of split
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #271 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.24    (2)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 158.86/25.24           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.86/25.24           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 158.86/25.24           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 158.86/25.24             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.86/25.24    (3)  op(e2, e2) = e0
% 158.86/25.24    (4)   ~ (e1 = e0)
% 158.86/25.24    (5)  op(e3, e3) = e2
% 158.86/25.24    (6)   ~ (e2 = e1)
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | BETA: splitting (2) gives:
% 158.86/25.24  | 
% 158.86/25.24  | Case 1:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (7)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 158.86/25.24  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.86/25.24  | |        all_57_14 & $i(all_57_14)
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (7) implies:
% 158.86/25.24  | |   (8)  op(e3, e3) = e1
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #828.
% 158.86/25.24  | | 
% 158.86/25.24  | Case 2:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 158.86/25.24  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.86/25.24  | |        all_57_14 & $i(all_57_14)
% 158.86/25.24  | | 
% 158.86/25.24  | | ALPHA: (9) implies:
% 158.86/25.24  | |   (10)  op(e2, e2) = e1
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #960.
% 158.86/25.24  | | 
% 158.86/25.24  | End of split
% 158.86/25.24  | 
% 158.86/25.24  End of proof
% 158.86/25.24  
% 158.86/25.24  Sub-proof #272 shows that the following formulas are inconsistent:
% 158.86/25.24  ----------------------------------------------------------------
% 158.86/25.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.24    (2)  op(e0, e0) = e0
% 158.86/25.24    (3)  op(e2, e2) = e0
% 158.86/25.24    (4)  op(e3, e3) = e2
% 158.86/25.24    (5)   ~ (e2 = e1)
% 158.86/25.24    (6)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 158.86/25.24           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.86/25.24           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 158.86/25.24           & op(e3, e3) = e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2
% 158.86/25.24           & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 158.86/25.24           e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 158.86/25.24         (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3) &
% 158.86/25.24           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.86/25.24           all_57_14 & $i(all_57_14))
% 158.86/25.24    (7)   ~ (e3 = e0)
% 158.86/25.24  
% 158.86/25.24  Begin of proof
% 158.86/25.24  | 
% 158.86/25.24  | BETA: splitting (6) gives:
% 158.86/25.24  | 
% 158.86/25.24  | Case 1:
% 158.86/25.24  | | 
% 158.86/25.24  | |   (8)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 158.86/25.24  | |          & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 158.86/25.24  | |          op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3
% 158.86/25.24  | |          &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 158.86/25.24  | | 
% 158.86/25.24  | | REF_CLOSE: (1), (2), (4), (7), (8) are inconsistent by sub-proof #287.
% 158.86/25.24  | | 
% 158.86/25.24  | Case 2:
% 158.86/25.24  | | 
% 158.86/25.25  | |   (9)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 =
% 158.86/25.25  | |            e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12
% 158.86/25.25  | |          & op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3
% 158.86/25.25  | |          & all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 158.86/25.25  | |            e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.86/25.25  | |          $i(all_57_14))
% 158.86/25.25  | | 
% 158.86/25.25  | | BETA: splitting (9) gives:
% 158.86/25.25  | | 
% 158.86/25.25  | | Case 1:
% 158.86/25.25  | | | 
% 158.86/25.25  | | |   (10)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 =
% 158.86/25.25  | | |           e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12
% 158.86/25.25  | | |         & op(e2, e0) = e2 & $i(all_57_12)
% 158.86/25.25  | | | 
% 158.86/25.25  | | | ALPHA: (10) implies:
% 158.86/25.25  | | |   (11)   ~ (all_57_12 = e0)
% 158.86/25.25  | | |   (12)  op(e2, e2) = all_57_12
% 158.86/25.25  | | | 
% 158.86/25.25  | | | REF_CLOSE: (1), (3), (11), (12) are inconsistent by sub-proof #811.
% 158.86/25.25  | | | 
% 158.86/25.25  | | Case 2:
% 158.86/25.25  | | | 
% 158.86/25.25  | | |   (13)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 158.86/25.25  | | |           e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 158.86/25.25  | | |         op(e1, e1) = all_57_14 & $i(all_57_14)
% 158.86/25.25  | | | 
% 158.86/25.25  | | | ALPHA: (13) implies:
% 158.86/25.25  | | |   (14)  op(e3, e3) = e1
% 158.86/25.25  | | | 
% 158.86/25.25  | | | REF_CLOSE: (1), (4), (5), (14) are inconsistent by sub-proof #828.
% 158.86/25.25  | | | 
% 158.86/25.25  | | End of split
% 158.86/25.25  | | 
% 158.86/25.25  | End of split
% 158.86/25.25  | 
% 158.86/25.25  End of proof
% 158.86/25.25  
% 158.86/25.25  Sub-proof #273 shows that the following formulas are inconsistent:
% 158.86/25.25  ----------------------------------------------------------------
% 158.86/25.25    (1)  op(e1, e3) = e0
% 158.86/25.25    (2)   ~ (e3 = e2)
% 158.86/25.25    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.25    (4)  op(e1, e1) = e1
% 158.86/25.25    (5)   ~ (all_52_6 = e3)
% 158.86/25.25    (6)  op(e1, e2) = all_52_6
% 158.86/25.25    (7)  all_56_11 = e2
% 158.86/25.25    (8)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.86/25.25         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.86/25.25    (9)   ~ (e3 = e1)
% 158.86/25.25    (10)   ~ (e3 = e0)
% 158.86/25.25  
% 158.86/25.25  Begin of proof
% 158.86/25.25  | 
% 158.86/25.25  | BETA: splitting (8) gives:
% 158.86/25.25  | 
% 158.86/25.25  | Case 1:
% 158.86/25.25  | | 
% 158.86/25.25  | |   (11)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) =
% 158.86/25.25  | |           e3)
% 158.86/25.25  | | 
% 158.86/25.25  | | BETA: splitting (11) gives:
% 158.86/25.25  | | 
% 158.86/25.25  | | Case 1:
% 158.86/25.25  | | | 
% 158.86/25.25  | | |   (12)  all_56_6 = e3 & op(e1, e3) = e3
% 158.86/25.25  | | | 
% 158.86/25.25  | | | ALPHA: (12) implies:
% 158.86/25.25  | | |   (13)  op(e1, e3) = e3
% 158.86/25.25  | | | 
% 158.86/25.25  | | | REF_CLOSE: (1), (3), (10), (13) are inconsistent by sub-proof #913.
% 158.86/25.25  | | | 
% 158.86/25.25  | | Case 2:
% 158.86/25.25  | | | 
% 158.86/25.25  | | |   (14)  all_56_7 = e3 & op(e1, e2) = e3
% 158.86/25.25  | | | 
% 158.86/25.25  | | | REF_CLOSE: (3), (5), (6), (14) are inconsistent by sub-proof #388.
% 158.86/25.25  | | | 
% 158.86/25.25  | | End of split
% 158.86/25.25  | | 
% 158.86/25.25  | Case 2:
% 158.86/25.25  | | 
% 158.86/25.25  | |   (15)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) =
% 158.86/25.25  | |           e3)
% 158.86/25.25  | | 
% 158.86/25.25  | | BETA: splitting (15) gives:
% 158.86/25.25  | | 
% 158.86/25.25  | | Case 1:
% 158.86/25.25  | | | 
% 158.86/25.25  | | |   (16)  all_56_8 = e3 & op(e1, e1) = e3
% 158.86/25.25  | | | 
% 158.86/25.25  | | | ALPHA: (16) implies:
% 158.86/25.25  | | |   (17)  op(e1, e1) = e3
% 158.86/25.25  | | | 
% 158.86/25.25  | | | REF_CLOSE: (3), (4), (9), (17) are inconsistent by sub-proof #1003.
% 158.86/25.25  | | | 
% 158.86/25.25  | | Case 2:
% 158.86/25.25  | | | 
% 158.86/25.25  | | |   (18)  all_56_11 = e3 & op(e1, e0) = e3
% 158.86/25.25  | | | 
% 158.86/25.25  | | | ALPHA: (18) implies:
% 158.86/25.25  | | |   (19)  all_56_11 = e3
% 158.86/25.25  | | | 
% 158.86/25.25  | | | REF_CLOSE: (2), (7), (19) are inconsistent by sub-proof #319.
% 158.86/25.25  | | | 
% 158.86/25.25  | | End of split
% 158.86/25.25  | | 
% 158.86/25.25  | End of split
% 158.86/25.25  | 
% 158.86/25.25  End of proof
% 158.86/25.25  
% 158.86/25.25  Sub-proof #274 shows that the following formulas are inconsistent:
% 158.86/25.25  ----------------------------------------------------------------
% 158.86/25.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.25    (2)  op(e2, e2) = all_57_12
% 158.86/25.25    (3)   ~ (all_57_12 = e1)
% 158.86/25.25    (4)  all_57_5 = e2
% 158.86/25.25    (5)  (all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 158.86/25.25           all_57_5 & $i(all_57_5))
% 158.86/25.25  
% 158.86/25.25  Begin of proof
% 158.86/25.25  | 
% 158.86/25.25  | BETA: splitting (5) gives:
% 158.86/25.25  | 
% 158.86/25.25  | Case 1:
% 158.86/25.25  | | 
% 158.86/25.25  | |   (6)  all_57_12 = e1 & op(e2, e2) = e1
% 158.86/25.25  | | 
% 158.86/25.25  | | ALPHA: (6) implies:
% 158.86/25.25  | |   (7)  op(e2, e2) = e1
% 158.86/25.25  | | 
% 158.86/25.25  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #795.
% 158.86/25.25  | | 
% 158.86/25.25  | Case 2:
% 158.86/25.25  | | 
% 158.86/25.25  | |   (8)   ~ (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5)
% 158.86/25.25  | | 
% 158.86/25.25  | | ALPHA: (8) implies:
% 158.86/25.25  | |   (9)   ~ (all_57_5 = e2)
% 158.86/25.25  | | 
% 158.86/25.25  | | REDUCE: (4), (9) imply:
% 158.86/25.25  | |   (10)  $false
% 158.86/25.25  | | 
% 158.86/25.25  | | CLOSE: (10) is inconsistent.
% 158.86/25.25  | | 
% 158.86/25.25  | End of split
% 158.86/25.25  | 
% 158.86/25.25  End of proof
% 158.86/25.25  
% 158.86/25.25  Sub-proof #275 shows that the following formulas are inconsistent:
% 158.86/25.25  ----------------------------------------------------------------
% 158.86/25.25    (1)  all_56_2 = e3
% 158.86/25.25    (2)  all_56_2 = e0
% 158.86/25.25    (3)   ~ (e3 = e0)
% 158.86/25.25  
% 158.86/25.25  Begin of proof
% 158.86/25.25  | 
% 158.86/25.25  | COMBINE_EQS: (1), (2) imply:
% 158.86/25.25  |   (4)  e3 = e0
% 158.86/25.25  | 
% 158.86/25.25  | SIMP: (4) implies:
% 158.86/25.25  |   (5)  e3 = e0
% 158.86/25.25  | 
% 158.86/25.25  | REDUCE: (3), (5) imply:
% 158.86/25.25  |   (6)  $false
% 158.86/25.25  | 
% 158.86/25.25  | CLOSE: (6) is inconsistent.
% 158.86/25.25  | 
% 158.86/25.25  End of proof
% 158.86/25.25  
% 158.86/25.25  Sub-proof #276 shows that the following formulas are inconsistent:
% 158.86/25.25  ----------------------------------------------------------------
% 158.86/25.25    (1)   ~ (all_52_7 = e0)
% 158.86/25.25    (2)  op(e0, e1) = all_52_11
% 158.86/25.25    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.25    (4)  op(e0, e3) = all_52_3
% 158.86/25.25    (5)  op(e1, e1) = e1
% 158.86/25.25    (6)   ~ (all_52_3 = e0)
% 158.86/25.25    (7)  op(e0, e2) = all_52_7
% 158.86/25.25    (8)  op(e1, e0) = all_52_14
% 158.86/25.25    (9)   ~ (e1 = e0)
% 158.86/25.25    (10)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.86/25.25            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.86/25.25            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.86/25.25                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.86/25.25                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.86/25.25                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.86/25.25                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.86/25.25                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.86/25.25                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.86/25.25                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.86/25.25                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.86/25.25                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.86/25.25                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.86/25.25                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.86/25.25                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.86/25.25                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.86/25.25                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.25                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.86/25.25                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.25                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.86/25.25                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.25                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.86/25.25                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.86/25.25                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.86/25.25                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.86/25.25                op(e0, e1) = e0)))
% 158.86/25.25    (11)  op(e3, e3) = e2
% 158.86/25.25    (12)   ~ (all_52_11 = e0)
% 158.86/25.25    (13)   ~ (all_52_14 = e1)
% 158.86/25.25    (14)   ~ (e2 = e0)
% 158.86/25.25  
% 158.86/25.25  Begin of proof
% 158.86/25.25  | 
% 158.86/25.25  | BETA: splitting (10) gives:
% 158.86/25.25  | 
% 158.86/25.25  | Case 1:
% 158.86/25.25  | | 
% 158.86/25.25  | |   (15)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.86/25.25  | |         op(e1, e0) = e1
% 158.86/25.25  | | 
% 158.86/25.25  | | ALPHA: (15) implies:
% 158.86/25.25  | |   (16)  op(e1, e0) = e1
% 158.86/25.25  | | 
% 158.86/25.25  | | REF_CLOSE: (3), (8), (13), (16) are inconsistent by sub-proof #974.
% 158.86/25.25  | | 
% 158.86/25.25  | Case 2:
% 158.86/25.25  | | 
% 158.86/25.25  | |   (17)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9
% 158.86/25.25  | |             = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 158.86/25.25  | |             op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 158.86/25.25  | |             = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 158.86/25.25  | |             op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13
% 158.86/25.25  | |             = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 158.86/25.25  | |             op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15
% 158.86/25.25  | |             = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.86/25.25  | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 158.86/25.25  | |               e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 158.86/25.25  | |             & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.86/25.25  | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0
% 158.86/25.25  | |             & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 158.86/25.25  | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0
% 158.86/25.25  | |             & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 =
% 158.86/25.25  | |             e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.25  | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8
% 158.86/25.25  | |             = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.25  | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8
% 158.86/25.25  | |             = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.25  | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8
% 158.86/25.25  | |             = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.86/25.25  | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.86/25.25  | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 158.86/25.25  | |             & op(e0, e1) = e0))
% 158.86/25.25  | | 
% 158.86/25.25  | | ALPHA: (17) implies:
% 158.86/25.25  | |   (18)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.86/25.25  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.86/25.25  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 158.86/25.25  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.86/25.25  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.86/25.25  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) |
% 158.86/25.25  | |         (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.86/25.25  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.86/25.25  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.86/25.25  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.86/25.25  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.86/25.25  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.86/25.25  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 158.86/25.25  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 158.86/25.25  | |           & op(e0, e1) = e0)
% 158.86/25.25  | | 
% 158.86/25.25  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (14), (18)
% 158.86/25.25  | |            are inconsistent by sub-proof #277.
% 158.86/25.25  | | 
% 158.86/25.25  | End of split
% 158.86/25.25  | 
% 158.86/25.25  End of proof
% 158.86/25.25  
% 158.86/25.25  Sub-proof #277 shows that the following formulas are inconsistent:
% 158.86/25.25  ----------------------------------------------------------------
% 158.86/25.25    (1)   ~ (all_52_7 = e0)
% 158.86/25.25    (2)  op(e0, e1) = all_52_11
% 158.86/25.25    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.25    (4)  op(e0, e3) = all_52_3
% 158.86/25.25    (5)  op(e1, e1) = e1
% 158.86/25.25    (6)   ~ (all_52_3 = e0)
% 158.86/25.25    (7)  op(e0, e2) = all_52_7
% 158.86/25.25    (8)   ~ (e1 = e0)
% 158.86/25.25    (9)  op(e3, e3) = e2
% 158.86/25.25    (10)   ~ (all_52_11 = e0)
% 158.86/25.25    (11)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.86/25.25            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.86/25.25            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 158.86/25.25            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.86/25.25            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.86/25.25              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.86/25.25            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 158.86/25.25            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 158.86/25.25            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 158.86/25.25            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 158.86/25.25              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.86/25.25            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 158.86/25.25            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.86/25.25            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.86/25.25              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.86/25.25          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.25            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 158.86/25.25            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 158.86/25.25            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.86/25.25            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 158.86/25.25            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.86/25.25            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.86/25.25    (12)   ~ (e2 = e0)
% 158.86/25.25  
% 158.86/25.25  Begin of proof
% 158.86/25.25  | 
% 158.86/25.25  | BETA: splitting (11) gives:
% 158.86/25.25  | 
% 158.86/25.25  | Case 1:
% 158.86/25.25  | | 
% 158.86/25.25  | |   (13)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.86/25.25  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.86/25.25  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 158.86/25.25  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.86/25.25  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.86/25.25  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.25  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.86/25.25  | | 
% 158.86/25.25  | | BETA: splitting (13) gives:
% 158.86/25.25  | | 
% 158.86/25.25  | | Case 1:
% 158.86/25.25  | | | 
% 158.86/25.25  | | |   (14)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.86/25.26  | | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.86/25.26  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 158.86/25.26  | | | 
% 158.86/25.26  | | | REF_CLOSE: (3), (4), (5), (6), (8), (14) are inconsistent by sub-proof
% 158.86/25.26  | | |            #821.
% 158.86/25.26  | | | 
% 158.86/25.26  | | Case 2:
% 158.86/25.26  | | | 
% 158.86/25.26  | | |   (15)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0)
% 158.86/25.26  | | |         | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.86/25.26  | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.86/25.26  | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.86/25.26  | | | 
% 158.86/25.26  | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (12), (15) are inconsistent by
% 158.86/25.26  | | |            sub-proof #280.
% 158.86/25.26  | | | 
% 158.86/25.26  | | End of split
% 158.86/25.26  | | 
% 158.86/25.26  | Case 2:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (16)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.86/25.26  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.86/25.26  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.86/25.26  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.86/25.26  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.86/25.26  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.86/25.26  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 158.86/25.26  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 158.86/25.26  | |           & op(e0, e1) = e0)
% 158.86/25.26  | | 
% 158.86/25.26  | | BETA: splitting (16) gives:
% 158.86/25.26  | | 
% 158.86/25.26  | | Case 1:
% 158.86/25.26  | | | 
% 158.86/25.26  | | |   (17)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.86/25.26  | | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.86/25.26  | | |         | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 158.86/25.26  | | |             = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.86/25.26  | | | 
% 158.86/25.26  | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (12), (17) are inconsistent by
% 158.86/25.26  | | |            sub-proof #278.
% 158.86/25.26  | | | 
% 158.86/25.26  | | Case 2:
% 158.86/25.26  | | | 
% 158.86/25.26  | | |   (18)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 158.86/25.26  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.86/25.26  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.86/25.26  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.86/25.26  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 158.86/25.26  | | |             e0) & op(e0, e1) = e0)
% 158.86/25.26  | | | 
% 158.86/25.26  | | | REF_CLOSE: (2), (3), (5), (8), (10), (18) are inconsistent by sub-proof
% 158.86/25.26  | | |            #820.
% 158.86/25.26  | | | 
% 158.86/25.26  | | End of split
% 158.86/25.26  | | 
% 158.86/25.26  | End of split
% 158.86/25.26  | 
% 158.86/25.26  End of proof
% 158.86/25.26  
% 158.86/25.26  Sub-proof #278 shows that the following formulas are inconsistent:
% 158.86/25.26  ----------------------------------------------------------------
% 158.86/25.26    (1)   ~ (all_52_7 = e0)
% 158.86/25.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.26    (3)  op(e1, e1) = e1
% 158.86/25.26    (4)  op(e0, e2) = all_52_7
% 158.86/25.26    (5)   ~ (e1 = e0)
% 158.86/25.26    (6)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.86/25.26           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.86/25.26           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.86/25.26           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 158.86/25.26           & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.86/25.26    (7)  op(e3, e3) = e2
% 158.86/25.26    (8)   ~ (e2 = e0)
% 158.86/25.26  
% 158.86/25.26  Begin of proof
% 158.86/25.26  | 
% 158.86/25.26  | BETA: splitting (6) gives:
% 158.86/25.26  | 
% 158.86/25.26  | Case 1:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (9)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 158.86/25.26  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 158.86/25.26  | | 
% 158.86/25.26  | | ALPHA: (9) implies:
% 158.86/25.26  | |   (10)  op(e1, e1) = e0
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #903.
% 158.86/25.26  | | 
% 158.86/25.26  | Case 2:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (11)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.86/25.26  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (1), (2), (4), (7), (8), (11) are inconsistent by sub-proof #279.
% 158.86/25.26  | | 
% 158.86/25.26  | End of split
% 158.86/25.26  | 
% 158.86/25.26  End of proof
% 158.86/25.26  
% 158.86/25.26  Sub-proof #279 shows that the following formulas are inconsistent:
% 158.86/25.26  ----------------------------------------------------------------
% 158.86/25.26    (1)   ~ (all_52_7 = e0)
% 158.86/25.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.26    (3)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.86/25.26         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.26           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.86/25.26    (4)  op(e0, e2) = all_52_7
% 158.86/25.26    (5)  op(e3, e3) = e2
% 158.86/25.26    (6)   ~ (e2 = e0)
% 158.86/25.26  
% 158.86/25.26  Begin of proof
% 158.86/25.26  | 
% 158.86/25.26  | BETA: splitting (3) gives:
% 158.86/25.26  | 
% 158.86/25.26  | Case 1:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (7)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 158.86/25.26  | | 
% 158.86/25.26  | | ALPHA: (7) implies:
% 158.86/25.26  | |   (8)  op(e0, e2) = e0
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #969.
% 158.86/25.26  | | 
% 158.86/25.26  | Case 2:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (9)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 158.86/25.26  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 158.86/25.26  | | 
% 158.86/25.26  | | ALPHA: (9) implies:
% 158.86/25.26  | |   (10)  op(e3, e3) = e0
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #281.
% 158.86/25.26  | | 
% 158.86/25.26  | End of split
% 158.86/25.26  | 
% 158.86/25.26  End of proof
% 158.86/25.26  
% 158.86/25.26  Sub-proof #280 shows that the following formulas are inconsistent:
% 158.86/25.26  ----------------------------------------------------------------
% 158.86/25.26    (1)   ~ (all_52_7 = e0)
% 158.86/25.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.26    (3)  op(e0, e3) = all_52_3
% 158.86/25.26    (4)   ~ (all_52_3 = e0)
% 158.86/25.26    (5)  op(e0, e2) = all_52_7
% 158.86/25.26    (6)  op(e3, e3) = e2
% 158.86/25.26    (7)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.86/25.26         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.86/25.26           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.86/25.26           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 158.86/25.26           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.86/25.26    (8)   ~ (e2 = e0)
% 158.86/25.26  
% 158.86/25.26  Begin of proof
% 158.86/25.26  | 
% 158.86/25.26  | BETA: splitting (7) gives:
% 158.86/25.26  | 
% 158.86/25.26  | Case 1:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (9)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 158.86/25.26  | | 
% 158.86/25.26  | | ALPHA: (9) implies:
% 158.86/25.26  | |   (10)  op(e0, e3) = e0
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #973.
% 158.86/25.26  | | 
% 158.86/25.26  | Case 2:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (11)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 158.86/25.26  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.86/25.26  | | 
% 158.86/25.26  | | BETA: splitting (11) gives:
% 158.86/25.26  | | 
% 158.86/25.26  | | Case 1:
% 158.86/25.26  | | | 
% 158.86/25.26  | | |   (12)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | | |           e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 158.86/25.26  | | | 
% 158.86/25.26  | | | ALPHA: (12) implies:
% 158.86/25.26  | | |   (13)  op(e3, e3) = e0
% 158.86/25.26  | | | 
% 158.86/25.26  | | | REF_CLOSE: (2), (6), (8), (13) are inconsistent by sub-proof #281.
% 158.86/25.26  | | | 
% 158.86/25.26  | | Case 2:
% 158.86/25.26  | | | 
% 158.86/25.26  | | |   (14)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.86/25.26  | | |           e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 158.86/25.26  | | | 
% 158.86/25.26  | | | ALPHA: (14) implies:
% 158.86/25.26  | | |   (15)  op(e0, e2) = e0
% 158.86/25.26  | | | 
% 158.86/25.26  | | | REF_CLOSE: (1), (2), (5), (15) are inconsistent by sub-proof #969.
% 158.86/25.26  | | | 
% 158.86/25.26  | | End of split
% 158.86/25.26  | | 
% 158.86/25.26  | End of split
% 158.86/25.26  | 
% 158.86/25.26  End of proof
% 158.86/25.26  
% 158.86/25.26  Sub-proof #281 shows that the following formulas are inconsistent:
% 158.86/25.26  ----------------------------------------------------------------
% 158.86/25.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.26    (2)  op(e3, e3) = e2
% 158.86/25.26    (3)  op(e3, e3) = e0
% 158.86/25.26    (4)   ~ (e2 = e0)
% 158.86/25.26  
% 158.86/25.26  Begin of proof
% 158.86/25.26  | 
% 158.86/25.26  | GROUND_INST: instantiating (1) with e2, e0, e3, e3, simplifying with (2), (3)
% 158.86/25.26  |              gives:
% 158.86/25.26  |   (5)  e2 = e0
% 158.86/25.26  | 
% 158.86/25.26  | REDUCE: (4), (5) imply:
% 158.86/25.26  |   (6)  $false
% 158.86/25.26  | 
% 158.86/25.26  | CLOSE: (6) is inconsistent.
% 158.86/25.26  | 
% 158.86/25.26  End of proof
% 158.86/25.26  
% 158.86/25.26  Sub-proof #282 shows that the following formulas are inconsistent:
% 158.86/25.26  ----------------------------------------------------------------
% 158.86/25.26    (1)   ~ (e3 = e2)
% 158.86/25.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.26    (3)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.86/25.26           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 158.86/25.26           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 158.86/25.26           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 158.86/25.26    (4)  op(e0, e0) = e0
% 158.86/25.26    (5)  op(e3, e3) = e2
% 158.86/25.26    (6)   ~ (e2 = e0)
% 158.86/25.26  
% 158.86/25.26  Begin of proof
% 158.86/25.26  | 
% 158.86/25.26  | BETA: splitting (3) gives:
% 158.86/25.26  | 
% 158.86/25.26  | Case 1:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (7)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 158.86/25.26  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.86/25.26  | |          e0) = e2 & $i(all_57_12)
% 158.86/25.26  | | 
% 158.86/25.26  | | ALPHA: (7) implies:
% 158.86/25.26  | |   (8)  op(e0, e0) = e2
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #979.
% 158.86/25.26  | | 
% 158.86/25.26  | Case 2:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (9)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 158.86/25.26  | |        op(e3, e0) = e3
% 158.86/25.26  | | 
% 158.86/25.26  | | ALPHA: (9) implies:
% 158.86/25.26  | |   (10)  op(e3, e3) = e3
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #958.
% 158.86/25.26  | | 
% 158.86/25.26  | End of split
% 158.86/25.26  | 
% 158.86/25.26  End of proof
% 158.86/25.26  
% 158.86/25.26  Sub-proof #283 shows that the following formulas are inconsistent:
% 158.86/25.26  ----------------------------------------------------------------
% 158.86/25.26    (1)   ~ (e3 = e2)
% 158.86/25.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.26    (3)  op(e0, e0) = e0
% 158.86/25.26    (4)  op(e3, e3) = e2
% 158.86/25.26    (5)   ~ (e2 = e1)
% 158.86/25.26    (6)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.86/25.26           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.86/25.26           = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1)
% 158.86/25.26           & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 158.86/25.26           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 158.86/25.26           e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.86/25.26    (7)   ~ (e3 = e0)
% 158.86/25.26  
% 158.86/25.26  Begin of proof
% 158.86/25.26  | 
% 158.86/25.26  | BETA: splitting (6) gives:
% 158.86/25.26  | 
% 158.86/25.26  | Case 1:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (8)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1)
% 158.86/25.26  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.86/25.26  | |          e0) = e3 & $i(all_57_10)
% 158.86/25.26  | | 
% 158.86/25.26  | | ALPHA: (8) implies:
% 158.86/25.26  | |   (9)  op(e0, e0) = e3
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (2), (3), (7), (9) are inconsistent by sub-proof #999.
% 158.86/25.26  | | 
% 158.86/25.26  | Case 2:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (10)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.86/25.26  | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 =
% 158.86/25.26  | |           e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.86/25.26  | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (1), (2), (4), (5), (10) are inconsistent by sub-proof #284.
% 158.86/25.26  | | 
% 158.86/25.26  | End of split
% 158.86/25.26  | 
% 158.86/25.26  End of proof
% 158.86/25.26  
% 158.86/25.26  Sub-proof #284 shows that the following formulas are inconsistent:
% 158.86/25.26  ----------------------------------------------------------------
% 158.86/25.26    (1)   ~ (e3 = e2)
% 158.86/25.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.26    (3)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 158.86/25.26             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.86/25.26           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.86/25.26           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.86/25.26    (4)  op(e3, e3) = e2
% 158.86/25.26    (5)   ~ (e2 = e1)
% 158.86/25.26  
% 158.86/25.26  Begin of proof
% 158.86/25.26  | 
% 158.86/25.26  | BETA: splitting (3) gives:
% 158.86/25.26  | 
% 158.86/25.26  | Case 1:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (6)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.86/25.26  | |        op(e3, e1) = e3
% 158.86/25.26  | | 
% 158.86/25.26  | | ALPHA: (6) implies:
% 158.86/25.26  | |   (7)  op(e3, e3) = e3
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #958.
% 158.86/25.26  | | 
% 158.86/25.26  | Case 2:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (8)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 158.86/25.26  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 158.86/25.26  | |          e0) = e1 & $i(all_57_14)
% 158.86/25.26  | | 
% 158.86/25.26  | | ALPHA: (8) implies:
% 158.86/25.26  | |   (9)  op(e3, e3) = e1
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #828.
% 158.86/25.26  | | 
% 158.86/25.26  | End of split
% 158.86/25.26  | 
% 158.86/25.26  End of proof
% 158.86/25.26  
% 158.86/25.26  Sub-proof #285 shows that the following formulas are inconsistent:
% 158.86/25.26  ----------------------------------------------------------------
% 158.86/25.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.26    (2)  op(e2, e2) = e2
% 158.86/25.26    (3)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 158.86/25.26           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.86/25.26           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 158.86/25.26           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 158.86/25.26             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.86/25.26    (4)  op(e3, e3) = e2
% 158.86/25.26    (5)   ~ (e2 = e1)
% 158.86/25.26  
% 158.86/25.26  Begin of proof
% 158.86/25.26  | 
% 158.86/25.26  | BETA: splitting (3) gives:
% 158.86/25.26  | 
% 158.86/25.26  | Case 1:
% 158.86/25.26  | | 
% 158.86/25.26  | |   (6)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 158.86/25.26  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 158.86/25.26  | |        all_57_14 & $i(all_57_14)
% 158.86/25.26  | | 
% 158.86/25.26  | | ALPHA: (6) implies:
% 158.86/25.26  | |   (7)  op(e3, e3) = e1
% 158.86/25.26  | | 
% 158.86/25.26  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #828.
% 158.86/25.26  | | 
% 158.86/25.26  | Case 2:
% 158.86/25.26  | | 
% 158.86/25.27  | |   (8)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 158.86/25.27  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.86/25.27  | |        all_57_14 & $i(all_57_14)
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (8) implies:
% 158.86/25.27  | |   (9)  op(e2, e2) = e1
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #993.
% 158.86/25.27  | | 
% 158.86/25.27  | End of split
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #286 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.27    (2)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.86/25.27           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.86/25.27           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 158.86/25.27           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 158.86/25.27           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.86/25.27    (3)  op(e2, e0) = all_52_13
% 158.86/25.27    (4)  op(e3, e3) = e2
% 158.86/25.27    (5)   ~ (e2 = e1)
% 158.86/25.27    (6)   ~ (all_52_13 = e2)
% 158.86/25.27  
% 158.86/25.27  Begin of proof
% 158.86/25.27  | 
% 158.86/25.27  | BETA: splitting (2) gives:
% 158.86/25.27  | 
% 158.86/25.27  | Case 1:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (7)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 158.86/25.27  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.86/25.27  | |          e0) = e2 & $i(all_57_12)
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (7) implies:
% 158.86/25.27  | |   (8)  op(e2, e0) = e2
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #996.
% 158.86/25.27  | | 
% 158.86/25.27  | Case 2:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (9)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 158.86/25.27  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.86/25.27  | |        all_57_14 & $i(all_57_14)
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (9) implies:
% 158.86/25.27  | |   (10)  op(e3, e3) = e1
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #828.
% 158.86/25.27  | | 
% 158.86/25.27  | End of split
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #287 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.27    (2)  op(e0, e0) = e0
% 158.86/25.27    (3)  op(e3, e3) = e2
% 158.86/25.27    (4)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 158.86/25.27           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.86/25.27           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 158.86/25.27           & op(e3, e3) = e3 & op(e3, e2) = e3)
% 158.86/25.27    (5)   ~ (e3 = e0)
% 158.86/25.27  
% 158.86/25.27  Begin of proof
% 158.86/25.27  | 
% 158.86/25.27  | BETA: splitting (4) gives:
% 158.86/25.27  | 
% 158.86/25.27  | Case 1:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (6)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 158.86/25.27  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 158.86/25.27  | |          e0) = e3 & $i(all_57_10)
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (6) implies:
% 158.86/25.27  | |   (7)  op(e0, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #999.
% 158.86/25.27  | | 
% 158.86/25.27  | Case 2:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (8)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 158.86/25.27  | |        op(e3, e2) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (8) implies:
% 158.86/25.27  | |   (9)   ~ (e3 = e2)
% 158.86/25.27  | |   (10)  op(e3, e3) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (3), (9), (10) are inconsistent by sub-proof #958.
% 158.86/25.27  | | 
% 158.86/25.27  | End of split
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #288 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)   ~ (all_14_1 = e3) & op(e1, e1) = all_14_1 & $i(all_14_1)
% 158.86/25.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.27    (3)  op(e1, e1) = e3
% 158.86/25.27  
% 158.86/25.27  Begin of proof
% 158.86/25.27  | 
% 158.86/25.27  | ALPHA: (1) implies:
% 158.86/25.27  |   (4)   ~ (all_14_1 = e3)
% 158.86/25.27  |   (5)  op(e1, e1) = all_14_1
% 158.86/25.27  | 
% 158.86/25.27  | GROUND_INST: instantiating (2) with e3, all_14_1, e1, e1, simplifying with
% 158.86/25.27  |              (3), (5) gives:
% 158.86/25.27  |   (6)  all_14_1 = e3
% 158.86/25.27  | 
% 158.86/25.27  | REDUCE: (4), (6) imply:
% 158.86/25.27  |   (7)  $false
% 158.86/25.27  | 
% 158.86/25.27  | CLOSE: (7) is inconsistent.
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #289 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)  op(e0, e0) = e1
% 158.86/25.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.27    (3)  op(e1, e0) = e0
% 158.86/25.27    (4)  op(e0, e0) = all_57_15
% 158.86/25.27    (5)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.86/25.27           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.86/25.27           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.86/25.27           op(e0, e1) = e0)
% 158.86/25.27    (6)  op(e0, e0) = all_14_2
% 158.86/25.27    (7)   ~ (e1 = e0)
% 158.86/25.27  
% 158.86/25.27  Begin of proof
% 158.86/25.27  | 
% 158.86/25.27  | BETA: splitting (5) gives:
% 158.86/25.27  | 
% 158.86/25.27  | Case 1:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (8)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 158.86/25.27  | |        & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.86/25.27  | |        $i(all_57_14)
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (8) implies:
% 158.86/25.27  | |   (9)  op(e1, e0) = e1
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (2), (3), (7), (9) are inconsistent by sub-proof #545.
% 158.86/25.27  | | 
% 158.86/25.27  | Case 2:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (10)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (10) implies:
% 158.86/25.27  | |   (11)  all_57_15 = e0
% 158.86/25.27  | | 
% 158.86/25.27  | | REDUCE: (4), (11) imply:
% 158.86/25.27  | |   (12)  op(e0, e0) = e0
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (2), (6), (7), (12) are inconsistent by sub-proof #991.
% 158.86/25.27  | | 
% 158.86/25.27  | End of split
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #290 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)  op(e0, e0) = e1
% 158.86/25.27    (2)  op(e0, e1) = all_52_11
% 158.86/25.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.27    (4)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.86/25.27    (5)   ~ (e3 = e1)
% 158.86/25.27    (6)   ~ (all_52_11 = e3)
% 158.86/25.27  
% 158.86/25.27  Begin of proof
% 158.86/25.27  | 
% 158.86/25.27  | BETA: splitting (4) gives:
% 158.86/25.27  | 
% 158.86/25.27  | Case 1:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (7)  all_56_14 = e3 & op(e0, e1) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (7) implies:
% 158.86/25.27  | |   (8)  op(e0, e1) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #720.
% 158.86/25.27  | | 
% 158.86/25.27  | Case 2:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (9)  all_56_15 = e3 & op(e0, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (9) implies:
% 158.86/25.27  | |   (10)  op(e0, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #473.
% 158.86/25.27  | | 
% 158.86/25.27  | End of split
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #291 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)  op(e0, e0) = e1
% 158.86/25.27    (2)   ~ (all_52_14 = e3)
% 158.86/25.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.27    (4)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.86/25.27    (5)  op(e1, e0) = all_52_14
% 158.86/25.27    (6)   ~ (e3 = e1)
% 158.86/25.27  
% 158.86/25.27  Begin of proof
% 158.86/25.27  | 
% 158.86/25.27  | BETA: splitting (4) gives:
% 158.86/25.27  | 
% 158.86/25.27  | Case 1:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (7)  all_56_11 = e3 & op(e1, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (7) implies:
% 158.86/25.27  | |   (8)  op(e1, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #677.
% 158.86/25.27  | | 
% 158.86/25.27  | Case 2:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (9)  all_56_15 = e3 & op(e0, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (9) implies:
% 158.86/25.27  | |   (10)  op(e0, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #473.
% 158.86/25.27  | | 
% 158.86/25.27  | End of split
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #292 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)  op(e0, e0) = e1
% 158.86/25.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.27    (3)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.86/25.27    (4)  op(e1, e0) = e0
% 158.86/25.27    (5)   ~ (e2 = e1)
% 158.86/25.27    (6)   ~ (e2 = e0)
% 158.86/25.27  
% 158.86/25.27  Begin of proof
% 158.86/25.27  | 
% 158.86/25.27  | BETA: splitting (3) gives:
% 158.86/25.27  | 
% 158.86/25.27  | Case 1:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (7)  all_56_11 = e2 & op(e1, e0) = e2
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (7) implies:
% 158.86/25.27  | |   (8)  op(e1, e0) = e2
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #397.
% 158.86/25.27  | | 
% 158.86/25.27  | Case 2:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (9)  all_56_15 = e2 & op(e0, e0) = e2
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (9) implies:
% 158.86/25.27  | |   (10)  op(e0, e0) = e2
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #875.
% 158.86/25.27  | | 
% 158.86/25.27  | End of split
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #293 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)  op(e0, e0) = e1
% 158.86/25.27    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.86/25.27         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.86/25.27    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.86/25.27         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.86/25.27    (4)   ~ (e3 = e2)
% 158.86/25.27    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.27    (6)  op(e1, e0) = e0
% 158.86/25.27    (7)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.86/25.27         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.86/25.27    (8)  op(e3, e3) = e3
% 158.86/25.27    (9)  all_56_10 = e1 & op(e2, e0) = e1
% 158.86/25.27    (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.86/25.27          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.86/25.27    (11)   ~ (e1 = e0)
% 158.86/25.27    (12)   ~ (e2 = e1)
% 158.86/25.27    (13)   ~ (e3 = e1)
% 158.86/25.27    (14)   ~ (e2 = e0)
% 158.86/25.27    (15)   ~ (e3 = e0)
% 158.86/25.27  
% 158.86/25.27  Begin of proof
% 158.86/25.27  | 
% 158.86/25.27  | ALPHA: (9) implies:
% 158.86/25.27  |   (16)  all_56_10 = e1
% 158.86/25.27  | 
% 158.86/25.27  | BETA: splitting (7) gives:
% 158.86/25.27  | 
% 158.86/25.27  | Case 1:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (17)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 158.86/25.27  | |           e3)
% 158.86/25.27  | | 
% 158.86/25.27  | | BETA: splitting (17) gives:
% 158.86/25.27  | | 
% 158.86/25.27  | | Case 1:
% 158.86/25.27  | | | 
% 158.86/25.27  | | |   (18)  all_56_9 = e3 & op(e3, e0) = e3
% 158.86/25.27  | | | 
% 158.86/25.27  | | | ALPHA: (18) implies:
% 158.86/25.27  | | |   (19)  all_56_9 = e3
% 158.86/25.27  | | | 
% 158.86/25.27  | | | REF_CLOSE: (2), (3), (4), (5), (8), (10), (11), (12), (13), (14), (15),
% 158.86/25.27  | | |            (19) are inconsistent by sub-proof #632.
% 158.86/25.27  | | | 
% 158.86/25.27  | | Case 2:
% 158.86/25.27  | | | 
% 158.86/25.27  | | |   (20)  all_56_10 = e3 & op(e2, e0) = e3
% 158.86/25.27  | | | 
% 158.86/25.27  | | | REF_CLOSE: (13), (16), (20) are inconsistent by sub-proof #295.
% 158.86/25.27  | | | 
% 158.86/25.27  | | End of split
% 158.86/25.27  | | 
% 158.86/25.27  | Case 2:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (21)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.86/25.27  | |           e3)
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (5), (6), (13), (15), (21) are inconsistent by sub-proof
% 158.86/25.27  | |            #294.
% 158.86/25.27  | | 
% 158.86/25.27  | End of split
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #294 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)  op(e0, e0) = e1
% 158.86/25.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.27    (3)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.86/25.27    (4)  op(e1, e0) = e0
% 158.86/25.27    (5)   ~ (e3 = e1)
% 158.86/25.27    (6)   ~ (e3 = e0)
% 158.86/25.27  
% 158.86/25.27  Begin of proof
% 158.86/25.27  | 
% 158.86/25.27  | BETA: splitting (3) gives:
% 158.86/25.27  | 
% 158.86/25.27  | Case 1:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (7)  all_56_11 = e3 & op(e1, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (7) implies:
% 158.86/25.27  | |   (8)  op(e1, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #314.
% 158.86/25.27  | | 
% 158.86/25.27  | Case 2:
% 158.86/25.27  | | 
% 158.86/25.27  | |   (9)  all_56_15 = e3 & op(e0, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | ALPHA: (9) implies:
% 158.86/25.27  | |   (10)  op(e0, e0) = e3
% 158.86/25.27  | | 
% 158.86/25.27  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #473.
% 158.86/25.27  | | 
% 158.86/25.27  | End of split
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #295 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)  all_56_10 = e3 & op(e2, e0) = e3
% 158.86/25.27    (2)  all_56_10 = e1
% 158.86/25.27    (3)   ~ (e3 = e1)
% 158.86/25.27  
% 158.86/25.27  Begin of proof
% 158.86/25.27  | 
% 158.86/25.27  | ALPHA: (1) implies:
% 158.86/25.27  |   (4)  all_56_10 = e3
% 158.86/25.27  | 
% 158.86/25.27  | COMBINE_EQS: (2), (4) imply:
% 158.86/25.27  |   (5)  e3 = e1
% 158.86/25.27  | 
% 158.86/25.27  | REDUCE: (3), (5) imply:
% 158.86/25.27  |   (6)  $false
% 158.86/25.27  | 
% 158.86/25.27  | CLOSE: (6) is inconsistent.
% 158.86/25.27  | 
% 158.86/25.27  End of proof
% 158.86/25.27  
% 158.86/25.27  Sub-proof #296 shows that the following formulas are inconsistent:
% 158.86/25.27  ----------------------------------------------------------------
% 158.86/25.27    (1)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.86/25.27    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.86/25.27         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.86/25.27    (3)  op(e0, e0) = e1
% 158.86/25.27    (4)  all_54_9 = all_52_6
% 158.86/25.27    (5)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.86/25.27         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.86/25.27    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.86/25.27         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.86/25.27    (7)   ~ (all_52_4 = e3)
% 158.86/25.27    (8)  op(e1, e1) = e3
% 158.86/25.28    (9)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.86/25.28             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.86/25.28           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.86/25.28               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.86/25.28             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.86/25.28         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.86/25.28             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.86/25.28           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.86/25.28               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.86/25.28             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.86/25.28         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.86/25.28             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.86/25.28           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.86/25.28               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.86/25.28             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.86/25.28         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.86/25.28             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.86/25.28           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.86/25.28               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.86/25.28             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.86/25.28    (10)   ~ (all_52_4 = all_52_6)
% 158.86/25.28    (11)  all_56_9 = e2
% 158.86/25.28    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.28    (13)  all_56_11 = e0
% 158.86/25.28    (14)  op(e0, e3) = all_52_3
% 158.86/25.28    (15)  op(e3, e1) = all_52_8
% 158.86/25.28    (16)   ~ (all_52_6 = e0)
% 158.86/25.28    (17)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.86/25.28              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 158.86/25.28                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.86/25.28                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.86/25.28    (18)   ~ (all_52_6 = e3)
% 158.86/25.28    (19)  op(e1, e3) = all_52_2
% 158.86/25.28    (20)  all_54_1 = all_52_4
% 158.86/25.28    (21)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.86/25.28    (22)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.86/25.28          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.86/25.28    (23)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 158.86/25.28          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 158.86/25.28    (24)   ~ (all_52_2 = all_52_6)
% 158.86/25.28    (25)  op(e2, e2) = e0
% 158.86/25.28    (26)  op(e0, e0) = all_14_2
% 158.86/25.28    (27)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.86/25.28          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.86/25.28    (28)   ~ (e1 = e0)
% 158.86/25.28    (29)  all_56_14 = e2
% 158.86/25.28    (30)  all_56_13 = e3
% 158.86/25.28    (31)   ~ (all_52_8 = e2)
% 158.86/25.28    (32)   ~ (all_52_4 = e0)
% 158.86/25.28    (33)   ~ (e3 = e1)
% 158.86/25.28    (34)   ~ (all_52_4 = e2)
% 158.86/25.28    (35)   ~ (e2 = e0)
% 158.86/25.28    (36)   ~ (e3 = e0)
% 158.86/25.28    (37)  all_56_4 = e0
% 158.86/25.28  
% 158.86/25.28  Begin of proof
% 158.86/25.28  | 
% 158.86/25.28  | BETA: splitting (21) gives:
% 158.86/25.28  | 
% 158.86/25.28  | Case 1:
% 158.86/25.28  | | 
% 158.86/25.28  | |   (38)  all_54_1 = e3
% 158.86/25.28  | | 
% 158.86/25.28  | | REF_CLOSE: (7), (20), (38) are inconsistent by sub-proof #299.
% 158.86/25.28  | | 
% 158.86/25.28  | Case 2:
% 158.86/25.28  | | 
% 158.86/25.28  | |   (39)   ~ (all_54_1 = e3)
% 158.86/25.28  | |   (40)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.86/25.28  | | 
% 158.86/25.28  | | BETA: splitting (9) gives:
% 158.86/25.28  | | 
% 158.86/25.28  | | Case 1:
% 158.86/25.28  | | | 
% 158.86/25.28  | | |   (41)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2)
% 158.86/25.28  | | |               = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.86/25.28  | | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.86/25.28  | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.86/25.28  | | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 158.86/25.28  | | |               op(e0, e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 &
% 158.86/25.28  | | |           op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 158.86/25.28  | | |               (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.86/25.28  | | |           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 158.86/25.28  | | |               op(e1, e2) = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 &
% 158.86/25.28  | | |               op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 158.86/25.28  | | |               all_57_7 & $i(all_57_7))))
% 158.86/25.28  | | | 
% 158.86/25.28  | | | BETA: splitting (41) gives:
% 158.86/25.28  | | | 
% 158.86/25.28  | | | Case 1:
% 158.86/25.28  | | | | 
% 158.86/25.28  | | | |   (42)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2)
% 158.86/25.28  | | | |             = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.86/25.28  | | | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 158.86/25.28  | | | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 158.86/25.28  | | | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 158.86/25.28  | | | |             op(e0, e3) = all_57_6 & $i(all_57_6)))
% 158.86/25.28  | | | | 
% 158.86/25.28  | | | | ALPHA: (42) implies:
% 158.86/25.28  | | | |   (43)  op(e3, e3) = e3
% 158.86/25.28  | | | |   (44)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 158.86/25.28  | | | |           op(e2, e3) = all_57_0 & $i(all_57_0))
% 158.86/25.28  | | | | 
% 158.86/25.28  | | | | BETA: splitting (44) gives:
% 158.86/25.28  | | | | 
% 158.86/25.28  | | | | Case 1:
% 158.86/25.28  | | | | | 
% 158.86/25.28  | | | | |   (45)  all_57_12 = e3 & op(e2, e2) = e3
% 158.86/25.28  | | | | | 
% 158.86/25.28  | | | | | ALPHA: (45) implies:
% 158.86/25.28  | | | | |   (46)  op(e2, e2) = e3
% 158.86/25.28  | | | | | 
% 158.86/25.28  | | | | | REF_CLOSE: (12), (25), (36), (46) are inconsistent by sub-proof #945.
% 158.86/25.28  | | | | | 
% 158.86/25.28  | | | | Case 2:
% 158.86/25.28  | | | | | 
% 158.86/25.28  | | | | |   (47)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0)
% 158.86/25.28  | | | | | 
% 158.86/25.28  | | | | | ALPHA: (47) implies:
% 158.86/25.28  | | | | |   (48)   ~ (all_57_0 = e2)
% 158.86/25.28  | | | | |   (49)  op(e2, e3) = all_57_0
% 158.86/25.28  | | | | | 
% 158.86/25.28  | | | | | BETA: splitting (40) gives:
% 158.86/25.28  | | | | | 
% 158.86/25.28  | | | | | Case 1:
% 158.86/25.28  | | | | | | 
% 158.86/25.28  | | | | | |   (50)  all_54_1 = e2
% 158.86/25.28  | | | | | | 
% 158.86/25.28  | | | | | | COMBINE_EQS: (20), (50) imply:
% 158.86/25.28  | | | | | |   (51)  all_52_4 = e2
% 158.86/25.28  | | | | | | 
% 158.86/25.28  | | | | | | REDUCE: (34), (51) imply:
% 158.86/25.28  | | | | | |   (52)  $false
% 158.86/25.28  | | | | | | 
% 158.86/25.28  | | | | | | CLOSE: (52) is inconsistent.
% 158.86/25.28  | | | | | | 
% 158.86/25.28  | | | | | Case 2:
% 158.86/25.28  | | | | | | 
% 158.86/25.28  | | | | | |   (53)  all_54_1 = e1 | all_54_1 = e0
% 158.86/25.28  | | | | | | 
% 158.86/25.28  | | | | | | BETA: splitting (53) gives:
% 158.86/25.28  | | | | | | 
% 158.86/25.28  | | | | | | Case 1:
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | |   (54)  all_54_1 = e1
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | | COMBINE_EQS: (20), (54) imply:
% 158.86/25.28  | | | | | | |   (55)  all_52_4 = e1
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | | REDUCE: (10), (55) imply:
% 158.86/25.28  | | | | | | |   (56)   ~ (all_52_6 = e1)
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | | SIMP: (56) implies:
% 158.86/25.28  | | | | | | |   (57)   ~ (all_52_6 = e1)
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | | REDUCE: (7), (55) imply:
% 158.86/25.28  | | | | | | |   (58)   ~ (e3 = e1)
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | | BETA: splitting (1) gives:
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | | Case 1:
% 158.86/25.28  | | | | | | | | 
% 158.86/25.28  | | | | | | | |   (59)  all_54_9 = e3
% 158.86/25.28  | | | | | | | | 
% 158.86/25.28  | | | | | | | | REF_CLOSE: (4), (18), (59) are inconsistent by sub-proof #656.
% 158.86/25.28  | | | | | | | | 
% 158.86/25.28  | | | | | | | Case 2:
% 158.86/25.28  | | | | | | | | 
% 158.86/25.28  | | | | | | | |   (60)   ~ (all_54_9 = e3)
% 158.86/25.28  | | | | | | | |   (61)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.86/25.28  | | | | | | | | 
% 158.86/25.28  | | | | | | | | BETA: splitting (61) gives:
% 158.86/25.28  | | | | | | | | 
% 158.86/25.28  | | | | | | | | Case 1:
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | |   (62)  all_54_9 = e2
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | COMBINE_EQS: (4), (62) imply:
% 158.86/25.28  | | | | | | | | |   (63)  all_52_6 = e2
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | SIMP: (63) implies:
% 158.86/25.28  | | | | | | | | |   (64)  all_52_6 = e2
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | REDUCE: (24), (64) imply:
% 158.86/25.28  | | | | | | | | |   (65)   ~ (all_52_2 = e2)
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | REDUCE: (18), (64) imply:
% 158.86/25.28  | | | | | | | | |   (66)   ~ (e3 = e2)
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | SIMP: (66) implies:
% 158.86/25.28  | | | | | | | | |   (67)   ~ (e3 = e2)
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | REDUCE: (57), (64) imply:
% 158.86/25.28  | | | | | | | | |   (68)   ~ (e2 = e1)
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | BETA: splitting (17) gives:
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | Case 1:
% 158.86/25.28  | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | |   (69)  all_56_15 = e0 & op(e0, e0) = e0
% 158.86/25.28  | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | ALPHA: (69) implies:
% 158.86/25.28  | | | | | | | | | |   (70)  all_56_15 = e0
% 158.86/25.28  | | | | | | | | | |   (71)  op(e0, e0) = e0
% 158.86/25.28  | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | REF_CLOSE: (5), (12), (13), (22), (23), (28), (33), (35),
% 158.86/25.28  | | | | | | | | | |            (36), (67), (68), (70), (71) are inconsistent by
% 158.86/25.28  | | | | | | | | | |            sub-proof #883.
% 158.86/25.28  | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | Case 2:
% 158.86/25.28  | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | |   (72)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0
% 158.86/25.28  | | | | | | | | | |             & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 158.86/25.28  | | | | | | | | | |               e0) = e0)) & ((all_56_12 = e0 & op(e0, e3) =
% 158.86/25.28  | | | | | | | | | |             e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 158.86/25.28  | | | | | | | | | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 158.86/25.28  | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | ALPHA: (72) implies:
% 158.86/25.28  | | | | | | | | | |   (73)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0
% 158.86/25.28  | | | | | | | | | |           & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1)
% 158.86/25.28  | | | | | | | | | |           = e0)
% 158.86/25.28  | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | BETA: splitting (73) gives:
% 158.86/25.28  | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | Case 1:
% 158.86/25.28  | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | |   (74)  all_56_12 = e0 & op(e0, e3) = e0
% 158.86/25.28  | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | ALPHA: (74) implies:
% 158.86/25.28  | | | | | | | | | | |   (75)  op(e0, e3) = e0
% 158.86/25.28  | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | BETA: splitting (2) gives:
% 158.86/25.28  | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | Case 1:
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | |   (76)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 158.86/25.28  | | | | | | | | | | | |           & op(e2, e3) = e2)
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | REF_CLOSE: (12), (43), (48), (49), (67), (76) are
% 158.86/25.28  | | | | | | | | | | | |            inconsistent by sub-proof #550.
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | Case 2:
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | |   (77)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 158.86/25.28  | | | | | | | | | | | |           e2 & op(e0, e3) = e2)
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | REF_CLOSE: (12), (14), (19), (35), (65), (75), (77) are
% 158.86/25.28  | | | | | | | | | | | |            inconsistent by sub-proof #589.
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | End of split
% 158.86/25.28  | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | Case 2:
% 158.86/25.28  | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | |   (78)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 158.86/25.28  | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 158.86/25.28  | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | BETA: splitting (78) gives:
% 158.86/25.28  | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | Case 1:
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | |   (79)  all_56_13 = e0 & op(e0, e2) = e0
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | REF_CLOSE: (30), (36), (79) are inconsistent by sub-proof
% 158.86/25.28  | | | | | | | | | | | |            #298.
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | Case 2:
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | |   (80)  all_56_14 = e0 & op(e0, e1) = e0
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | ALPHA: (80) implies:
% 158.86/25.28  | | | | | | | | | | | |   (81)  all_56_14 = e0
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | COMBINE_EQS: (29), (81) imply:
% 158.86/25.28  | | | | | | | | | | | |   (82)  e2 = e0
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | SIMP: (82) implies:
% 158.86/25.28  | | | | | | | | | | | |   (83)  e2 = e0
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | COMBINE_EQS: (11), (83) imply:
% 158.86/25.28  | | | | | | | | | | | |   (84)  all_56_9 = e0
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | BETA: splitting (6) gives:
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | Case 1:
% 158.86/25.28  | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | |   (85)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 158.86/25.28  | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 158.86/25.28  | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | BETA: splitting (85) gives:
% 158.86/25.28  | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | Case 1:
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | |   (86)  all_56_0 = e2 & op(e3, e3) = e2
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | | ALPHA: (86) implies:
% 158.86/25.28  | | | | | | | | | | | | | |   (87)  op(e3, e3) = e2
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | | REF_CLOSE: (12), (43), (67), (87) are inconsistent by
% 158.86/25.28  | | | | | | | | | | | | | |            sub-proof #958.
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | Case 2:
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | |   (88)  all_56_1 = e2 & op(e3, e2) = e2
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | | ALPHA: (88) implies:
% 158.86/25.28  | | | | | | | | | | | | | |   (89)  all_56_1 = e2
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (28), (33), (37), (43), (68), (84),
% 158.86/25.28  | | | | | | | | | | | | | |            (89) are inconsistent by sub-proof #525.
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | End of split
% 158.86/25.28  | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | Case 2:
% 158.86/25.28  | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | |   (90)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 158.86/25.28  | | | | | | | | | | | | |           & op(e3, e0) = e2)
% 158.86/25.28  | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | BETA: splitting (90) gives:
% 158.86/25.28  | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | Case 1:
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | |   (91)  all_56_4 = e2 & op(e3, e1) = e2
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | | ALPHA: (91) implies:
% 158.86/25.28  | | | | | | | | | | | | | |   (92)  op(e3, e1) = e2
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (31), (92) are inconsistent by
% 158.86/25.28  | | | | | | | | | | | | | |            sub-proof #670.
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | Case 2:
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | |   (93)  all_56_9 = e2 & op(e3, e0) = e2
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | | REF_CLOSE: (11), (35), (84) are inconsistent by sub-proof
% 158.86/25.28  | | | | | | | | | | | | | |            #316.
% 158.86/25.28  | | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | | End of split
% 158.86/25.28  | | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | | End of split
% 158.86/25.28  | | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | | End of split
% 158.86/25.28  | | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | | End of split
% 158.86/25.28  | | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | End of split
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | Case 2:
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | |   (94)  all_54_9 = e1 | all_54_9 = e0
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | | REF_CLOSE: (4), (16), (57), (94) are inconsistent by sub-proof
% 158.86/25.28  | | | | | | | | |            #478.
% 158.86/25.28  | | | | | | | | | 
% 158.86/25.28  | | | | | | | | End of split
% 158.86/25.28  | | | | | | | | 
% 158.86/25.28  | | | | | | | End of split
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | Case 2:
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | |   (95)  all_54_1 = e0
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | | COMBINE_EQS: (20), (95) imply:
% 158.86/25.28  | | | | | | |   (96)  all_52_4 = e0
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | | REDUCE: (32), (96) imply:
% 158.86/25.28  | | | | | | |   (97)  $false
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | | CLOSE: (97) is inconsistent.
% 158.86/25.28  | | | | | | | 
% 158.86/25.28  | | | | | | End of split
% 158.86/25.28  | | | | | | 
% 158.86/25.28  | | | | | End of split
% 158.86/25.28  | | | | | 
% 158.86/25.28  | | | | End of split
% 158.86/25.28  | | | | 
% 158.86/25.28  | | | Case 2:
% 158.86/25.28  | | | | 
% 158.86/25.28  | | | |   (98)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3)
% 158.86/25.28  | | | |             = e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 158.86/25.28  | | | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 158.86/25.28  | | | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 158.86/25.28  | | | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) &
% 158.86/25.28  | | | |             op(e0, e2) = all_57_7 & $i(all_57_7)))
% 158.86/25.28  | | | | 
% 158.86/25.28  | | | | ALPHA: (98) implies:
% 158.86/25.28  | | | |   (99)  op(e2, e2) = e2
% 158.86/25.28  | | | | 
% 158.86/25.28  | | | | REF_CLOSE: (12), (25), (35), (99) are inconsistent by sub-proof #942.
% 158.86/25.28  | | | | 
% 158.86/25.28  | | | End of split
% 158.86/25.28  | | | 
% 158.86/25.28  | | Case 2:
% 158.86/25.28  | | | 
% 158.86/25.28  | | |   (100)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3)
% 158.86/25.28  | | |                = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 158.86/25.28  | | |                $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 158.86/25.28  | | |                (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 158.86/25.28  | | |            ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) &
% 158.86/25.28  | | |                op(e0, e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 &
% 158.86/25.28  | | |            op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 158.86/25.28  | | |                (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.86/25.28  | | |            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 158.86/25.28  | | |                op(e2, e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0
% 158.86/25.28  | | |                & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) =
% 158.86/25.28  | | |                all_57_13 & $i(all_57_13))))
% 158.86/25.28  | | | 
% 158.86/25.28  | | | REF_CLOSE: (3), (8), (12), (26), (28), (33), (100) are inconsistent by
% 158.86/25.28  | | |            sub-proof #297.
% 158.86/25.28  | | | 
% 158.86/25.28  | | End of split
% 158.86/25.28  | | 
% 158.86/25.28  | End of split
% 158.86/25.28  | 
% 158.86/25.28  End of proof
% 158.86/25.28  
% 158.86/25.28  Sub-proof #297 shows that the following formulas are inconsistent:
% 158.86/25.28  ----------------------------------------------------------------
% 158.86/25.28    (1)  op(e0, e0) = e1
% 158.86/25.28    (2)  op(e1, e1) = e3
% 158.86/25.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.28    (4)  op(e0, e0) = all_14_2
% 158.86/25.28    (5)   ~ (e1 = e0)
% 158.86/25.28    (6)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.86/25.28             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.86/25.28           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.86/25.28               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.86/25.28             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.86/25.28         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.86/25.28             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.86/25.28           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.86/25.28               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.86/25.28             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.86/25.28    (7)   ~ (e3 = e1)
% 158.86/25.28  
% 158.86/25.28  Begin of proof
% 158.86/25.28  | 
% 158.86/25.28  | BETA: splitting (6) gives:
% 158.86/25.28  | 
% 158.86/25.28  | Case 1:
% 158.86/25.28  | | 
% 158.86/25.28  | |   (8)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 158.86/25.28  | |            e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 158.86/25.28  | |            $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 158.86/25.28  | |            (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 158.86/25.28  | |        ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 158.86/25.28  | |              e1) = all_57_8 & $i(all_57_8)))
% 158.86/25.28  | | 
% 158.86/25.28  | | ALPHA: (8) implies:
% 158.86/25.28  | |   (9)  op(e1, e1) = e1
% 158.86/25.28  | | 
% 158.86/25.28  | | REF_CLOSE: (2), (3), (7), (9) are inconsistent by sub-proof #1003.
% 158.86/25.28  | | 
% 158.86/25.28  | Case 2:
% 158.86/25.28  | | 
% 158.86/25.29  | |   (10)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 158.86/25.29  | |             e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 158.86/25.29  | |             $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 158.86/25.29  | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 158.86/25.29  | |         ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 158.86/25.29  | |               e0) = all_57_13 & $i(all_57_13)))
% 158.86/25.29  | | 
% 158.86/25.29  | | ALPHA: (10) implies:
% 158.86/25.29  | |   (11)  op(e0, e0) = e0
% 158.86/25.29  | | 
% 158.86/25.29  | | REF_CLOSE: (1), (3), (4), (5), (11) are inconsistent by sub-proof #991.
% 158.86/25.29  | | 
% 158.86/25.29  | End of split
% 158.86/25.29  | 
% 158.86/25.29  End of proof
% 158.86/25.29  
% 158.86/25.29  Sub-proof #298 shows that the following formulas are inconsistent:
% 158.86/25.29  ----------------------------------------------------------------
% 158.86/25.29    (1)  all_56_13 = e0 & op(e0, e2) = e0
% 158.86/25.29    (2)  all_56_13 = e3
% 158.86/25.29    (3)   ~ (e3 = e0)
% 158.86/25.29  
% 158.86/25.29  Begin of proof
% 158.86/25.29  | 
% 158.86/25.29  | ALPHA: (1) implies:
% 158.86/25.29  |   (4)  all_56_13 = e0
% 158.86/25.29  | 
% 158.86/25.29  | COMBINE_EQS: (2), (4) imply:
% 158.86/25.29  |   (5)  e3 = e0
% 158.86/25.29  | 
% 158.86/25.29  | SIMP: (5) implies:
% 158.86/25.29  |   (6)  e3 = e0
% 158.86/25.29  | 
% 158.86/25.29  | REDUCE: (3), (6) imply:
% 158.86/25.29  |   (7)  $false
% 158.86/25.29  | 
% 158.86/25.29  | CLOSE: (7) is inconsistent.
% 158.86/25.29  | 
% 158.86/25.29  End of proof
% 158.86/25.29  
% 158.86/25.29  Sub-proof #299 shows that the following formulas are inconsistent:
% 158.86/25.29  ----------------------------------------------------------------
% 158.86/25.29    (1)  all_54_1 = all_52_4
% 158.86/25.29    (2)  all_54_1 = e3
% 158.86/25.29    (3)   ~ (all_52_4 = e3)
% 158.86/25.29  
% 158.86/25.29  Begin of proof
% 158.86/25.29  | 
% 158.86/25.29  | COMBINE_EQS: (1), (2) imply:
% 158.86/25.29  |   (4)  all_52_4 = e3
% 158.86/25.29  | 
% 158.86/25.29  | SIMP: (4) implies:
% 158.86/25.29  |   (5)  all_52_4 = e3
% 158.86/25.29  | 
% 158.86/25.29  | REDUCE: (3), (5) imply:
% 158.86/25.29  |   (6)  $false
% 158.86/25.29  | 
% 158.86/25.29  | CLOSE: (6) is inconsistent.
% 158.86/25.29  | 
% 158.86/25.29  End of proof
% 158.86/25.29  
% 158.86/25.29  Sub-proof #300 shows that the following formulas are inconsistent:
% 158.86/25.29  ----------------------------------------------------------------
% 158.86/25.29    (1)  all_56_9 = e2
% 158.86/25.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.29    (3)  all_56_1 = e2
% 158.86/25.29    (4)  op(e3, e3) = e3
% 158.86/25.29    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.86/25.29         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.86/25.29    (6)   ~ (e1 = e0)
% 158.86/25.29    (7)   ~ (e2 = e1)
% 158.86/25.29    (8)   ~ (e3 = e1)
% 158.86/25.29    (9)  all_56_4 = e0
% 158.86/25.29  
% 158.86/25.29  Begin of proof
% 158.86/25.29  | 
% 158.86/25.29  | BETA: splitting (5) gives:
% 158.86/25.29  | 
% 158.86/25.29  | Case 1:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 158.86/25.29  | |           e1)
% 158.86/25.29  | | 
% 158.86/25.29  | | REF_CLOSE: (2), (3), (4), (7), (8), (10) are inconsistent by sub-proof #635.
% 158.86/25.29  | | 
% 158.86/25.29  | Case 2:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (11)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 158.86/25.29  | |           e1)
% 158.86/25.29  | | 
% 158.86/25.29  | | REF_CLOSE: (1), (6), (7), (9), (11) are inconsistent by sub-proof #516.
% 158.86/25.29  | | 
% 158.86/25.29  | End of split
% 158.86/25.29  | 
% 158.86/25.29  End of proof
% 158.86/25.29  
% 158.86/25.29  Sub-proof #301 shows that the following formulas are inconsistent:
% 158.86/25.29  ----------------------------------------------------------------
% 158.86/25.29    (1)  all_56_9 = e2
% 158.86/25.29    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.86/25.29         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.86/25.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.29    (4)  all_56_1 = e2 & op(e3, e2) = e2
% 158.86/25.29    (5)  op(e3, e3) = e3
% 158.86/25.29    (6)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.86/25.29         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.86/25.29    (7)   ~ (e1 = e0)
% 158.86/25.29    (8)   ~ (e2 = e1)
% 158.86/25.29    (9)   ~ (e3 = e1)
% 158.86/25.29    (10)   ~ (e2 = e0)
% 158.86/25.29    (11)   ~ (e3 = e0)
% 158.86/25.29  
% 158.86/25.29  Begin of proof
% 158.86/25.29  | 
% 158.86/25.29  | ALPHA: (4) implies:
% 158.86/25.29  |   (12)  all_56_1 = e2
% 158.86/25.29  | 
% 158.86/25.29  | BETA: splitting (2) gives:
% 158.86/25.29  | 
% 158.86/25.29  | Case 1:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (13)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 158.86/25.29  | |           e0)
% 158.86/25.29  | | 
% 158.86/25.29  | | REF_CLOSE: (3), (5), (10), (11), (12), (13) are inconsistent by sub-proof
% 158.86/25.29  | |            #634.
% 158.86/25.29  | | 
% 158.86/25.29  | Case 2:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (14)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 158.86/25.29  | |           e0)
% 158.86/25.29  | | 
% 158.86/25.29  | | BETA: splitting (14) gives:
% 158.86/25.29  | | 
% 158.86/25.29  | | Case 1:
% 158.86/25.29  | | | 
% 158.86/25.29  | | |   (15)  all_56_4 = e0 & op(e3, e1) = e0
% 158.86/25.29  | | | 
% 158.86/25.29  | | | ALPHA: (15) implies:
% 158.86/25.29  | | |   (16)  all_56_4 = e0
% 158.86/25.29  | | | 
% 158.86/25.29  | | | BETA: splitting (6) gives:
% 158.86/25.29  | | | 
% 158.86/25.29  | | | Case 1:
% 158.86/25.29  | | | | 
% 158.86/25.29  | | | |   (17)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2)
% 158.86/25.29  | | | |           = e1)
% 158.86/25.29  | | | | 
% 158.86/25.29  | | | | REF_CLOSE: (3), (5), (8), (9), (12), (17) are inconsistent by sub-proof
% 158.86/25.29  | | | |            #635.
% 158.86/25.29  | | | | 
% 158.86/25.29  | | | Case 2:
% 158.86/25.29  | | | | 
% 158.86/25.29  | | | |   (18)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0)
% 158.86/25.29  | | | |           = e1)
% 158.86/25.29  | | | | 
% 158.86/25.29  | | | | REF_CLOSE: (1), (7), (8), (16), (18) are inconsistent by sub-proof #516.
% 158.86/25.29  | | | | 
% 158.86/25.29  | | | End of split
% 158.86/25.29  | | | 
% 158.86/25.29  | | Case 2:
% 158.86/25.29  | | | 
% 158.86/25.29  | | |   (19)  all_56_9 = e0 & op(e3, e0) = e0
% 158.86/25.29  | | | 
% 158.86/25.29  | | | REF_CLOSE: (1), (10), (19) are inconsistent by sub-proof #950.
% 158.86/25.29  | | | 
% 158.86/25.29  | | End of split
% 158.86/25.29  | | 
% 158.86/25.29  | End of split
% 158.86/25.29  | 
% 158.86/25.29  End of proof
% 158.86/25.29  
% 158.86/25.29  Sub-proof #302 shows that the following formulas are inconsistent:
% 158.86/25.29  ----------------------------------------------------------------
% 158.86/25.29    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.86/25.29         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.86/25.29    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.86/25.29         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.86/25.29    (3)  all_56_9 = e2
% 158.86/25.29    (4)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.86/25.29         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.86/25.29    (5)   ~ (e3 = e2)
% 158.86/25.29    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.29    (7)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.86/25.29         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.86/25.29    (8)  op(e3, e3) = e3
% 158.86/25.29    (9)  all_56_11 = e2
% 158.86/25.29    (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.86/25.29          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.86/25.29    (11)   ~ (e1 = e0)
% 158.86/25.29    (12)   ~ (e2 = e1)
% 158.86/25.29    (13)  all_56_15 = e0
% 158.86/25.29    (14)   ~ (e3 = e1)
% 158.86/25.29    (15)   ~ (e2 = e0)
% 158.86/25.29    (16)   ~ (e3 = e0)
% 158.86/25.29  
% 158.86/25.29  Begin of proof
% 158.86/25.29  | 
% 158.86/25.29  | BETA: splitting (1) gives:
% 158.86/25.29  | 
% 158.86/25.29  | Case 1:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (17)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 158.86/25.29  | |           e1)
% 158.86/25.29  | | 
% 158.86/25.29  | | BETA: splitting (17) gives:
% 158.86/25.29  | | 
% 158.86/25.29  | | Case 1:
% 158.86/25.29  | | | 
% 158.86/25.29  | | |   (18)  all_56_9 = e1 & op(e3, e0) = e1
% 158.86/25.29  | | | 
% 158.86/25.29  | | | REF_CLOSE: (3), (12), (18) are inconsistent by sub-proof #948.
% 158.86/25.29  | | | 
% 158.86/25.29  | | Case 2:
% 158.86/25.29  | | | 
% 158.86/25.29  | | |   (19)  all_56_10 = e1 & op(e2, e0) = e1
% 158.86/25.29  | | | 
% 158.86/25.29  | | | ALPHA: (19) implies:
% 158.86/25.29  | | |   (20)  all_56_10 = e1
% 158.86/25.29  | | | 
% 158.86/25.29  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 158.86/25.29  | | |            (14), (15), (16), (20) are inconsistent by sub-proof #303.
% 158.86/25.29  | | | 
% 158.86/25.29  | | End of split
% 158.86/25.29  | | 
% 158.86/25.29  | Case 2:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (21)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 158.86/25.29  | |           e1)
% 158.86/25.29  | | 
% 158.86/25.29  | | BETA: splitting (21) gives:
% 158.86/25.29  | | 
% 158.86/25.29  | | Case 1:
% 158.86/25.29  | | | 
% 158.86/25.29  | | |   (22)  all_56_11 = e1 & op(e1, e0) = e1
% 158.86/25.29  | | | 
% 158.86/25.29  | | | REF_CLOSE: (9), (12), (22) are inconsistent by sub-proof #469.
% 158.86/25.29  | | | 
% 158.86/25.29  | | Case 2:
% 158.86/25.29  | | | 
% 158.86/25.29  | | |   (23)  all_56_15 = e1 & op(e0, e0) = e1
% 158.86/25.29  | | | 
% 158.86/25.29  | | | REF_CLOSE: (11), (13), (23) are inconsistent by sub-proof #884.
% 158.86/25.29  | | | 
% 158.86/25.29  | | End of split
% 158.86/25.29  | | 
% 158.86/25.29  | End of split
% 158.86/25.29  | 
% 158.86/25.29  End of proof
% 158.86/25.29  
% 158.86/25.29  Sub-proof #303 shows that the following formulas are inconsistent:
% 158.86/25.29  ----------------------------------------------------------------
% 158.86/25.29    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.86/25.29         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.86/25.29    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.86/25.29         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.86/25.29    (3)   ~ (e3 = e2)
% 158.86/25.29    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.29    (5)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.86/25.29         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.86/25.29    (6)  op(e3, e3) = e3
% 158.86/25.29    (7)  all_56_10 = e1
% 158.86/25.29    (8)  all_56_11 = e2
% 158.86/25.29    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.86/25.29         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.86/25.29    (10)   ~ (e1 = e0)
% 158.86/25.29    (11)   ~ (e2 = e1)
% 158.86/25.29    (12)  all_56_15 = e0
% 158.86/25.29    (13)   ~ (e3 = e1)
% 158.86/25.29    (14)   ~ (e2 = e0)
% 158.86/25.29    (15)   ~ (e3 = e0)
% 158.86/25.29  
% 158.86/25.29  Begin of proof
% 158.86/25.29  | 
% 158.86/25.29  | BETA: splitting (5) gives:
% 158.86/25.29  | 
% 158.86/25.29  | Case 1:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (16)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 158.86/25.29  | |           e3)
% 158.86/25.29  | | 
% 158.86/25.29  | | BETA: splitting (16) gives:
% 158.86/25.29  | | 
% 158.86/25.29  | | Case 1:
% 158.86/25.29  | | | 
% 158.86/25.29  | | |   (17)  all_56_9 = e3 & op(e3, e0) = e3
% 158.86/25.29  | | | 
% 158.86/25.29  | | | ALPHA: (17) implies:
% 158.86/25.29  | | |   (18)  all_56_9 = e3
% 158.86/25.29  | | | 
% 158.86/25.29  | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (13), (14), (15),
% 158.86/25.29  | | |            (18) are inconsistent by sub-proof #632.
% 158.86/25.29  | | | 
% 158.86/25.29  | | Case 2:
% 158.86/25.29  | | | 
% 158.86/25.29  | | |   (19)  all_56_10 = e3 & op(e2, e0) = e3
% 158.86/25.29  | | | 
% 158.86/25.29  | | | ALPHA: (19) implies:
% 158.86/25.29  | | |   (20)  all_56_10 = e3
% 158.86/25.29  | | | 
% 158.86/25.29  | | | REF_CLOSE: (7), (13), (20) are inconsistent by sub-proof #887.
% 158.86/25.29  | | | 
% 158.86/25.29  | | End of split
% 158.86/25.29  | | 
% 158.86/25.29  | Case 2:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (21)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.86/25.29  | |           e3)
% 158.86/25.29  | | 
% 158.86/25.29  | | BETA: splitting (21) gives:
% 158.86/25.29  | | 
% 158.86/25.29  | | Case 1:
% 158.86/25.29  | | | 
% 158.86/25.29  | | |   (22)  all_56_11 = e3 & op(e1, e0) = e3
% 158.86/25.29  | | | 
% 158.86/25.29  | | | ALPHA: (22) implies:
% 158.86/25.29  | | |   (23)  all_56_11 = e3
% 158.86/25.29  | | | 
% 158.86/25.29  | | | REF_CLOSE: (3), (8), (23) are inconsistent by sub-proof #319.
% 158.86/25.29  | | | 
% 158.86/25.29  | | Case 2:
% 158.86/25.29  | | | 
% 158.86/25.29  | | |   (24)  all_56_15 = e3 & op(e0, e0) = e3
% 158.86/25.29  | | | 
% 158.86/25.29  | | | REF_CLOSE: (12), (15), (24) are inconsistent by sub-proof #892.
% 158.86/25.29  | | | 
% 158.86/25.29  | | End of split
% 158.86/25.29  | | 
% 158.86/25.29  | End of split
% 158.86/25.29  | 
% 158.86/25.29  End of proof
% 158.86/25.29  
% 158.86/25.29  Sub-proof #304 shows that the following formulas are inconsistent:
% 158.86/25.29  ----------------------------------------------------------------
% 158.86/25.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.29    (2)  op(e0, e3) = all_52_3
% 158.86/25.29    (3)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.86/25.29    (4)  all_56_6 = e2
% 158.86/25.29    (5)   ~ (all_52_3 = e1)
% 158.86/25.29    (6)   ~ (e2 = e1)
% 158.86/25.29  
% 158.86/25.29  Begin of proof
% 158.86/25.29  | 
% 158.86/25.29  | BETA: splitting (3) gives:
% 158.86/25.29  | 
% 158.86/25.29  | Case 1:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (7)  all_56_6 = e1 & op(e1, e3) = e1
% 158.86/25.29  | | 
% 158.86/25.29  | | ALPHA: (7) implies:
% 158.86/25.29  | |   (8)  all_56_6 = e1
% 158.86/25.29  | | 
% 158.86/25.29  | | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #533.
% 158.86/25.29  | | 
% 158.86/25.29  | Case 2:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (9)  all_56_12 = e1 & op(e0, e3) = e1
% 158.86/25.29  | | 
% 158.86/25.29  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #852.
% 158.86/25.29  | | 
% 158.86/25.29  | End of split
% 158.86/25.29  | 
% 158.86/25.29  End of proof
% 158.86/25.29  
% 158.86/25.29  Sub-proof #305 shows that the following formulas are inconsistent:
% 158.86/25.29  ----------------------------------------------------------------
% 158.86/25.29    (1)  op(e0, e0) = e1
% 158.86/25.29    (2)  op(e1, e1) = e3
% 158.86/25.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.29    (4)  op(e0, e0) = all_57_15
% 158.86/25.29    (5)  op(e3, e3) = e3
% 158.86/25.29    (6)  op(e0, e0) = all_14_2
% 158.86/25.29    (7)   ~ (e1 = e0)
% 158.86/25.29    (8)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.86/25.29           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.86/25.29           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.86/25.29           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 158.86/25.29           & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.86/25.29    (9)   ~ (e3 = e0)
% 158.86/25.29  
% 158.86/25.29  Begin of proof
% 158.86/25.29  | 
% 158.86/25.29  | BETA: splitting (8) gives:
% 158.86/25.29  | 
% 158.86/25.29  | Case 1:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (10)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.86/25.29  | |           e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 158.86/25.29  | | 
% 158.86/25.29  | | ALPHA: (10) implies:
% 158.86/25.29  | |   (11)  op(e1, e1) = e0
% 158.86/25.29  | | 
% 158.86/25.29  | | REF_CLOSE: (2), (3), (9), (11) are inconsistent by sub-proof #912.
% 158.86/25.29  | | 
% 158.86/25.29  | Case 2:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (12)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.86/25.29  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.86/25.29  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.86/25.29  | | 
% 158.86/25.29  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (12) are inconsistent by
% 158.86/25.29  | |            sub-proof #306.
% 158.86/25.29  | | 
% 158.86/25.29  | End of split
% 158.86/25.29  | 
% 158.86/25.29  End of proof
% 158.86/25.29  
% 158.86/25.29  Sub-proof #306 shows that the following formulas are inconsistent:
% 158.86/25.29  ----------------------------------------------------------------
% 158.86/25.29    (1)  op(e0, e0) = e1
% 158.86/25.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.29    (3)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.86/25.29         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.29           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 158.86/25.29    (4)  op(e0, e0) = all_57_15
% 158.86/25.29    (5)  op(e3, e3) = e3
% 158.86/25.29    (6)  op(e0, e0) = all_14_2
% 158.86/25.29    (7)   ~ (e1 = e0)
% 158.86/25.29    (8)   ~ (e3 = e0)
% 158.86/25.29  
% 158.86/25.29  Begin of proof
% 158.86/25.29  | 
% 158.86/25.29  | BETA: splitting (3) gives:
% 158.86/25.29  | 
% 158.86/25.29  | Case 1:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (9)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 158.86/25.29  | | 
% 158.86/25.29  | | ALPHA: (9) implies:
% 158.86/25.29  | |   (10)  all_57_15 = e0
% 158.86/25.29  | | 
% 158.86/25.29  | | REDUCE: (4), (10) imply:
% 158.86/25.29  | |   (11)  op(e0, e0) = e0
% 158.86/25.29  | | 
% 158.86/25.29  | | REF_CLOSE: (1), (2), (6), (7), (11) are inconsistent by sub-proof #991.
% 158.86/25.29  | | 
% 158.86/25.29  | Case 2:
% 158.86/25.29  | | 
% 158.86/25.29  | |   (12)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 158.86/25.29  | |         & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 158.86/25.29  | | 
% 158.86/25.29  | | ALPHA: (12) implies:
% 158.86/25.29  | |   (13)  op(e3, e3) = e0
% 158.86/25.29  | | 
% 158.86/25.29  | | REF_CLOSE: (2), (5), (8), (13) are inconsistent by sub-proof #971.
% 158.86/25.29  | | 
% 158.86/25.29  | End of split
% 158.86/25.29  | 
% 158.86/25.29  End of proof
% 158.86/25.29  
% 158.86/25.29  Sub-proof #307 shows that the following formulas are inconsistent:
% 158.86/25.29  ----------------------------------------------------------------
% 158.86/25.29    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.86/25.29         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.86/25.29    (2)  op(e1, e1) = e3
% 158.86/25.29    (3)  all_56_9 = e2
% 158.86/25.29    (4)   ~ (e3 = e2)
% 158.86/25.29    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.29    (6)  op(e3, e1) = all_52_8
% 158.86/25.30    (7)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.86/25.30             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 158.86/25.30               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.86/25.30               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.86/25.30    (8)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 158.86/25.30           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 158.86/25.30           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1)
% 158.86/25.30           & op(e1, e2) = e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.86/25.30           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.86/25.30             e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.86/25.30         (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 158.86/25.30             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.86/25.30           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.86/25.30           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.86/25.30    (9)  all_56_10 = e3
% 158.86/25.30    (10)  op(e3, e3) = e3
% 158.86/25.30    (11)   ~ (e1 = e0)
% 158.86/25.30    (12)   ~ (e2 = e1)
% 158.86/25.30    (13)   ~ (e3 = e1)
% 158.86/25.30    (14)   ~ (e2 = e0)
% 158.86/25.30    (15)   ~ (all_52_8 = e3)
% 158.86/25.30    (16)   ~ (e3 = e0)
% 158.86/25.30  
% 158.86/25.30  Begin of proof
% 158.86/25.30  | 
% 158.86/25.30  | BETA: splitting (8) gives:
% 158.86/25.30  | 
% 158.86/25.30  | Case 1:
% 158.86/25.30  | | 
% 158.86/25.30  | |   (17)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 158.86/25.30  | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1
% 158.86/25.30  | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 =
% 158.86/25.30  | |           e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1)
% 158.86/25.30  | | 
% 158.86/25.30  | | REF_CLOSE: (2), (4), (5), (13), (17) are inconsistent by sub-proof #644.
% 158.86/25.30  | | 
% 158.86/25.30  | Case 2:
% 158.86/25.30  | | 
% 158.86/25.30  | |   (18)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 158.86/25.30  | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0
% 158.86/25.30  | |           & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 =
% 158.86/25.30  | |           e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4
% 158.86/25.30  | |           = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.86/25.30  | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.86/25.30  | |           op(e1, e0) = e1 & $i(all_57_14))
% 158.86/25.30  | | 
% 158.86/25.30  | | BETA: splitting (18) gives:
% 158.86/25.30  | | 
% 158.86/25.30  | | Case 1:
% 158.86/25.30  | | | 
% 158.86/25.30  | | |   (19)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 158.86/25.30  | | |           e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0
% 158.86/25.30  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 158.86/25.30  | | | 
% 158.86/25.30  | | | ALPHA: (19) implies:
% 158.86/25.30  | | |   (20)  op(e0, e0) = e3
% 158.86/25.30  | | | 
% 158.86/25.30  | | | REF_CLOSE: (1), (3), (5), (7), (9), (11), (12), (13), (14), (16), (20) are
% 158.86/25.30  | | |            inconsistent by sub-proof #471.
% 158.86/25.30  | | | 
% 158.86/25.30  | | Case 2:
% 158.86/25.30  | | | 
% 158.86/25.30  | | |   (21)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 158.86/25.30  | | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 =
% 158.86/25.30  | | |           e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.86/25.30  | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.86/25.30  | | | 
% 158.86/25.30  | | | REF_CLOSE: (5), (6), (10), (13), (15), (21) are inconsistent by sub-proof
% 158.86/25.30  | | |            #981.
% 158.86/25.30  | | | 
% 158.86/25.30  | | End of split
% 158.86/25.30  | | 
% 158.86/25.30  | End of split
% 158.86/25.30  | 
% 158.86/25.30  End of proof
% 158.86/25.30  
% 158.86/25.30  Sub-proof #308 shows that the following formulas are inconsistent:
% 158.86/25.30  ----------------------------------------------------------------
% 158.86/25.30    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 158.86/25.30         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 158.86/25.30    (2)   ~ (all_52_4 = e3)
% 158.86/25.30    (3)  all_56_9 = e2
% 158.86/25.30    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.30    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 158.86/25.30             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 158.86/25.30               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 158.86/25.30               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 158.86/25.30    (6)  all_56_10 = e3
% 158.86/25.30    (7)  op(e3, e2) = all_52_4
% 158.86/25.30    (8)   ~ (e1 = e0)
% 158.86/25.30    (9)   ~ (e2 = e1)
% 158.86/25.30    (10)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 158.86/25.30            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 158.86/25.30              e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3
% 158.86/25.30              = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 158.86/25.30    (11)   ~ (e3 = e1)
% 158.86/25.30    (12)   ~ (e2 = e0)
% 158.86/25.30    (13)   ~ (e3 = e0)
% 158.86/25.30  
% 158.86/25.30  Begin of proof
% 158.86/25.30  | 
% 158.86/25.30  | BETA: splitting (10) gives:
% 158.86/25.30  | 
% 158.86/25.30  | Case 1:
% 158.86/25.30  | | 
% 158.86/25.30  | |   (14)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 158.86/25.30  | |         & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 158.86/25.30  | |         op(e0, e0) = e3 & $i(all_57_10)
% 158.86/25.30  | | 
% 158.86/25.30  | | ALPHA: (14) implies:
% 158.86/25.30  | |   (15)  op(e0, e0) = e3
% 158.86/25.30  | | 
% 158.86/25.30  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (11), (12), (13), (15) are
% 158.86/25.30  | |            inconsistent by sub-proof #471.
% 158.86/25.30  | | 
% 158.86/25.30  | Case 2:
% 158.86/25.30  | | 
% 158.86/25.30  | |   (16)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 158.86/25.30  | |         op(e3, e2) = e3
% 158.86/25.30  | | 
% 158.86/25.30  | | ALPHA: (16) implies:
% 158.86/25.30  | |   (17)  op(e3, e2) = e3
% 158.86/25.30  | | 
% 158.86/25.30  | | REF_CLOSE: (2), (4), (7), (17) are inconsistent by sub-proof #998.
% 158.86/25.30  | | 
% 158.86/25.30  | End of split
% 158.86/25.30  | 
% 158.86/25.30  End of proof
% 158.86/25.30  
% 158.86/25.30  Sub-proof #309 shows that the following formulas are inconsistent:
% 158.86/25.30  ----------------------------------------------------------------
% 158.86/25.30    (1)  all_54_8 = all_52_2
% 158.86/25.30    (2)  all_54_8 = e3
% 158.86/25.30    (3)   ~ (all_52_2 = e3)
% 158.86/25.30  
% 158.86/25.30  Begin of proof
% 158.86/25.30  | 
% 158.86/25.30  | COMBINE_EQS: (1), (2) imply:
% 158.86/25.30  |   (4)  all_52_2 = e3
% 158.86/25.30  | 
% 158.86/25.30  | SIMP: (4) implies:
% 158.86/25.30  |   (5)  all_52_2 = e3
% 158.86/25.30  | 
% 158.86/25.30  | REDUCE: (3), (5) imply:
% 158.86/25.30  |   (6)  $false
% 158.86/25.30  | 
% 158.86/25.30  | CLOSE: (6) is inconsistent.
% 158.86/25.30  | 
% 158.86/25.30  End of proof
% 158.86/25.30  
% 158.86/25.30  Sub-proof #310 shows that the following formulas are inconsistent:
% 158.86/25.30  ----------------------------------------------------------------
% 158.86/25.30    (1)  all_54_3 = all_52_12
% 158.86/25.30    (2)  all_54_3 = e3
% 158.86/25.30    (3)   ~ (all_52_12 = e3)
% 158.86/25.30  
% 158.86/25.30  Begin of proof
% 158.86/25.30  | 
% 158.86/25.30  | COMBINE_EQS: (1), (2) imply:
% 158.86/25.30  |   (4)  all_52_12 = e3
% 158.86/25.30  | 
% 158.86/25.30  | SIMP: (4) implies:
% 158.86/25.30  |   (5)  all_52_12 = e3
% 158.86/25.30  | 
% 158.86/25.30  | REDUCE: (3), (5) imply:
% 158.86/25.30  |   (6)  $false
% 158.86/25.30  | 
% 158.86/25.30  | CLOSE: (6) is inconsistent.
% 158.86/25.30  | 
% 158.86/25.30  End of proof
% 158.86/25.30  
% 158.86/25.30  Sub-proof #311 shows that the following formulas are inconsistent:
% 158.86/25.30  ----------------------------------------------------------------
% 158.86/25.30    (1)  op(e1, e1) = e3
% 158.86/25.30    (2)   ~ (e3 = e2)
% 158.86/25.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.30    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.86/25.30         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.86/25.30    (5)  op(e1, e0) = e0
% 158.86/25.30    (6)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.86/25.30         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.86/25.30    (7)   ~ (e1 = e0)
% 158.86/25.30    (8)   ~ (e2 = e1)
% 158.86/25.30    (9)  all_56_7 = e0
% 158.86/25.30    (10)   ~ (e3 = e1)
% 158.86/25.30    (11)   ~ (e2 = e0)
% 158.86/25.30    (12)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 158.86/25.30          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 158.86/25.30    (13)   ~ (e3 = e0)
% 158.86/25.30  
% 158.86/25.30  Begin of proof
% 158.86/25.30  | 
% 158.86/25.30  | BETA: splitting (12) gives:
% 158.86/25.30  | 
% 158.86/25.30  | Case 1:
% 158.86/25.30  | | 
% 158.86/25.30  | |   (14)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 158.86/25.30  | |           e2)
% 158.86/25.30  | | 
% 158.86/25.30  | | BETA: splitting (14) gives:
% 158.86/25.30  | | 
% 158.86/25.30  | | Case 1:
% 158.86/25.30  | | | 
% 158.86/25.30  | | |   (15)  all_56_6 = e2 & op(e1, e3) = e2
% 158.86/25.30  | | | 
% 158.86/25.30  | | | ALPHA: (15) implies:
% 158.86/25.30  | | |   (16)  all_56_6 = e2
% 158.86/25.30  | | | 
% 158.86/25.30  | | | BETA: splitting (4) gives:
% 158.86/25.30  | | | 
% 158.86/25.30  | | | Case 1:
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | |   (17)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2)
% 158.86/25.30  | | | |           = e1)
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | | REF_CLOSE: (7), (8), (9), (16), (17) are inconsistent by sub-proof #527.
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | Case 2:
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | |   (18)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0)
% 158.86/25.30  | | | |           = e1)
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | | REF_CLOSE: (1), (3), (5), (7), (10), (18) are inconsistent by sub-proof
% 158.86/25.30  | | | |            #544.
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | End of split
% 158.86/25.30  | | | 
% 158.86/25.30  | | Case 2:
% 158.86/25.30  | | | 
% 158.86/25.30  | | |   (19)  all_56_7 = e2 & op(e1, e2) = e2
% 158.86/25.30  | | | 
% 158.86/25.30  | | | ALPHA: (19) implies:
% 158.86/25.30  | | |   (20)  all_56_7 = e2
% 158.86/25.30  | | | 
% 158.86/25.30  | | | REF_CLOSE: (9), (11), (20) are inconsistent by sub-proof #523.
% 158.86/25.30  | | | 
% 158.86/25.30  | | End of split
% 158.86/25.30  | | 
% 158.86/25.30  | Case 2:
% 158.86/25.30  | | 
% 158.86/25.30  | |   (21)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 158.86/25.30  | |           e2)
% 158.86/25.30  | | 
% 158.86/25.30  | | BETA: splitting (21) gives:
% 158.86/25.30  | | 
% 158.86/25.30  | | Case 1:
% 158.86/25.30  | | | 
% 158.86/25.30  | | |   (22)  all_56_8 = e2 & op(e1, e1) = e2
% 158.86/25.30  | | | 
% 158.86/25.30  | | | ALPHA: (22) implies:
% 158.86/25.30  | | |   (23)  op(e1, e1) = e2
% 158.86/25.30  | | | 
% 158.86/25.30  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (23) are
% 158.86/25.30  | | |            inconsistent by sub-proof #312.
% 158.86/25.30  | | | 
% 158.86/25.30  | | Case 2:
% 158.86/25.30  | | | 
% 158.86/25.30  | | |   (24)  all_56_11 = e2 & op(e1, e0) = e2
% 158.86/25.30  | | | 
% 158.86/25.30  | | | ALPHA: (24) implies:
% 158.86/25.30  | | |   (25)  op(e1, e0) = e2
% 158.86/25.30  | | | 
% 158.86/25.30  | | | REF_CLOSE: (3), (5), (11), (25) are inconsistent by sub-proof #397.
% 158.86/25.30  | | | 
% 158.86/25.30  | | End of split
% 158.86/25.30  | | 
% 158.86/25.30  | End of split
% 158.86/25.30  | 
% 158.86/25.30  End of proof
% 158.86/25.30  
% 158.86/25.30  Sub-proof #312 shows that the following formulas are inconsistent:
% 158.86/25.30  ----------------------------------------------------------------
% 158.86/25.30    (1)   ~ (e3 = e2)
% 158.86/25.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.30    (3)  op(e1, e1) = e2
% 158.86/25.30    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.86/25.30         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.86/25.30    (5)  op(e1, e0) = e0
% 158.86/25.30    (6)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 158.86/25.30         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.86/25.30    (7)   ~ (e1 = e0)
% 158.86/25.30    (8)   ~ (e2 = e1)
% 158.86/25.30    (9)  all_56_7 = e0
% 158.86/25.30    (10)   ~ (e3 = e1)
% 158.86/25.30    (11)   ~ (e3 = e0)
% 158.86/25.30  
% 158.86/25.30  Begin of proof
% 158.86/25.30  | 
% 158.86/25.30  | BETA: splitting (6) gives:
% 158.86/25.30  | 
% 158.86/25.30  | Case 1:
% 158.86/25.30  | | 
% 158.86/25.30  | |   (12)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) =
% 158.86/25.30  | |           e3)
% 158.86/25.30  | | 
% 158.86/25.30  | | BETA: splitting (12) gives:
% 158.86/25.30  | | 
% 158.86/25.30  | | Case 1:
% 158.86/25.30  | | | 
% 158.86/25.30  | | |   (13)  all_56_6 = e3 & op(e1, e3) = e3
% 158.86/25.30  | | | 
% 158.86/25.30  | | | ALPHA: (13) implies:
% 158.86/25.30  | | |   (14)  all_56_6 = e3
% 158.86/25.30  | | | 
% 158.86/25.30  | | | BETA: splitting (4) gives:
% 158.86/25.30  | | | 
% 158.86/25.30  | | | Case 1:
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | |   (15)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2)
% 158.86/25.30  | | | |           = e1)
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | | BETA: splitting (15) gives:
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | | Case 1:
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | |   (16)  all_56_6 = e1 & op(e1, e3) = e1
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | ALPHA: (16) implies:
% 158.86/25.30  | | | | |   (17)  all_56_6 = e1
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | COMBINE_EQS: (14), (17) imply:
% 158.86/25.30  | | | | |   (18)  e3 = e1
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | SIMP: (18) implies:
% 158.86/25.30  | | | | |   (19)  e3 = e1
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | REDUCE: (10), (19) imply:
% 158.86/25.30  | | | | |   (20)  $false
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | CLOSE: (20) is inconsistent.
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | Case 2:
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | |   (21)  all_56_7 = e1 & op(e1, e2) = e1
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | ALPHA: (21) implies:
% 158.86/25.30  | | | | |   (22)  all_56_7 = e1
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | REF_CLOSE: (7), (9), (22) are inconsistent by sub-proof #560.
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | End of split
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | Case 2:
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | |   (23)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0)
% 158.86/25.30  | | | |           = e1)
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | | BETA: splitting (23) gives:
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | | Case 1:
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | |   (24)  all_56_8 = e1 & op(e1, e1) = e1
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | ALPHA: (24) implies:
% 158.86/25.30  | | | | |   (25)  op(e1, e1) = e1
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | REF_CLOSE: (2), (3), (8), (25) are inconsistent by sub-proof #986.
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | Case 2:
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | |   (26)  all_56_11 = e1 & op(e1, e0) = e1
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | ALPHA: (26) implies:
% 158.86/25.30  | | | | |   (27)  op(e1, e0) = e1
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | | REF_CLOSE: (2), (5), (7), (27) are inconsistent by sub-proof #545.
% 158.86/25.30  | | | | | 
% 158.86/25.30  | | | | End of split
% 158.86/25.30  | | | | 
% 158.86/25.30  | | | End of split
% 158.86/25.30  | | | 
% 158.86/25.30  | | Case 2:
% 158.86/25.30  | | | 
% 158.86/25.30  | | |   (28)  all_56_7 = e3 & op(e1, e2) = e3
% 158.86/25.30  | | | 
% 158.86/25.30  | | | REF_CLOSE: (9), (11), (28) are inconsistent by sub-proof #522.
% 158.86/25.30  | | | 
% 158.86/25.30  | | End of split
% 158.86/25.30  | | 
% 158.86/25.30  | Case 2:
% 158.86/25.30  | | 
% 158.86/25.30  | |   (29)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) =
% 158.86/25.30  | |           e3)
% 158.86/25.30  | | 
% 158.86/25.30  | | REF_CLOSE: (1), (2), (3), (5), (11), (29) are inconsistent by sub-proof
% 158.86/25.30  | |            #313.
% 158.86/25.30  | | 
% 158.86/25.30  | End of split
% 158.86/25.30  | 
% 158.86/25.30  End of proof
% 158.86/25.30  
% 158.86/25.30  Sub-proof #313 shows that the following formulas are inconsistent:
% 158.86/25.30  ----------------------------------------------------------------
% 158.86/25.30    (1)   ~ (e3 = e2)
% 158.86/25.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.30    (3)  op(e1, e1) = e2
% 158.86/25.30    (4)  op(e1, e0) = e0
% 158.86/25.30    (5)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 158.86/25.30    (6)   ~ (e3 = e0)
% 158.86/25.30  
% 158.86/25.30  Begin of proof
% 158.86/25.30  | 
% 158.86/25.30  | BETA: splitting (5) gives:
% 158.86/25.30  | 
% 158.86/25.30  | Case 1:
% 158.86/25.30  | | 
% 158.86/25.30  | |   (7)  all_56_8 = e3 & op(e1, e1) = e3
% 158.86/25.30  | | 
% 158.86/25.30  | | ALPHA: (7) implies:
% 158.86/25.30  | |   (8)  op(e1, e1) = e3
% 158.86/25.30  | | 
% 158.86/25.30  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #646.
% 158.86/25.30  | | 
% 158.86/25.30  | Case 2:
% 158.86/25.30  | | 
% 158.86/25.30  | |   (9)  all_56_11 = e3 & op(e1, e0) = e3
% 158.86/25.30  | | 
% 158.86/25.30  | | ALPHA: (9) implies:
% 158.86/25.30  | |   (10)  op(e1, e0) = e3
% 158.86/25.30  | | 
% 158.86/25.30  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #314.
% 158.86/25.30  | | 
% 158.86/25.30  | End of split
% 158.86/25.30  | 
% 158.86/25.30  End of proof
% 158.86/25.30  
% 158.86/25.30  Sub-proof #314 shows that the following formulas are inconsistent:
% 158.86/25.30  ----------------------------------------------------------------
% 158.86/25.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.30    (2)  op(e1, e0) = e3
% 158.86/25.30    (3)  op(e1, e0) = e0
% 158.86/25.30    (4)   ~ (e3 = e0)
% 158.86/25.30  
% 158.86/25.30  Begin of proof
% 158.86/25.30  | 
% 158.86/25.30  | GROUND_INST: instantiating (1) with e0, e3, e0, e1, simplifying with (2), (3)
% 158.86/25.30  |              gives:
% 158.86/25.30  |   (5)  e3 = e0
% 158.86/25.30  | 
% 158.86/25.30  | REDUCE: (4), (5) imply:
% 158.86/25.30  |   (6)  $false
% 158.86/25.30  | 
% 158.86/25.30  | CLOSE: (6) is inconsistent.
% 158.86/25.30  | 
% 158.86/25.30  End of proof
% 158.86/25.30  
% 158.86/25.30  Sub-proof #315 shows that the following formulas are inconsistent:
% 158.86/25.30  ----------------------------------------------------------------
% 158.86/25.30    (1)  op(e1, e1) = e3
% 158.86/25.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.30    (3)  all_56_7 = e2
% 158.86/25.30    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.86/25.30         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.86/25.31    (5)  op(e1, e0) = e0
% 158.86/25.31    (6)  all_56_6 = e0
% 158.86/25.31    (7)   ~ (e1 = e0)
% 158.86/25.31    (8)   ~ (e2 = e1)
% 158.86/25.31    (9)   ~ (e3 = e1)
% 158.86/25.31  
% 158.86/25.31  Begin of proof
% 158.86/25.31  | 
% 158.86/25.31  | BETA: splitting (4) gives:
% 158.86/25.31  | 
% 158.86/25.31  | Case 1:
% 158.86/25.31  | | 
% 158.86/25.31  | |   (10)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 158.86/25.31  | |           e1)
% 158.86/25.31  | | 
% 158.86/25.31  | | BETA: splitting (10) gives:
% 158.86/25.31  | | 
% 158.86/25.31  | | Case 1:
% 158.86/25.31  | | | 
% 158.86/25.31  | | |   (11)  all_56_6 = e1 & op(e1, e3) = e1
% 158.86/25.31  | | | 
% 158.86/25.31  | | | REF_CLOSE: (6), (7), (11) are inconsistent by sub-proof #917.
% 158.86/25.31  | | | 
% 158.86/25.31  | | Case 2:
% 158.86/25.31  | | | 
% 158.86/25.31  | | |   (12)  all_56_7 = e1 & op(e1, e2) = e1
% 158.86/25.31  | | | 
% 158.86/25.31  | | | REF_CLOSE: (3), (8), (12) are inconsistent by sub-proof #604.
% 158.86/25.31  | | | 
% 158.86/25.31  | | End of split
% 158.86/25.31  | | 
% 158.86/25.31  | Case 2:
% 158.86/25.31  | | 
% 158.86/25.31  | |   (13)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 158.86/25.31  | |           e1)
% 158.86/25.31  | | 
% 158.86/25.31  | | REF_CLOSE: (1), (2), (5), (7), (9), (13) are inconsistent by sub-proof #544.
% 158.86/25.31  | | 
% 158.86/25.31  | End of split
% 158.86/25.31  | 
% 158.86/25.31  End of proof
% 158.86/25.31  
% 158.86/25.31  Sub-proof #316 shows that the following formulas are inconsistent:
% 158.86/25.31  ----------------------------------------------------------------
% 158.86/25.31    (1)  all_56_9 = e2
% 158.86/25.31    (2)  all_56_9 = e0
% 158.86/25.31    (3)   ~ (e2 = e0)
% 158.86/25.31  
% 158.86/25.31  Begin of proof
% 158.86/25.31  | 
% 158.86/25.31  | COMBINE_EQS: (1), (2) imply:
% 158.86/25.31  |   (4)  e2 = e0
% 158.86/25.31  | 
% 158.86/25.31  | SIMP: (4) implies:
% 158.86/25.31  |   (5)  e2 = e0
% 158.86/25.31  | 
% 158.86/25.31  | REDUCE: (3), (5) imply:
% 158.86/25.31  |   (6)  $false
% 158.86/25.31  | 
% 158.86/25.31  | CLOSE: (6) is inconsistent.
% 158.86/25.31  | 
% 158.86/25.31  End of proof
% 158.86/25.31  
% 158.86/25.31  Sub-proof #317 shows that the following formulas are inconsistent:
% 158.86/25.31  ----------------------------------------------------------------
% 158.86/25.31    (1)  all_56_4 = e2 & op(e3, e1) = e2
% 158.86/25.31    (2)  all_56_4 = e1
% 158.86/25.31    (3)   ~ (e2 = e1)
% 158.86/25.31  
% 158.86/25.31  Begin of proof
% 158.86/25.31  | 
% 158.86/25.31  | ALPHA: (1) implies:
% 158.86/25.31  |   (4)  all_56_4 = e2
% 158.86/25.31  | 
% 158.86/25.31  | COMBINE_EQS: (2), (4) imply:
% 158.86/25.31  |   (5)  e2 = e1
% 158.86/25.31  | 
% 158.86/25.31  | SIMP: (5) implies:
% 158.86/25.31  |   (6)  e2 = e1
% 158.86/25.31  | 
% 158.86/25.31  | REDUCE: (3), (6) imply:
% 158.86/25.31  |   (7)  $false
% 158.86/25.31  | 
% 158.86/25.31  | CLOSE: (7) is inconsistent.
% 158.86/25.31  | 
% 158.86/25.31  End of proof
% 158.86/25.31  
% 158.86/25.31  Sub-proof #318 shows that the following formulas are inconsistent:
% 158.86/25.31  ----------------------------------------------------------------
% 158.86/25.31    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.86/25.31         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.86/25.31    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.86/25.31         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.86/25.31    (3)   ~ (e3 = e2)
% 158.86/25.31    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.31    (5)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 158.86/25.31         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 158.86/25.31    (6)  op(e3, e3) = e3
% 158.86/25.31    (7)  all_56_11 = e2
% 158.86/25.31    (8)  all_56_15 = e1
% 158.86/25.31    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.86/25.31         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.86/25.31    (10)   ~ (e1 = e0)
% 158.86/25.31    (11)  all_56_10 = e0
% 158.86/25.31    (12)   ~ (e2 = e1)
% 158.86/25.31    (13)   ~ (e3 = e1)
% 158.86/25.31    (14)   ~ (e2 = e0)
% 158.86/25.31    (15)   ~ (e3 = e0)
% 158.86/25.31  
% 158.86/25.31  Begin of proof
% 158.86/25.31  | 
% 158.86/25.31  | BETA: splitting (5) gives:
% 158.86/25.31  | 
% 158.86/25.31  | Case 1:
% 158.86/25.31  | | 
% 158.86/25.31  | |   (16)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 158.86/25.31  | |           e3)
% 158.86/25.31  | | 
% 158.86/25.31  | | BETA: splitting (16) gives:
% 158.86/25.31  | | 
% 158.86/25.31  | | Case 1:
% 158.86/25.31  | | | 
% 158.86/25.31  | | |   (17)  all_56_9 = e3 & op(e3, e0) = e3
% 158.86/25.31  | | | 
% 158.86/25.31  | | | ALPHA: (17) implies:
% 158.86/25.31  | | |   (18)  all_56_9 = e3
% 158.86/25.31  | | | 
% 158.86/25.31  | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (12), (13), (14), (15),
% 158.86/25.31  | | |            (18) are inconsistent by sub-proof #632.
% 158.86/25.31  | | | 
% 158.86/25.31  | | Case 2:
% 158.86/25.31  | | | 
% 158.86/25.31  | | |   (19)  all_56_10 = e3 & op(e2, e0) = e3
% 158.86/25.31  | | | 
% 158.86/25.31  | | | ALPHA: (19) implies:
% 158.86/25.31  | | |   (20)  all_56_10 = e3
% 158.86/25.31  | | | 
% 158.86/25.31  | | | REF_CLOSE: (11), (15), (20) are inconsistent by sub-proof #740.
% 158.86/25.31  | | | 
% 158.86/25.31  | | End of split
% 158.86/25.31  | | 
% 158.86/25.31  | Case 2:
% 158.86/25.31  | | 
% 158.86/25.31  | |   (21)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 158.86/25.31  | |           e3)
% 158.86/25.31  | | 
% 158.86/25.31  | | BETA: splitting (21) gives:
% 158.86/25.31  | | 
% 158.86/25.31  | | Case 1:
% 158.86/25.31  | | | 
% 158.86/25.31  | | |   (22)  all_56_11 = e3 & op(e1, e0) = e3
% 158.86/25.31  | | | 
% 158.86/25.31  | | | ALPHA: (22) implies:
% 158.86/25.31  | | |   (23)  all_56_11 = e3
% 158.86/25.31  | | | 
% 158.86/25.31  | | | REF_CLOSE: (3), (7), (23) are inconsistent by sub-proof #319.
% 158.86/25.31  | | | 
% 158.86/25.31  | | Case 2:
% 158.86/25.31  | | | 
% 158.86/25.31  | | |   (24)  all_56_15 = e3 & op(e0, e0) = e3
% 158.86/25.31  | | | 
% 158.86/25.31  | | | ALPHA: (24) implies:
% 158.86/25.31  | | |   (25)  all_56_15 = e3
% 158.86/25.31  | | | 
% 158.86/25.31  | | | COMBINE_EQS: (8), (25) imply:
% 158.86/25.31  | | |   (26)  e3 = e1
% 158.86/25.31  | | | 
% 158.86/25.31  | | | SIMP: (26) implies:
% 158.86/25.31  | | |   (27)  e3 = e1
% 158.86/25.31  | | | 
% 158.86/25.31  | | | REDUCE: (13), (27) imply:
% 158.86/25.31  | | |   (28)  $false
% 158.86/25.31  | | | 
% 158.86/25.31  | | | CLOSE: (28) is inconsistent.
% 158.86/25.31  | | | 
% 158.86/25.31  | | End of split
% 158.86/25.31  | | 
% 158.86/25.31  | End of split
% 158.86/25.31  | 
% 158.86/25.31  End of proof
% 158.86/25.31  
% 158.86/25.31  Sub-proof #319 shows that the following formulas are inconsistent:
% 158.86/25.31  ----------------------------------------------------------------
% 158.86/25.31    (1)  all_56_11 = e3
% 158.86/25.31    (2)  all_56_11 = e2
% 158.86/25.31    (3)   ~ (e3 = e2)
% 158.86/25.31  
% 158.86/25.31  Begin of proof
% 158.86/25.31  | 
% 158.86/25.31  | COMBINE_EQS: (1), (2) imply:
% 158.86/25.31  |   (4)  e3 = e2
% 158.86/25.31  | 
% 158.86/25.31  | SIMP: (4) implies:
% 158.86/25.31  |   (5)  e3 = e2
% 158.86/25.31  | 
% 158.86/25.31  | REDUCE: (3), (5) imply:
% 158.86/25.31  |   (6)  $false
% 158.86/25.31  | 
% 158.86/25.31  | CLOSE: (6) is inconsistent.
% 158.86/25.31  | 
% 158.86/25.31  End of proof
% 158.86/25.31  
% 158.86/25.31  Sub-proof #320 shows that the following formulas are inconsistent:
% 158.86/25.31  ----------------------------------------------------------------
% 158.86/25.31    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.86/25.31         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.86/25.31    (2)   ~ (all_52_7 = e0)
% 158.86/25.31    (3)  op(e0, e0) = e1
% 158.86/25.31    (4)   ~ (all_52_12 = e1)
% 158.86/25.31    (5)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.86/25.31         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.86/25.31    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.86/25.31         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.86/25.31    (7)   ~ (all_52_4 = e3)
% 158.86/25.31    (8)  op(e1, e1) = e0
% 158.86/25.31    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.86/25.31         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.86/25.31    (10)  op(e0, e1) = all_52_11
% 158.86/25.31    (11)   ~ (e3 = e2)
% 158.86/25.31    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.86/25.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.86/25.31    (13)  op(e0, e3) = all_52_3
% 158.86/25.31    (14)  op(e3, e1) = all_52_8
% 158.86/25.31    (15)   ~ (all_52_12 = e3)
% 158.86/25.31    (16)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.86/25.31          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.86/25.31    (17)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 158.86/25.31          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.86/25.31    (18)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.86/25.31          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.86/25.31    (19)  op(e0, e2) = all_52_7
% 158.86/25.31    (20)   ~ (all_52_11 = e1)
% 158.86/25.31    (21)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.86/25.31          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.86/25.31    (22)  op(e0, e3) = e0
% 158.86/25.31    (23)  op(e1, e0) = all_52_14
% 158.86/25.31    (24)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.86/25.31          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.86/25.31    (25)  op(e3, e3) = e3
% 158.86/25.31    (26)  op(e2, e2) = e0
% 158.86/25.31    (27)  op(e3, e2) = all_52_4
% 158.86/25.31    (28)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.86/25.31          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 158.86/25.31            e2)
% 158.86/25.31    (29)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.86/25.31          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.86/25.31    (30)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 158.86/25.31            all_57_0 & $i(all_57_0))
% 158.86/25.31    (31)   ~ (e1 = e0)
% 158.86/25.31    (32)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.86/25.31          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.86/25.31    (33)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.86/25.31          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.86/25.31    (34)   ~ (all_52_11 = e0)
% 158.86/25.31    (35)   ~ (e2 = e1)
% 158.86/25.31    (36)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 158.86/25.31            all_57_6 & $i(all_57_6))
% 158.86/25.31    (37)  op(e3, e0) = all_52_12
% 158.86/25.31    (38)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.86/25.31          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.86/25.31    (39)   ~ (all_52_3 = all_52_11)
% 158.86/25.31    (40)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.86/25.31          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.86/25.31    (41)   ~ (all_52_14 = e1)
% 158.86/25.32    (42)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.86/25.32            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.86/25.32            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.86/25.32            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.86/25.32              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.86/25.32          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.86/25.32            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.86/25.32              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.86/25.32            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.86/25.32              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.86/25.32          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.86/25.32            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.86/25.32              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.86/25.32            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.86/25.32              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.86/25.32          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.86/25.32            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.86/25.32            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.86/25.32              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.86/25.32            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.86/25.32            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.86/25.32            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.86/25.32            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.86/25.32              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.86/25.32            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.86/25.32          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.86/25.32            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.86/25.32              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.86/25.32            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.86/25.32            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.86/25.32          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.86/25.32            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.86/25.32              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.86/25.32            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.86/25.32            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.86/25.32          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.86/25.32            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.86/25.32              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.86/25.32            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.86/25.32              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.86/25.32          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.86/25.32            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.86/25.32            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.86/25.32            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.86/25.32            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.86/25.32            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.86/25.32            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.86/25.32            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.86/25.32              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.86/25.32            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.86/25.32            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.86/25.32            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.86/25.32            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.86/25.32              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.86/25.32            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.86/25.32          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.86/25.32            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.86/25.32              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.86/25.32              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.86/25.32            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.86/25.32            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.86/25.32            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.86/25.32            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.86/25.32              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.86/25.32            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.86/25.32          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.86/25.32            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.86/25.32              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.86/25.32            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.86/25.32              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.86/25.32          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.86/25.32            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.86/25.32              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.86/25.32              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.86/25.32            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.86/25.32          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.86/25.32            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.86/25.32            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.86/25.32                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.86/25.32                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.86/25.32                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.86/25.32                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.86/25.32                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.86/25.32                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.86/25.32                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.86/25.32                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.86/25.32                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.86/25.32                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.86/25.32                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.86/25.32                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.86/25.32                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.86/25.32                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.32                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.86/25.32                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.32                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.86/25.32                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.86/25.32                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.86/25.32                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.86/25.32                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.86/25.32                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.86/25.32                op(e0, e1) = e0)))
% 158.86/25.32    (43)   ~ (all_52_7 = e1)
% 158.86/25.32    (44)   ~ (e3 = e1)
% 158.86/25.32    (45)   ~ (e2 = e0)
% 158.86/25.32    (46)   ~ (all_52_8 = e3)
% 158.86/25.32    (47)   ~ (e3 = e0)
% 158.86/25.32  
% 158.86/25.32  Begin of proof
% 158.86/25.32  | 
% 158.86/25.32  | BETA: splitting (9) gives:
% 158.86/25.32  | 
% 158.86/25.32  | Case 1:
% 158.86/25.32  | | 
% 158.86/25.32  | |   (48)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 158.86/25.32  | |           e0)
% 158.86/25.32  | | 
% 158.86/25.32  | | REF_CLOSE: (5), (6), (9), (11), (12), (18), (19), (24), (25), (26), (29),
% 158.86/25.32  | |            (31), (35), (43), (44), (45), (47), (48) are inconsistent by
% 158.86/25.32  | |            sub-proof #326.
% 158.86/25.32  | | 
% 158.86/25.32  | Case 2:
% 158.86/25.32  | | 
% 158.86/25.32  | |   (49)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 158.86/25.32  | |           e0)
% 158.86/25.32  | | 
% 158.86/25.32  | | BETA: splitting (49) gives:
% 158.86/25.32  | | 
% 158.86/25.32  | | Case 1:
% 158.86/25.32  | | | 
% 158.86/25.32  | | |   (50)  all_56_4 = e0 & op(e3, e1) = e0
% 158.86/25.32  | | | 
% 158.86/25.32  | | | REF_CLOSE: (1), (3), (6), (8), (9), (10), (11), (12), (14), (16), (17),
% 158.86/25.32  | | |            (20), (21), (23), (24), (25), (26), (28), (29), (30), (31),
% 158.86/25.32  | | |            (32), (33), (35), (38), (40), (41), (44), (45), (46), (47),
% 158.86/25.32  | | |            (50) are inconsistent by sub-proof #323.
% 158.86/25.32  | | | 
% 158.86/25.32  | | Case 2:
% 158.86/25.32  | | | 
% 158.86/25.32  | | |   (51)  all_56_9 = e0 & op(e3, e0) = e0
% 158.86/25.32  | | | 
% 158.86/25.32  | | | ALPHA: (51) implies:
% 158.86/25.32  | | |   (52)  op(e3, e0) = e0
% 158.86/25.32  | | | 
% 158.86/25.32  | | | BETA: splitting (42) gives:
% 158.86/25.32  | | | 
% 158.86/25.32  | | | Case 1:
% 158.86/25.32  | | | | 
% 158.86/25.32  | | | |   (53)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12
% 158.86/25.32  | | | |             = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2
% 158.86/25.32  | | | |           & op(e2, e2) = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.86/25.32  | | | |           all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3,
% 158.86/25.32  | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 158.86/25.32  | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 &
% 158.86/25.32  | | | |           all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 158.86/25.32  | | | |           op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.86/25.32  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 =
% 158.86/25.32  | | | |           e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 158.86/25.32  | | | |           = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.86/25.32  | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12
% 158.86/25.32  | | | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0,
% 158.86/25.32  | | | |             e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 158.86/25.32  | | | |           & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) &
% 158.86/25.32  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 158.86/25.32  | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_12
% 158.86/25.32  | | | |           = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 158.86/25.32  | | | |         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 158.86/25.32  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.86/25.32  | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 158.86/25.32  | | | |           & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.86/25.32  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.86/25.32  | | | |           op(e2, e1) = e2 & $i(all_57_12)) | (all_57_1 = e3 & all_57_6 =
% 158.86/25.32  | | | |           e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.86/25.32  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.86/25.32  | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3
% 158.86/25.32  | | | |             = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) | (all_57_1 = e3
% 158.86/25.32  | | | |           & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.86/25.32  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.86/25.32  | | | |           op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 =
% 158.86/25.32  | | | |           e3 & all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 158.86/25.32  | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.86/25.32  | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_14 =
% 158.86/25.32  | | | |           e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 158.86/25.32  | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.86/25.32  | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14
% 158.86/25.32  | | | |             = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1
% 158.86/25.32  | | | |           & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.86/25.32  | | | |           all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1,
% 158.86/25.32  | | | |             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.86/25.32  | | | |             e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.86/25.32  | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 158.86/25.32  | | | |           & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.86/25.32  | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 =
% 158.86/25.32  | | | |             e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.86/25.32  | | | | 
% 158.86/25.32  | | | | BETA: splitting (53) gives:
% 158.86/25.32  | | | | 
% 158.86/25.32  | | | | Case 1:
% 158.86/25.32  | | | | | 
% 158.86/25.32  | | | | |   (54)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.86/25.32  | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.86/25.32  | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12)) |
% 158.86/25.32  | | | | |         (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 158.86/25.32  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 158.86/25.32  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.86/25.32  | | | | |         (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.86/25.32  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 158.86/25.32  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.86/25.32  | | | | |         (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.86/25.32  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 158.86/25.32  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.86/25.32  | | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.86/25.32  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 158.86/25.32  | | | | |           & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.86/25.32  | | | | |         (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 158.86/25.32  | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.86/25.32  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.86/25.32  | | | | |         (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) =
% 158.86/25.32  | | | | |           e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 158.86/25.32  | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.86/25.32  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.86/25.32  | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 158.86/25.32  | | | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 158.86/25.32  | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.86/25.32  | | | | |           $i(all_57_12))
% 158.86/25.32  | | | | | 
% 158.86/25.32  | | | | | BETA: splitting (54) gives:
% 158.86/25.32  | | | | | 
% 158.86/25.32  | | | | | Case 1:
% 158.86/25.32  | | | | | | 
% 158.86/25.32  | | | | | |   (55)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.86/25.32  | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.86/25.32  | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12))
% 158.86/25.32  | | | | | |         | (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 158.86/25.32  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.86/25.32  | | | | | |           e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.86/25.32  | | | | | |         (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.86/25.32  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.86/25.32  | | | | | |           all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.86/25.32  | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.86/25.32  | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.86/25.32  | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 158.86/25.32  | | | | | |           = e3 & $i(all_57_10))
% 158.86/25.32  | | | | | | 
% 158.86/25.32  | | | | | | BETA: splitting (55) gives:
% 158.86/25.32  | | | | | | 
% 158.86/25.32  | | | | | | Case 1:
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | |   (56)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.86/25.32  | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.86/25.32  | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.86/25.32  | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.86/25.32  | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.86/25.32  | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 158.86/25.32  | | | | | | |             e2) = e3 & $i(all_57_10))
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | | BETA: splitting (56) gives:
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | | Case 1:
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | |   (57)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.86/25.32  | | | | | | | |         (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.86/25.32  | | | | | | | |         op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12)
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | ALPHA: (57) implies:
% 158.86/25.32  | | | | | | | |   (58)  op(e2, e3) = e2
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | REF_CLOSE: (12), (26), (30), (47), (58) are inconsistent by
% 158.86/25.32  | | | | | | | |            sub-proof #322.
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | Case 2:
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | |   (59)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 158.86/25.32  | | | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.86/25.32  | | | | | | | |         e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | ALPHA: (59) implies:
% 158.86/25.32  | | | | | | | |   (60)  op(e2, e3) = e2
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | REF_CLOSE: (12), (26), (30), (47), (60) are inconsistent by
% 158.86/25.32  | | | | | | | |            sub-proof #322.
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | End of split
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | Case 2:
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | |   (61)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.86/25.32  | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.86/25.32  | | | | | | |           all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.86/25.32  | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.86/25.32  | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.86/25.32  | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 158.86/25.32  | | | | | | |             e2) = e3 & $i(all_57_10))
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | | BETA: splitting (61) gives:
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | | Case 1:
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | |   (62)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.86/25.32  | | | | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.86/25.32  | | | | | | | |         all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.86/25.32  | | | | | | | |         $i(all_57_12)
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | ALPHA: (62) implies:
% 158.86/25.32  | | | | | | | |   (63)  op(e2, e3) = e2
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | REF_CLOSE: (12), (26), (30), (47), (63) are inconsistent by
% 158.86/25.32  | | | | | | | |            sub-proof #322.
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | Case 2:
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | |   (64)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.86/25.32  | | | | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 158.86/25.32  | | | | | | | |         e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | ALPHA: (64) implies:
% 158.86/25.32  | | | | | | | |   (65)  op(e2, e3) = e2
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | REF_CLOSE: (12), (26), (30), (47), (65) are inconsistent by
% 158.86/25.32  | | | | | | | |            sub-proof #322.
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | End of split
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | End of split
% 158.86/25.32  | | | | | | 
% 158.86/25.32  | | | | | Case 2:
% 158.86/25.32  | | | | | | 
% 158.86/25.32  | | | | | |   (66)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.86/25.32  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.86/25.32  | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.86/25.32  | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.86/25.32  | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.86/25.32  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 158.86/25.32  | | | | | |           = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 & 
% 158.86/25.32  | | | | | |           ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 158.86/25.32  | | | | | |         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.86/25.32  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.86/25.32  | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.86/25.32  | | | | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 158.86/25.32  | | | | | |           (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.86/25.32  | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.86/25.32  | | | | | | 
% 158.86/25.32  | | | | | | BETA: splitting (66) gives:
% 158.86/25.32  | | | | | | 
% 158.86/25.32  | | | | | | Case 1:
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | |   (67)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.86/25.32  | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.86/25.32  | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.86/25.32  | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.86/25.32  | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.86/25.32  | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.86/25.32  | | | | | | |             e2) = e3 & $i(all_57_10))
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | | BETA: splitting (67) gives:
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | | Case 1:
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | |   (68)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.86/25.32  | | | | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.86/25.32  | | | | | | | |         all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.86/25.32  | | | | | | | |         $i(all_57_12)
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | ALPHA: (68) implies:
% 158.86/25.32  | | | | | | | |   (69)  op(e2, e3) = e2
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | REF_CLOSE: (12), (26), (30), (47), (69) are inconsistent by
% 158.86/25.32  | | | | | | | |            sub-proof #322.
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | Case 2:
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | |   (70)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 158.86/25.32  | | | | | | | |         (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 158.86/25.32  | | | | | | | |         e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | ALPHA: (70) implies:
% 158.86/25.32  | | | | | | | |   (71)  op(e2, e3) = e2
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | | REF_CLOSE: (12), (26), (30), (47), (71) are inconsistent by
% 158.86/25.32  | | | | | | | |            sub-proof #322.
% 158.86/25.32  | | | | | | | | 
% 158.86/25.32  | | | | | | | End of split
% 158.86/25.32  | | | | | | | 
% 158.86/25.32  | | | | | | Case 2:
% 158.86/25.32  | | | | | | | 
% 158.93/25.32  | | | | | | |   (72)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2,
% 158.93/25.32  | | | | | | |             e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 &
% 158.93/25.32  | | | | | | |           all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.93/25.32  | | | | | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) =
% 158.93/25.32  | | | | | | |           e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.93/25.32  | | | | | | |           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.93/25.32  | | | | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.93/25.32  | | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.93/25.32  | | | | | | | 
% 158.93/25.32  | | | | | | | BETA: splitting (72) gives:
% 158.93/25.32  | | | | | | | 
% 158.93/25.32  | | | | | | | Case 1:
% 158.93/25.32  | | | | | | | | 
% 158.93/25.32  | | | | | | | |   (73)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2,
% 158.93/25.32  | | | | | | | |           e3) = e2 & op(e2, e2) = e2
% 158.93/25.32  | | | | | | | | 
% 158.93/25.32  | | | | | | | | ALPHA: (73) implies:
% 158.93/25.32  | | | | | | | |   (74)  op(e2, e3) = e2
% 158.93/25.32  | | | | | | | | 
% 158.93/25.32  | | | | | | | | REF_CLOSE: (12), (26), (30), (47), (74) are inconsistent by
% 158.93/25.32  | | | | | | | |            sub-proof #322.
% 158.93/25.32  | | | | | | | | 
% 158.93/25.32  | | | | | | | Case 2:
% 158.93/25.32  | | | | | | | | 
% 158.93/25.32  | | | | | | | |   (75)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.93/25.32  | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2)
% 158.93/25.32  | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.93/25.32  | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 158.93/25.32  | | | | | | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.93/25.32  | | | | | | | |           & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.93/25.32  | | | | | | | |             e1) = e2 & $i(all_57_12))
% 158.93/25.32  | | | | | | | | 
% 158.93/25.32  | | | | | | | | REF_CLOSE: (8), (11), (12), (25), (47), (75) are inconsistent by
% 158.93/25.32  | | | | | | | |            sub-proof #321.
% 158.93/25.32  | | | | | | | | 
% 158.93/25.32  | | | | | | | End of split
% 158.93/25.32  | | | | | | | 
% 158.93/25.32  | | | | | | End of split
% 158.93/25.32  | | | | | | 
% 158.93/25.32  | | | | | End of split
% 158.93/25.32  | | | | | 
% 158.93/25.32  | | | | Case 2:
% 158.93/25.32  | | | | | 
% 158.93/25.33  | | | | |   (76)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.33  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 158.93/25.33  | | | | |           & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.93/25.33  | | | | |         (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) =
% 158.93/25.33  | | | | |           e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 158.93/25.33  | | | | |           all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 &
% 158.93/25.33  | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.93/25.33  | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10
% 158.93/25.33  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.93/25.33  | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.93/25.33  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_14
% 158.93/25.33  | | | | |           = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.33  | | | | |             e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.93/25.33  | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12
% 158.93/25.33  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.93/25.33  | | | | |           e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.93/25.33  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 & all_57_15
% 158.93/25.33  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 158.93/25.33  | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.33  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14
% 158.93/25.33  | | | | |           = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.33  | | | | |             e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.93/25.33  | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 =
% 158.93/25.33  | | | | |             e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.93/25.33  | | | | | 
% 158.93/25.33  | | | | | BETA: splitting (76) gives:
% 158.93/25.33  | | | | | 
% 158.93/25.33  | | | | | Case 1:
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | |   (77)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.33  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.93/25.33  | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.93/25.33  | | | | | |         (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3)
% 158.93/25.33  | | | | | |           = e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2
% 158.93/25.33  | | | | | |           & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 &
% 158.93/25.33  | | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 158.93/25.33  | | | | | |           & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.93/25.33  | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 158.93/25.33  | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 158.93/25.33  | | | | | |           & $i(all_57_14))
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | | BETA: splitting (77) gives:
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | | Case 1:
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | |   (78)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.33  | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.93/25.33  | | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 158.93/25.33  | | | | | | |         | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3,
% 158.93/25.33  | | | | | | |             e3) = e3 & op(e3, e2) = e3)
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | | REF_CLOSE: (3), (7), (12), (27), (44), (78) are inconsistent by
% 158.93/25.33  | | | | | | |            sub-proof #378.
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | Case 2:
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | |   (79)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.93/25.33  | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.93/25.33  | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.93/25.33  | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.93/25.33  | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 158.93/25.33  | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.93/25.33  | | | | | | |           all_57_14 & $i(all_57_14))
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | | REF_CLOSE: (11), (12), (25), (44), (79) are inconsistent by
% 158.93/25.33  | | | | | | |            sub-proof #922.
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | End of split
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | Case 2:
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | |   (80)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.93/25.33  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 158.93/25.33  | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.93/25.33  | | | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.93/25.33  | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.93/25.33  | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.93/25.33  | | | | | |         | (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.93/25.33  | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 158.93/25.33  | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.33  | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.93/25.33  | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.93/25.33  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.93/25.33  | | | | | |           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 & 
% 158.93/25.33  | | | | | |           ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | | BETA: splitting (80) gives:
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | | Case 1:
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | |   (81)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.93/25.33  | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 158.93/25.33  | | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 158.93/25.33  | | | | | | |         | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.93/25.33  | | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.93/25.33  | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.93/25.33  | | | | | | |           $i(all_57_14))
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | | REF_CLOSE: (8), (12), (26), (31), (47), (81) are inconsistent by
% 158.93/25.33  | | | | | | |            sub-proof #366.
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | Case 2:
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | |   (82)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.93/25.33  | | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 158.93/25.33  | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.33  | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.93/25.33  | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.93/25.33  | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 158.93/25.33  | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 158.93/25.33  | | | | | | |           = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | | REF_CLOSE: (8), (10), (12), (31), (34), (47), (82) are
% 158.93/25.33  | | | | | | |            inconsistent by sub-proof #377.
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | End of split
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | End of split
% 158.93/25.33  | | | | | 
% 158.93/25.33  | | | | End of split
% 158.93/25.33  | | | | 
% 158.93/25.33  | | | Case 2:
% 158.93/25.33  | | | | 
% 158.93/25.33  | | | |   (83)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14
% 158.93/25.33  | | | |             = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1
% 158.93/25.33  | | | |           & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.93/25.33  | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2,
% 158.93/25.33  | | | |             e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.93/25.33  | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.93/25.33  | | | |           all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12
% 158.93/25.33  | | | |           & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.93/25.33  | | | |           $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 =
% 158.93/25.33  | | | |           e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.93/25.33  | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 158.93/25.33  | | | |         | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.93/25.33  | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.93/25.33  | | | |           op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3
% 158.93/25.33  | | | |           = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.93/25.33  | | | |           op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 158.93/25.33  | | | |           = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.33  | | | |             e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.93/25.33  | | | |           $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 =
% 158.93/25.33  | | | |             e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.93/25.33  | | | |           all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 158.93/25.33  | | | |             e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 158.93/25.33  | | | |             e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 &
% 158.93/25.33  | | | |           all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12
% 158.93/25.33  | | | |           & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.93/25.33  | | | |           $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 =
% 158.93/25.33  | | | |             e1) & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 &
% 158.93/25.33  | | | |           all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 158.93/25.33  | | | |             e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.93/25.33  | | | |             e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.93/25.33  | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 158.93/25.33  | | | |           & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.93/25.33  | | | |           $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 & all_57_15 =
% 158.93/25.33  | | | |           e2 &  ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.93/25.33  | | | |           = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.93/25.33  | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3
% 158.93/25.33  | | | |           & op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 158.93/25.33  | | | |             = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 158.93/25.33  | | | |           & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0)
% 158.93/25.33  | | | |           = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 =
% 158.93/25.33  | | | |               e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.93/25.33  | | | |               & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.93/25.33  | | | |             (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.93/25.33  | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.93/25.33  | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 158.93/25.33  | | | |               all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 158.93/25.33  | | | |               op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.93/25.33  | | | |               all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.93/25.33  | | | |             (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.93/25.33  | | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.93/25.33  | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.93/25.33  | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 158.93/25.33  | | | |               op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.93/25.33  | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.93/25.33  | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.93/25.33  | | | |             (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2)
% 158.93/25.33  | | | |               = e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.93/25.33  | | | |               ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.93/25.33  | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.93/25.33  | | | |               all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.93/25.33  | | | |               op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.93/25.33  | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.33  | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.93/25.33  | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 158.93/25.33  | | | |               (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.93/25.33  | | | |               e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.93/25.33  | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.93/25.33  | | | | 
% 158.93/25.33  | | | | BETA: splitting (83) gives:
% 158.93/25.33  | | | | 
% 158.93/25.33  | | | | Case 1:
% 158.93/25.33  | | | | | 
% 158.93/25.33  | | | | |   (84)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.93/25.33  | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.93/25.33  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.93/25.33  | | | | |         (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.93/25.33  | | | | |           (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.93/25.33  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.93/25.33  | | | | |         (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.93/25.33  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 158.93/25.33  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.93/25.33  | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.93/25.33  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 158.93/25.33  | | | | |           & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 158.93/25.33  | | | | |         (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.93/25.33  | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 158.93/25.33  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.93/25.33  | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) =
% 158.93/25.33  | | | | |           e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.93/25.33  | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.93/25.33  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.93/25.33  | | | | |           e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~
% 158.93/25.33  | | | | |           (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 158.93/25.33  | | | | |           e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.93/25.33  | | | | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.93/25.33  | | | | |           op(e1, e0) = e1 & $i(all_57_14))
% 158.93/25.33  | | | | | 
% 158.93/25.33  | | | | | BETA: splitting (84) gives:
% 158.93/25.33  | | | | | 
% 158.93/25.33  | | | | | Case 1:
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | |   (85)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.93/25.33  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.93/25.33  | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.93/25.33  | | | | | |         | (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.93/25.33  | | | | | |           (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.93/25.33  | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.93/25.33  | | | | | |         | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.93/25.33  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 158.93/25.33  | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.93/25.33  | | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.93/25.33  | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.93/25.33  | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.33  | | | | | |           $i(all_57_14))
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | | BETA: splitting (85) gives:
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | | Case 1:
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | |   (86)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.93/25.33  | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.93/25.33  | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.93/25.33  | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.93/25.33  | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 &
% 158.93/25.33  | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.93/25.33  | | | | | | |           all_57_14 & $i(all_57_14))
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | | REF_CLOSE: (12), (25), (26), (31), (44), (86) are inconsistent by
% 158.93/25.33  | | | | | | |            sub-proof #920.
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | Case 2:
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | |   (87)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.93/25.33  | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 158.93/25.33  | | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 158.93/25.33  | | | | | | |         | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.93/25.33  | | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.93/25.33  | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.33  | | | | | | |           $i(all_57_14))
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | | REF_CLOSE: (8), (10), (12), (34), (45), (87) are inconsistent by
% 158.93/25.33  | | | | | | |            sub-proof #376.
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | End of split
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | Case 2:
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | |   (88)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.93/25.33  | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 158.93/25.33  | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.93/25.33  | | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2)
% 158.93/25.33  | | | | | |           = e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.93/25.33  | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.93/25.33  | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.93/25.33  | | | | | |           = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 & 
% 158.93/25.33  | | | | | |           ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) |
% 158.93/25.33  | | | | | |         (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.93/25.33  | | | | | |           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.93/25.33  | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | | BETA: splitting (88) gives:
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | | Case 1:
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | |   (89)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.93/25.33  | | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 158.93/25.33  | | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 158.93/25.33  | | | | | | |         | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1,
% 158.93/25.33  | | | | | | |             e2) = e1 & op(e1, e1) = e1)
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | | REF_CLOSE: (8), (12), (31), (45), (89) are inconsistent by
% 158.93/25.33  | | | | | | |            sub-proof #701.
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | Case 2:
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | |   (90)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.33  | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 158.93/25.33  | | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 158.93/25.33  | | | | | | |         | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3,
% 158.93/25.33  | | | | | | |             e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.93/25.33  | | | | | | |           all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.93/25.33  | | | | | | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.93/25.33  | | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | | REF_CLOSE: (3), (12), (14), (25), (44), (46), (90) are
% 158.93/25.33  | | | | | | |            inconsistent by sub-proof #375.
% 158.93/25.33  | | | | | | | 
% 158.93/25.33  | | | | | | End of split
% 158.93/25.33  | | | | | | 
% 158.93/25.33  | | | | | End of split
% 158.93/25.33  | | | | | 
% 158.93/25.33  | | | | Case 2:
% 158.93/25.33  | | | | | 
% 158.93/25.34  | | | | |   (91)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.93/25.34  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 158.93/25.34  | | | | |           & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.93/25.34  | | | | |         (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) =
% 158.93/25.34  | | | | |           e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.93/25.34  | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 &
% 158.93/25.34  | | | | |           op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.93/25.34  | | | | |           $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15
% 158.93/25.34  | | | | |           = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.34  | | | | |             e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.93/25.34  | | | | |           $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 & all_57_15
% 158.93/25.34  | | | | |           = e2 &  ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 158.93/25.34  | | | | |             e0) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.93/25.34  | | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 =
% 158.93/25.34  | | | | |             e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2
% 158.93/25.34  | | | | |           & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2,
% 158.93/25.34  | | | | |             e0) = e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 =
% 158.93/25.34  | | | | |             e0) & op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.93/25.34  | | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3
% 158.93/25.34  | | | | |               & all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0
% 158.93/25.34  | | | | |               & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.93/25.34  | | | | |               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.93/25.34  | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.93/25.34  | | | | |             (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.93/25.34  | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.93/25.34  | | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.93/25.34  | | | | |               (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9
% 158.93/25.34  | | | | |               = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3)
% 158.93/25.34  | | | | |               = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.93/25.34  | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.93/25.34  | | | | |                 e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.93/25.34  | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.93/25.34  | | | | |                ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1
% 158.93/25.34  | | | | |               & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 & 
% 158.93/25.34  | | | | |               ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.93/25.34  | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.34  | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.93/25.34  | | | | |             (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.93/25.34  | | | | |               (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.93/25.34  | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.93/25.34  | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.93/25.34  | | | | |               op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.93/25.34  | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.93/25.34  | | | | |               op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.93/25.34  | | | | |               e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 158.93/25.34  | | | | |               ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.93/25.34  | | | | | 
% 158.93/25.34  | | | | | BETA: splitting (91) gives:
% 158.93/25.34  | | | | | 
% 158.93/25.34  | | | | | Case 1:
% 158.93/25.34  | | | | | | 
% 158.93/25.34  | | | | | |   (92)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.93/25.34  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 158.93/25.34  | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.93/25.34  | | | | | |         (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2)
% 158.93/25.34  | | | | | |           = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 158.93/25.34  | | | | | |           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 &
% 158.93/25.34  | | | | | |           op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 158.93/25.34  | | | | | |           & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.93/25.34  | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.93/25.34  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.93/25.34  | | | | | |           = e3 & $i(all_57_10))
% 158.93/25.34  | | | | | | 
% 158.93/25.34  | | | | | | REF_CLOSE: (3), (12), (26), (31), (35), (44), (45), (92) are
% 158.93/25.34  | | | | | |            inconsistent by sub-proof #342.
% 158.93/25.34  | | | | | | 
% 158.93/25.34  | | | | | Case 2:
% 158.93/25.34  | | | | | | 
% 158.93/25.34  | | | | | |   (93)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 158.93/25.34  | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 158.93/25.34  | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.93/25.34  | | | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3)
% 158.93/25.34  | | | | | |           = e3 & op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2
% 158.93/25.34  | | | | | |           &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.93/25.34  | | | | | |         (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1)
% 158.93/25.34  | | | | | |           = e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 158.93/25.34  | | | | | |           $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 158.93/25.34  | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0
% 158.93/25.34  | | | | | |               & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 158.93/25.34  | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.93/25.34  | | | | | |                 e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3)
% 158.93/25.34  | | | | | |               = e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 158.93/25.34  | | | | | |               e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.93/25.34  | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.93/25.34  | | | | | |               all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.93/25.34  | | | | | |             (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.93/25.34  | | | | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.93/25.34  | | | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.93/25.34  | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 158.93/25.34  | | | | | |               & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0
% 158.93/25.34  | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.93/25.34  | | | | | |                 e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2)
% 158.93/25.34  | | | | | |               = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 158.93/25.34  | | | | | |               & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 158.93/25.34  | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 158.93/25.34  | | | | | |               & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0
% 158.93/25.34  | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.93/25.34  | | | | | |                 e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 158.93/25.34  | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.93/25.34  | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.93/25.34  | | | | | |                 e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.93/25.34  | | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 158.93/25.34  | | | | | |               & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.93/25.34  | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.93/25.34  | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.93/25.34  | | | | | | 
% 158.93/25.34  | | | | | | BETA: splitting (93) gives:
% 158.93/25.34  | | | | | | 
% 158.93/25.34  | | | | | | Case 1:
% 158.93/25.34  | | | | | | | 
% 158.93/25.34  | | | | | | |   (94)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 158.93/25.34  | | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 158.93/25.34  | | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 158.93/25.34  | | | | | | |         | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3,
% 158.93/25.34  | | | | | | |             e3) = e3 & op(e3, e0) = e3)
% 158.93/25.34  | | | | | | | 
% 158.93/25.34  | | | | | | | REF_CLOSE: (3), (12), (15), (35), (37), (94) are inconsistent by
% 158.93/25.34  | | | | | | |            sub-proof #373.
% 158.93/25.34  | | | | | | | 
% 158.93/25.34  | | | | | | Case 2:
% 158.93/25.34  | | | | | | | 
% 158.93/25.34  | | | | | | |   (95)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 158.93/25.34  | | | | | | |             e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 158.93/25.34  | | | | | | |           all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1,
% 158.93/25.34  | | | | | | |             e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.93/25.34  | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.93/25.34  | | | | | | |               (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3
% 158.93/25.34  | | | | | | |               & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2
% 158.93/25.34  | | | | | | |               & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2)
% 158.93/25.34  | | | | | | |               = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.93/25.34  | | | | | | |             (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.93/25.34  | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1
% 158.93/25.34  | | | | | | |               & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0
% 158.93/25.34  | | | | | | |               &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.93/25.34  | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 158.93/25.34  | | | | | | |               & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.93/25.34  | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 158.93/25.34  | | | | | | |               e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 158.93/25.34  | | | | | | |                 e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.93/25.34  | | | | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.93/25.34  | | | | | | |                 e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.93/25.34  | | | | | | |                 e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~
% 158.93/25.34  | | | | | | |               (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.93/25.34  | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 158.93/25.34  | | | | | | |               & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.93/25.34  | | | | | | |               e0) | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 158.93/25.34  | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.93/25.34  | | | | | | |                 e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.93/25.34  | | | | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.93/25.34  | | | | | | |                 e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 158.93/25.34  | | | | | | |                 e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.93/25.34  | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.93/25.34  | | | | | | |               all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.93/25.34  | | | | | | |               $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 158.93/25.34  | | | | | | |               ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.93/25.34  | | | | | | | 
% 158.93/25.34  | | | | | | | BETA: splitting (95) gives:
% 158.93/25.34  | | | | | | | 
% 158.93/25.34  | | | | | | | Case 1:
% 158.93/25.34  | | | | | | | | 
% 158.93/25.34  | | | | | | | |   (96)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 158.93/25.34  | | | | | | | |           e2) = e2 & op(e2, e0) = e2
% 158.93/25.34  | | | | | | | | 
% 158.93/25.34  | | | | | | | | ALPHA: (96) implies:
% 158.93/25.34  | | | | | | | |   (97)  op(e2, e2) = e2
% 158.93/25.34  | | | | | | | | 
% 158.93/25.34  | | | | | | | | REF_CLOSE: (12), (26), (45), (97) are inconsistent by sub-proof
% 158.93/25.34  | | | | | | | |            #942.
% 158.93/25.34  | | | | | | | | 
% 158.93/25.34  | | | | | | | Case 2:
% 158.93/25.34  | | | | | | | | 
% 158.93/25.34  | | | | | | | |   (98)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 158.93/25.34  | | | | | | | |             e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.93/25.34  | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9
% 158.93/25.34  | | | | | | | |               = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 158.93/25.34  | | | | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 158.93/25.34  | | | | | | | |               e0) | (all_57_6 = e0 & all_57_11 = e2 & all_57_12
% 158.93/25.34  | | | | | | | |               = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 158.93/25.34  | | | | | | | |               op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.93/25.34  | | | | | | | |               e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.93/25.34  | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 158.93/25.34  | | | | | | | |               e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15
% 158.93/25.34  | | | | | | | |               = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.93/25.34  | | | | | | | |               = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.93/25.34  | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 158.93/25.34  | | | | | | | |               e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11
% 158.93/25.34  | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.93/25.34  | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.93/25.34  | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14
% 158.93/25.34  | | | | | | | |               = e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 158.93/25.34  | | | | | | | |               op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.93/25.34  | | | | | | | |               e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.93/25.34  | | | | | | | |               e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 158.93/25.34  | | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.93/25.34  | | | | | | | |               op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.93/25.34  | | | | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.93/25.34  | | | | | | | |               (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 158.93/25.34  | | | | | | | |               e2 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13
% 158.93/25.34  | | | | | | | |               = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.34  | | | | | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.93/25.34  | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15
% 158.93/25.34  | | | | | | | |               = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.93/25.34  | | | | | | | |               all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.93/25.34  | | | | | | | |               $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &
% 158.93/25.34  | | | | | | | |                ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.93/25.34  | | | | | | | | 
% 158.93/25.34  | | | | | | | | BETA: splitting (98) gives:
% 158.93/25.34  | | | | | | | | 
% 158.93/25.34  | | | | | | | | Case 1:
% 158.93/25.34  | | | | | | | | | 
% 158.93/25.34  | | | | | | | | |   (99)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 158.93/25.34  | | | | | | | | |         op(e1, e1) = e1 & op(e1, e0) = e1
% 158.93/25.34  | | | | | | | | | 
% 158.93/25.34  | | | | | | | | | ALPHA: (99) implies:
% 158.93/25.34  | | | | | | | | |   (100)  op(e1, e1) = e1
% 158.93/25.34  | | | | | | | | | 
% 158.93/25.34  | | | | | | | | | REF_CLOSE: (8), (12), (31), (100) are inconsistent by
% 158.93/25.34  | | | | | | | | |            sub-proof #903.
% 158.93/25.34  | | | | | | | | | 
% 158.93/25.34  | | | | | | | | Case 2:
% 158.93/25.34  | | | | | | | | | 
% 158.93/25.34  | | | | | | | | |   (101)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 =
% 158.93/25.34  | | | | | | | | |              e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.93/25.34  | | | | | | | | |              (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 158.93/25.34  | | | | | | | | |              e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.93/25.34  | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.93/25.34  | | | | | | | | |                e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.93/25.34  | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.93/25.34  | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.93/25.34  | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.93/25.34  | | | | | | | | |              e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.93/25.34  | | | | | | | | |                e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.93/25.34  | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.93/25.34  | | | | | | | | |                e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.93/25.34  | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.93/25.34  | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.93/25.34  | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.93/25.34  | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14
% 158.93/25.34  | | | | | | | | |              = e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 158.93/25.34  | | | | | | | | |              op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.93/25.34  | | | | | | | | |              e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 158.93/25.34  | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10
% 158.93/25.34  | | | | | | | | |              = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 158.93/25.34  | | | | | | | | |              op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.93/25.34  | | | | | | | | |              e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.93/25.34  | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 158.93/25.34  | | | | | | | | |              e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.93/25.34  | | | | | | | | |              all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 158.93/25.34  | | | | | | | | |                e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.93/25.34  | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.93/25.34  | | | | | | | | |              e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.93/25.34  | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 158.93/25.34  | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.93/25.34  | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0))
% 158.93/25.34  | | | | | | | | | 
% 158.93/25.34  | | | | | | | | | ALPHA: (101) implies:
% 158.93/25.34  | | | | | | | | |   (102)  op(e0, e0) = all_57_15
% 158.93/25.34  | | | | | | | | |   (103)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.93/25.34  | | | | | | | | |            (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 158.93/25.34  | | | | | | | | |            e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 158.93/25.34  | | | | | | | | |            = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.93/25.34  | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 158.93/25.34  | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 158.93/25.34  | | | | | | | | |            e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 158.93/25.34  | | | | | | | | |              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.93/25.34  | | | | | | | | |            all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.93/25.34  | | | | | | | | |          (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.93/25.34  | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 158.93/25.34  | | | | | | | | |            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11
% 158.93/25.34  | | | | | | | | |            = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.93/25.34  | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.93/25.34  | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 158.93/25.34  | | | | | | | | |            e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.93/25.34  | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.93/25.34  | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 158.93/25.34  | | | | | | | | |          (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.93/25.34  | | | | | | | | |            (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) =
% 158.93/25.34  | | | | | | | | |            e3 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 158.93/25.34  | | | | | | | | |            = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.34  | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) =
% 158.93/25.34  | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 158.93/25.34  | | | | | | | | |            e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 158.93/25.34  | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.93/25.34  | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 158.93/25.34  | | | | | | | | |              e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.93/25.34  | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.93/25.34  | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.93/25.34  | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | GROUND_INST: instantiating (12) with e1, all_57_15, e0, e0,
% 158.93/25.35  | | | | | | | | |              simplifying with (3), (102) gives:
% 158.93/25.35  | | | | | | | | |   (104)  all_57_15 = e1
% 158.93/25.35  | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | GROUND_INST: instantiating (12) with all_52_3, e0, e3, e0,
% 158.93/25.35  | | | | | | | | |              simplifying with (13), (22) gives:
% 158.93/25.35  | | | | | | | | |   (105)  all_52_3 = e0
% 158.93/25.35  | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | GROUND_INST: instantiating (12) with all_52_12, e0, e0, e3,
% 158.93/25.35  | | | | | | | | |              simplifying with (37), (52) gives:
% 158.93/25.35  | | | | | | | | |   (106)  all_52_12 = e0
% 158.93/25.35  | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | REDUCE: (39), (105) imply:
% 158.93/25.35  | | | | | | | | |   (107)   ~ (all_52_11 = e0)
% 158.93/25.35  | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | REDUCE: (15), (106) imply:
% 158.93/25.35  | | | | | | | | |   (108)   ~ (e3 = e0)
% 158.93/25.35  | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | REDUCE: (4), (106) imply:
% 158.93/25.35  | | | | | | | | |   (109)   ~ (e1 = e0)
% 158.93/25.35  | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | BETA: splitting (103) gives:
% 158.93/25.35  | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | Case 1:
% 158.93/25.35  | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | |   (110)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.93/25.35  | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 158.93/25.35  | | | | | | | | | |            = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.93/25.35  | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.93/25.35  | | | | | | | | | |              e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.93/25.35  | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.93/25.35  | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.93/25.35  | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.93/25.35  | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 158.93/25.35  | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 158.93/25.35  | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 158.93/25.35  | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.93/25.35  | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 158.93/25.35  | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.93/25.35  | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.93/25.35  | | | | | | | | | |            e0)
% 158.93/25.35  | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | BETA: splitting (110) gives:
% 158.93/25.35  | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | Case 1:
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | |   (111)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.93/25.35  | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 158.93/25.35  | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.93/25.35  | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.93/25.35  | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.93/25.35  | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 158.93/25.35  | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.93/25.35  | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 158.93/25.35  | | | | | | | | | | |            e0)
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | REF_CLOSE: (36), (111) are inconsistent by sub-proof #365.
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | Case 2:
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | |   (112)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.93/25.35  | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 158.93/25.35  | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.93/25.35  | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 158.93/25.35  | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.93/25.35  | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 158.93/25.35  | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | BETA: splitting (112) gives:
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | Case 1:
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | |   (113)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 158.93/25.35  | | | | | | | | | | | |          op(e0, e3) = e0
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | | REF_CLOSE: (31), (104), (113) are inconsistent by sub-proof
% 158.93/25.35  | | | | | | | | | | | |            #372.
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | Case 2:
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | |   (114)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.93/25.35  | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 158.93/25.35  | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.93/25.35  | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 158.93/25.35  | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.93/25.35  | | | | | | | | | | | |            op(e0, e2) = e0)
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | | REF_CLOSE: (2), (12), (19), (25), (47), (114) are
% 158.93/25.35  | | | | | | | | | | | |            inconsistent by sub-proof #900.
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | End of split
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | End of split
% 158.93/25.35  | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | Case 2:
% 158.93/25.35  | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | |   (115)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 158.93/25.35  | | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 158.93/25.35  | | | | | | | | | |            = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.93/25.35  | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.93/25.35  | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 158.93/25.35  | | | | | | | | | |             ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.93/25.35  | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.93/25.35  | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.93/25.35  | | | | | | | | | |              e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.93/25.35  | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.93/25.35  | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.35  | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 158.93/25.35  | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15
% 158.93/25.35  | | | | | | | | | |            = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 158.93/25.35  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.93/25.35  | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 158.93/25.35  | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 158.93/25.35  | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | BETA: splitting (115) gives:
% 158.93/25.35  | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | Case 1:
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | |   (116)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.93/25.35  | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 158.93/25.35  | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.93/25.35  | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 158.93/25.35  | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 158.93/25.35  | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 158.93/25.35  | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | BETA: splitting (116) gives:
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | Case 1:
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | |   (117)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 158.93/25.35  | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 158.93/25.35  | | | | | | | | | | | |          = e1 & op(e0, e2) = e0
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | | ALPHA: (117) implies:
% 158.93/25.35  | | | | | | | | | | | |   (118)  op(e1, e0) = e1
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | | REF_CLOSE: (12), (23), (41), (118) are inconsistent by
% 158.93/25.35  | | | | | | | | | | | |            sub-proof #974.
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | Case 2:
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | |   (119)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 158.93/25.35  | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 158.93/25.35  | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.35  | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 158.93/25.35  | | | | | | | | | | | |            e0)
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | | REF_CLOSE: (2), (12), (19), (25), (47), (119) are
% 158.93/25.35  | | | | | | | | | | | |            inconsistent by sub-proof #968.
% 158.93/25.35  | | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | End of split
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | Case 2:
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | |   (120)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 158.93/25.35  | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 158.93/25.35  | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.93/25.35  | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 158.93/25.35  | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.93/25.35  | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 158.93/25.35  | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.93/25.35  | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.93/25.35  | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 158.93/25.35  | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 158.93/25.35  | | | | | | | | | | |            = e0)
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | | REF_CLOSE: (10), (12), (34), (120) are inconsistent by
% 158.93/25.35  | | | | | | | | | | |            sub-proof #744.
% 158.93/25.35  | | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | | End of split
% 158.93/25.35  | | | | | | | | | | 
% 158.93/25.35  | | | | | | | | | End of split
% 158.93/25.35  | | | | | | | | | 
% 158.93/25.35  | | | | | | | | End of split
% 158.93/25.35  | | | | | | | | 
% 158.93/25.35  | | | | | | | End of split
% 158.93/25.35  | | | | | | | 
% 158.93/25.35  | | | | | | End of split
% 158.93/25.35  | | | | | | 
% 158.93/25.35  | | | | | End of split
% 158.93/25.35  | | | | | 
% 158.93/25.35  | | | | End of split
% 158.93/25.35  | | | | 
% 158.93/25.35  | | | End of split
% 158.93/25.35  | | | 
% 158.93/25.35  | | End of split
% 158.93/25.35  | | 
% 158.93/25.35  | End of split
% 158.93/25.35  | 
% 158.93/25.35  End of proof
% 158.93/25.35  
% 158.93/25.35  Sub-proof #321 shows that the following formulas are inconsistent:
% 158.93/25.35  ----------------------------------------------------------------
% 158.93/25.35    (1)  op(e1, e1) = e0
% 158.93/25.35    (2)   ~ (e3 = e2)
% 158.93/25.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.93/25.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.93/25.35    (4)  op(e3, e3) = e3
% 158.93/25.35    (5)   ~ (e3 = e0)
% 158.93/25.35    (6)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.93/25.35           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.93/25.35           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 158.93/25.35           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 158.93/25.35           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.93/25.35  
% 158.93/25.35  Begin of proof
% 158.93/25.35  | 
% 158.93/25.35  | BETA: splitting (6) gives:
% 158.93/25.35  | 
% 158.93/25.35  | Case 1:
% 158.93/25.35  | | 
% 158.93/25.35  | |   (7)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 158.93/25.35  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 158.93/25.35  | |          e1) = e3 & $i(all_57_10)
% 158.93/25.35  | | 
% 158.93/25.35  | | ALPHA: (7) implies:
% 158.93/25.35  | |   (8)  op(e1, e1) = e3
% 158.93/25.35  | | 
% 158.93/25.35  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #912.
% 158.93/25.35  | | 
% 158.93/25.35  | Case 2:
% 158.93/25.35  | | 
% 158.93/25.35  | |   (9)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 158.93/25.35  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.93/25.35  | |          e1) = e2 & $i(all_57_12)
% 158.93/25.35  | | 
% 158.93/25.35  | | ALPHA: (9) implies:
% 158.93/25.35  | |   (10)  op(e3, e3) = e2
% 158.93/25.35  | | 
% 158.93/25.35  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #958.
% 158.93/25.35  | | 
% 158.93/25.35  | End of split
% 158.93/25.35  | 
% 158.93/25.35  End of proof
% 158.93/25.35  
% 158.93/25.35  Sub-proof #322 shows that the following formulas are inconsistent:
% 158.93/25.35  ----------------------------------------------------------------
% 158.93/25.35    (1)  op(e2, e3) = e2
% 158.93/25.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.93/25.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.93/25.35    (3)  op(e2, e2) = e0
% 158.93/25.35    (4)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 158.93/25.35           all_57_0 & $i(all_57_0))
% 158.93/25.35    (5)   ~ (e3 = e0)
% 158.93/25.35  
% 158.93/25.35  Begin of proof
% 158.93/25.35  | 
% 158.93/25.35  | BETA: splitting (4) gives:
% 158.93/25.35  | 
% 158.93/25.35  | Case 1:
% 158.93/25.35  | | 
% 158.93/25.35  | |   (6)  all_57_12 = e3 & op(e2, e2) = e3
% 158.93/25.35  | | 
% 158.93/25.35  | | ALPHA: (6) implies:
% 158.93/25.35  | |   (7)  op(e2, e2) = e3
% 158.93/25.35  | | 
% 158.93/25.35  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #945.
% 158.93/25.35  | | 
% 158.93/25.35  | Case 2:
% 158.93/25.35  | | 
% 158.93/25.35  | |   (8)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0)
% 158.93/25.35  | | 
% 158.93/25.35  | | ALPHA: (8) implies:
% 158.93/25.35  | |   (9)   ~ (all_57_0 = e2)
% 158.93/25.35  | |   (10)  op(e2, e3) = all_57_0
% 158.93/25.35  | | 
% 158.93/25.35  | | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #783.
% 158.93/25.35  | | 
% 158.93/25.35  | End of split
% 158.93/25.35  | 
% 158.93/25.35  End of proof
% 158.93/25.35  
% 158.93/25.35  Sub-proof #323 shows that the following formulas are inconsistent:
% 158.93/25.35  ----------------------------------------------------------------
% 158.93/25.35    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.93/25.35         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.93/25.35    (2)  op(e0, e0) = e1
% 158.93/25.35    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.93/25.35         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.93/25.35    (4)  op(e1, e1) = e0
% 158.93/25.35    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.93/25.35         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.93/25.35    (6)  op(e0, e1) = all_52_11
% 158.93/25.35    (7)   ~ (e3 = e2)
% 158.93/25.35    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.93/25.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.93/25.35    (9)  op(e3, e1) = all_52_8
% 158.93/25.35    (10)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.93/25.35          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.93/25.35    (11)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 158.93/25.35          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.93/25.35    (12)   ~ (all_52_11 = e1)
% 158.93/25.35    (13)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.93/25.35          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.93/25.35    (14)  op(e1, e0) = all_52_14
% 158.93/25.35    (15)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.93/25.35          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.93/25.35    (16)  all_56_4 = e0 & op(e3, e1) = e0
% 158.93/25.35    (17)  op(e3, e3) = e3
% 158.93/25.35    (18)  op(e2, e2) = e0
% 158.93/25.35    (19)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.93/25.35          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 158.93/25.35            e2)
% 158.93/25.35    (20)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.93/25.35          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.93/25.35    (21)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 158.93/25.35            all_57_0 & $i(all_57_0))
% 158.93/25.35    (22)   ~ (e1 = e0)
% 158.93/25.35    (23)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.93/25.35          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.93/25.35    (24)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 158.93/25.35          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.93/25.35    (25)   ~ (e2 = e1)
% 158.93/25.35    (26)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.93/25.35          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.93/25.35    (27)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.93/25.35          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.93/25.35    (28)   ~ (all_52_14 = e1)
% 158.93/25.35    (29)   ~ (e3 = e1)
% 158.93/25.35    (30)   ~ (e2 = e0)
% 158.93/25.35    (31)   ~ (all_52_8 = e3)
% 158.93/25.35    (32)   ~ (e3 = e0)
% 158.93/25.35  
% 158.93/25.35  Begin of proof
% 158.93/25.35  | 
% 158.93/25.35  | ALPHA: (16) implies:
% 158.93/25.35  |   (33)  all_56_4 = e0
% 158.93/25.35  | 
% 158.93/25.35  | BETA: splitting (24) gives:
% 158.93/25.35  | 
% 158.93/25.35  | Case 1:
% 158.93/25.35  | | 
% 158.93/25.35  | |   (34)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) =
% 158.93/25.35  | |           e1)
% 158.93/25.35  | | 
% 158.93/25.35  | | BETA: splitting (34) gives:
% 158.93/25.35  | | 
% 158.93/25.35  | | Case 1:
% 158.93/25.35  | | | 
% 158.93/25.35  | | |   (35)  all_56_4 = e1 & op(e3, e1) = e1
% 158.93/25.35  | | | 
% 158.93/25.35  | | | ALPHA: (35) implies:
% 158.93/25.35  | | |   (36)  all_56_4 = e1
% 158.93/25.35  | | | 
% 158.93/25.35  | | | REF_CLOSE: (22), (33), (36) are inconsistent by sub-proof #526.
% 158.93/25.35  | | | 
% 158.93/25.35  | | Case 2:
% 158.93/25.35  | | | 
% 158.93/25.35  | | |   (37)  all_56_5 = e1 & op(e2, e1) = e1
% 158.93/25.35  | | | 
% 158.93/25.35  | | | ALPHA: (37) implies:
% 158.93/25.35  | | |   (38)  all_56_5 = e1
% 158.93/25.35  | | | 
% 158.93/25.35  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 158.93/25.35  | | |            (15), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 158.93/25.35  | | |            (27), (28), (29), (30), (31), (32), (38) are inconsistent by
% 158.93/25.35  | | |            sub-proof #325.
% 158.93/25.35  | | | 
% 158.93/25.35  | | End of split
% 158.93/25.35  | | 
% 158.93/25.35  | Case 2:
% 158.93/25.35  | | 
% 158.93/25.35  | |   (39)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) =
% 158.93/25.35  | |           e1)
% 158.93/25.35  | | 
% 158.93/25.35  | | REF_CLOSE: (4), (6), (8), (12), (22), (39) are inconsistent by sub-proof
% 158.93/25.35  | |            #324.
% 158.93/25.35  | | 
% 158.93/25.35  | End of split
% 158.93/25.35  | 
% 158.93/25.35  End of proof
% 158.93/25.35  
% 158.93/25.35  Sub-proof #324 shows that the following formulas are inconsistent:
% 158.93/25.35  ----------------------------------------------------------------
% 158.93/25.35    (1)  op(e1, e1) = e0
% 158.93/25.36    (2)  op(e0, e1) = all_52_11
% 158.93/25.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.93/25.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.93/25.36    (4)   ~ (all_52_11 = e1)
% 158.93/25.36    (5)   ~ (e1 = e0)
% 158.93/25.36    (6)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 158.93/25.36  
% 158.93/25.36  Begin of proof
% 158.93/25.36  | 
% 158.93/25.36  | BETA: splitting (6) gives:
% 158.93/25.36  | 
% 158.93/25.36  | Case 1:
% 158.93/25.36  | | 
% 158.93/25.36  | |   (7)  all_56_8 = e1 & op(e1, e1) = e1
% 158.93/25.36  | | 
% 158.93/25.36  | | ALPHA: (7) implies:
% 158.93/25.36  | |   (8)  op(e1, e1) = e1
% 158.93/25.36  | | 
% 158.93/25.36  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #903.
% 158.93/25.36  | | 
% 158.93/25.36  | Case 2:
% 158.93/25.36  | | 
% 158.93/25.36  | |   (9)  all_56_14 = e1 & op(e0, e1) = e1
% 158.93/25.36  | | 
% 158.93/25.36  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #803.
% 158.93/25.36  | | 
% 158.93/25.36  | End of split
% 158.93/25.36  | 
% 158.93/25.36  End of proof
% 158.93/25.36  
% 158.93/25.36  Sub-proof #325 shows that the following formulas are inconsistent:
% 158.93/25.36  ----------------------------------------------------------------
% 158.93/25.36    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.93/25.36         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.93/25.36    (2)  op(e0, e0) = e1
% 158.93/25.36    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.93/25.36         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.93/25.36    (4)  op(e1, e1) = e0
% 158.93/25.36    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.93/25.36         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.93/25.36    (6)   ~ (e3 = e2)
% 158.93/25.36    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.93/25.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.93/25.36    (8)  op(e3, e1) = all_52_8
% 158.93/25.36    (9)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.93/25.36         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.93/25.36    (10)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 158.93/25.36          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 158.93/25.36    (11)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.93/25.36          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.93/25.36    (12)  all_56_5 = e1
% 158.93/25.36    (13)  op(e1, e0) = all_52_14
% 158.93/25.36    (14)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.93/25.36          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.93/25.36    (15)  op(e3, e3) = e3
% 158.93/25.36    (16)  op(e2, e2) = e0
% 158.93/25.36    (17)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.93/25.36          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 158.93/25.36            e2)
% 158.93/25.36    (18)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.93/25.36          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.93/25.36    (19)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 158.93/25.36            all_57_0 & $i(all_57_0))
% 158.93/25.36    (20)   ~ (e1 = e0)
% 158.93/25.36    (21)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.93/25.36          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.93/25.36    (22)   ~ (e2 = e1)
% 158.93/25.36    (23)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.93/25.36          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.93/25.36    (24)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.93/25.36          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.93/25.36    (25)   ~ (all_52_14 = e1)
% 158.93/25.36    (26)   ~ (e3 = e1)
% 158.93/25.36    (27)   ~ (e2 = e0)
% 158.93/25.36    (28)   ~ (all_52_8 = e3)
% 158.93/25.36    (29)   ~ (e3 = e0)
% 158.93/25.36  
% 158.93/25.36  Begin of proof
% 158.93/25.36  | 
% 158.93/25.36  | BETA: splitting (10) gives:
% 158.93/25.36  | 
% 158.93/25.36  | Case 1:
% 158.93/25.36  | | 
% 158.93/25.36  | |   (30)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) =
% 158.93/25.36  | |           e3)
% 158.93/25.36  | | 
% 158.93/25.36  | | BETA: splitting (30) gives:
% 158.93/25.36  | | 
% 158.93/25.36  | | Case 1:
% 158.93/25.36  | | | 
% 158.93/25.36  | | |   (31)  all_56_4 = e3 & op(e3, e1) = e3
% 158.93/25.36  | | | 
% 158.93/25.36  | | | ALPHA: (31) implies:
% 158.93/25.36  | | |   (32)  op(e3, e1) = e3
% 158.93/25.36  | | | 
% 158.93/25.36  | | | REF_CLOSE: (7), (8), (28), (32) are inconsistent by sub-proof #982.
% 158.93/25.36  | | | 
% 158.93/25.36  | | Case 2:
% 158.93/25.36  | | | 
% 158.93/25.36  | | |   (33)  all_56_5 = e3 & op(e2, e1) = e3
% 158.93/25.36  | | | 
% 158.93/25.36  | | | ALPHA: (33) implies:
% 158.93/25.36  | | |   (34)  all_56_5 = e3
% 158.93/25.36  | | | 
% 158.93/25.36  | | | REF_CLOSE: (12), (26), (34) are inconsistent by sub-proof #531.
% 158.93/25.36  | | | 
% 158.93/25.36  | | End of split
% 158.93/25.36  | | 
% 158.93/25.36  | Case 2:
% 158.93/25.36  | | 
% 158.93/25.36  | |   (35)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 158.93/25.36  | |           e3)
% 158.93/25.36  | | 
% 158.93/25.36  | | BETA: splitting (35) gives:
% 158.93/25.36  | | 
% 158.93/25.36  | | Case 1:
% 158.93/25.36  | | | 
% 158.93/25.36  | | |   (36)  all_56_8 = e3 & op(e1, e1) = e3
% 158.93/25.36  | | | 
% 158.93/25.36  | | | ALPHA: (36) implies:
% 158.93/25.36  | | |   (37)  op(e1, e1) = e3
% 158.93/25.36  | | | 
% 158.93/25.36  | | | REF_CLOSE: (4), (7), (29), (37) are inconsistent by sub-proof #912.
% 158.93/25.36  | | | 
% 158.93/25.36  | | Case 2:
% 158.93/25.36  | | | 
% 158.93/25.36  | | |   (38)  all_56_14 = e3 & op(e0, e1) = e3
% 158.93/25.36  | | | 
% 158.93/25.36  | | | ALPHA: (38) implies:
% 158.93/25.36  | | |   (39)  all_56_14 = e3
% 158.93/25.36  | | | 
% 158.93/25.36  | | | BETA: splitting (11) gives:
% 158.93/25.36  | | | 
% 158.93/25.36  | | | Case 1:
% 158.93/25.36  | | | | 
% 158.93/25.36  | | | |   (40)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2)
% 158.93/25.36  | | | |           = e3)
% 158.93/25.36  | | | | 
% 158.93/25.36  | | | | REF_CLOSE: (1), (6), (7), (15), (16), (20), (21), (22), (24), (26),
% 158.93/25.36  | | | |            (27), (29), (40) are inconsistent by sub-proof #441.
% 158.93/25.36  | | | | 
% 158.93/25.36  | | | Case 2:
% 158.93/25.36  | | | | 
% 158.93/25.36  | | | |   (41)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0)
% 158.93/25.36  | | | |           = e3)
% 158.93/25.36  | | | | 
% 158.93/25.36  | | | | BETA: splitting (41) gives:
% 158.93/25.36  | | | | 
% 158.93/25.36  | | | | Case 1:
% 158.93/25.36  | | | | | 
% 158.93/25.36  | | | | |   (42)  all_56_5 = e3 & op(e2, e1) = e3
% 158.93/25.36  | | | | | 
% 158.93/25.36  | | | | | ALPHA: (42) implies:
% 158.93/25.36  | | | | |   (43)  all_56_5 = e3
% 158.93/25.36  | | | | | 
% 158.93/25.36  | | | | | REF_CLOSE: (12), (26), (43) are inconsistent by sub-proof #531.
% 158.93/25.36  | | | | | 
% 158.93/25.36  | | | | Case 2:
% 158.93/25.36  | | | | | 
% 158.93/25.36  | | | | |   (44)  all_56_10 = e3 & op(e2, e0) = e3
% 158.93/25.36  | | | | | 
% 158.93/25.36  | | | | | ALPHA: (44) implies:
% 158.93/25.36  | | | | |   (45)  op(e2, e0) = e3
% 158.93/25.36  | | | | | 
% 158.93/25.36  | | | | | BETA: splitting (17) gives:
% 158.93/25.36  | | | | | 
% 158.93/25.36  | | | | | Case 1:
% 158.93/25.36  | | | | | | 
% 158.93/25.36  | | | | | |   (46)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 &
% 158.93/25.36  | | | | | |           op(e0, e2) = e2)
% 158.93/25.36  | | | | | | 
% 158.93/25.36  | | | | | | BETA: splitting (46) gives:
% 158.93/25.36  | | | | | | 
% 158.93/25.36  | | | | | | Case 1:
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | |   (47)  all_56_12 = e2 & op(e0, e3) = e2
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | ALPHA: (47) implies:
% 158.93/25.36  | | | | | | |   (48)  all_56_12 = e2
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | REF_CLOSE: (6), (7), (12), (15), (16), (20), (21), (22), (23),
% 158.93/25.36  | | | | | | |            (24), (26), (27), (29), (45), (48) are inconsistent by
% 158.93/25.36  | | | | | | |            sub-proof #547.
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | Case 2:
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | |   (49)  all_56_13 = e2 & op(e0, e2) = e2
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | ALPHA: (49) implies:
% 158.93/25.36  | | | | | | |   (50)  all_56_13 = e2
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | BETA: splitting (19) gives:
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | Case 1:
% 158.93/25.36  | | | | | | | | 
% 158.93/25.36  | | | | | | | |   (51)  all_57_12 = e3 & op(e2, e2) = e3
% 158.93/25.36  | | | | | | | | 
% 158.93/25.36  | | | | | | | | ALPHA: (51) implies:
% 158.93/25.36  | | | | | | | |   (52)  op(e2, e2) = e3
% 158.93/25.36  | | | | | | | | 
% 158.93/25.36  | | | | | | | | REF_CLOSE: (7), (16), (29), (52) are inconsistent by sub-proof
% 158.93/25.36  | | | | | | | |            #945.
% 158.93/25.36  | | | | | | | | 
% 158.93/25.36  | | | | | | | Case 2:
% 158.93/25.36  | | | | | | | | 
% 158.93/25.36  | | | | | | | |   (53)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 158.93/25.36  | | | | | | | |         $i(all_57_0)
% 158.93/25.36  | | | | | | | | 
% 158.93/25.36  | | | | | | | | ALPHA: (53) implies:
% 158.93/25.36  | | | | | | | |   (54)   ~ (all_57_0 = e2)
% 158.93/25.36  | | | | | | | |   (55)  op(e2, e3) = all_57_0
% 158.93/25.36  | | | | | | | | 
% 158.93/25.36  | | | | | | | | BETA: splitting (14) gives:
% 158.93/25.36  | | | | | | | | 
% 158.93/25.36  | | | | | | | | Case 1:
% 158.93/25.36  | | | | | | | | | 
% 158.93/25.36  | | | | | | | | |   (56)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 &
% 158.93/25.36  | | | | | | | | |           op(e2, e2) = e3)
% 158.93/25.36  | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | REF_CLOSE: (3), (5), (6), (7), (15), (16), (18), (20), (22),
% 158.93/25.36  | | | | | | | | |            (26), (27), (29), (56) are inconsistent by
% 158.93/25.36  | | | | | | | | |            sub-proof #944.
% 158.93/25.36  | | | | | | | | | 
% 158.93/25.36  | | | | | | | | Case 2:
% 158.93/25.36  | | | | | | | | | 
% 158.93/25.36  | | | | | | | | |   (57)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 &
% 158.93/25.36  | | | | | | | | |           op(e0, e2) = e3)
% 158.93/25.36  | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | BETA: splitting (57) gives:
% 158.93/25.36  | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | Case 1:
% 158.93/25.36  | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | |   (58)  all_56_7 = e3 & op(e1, e2) = e3
% 158.93/25.36  | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | ALPHA: (58) implies:
% 158.93/25.36  | | | | | | | | | |   (59)  op(e1, e2) = e3
% 158.93/25.36  | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | BETA: splitting (9) gives:
% 158.93/25.36  | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | Case 1:
% 158.93/25.36  | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | |   (60)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 158.93/25.36  | | | | | | | | | | |           & op(e1, e2) = e1)
% 158.93/25.36  | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | | BETA: splitting (60) gives:
% 158.93/25.36  | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | | Case 1:
% 158.93/25.36  | | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | | |   (61)  all_56_6 = e1 & op(e1, e3) = e1
% 158.93/25.36  | | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | | | REF_CLOSE: (1), (6), (7), (12), (15), (16), (20), (21), (22),
% 158.93/25.36  | | | | | | | | | | | |            (23), (24), (26), (27), (29), (45), (54), (55),
% 158.93/25.36  | | | | | | | | | | | |            (61) are inconsistent by sub-proof #546.
% 158.93/25.36  | | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | | Case 2:
% 158.93/25.36  | | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | | |   (62)  all_56_7 = e1 & op(e1, e2) = e1
% 158.93/25.36  | | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | | | ALPHA: (62) implies:
% 158.93/25.36  | | | | | | | | | | | |   (63)  op(e1, e2) = e1
% 158.93/25.36  | | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | | | REF_CLOSE: (7), (26), (59), (63) are inconsistent by
% 158.93/25.36  | | | | | | | | | | | |            sub-proof #939.
% 158.93/25.36  | | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | | End of split
% 158.93/25.36  | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | Case 2:
% 158.93/25.36  | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | |   (64)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 158.93/25.36  | | | | | | | | | | |           e1 & op(e1, e0) = e1)
% 158.93/25.36  | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | | REF_CLOSE: (4), (7), (13), (20), (25), (64) are inconsistent
% 158.93/25.36  | | | | | | | | | | |            by sub-proof #902.
% 158.93/25.36  | | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | End of split
% 158.93/25.36  | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | Case 2:
% 158.93/25.36  | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | |   (65)  all_56_13 = e3 & op(e0, e2) = e3
% 158.93/25.36  | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | ALPHA: (65) implies:
% 158.93/25.36  | | | | | | | | | |   (66)  all_56_13 = e3
% 158.93/25.36  | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | | REF_CLOSE: (6), (50), (66) are inconsistent by sub-proof
% 158.93/25.36  | | | | | | | | | |            #688.
% 158.93/25.36  | | | | | | | | | | 
% 158.93/25.36  | | | | | | | | | End of split
% 158.93/25.36  | | | | | | | | | 
% 158.93/25.36  | | | | | | | | End of split
% 158.93/25.36  | | | | | | | | 
% 158.93/25.36  | | | | | | | End of split
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | End of split
% 158.93/25.36  | | | | | | 
% 158.93/25.36  | | | | | Case 2:
% 158.93/25.36  | | | | | | 
% 158.93/25.36  | | | | | |   (67)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 &
% 158.93/25.36  | | | | | |           op(e0, e0) = e2)
% 158.93/25.36  | | | | | | 
% 158.93/25.36  | | | | | | BETA: splitting (67) gives:
% 158.93/25.36  | | | | | | 
% 158.93/25.36  | | | | | | Case 1:
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | |   (68)  all_56_14 = e2 & op(e0, e1) = e2
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | ALPHA: (68) implies:
% 158.93/25.36  | | | | | | |   (69)  all_56_14 = e2
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | COMBINE_EQS: (39), (69) imply:
% 158.93/25.36  | | | | | | |   (70)  e3 = e2
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | REDUCE: (6), (70) imply:
% 158.93/25.36  | | | | | | |   (71)  $false
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | CLOSE: (71) is inconsistent.
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | Case 2:
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | |   (72)  all_56_15 = e2 & op(e0, e0) = e2
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | ALPHA: (72) implies:
% 158.93/25.36  | | | | | | |   (73)  op(e0, e0) = e2
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | | REF_CLOSE: (2), (7), (22), (73) are inconsistent by sub-proof
% 158.93/25.36  | | | | | | |            #875.
% 158.93/25.36  | | | | | | | 
% 158.93/25.36  | | | | | | End of split
% 158.93/25.36  | | | | | | 
% 158.93/25.36  | | | | | End of split
% 158.93/25.36  | | | | | 
% 158.93/25.36  | | | | End of split
% 158.93/25.36  | | | | 
% 158.93/25.36  | | | End of split
% 158.93/25.36  | | | 
% 158.93/25.36  | | End of split
% 158.93/25.36  | | 
% 158.93/25.36  | End of split
% 158.93/25.36  | 
% 158.93/25.36  End of proof
% 158.93/25.36  
% 158.93/25.36  Sub-proof #326 shows that the following formulas are inconsistent:
% 158.93/25.36  ----------------------------------------------------------------
% 158.93/25.36    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.93/25.36         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 158.93/25.36    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 158.93/25.36         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 158.93/25.36    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 158.93/25.36         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 158.93/25.36    (4)   ~ (e3 = e2)
% 158.93/25.36    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.93/25.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.93/25.36    (6)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.93/25.36         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.93/25.36    (7)  op(e0, e2) = all_52_7
% 158.93/25.36    (8)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.93/25.36         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.93/25.36    (9)  op(e3, e3) = e3
% 158.93/25.36    (10)  op(e2, e2) = e0
% 158.93/25.36    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 158.93/25.36    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.93/25.36          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.93/25.36    (13)   ~ (e1 = e0)
% 158.93/25.36    (14)   ~ (e2 = e1)
% 158.93/25.36    (15)   ~ (all_52_7 = e1)
% 158.93/25.36    (16)   ~ (e3 = e1)
% 158.93/25.36    (17)   ~ (e2 = e0)
% 158.93/25.36    (18)   ~ (e3 = e0)
% 158.93/25.36  
% 158.93/25.36  Begin of proof
% 158.93/25.36  | 
% 158.93/25.36  | BETA: splitting (11) gives:
% 158.93/25.36  | 
% 158.93/25.36  | Case 1:
% 158.93/25.36  | | 
% 158.93/25.36  | |   (19)  all_56_0 = e0 & op(e3, e3) = e0
% 158.93/25.36  | | 
% 158.93/25.36  | | ALPHA: (19) implies:
% 158.93/25.36  | |   (20)  op(e3, e3) = e0
% 158.93/25.36  | | 
% 158.93/25.36  | | REF_CLOSE: (5), (9), (18), (20) are inconsistent by sub-proof #971.
% 158.93/25.36  | | 
% 158.93/25.36  | Case 2:
% 158.93/25.36  | | 
% 158.93/25.36  | |   (21)  all_56_1 = e0 & op(e3, e2) = e0
% 158.93/25.36  | | 
% 158.93/25.36  | | ALPHA: (21) implies:
% 158.93/25.36  | |   (22)  all_56_1 = e0
% 158.93/25.36  | | 
% 158.93/25.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 158.93/25.36  | |            (14), (15), (16), (17), (18), (22) are inconsistent by sub-proof
% 158.93/25.36  | |            #340.
% 158.93/25.36  | | 
% 158.93/25.36  | End of split
% 158.93/25.36  | 
% 158.93/25.36  End of proof
% 158.93/25.36  
% 158.93/25.36  Sub-proof #327 shows that the following formulas are inconsistent:
% 158.93/25.37  ----------------------------------------------------------------
% 158.93/25.37    (1)   ~ (all_52_13 = e1)
% 158.93/25.37    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.93/25.37         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.93/25.37    (3)   ~ (e3 = e2)
% 158.93/25.37    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.93/25.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.93/25.37    (5)  op(e0, e3) = all_52_3
% 158.93/25.37    (6)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.93/25.37         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.93/25.37    (7)   ~ (all_52_3 = e1)
% 158.93/25.37    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 158.93/25.37    (9)  op(e3, e3) = e3
% 158.93/25.37    (10)  op(e2, e2) = e0
% 158.93/25.37    (11)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.93/25.37          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 158.93/25.37    (12)   ~ (e1 = e0)
% 158.93/25.37    (13)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.93/25.37          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.93/25.37    (14)  op(e2, e0) = all_52_13
% 158.93/25.37    (15)   ~ (e2 = e1)
% 158.93/25.37    (16)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.93/25.37          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.93/25.37    (17)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.93/25.37          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.93/25.37    (18)   ~ (e3 = e1)
% 158.93/25.37    (19)   ~ (e2 = e0)
% 158.93/25.37    (20)   ~ (e3 = e0)
% 158.93/25.37  
% 158.93/25.37  Begin of proof
% 158.93/25.37  | 
% 158.93/25.37  | BETA: splitting (8) gives:
% 158.93/25.37  | 
% 158.93/25.37  | Case 1:
% 158.93/25.37  | | 
% 158.93/25.37  | |   (21)  all_56_0 = e0 & op(e3, e3) = e0
% 158.93/25.37  | | 
% 158.93/25.37  | | ALPHA: (21) implies:
% 158.93/25.37  | |   (22)  op(e3, e3) = e0
% 158.93/25.37  | | 
% 158.93/25.37  | | REF_CLOSE: (4), (9), (20), (22) are inconsistent by sub-proof #971.
% 158.93/25.37  | | 
% 158.93/25.37  | Case 2:
% 158.93/25.37  | | 
% 158.93/25.37  | |   (23)  all_56_2 = e0 & op(e2, e3) = e0
% 158.93/25.37  | | 
% 158.93/25.37  | | ALPHA: (23) implies:
% 158.93/25.37  | |   (24)  all_56_2 = e0
% 158.93/25.37  | | 
% 158.93/25.37  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 158.93/25.37  | |            (14), (15), (16), (17), (18), (19), (20), (24) are inconsistent
% 158.93/25.37  | |            by sub-proof #328.
% 158.93/25.37  | | 
% 158.93/25.37  | End of split
% 158.93/25.37  | 
% 158.93/25.37  End of proof
% 158.93/25.37  
% 158.93/25.37  Sub-proof #328 shows that the following formulas are inconsistent:
% 158.93/25.37  ----------------------------------------------------------------
% 158.93/25.37    (1)   ~ (all_52_13 = e1)
% 158.93/25.37    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 158.93/25.37         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 158.93/25.37    (3)  all_56_2 = e0
% 158.93/25.37    (4)   ~ (e3 = e2)
% 158.93/25.37    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.93/25.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.93/25.37    (6)  op(e0, e3) = all_52_3
% 158.93/25.37    (7)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.93/25.37         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 158.93/25.37    (8)   ~ (all_52_3 = e1)
% 158.93/25.37    (9)  op(e3, e3) = e3
% 158.93/25.37    (10)  op(e2, e2) = e0
% 158.93/25.37    (11)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 158.93/25.37          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 158.93/25.37    (12)   ~ (e1 = e0)
% 158.93/25.37    (13)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 158.93/25.37          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 158.93/25.37    (14)  op(e2, e0) = all_52_13
% 158.93/25.37    (15)   ~ (e2 = e1)
% 158.93/25.37    (16)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.93/25.37          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 158.93/25.37    (17)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 158.93/25.37          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 158.93/25.37    (18)   ~ (e3 = e1)
% 158.93/25.37    (19)   ~ (e2 = e0)
% 158.93/25.37    (20)   ~ (e3 = e0)
% 158.93/25.37  
% 158.93/25.37  Begin of proof
% 158.93/25.37  | 
% 158.93/25.37  | BETA: splitting (11) gives:
% 158.93/25.37  | 
% 158.93/25.37  | Case 1:
% 158.93/25.37  | | 
% 158.93/25.37  | |   (21)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 158.93/25.37  | |           e1)
% 158.93/25.37  | | 
% 158.93/25.37  | | REF_CLOSE: (3), (5), (10), (12), (21) are inconsistent by sub-proof #535.
% 158.93/25.37  | | 
% 158.93/25.37  | Case 2:
% 158.93/25.37  | | 
% 158.93/25.37  | |   (22)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 158.93/25.37  | |           e1)
% 158.93/25.37  | | 
% 158.93/25.37  | | BETA: splitting (22) gives:
% 158.93/25.37  | | 
% 158.93/25.37  | | Case 1:
% 158.93/25.37  | | | 
% 158.93/25.37  | | |   (23)  all_56_5 = e1 & op(e2, e1) = e1
% 158.93/25.37  | | | 
% 158.93/25.37  | | | ALPHA: (23) implies:
% 158.93/25.37  | | |   (24)  all_56_5 = e1
% 158.93/25.37  | | | 
% 158.93/25.37  | | | BETA: splitting (17) gives:
% 158.93/25.37  | | | 
% 158.93/25.37  | | | Case 1:
% 158.93/25.37  | | | | 
% 158.93/25.37  | | | |   (25)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3)
% 158.93/25.37  | | | |           = e1)
% 158.93/25.37  | | | | 
% 158.93/25.37  | | | | REF_CLOSE: (3), (5), (9), (12), (18), (25) are inconsistent by sub-proof
% 158.93/25.37  | | | |            #732.
% 158.93/25.37  | | | | 
% 158.93/25.37  | | | Case 2:
% 158.93/25.37  | | | | 
% 158.93/25.37  | | | |   (26)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3)
% 158.93/25.37  | | | |           = e1)
% 158.93/25.37  | | | | 
% 158.93/25.37  | | | | BETA: splitting (26) gives:
% 158.93/25.37  | | | | 
% 158.93/25.37  | | | | Case 1:
% 158.93/25.37  | | | | | 
% 158.93/25.37  | | | | |   (27)  all_56_6 = e1 & op(e1, e3) = e1
% 158.93/25.37  | | | | | 
% 158.93/25.37  | | | | | ALPHA: (27) implies:
% 158.93/25.37  | | | | |   (28)  all_56_6 = e1
% 158.93/25.37  | | | | | 
% 158.93/25.37  | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (12), (13), (15), (16),
% 158.93/25.37  | | | | |            (17), (18), (19), (20), (24), (28) are inconsistent by
% 158.93/25.37  | | | | |            sub-proof #529.
% 158.93/25.37  | | | | | 
% 158.93/25.37  | | | | Case 2:
% 158.93/25.37  | | | | | 
% 158.93/25.37  | | | | |   (29)  all_56_12 = e1 & op(e0, e3) = e1
% 158.93/25.37  | | | | | 
% 158.93/25.37  | | | | | REF_CLOSE: (5), (6), (8), (29) are inconsistent by sub-proof #852.
% 158.93/25.37  | | | | | 
% 158.93/25.37  | | | | End of split
% 158.93/25.37  | | | | 
% 158.93/25.37  | | | End of split
% 158.93/25.37  | | | 
% 158.93/25.37  | | Case 2:
% 158.93/25.37  | | | 
% 158.93/25.37  | | |   (30)  all_56_10 = e1 & op(e2, e0) = e1
% 158.93/25.37  | | | 
% 158.93/25.37  | | | REF_CLOSE: (1), (5), (14), (30) are inconsistent by sub-proof #713.
% 158.93/25.37  | | | 
% 158.93/25.37  | | End of split
% 158.93/25.37  | | 
% 158.93/25.37  | End of split
% 158.93/25.37  | 
% 158.93/25.37  End of proof
% 158.93/25.37  
% 158.93/25.37  Sub-proof #329 shows that the following formulas are inconsistent:
% 158.93/25.37  ----------------------------------------------------------------
% 158.93/25.37    (1)  all_54_10 = all_10_2
% 158.93/25.37    (2)  all_54_10 = e0
% 158.93/25.37    (3)   ~ (all_10_2 = e0)
% 158.93/25.37  
% 158.93/25.37  Begin of proof
% 158.93/25.37  | 
% 158.93/25.37  | COMBINE_EQS: (1), (2) imply:
% 158.93/25.37  |   (4)  all_10_2 = e0
% 158.93/25.37  | 
% 158.93/25.37  | SIMP: (4) implies:
% 158.93/25.37  |   (5)  all_10_2 = e0
% 158.93/25.37  | 
% 158.93/25.37  | REDUCE: (3), (5) imply:
% 158.93/25.37  |   (6)  $false
% 158.93/25.37  | 
% 158.93/25.37  | CLOSE: (6) is inconsistent.
% 158.93/25.37  | 
% 158.93/25.37  End of proof
% 158.93/25.37  
% 158.93/25.37  Sub-proof #330 shows that the following formulas are inconsistent:
% 158.93/25.37  ----------------------------------------------------------------
% 158.93/25.37    (1)  op(e0, e0) = e1
% 158.93/25.37    (2)   ~ (all_52_6 = e1)
% 158.93/25.37    (3)   ~ (all_52_12 = e1)
% 158.93/25.37    (4)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 158.93/25.37         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 158.93/25.37    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 158.93/25.37             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 158.93/25.37           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 158.93/25.37               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 158.93/25.37             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 158.93/25.37         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 158.93/25.37             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 158.93/25.37           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 158.93/25.37               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 158.93/25.37             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 158.93/25.37         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 158.93/25.37             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 158.93/25.37           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 158.93/25.37               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 158.93/25.37             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 158.93/25.37         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 158.93/25.37             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 158.93/25.37           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 158.93/25.37               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 158.93/25.37             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 158.93/25.37    (6)   ~ (e3 = e2)
% 158.93/25.37    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 158.93/25.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 158.93/25.37    (8)  op(e3, e1) = all_52_8
% 158.93/25.37    (9)  op(e1, e1) = e1
% 158.93/25.37    (10)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 158.93/25.37          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 158.93/25.37    (11)  op(e1, e3) = all_52_2
% 158.93/25.37    (12)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 158.93/25.37          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 158.93/25.37    (13)   ~ (all_52_2 = e1)
% 158.93/25.37    (14)  op(e1, e2) = all_52_6
% 158.93/25.37    (15)  op(e1, e0) = all_52_14
% 158.93/25.37    (16)   ~ (all_52_8 = e1)
% 158.93/25.37    (17)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 158.93/25.37          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 158.93/25.37    (18)  op(e0, e0) = all_14_2
% 158.93/25.37    (19)  op(e2, e2) = e1
% 158.93/25.37    (20)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 158.93/25.37          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 158.93/25.37    (21)   ~ (e1 = e0)
% 158.93/25.37    (22)   ~ (e2 = e1)
% 158.93/25.37    (23)  op(e3, e0) = all_52_12
% 158.93/25.37    (24)   ~ (all_52_14 = e1)
% 158.93/25.38    (25)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 158.93/25.38            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 158.93/25.38            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.93/25.38            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.38              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.93/25.38          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 158.93/25.38            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 158.93/25.38              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.93/25.38            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.38              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.93/25.38          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 158.93/25.38            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 158.93/25.38              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.93/25.38            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.38              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.93/25.38          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 158.93/25.38            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 158.93/25.38            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.93/25.38              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.93/25.38            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.93/25.38            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.93/25.38            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.38            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 158.93/25.38              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.93/25.38            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 158.93/25.38          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.93/25.38            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.93/25.38              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.93/25.38            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.93/25.38            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.93/25.38          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 158.93/25.38            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 158.93/25.38              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 158.93/25.38            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.93/25.38            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.93/25.38          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 158.93/25.38            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.93/25.38              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.93/25.38            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.38              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.93/25.38          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 158.93/25.38            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 158.93/25.38            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 158.93/25.38            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.93/25.38            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 158.93/25.38            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.93/25.38            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.93/25.38            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 158.93/25.38              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.93/25.38            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 158.93/25.38            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.38            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.93/25.38            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 158.93/25.38              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 158.93/25.38            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 158.93/25.38          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 158.93/25.38            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 158.93/25.38              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 158.93/25.38              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.93/25.38            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 158.93/25.38            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.93/25.38            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.93/25.38            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 158.93/25.38              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 158.93/25.38            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 158.93/25.38          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.93/25.38            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.93/25.38              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.93/25.38            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.38              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.93/25.38          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 158.93/25.38            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 158.93/25.38              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 158.93/25.38              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 158.93/25.38            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 158.93/25.38          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 158.93/25.38            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 158.93/25.38            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.93/25.38                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 158.93/25.38                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.93/25.38                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 158.93/25.38                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 158.93/25.38                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 158.93/25.38                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 158.93/25.38                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 158.93/25.38                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.93/25.38                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 158.93/25.38                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 158.93/25.38                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.93/25.38                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 158.93/25.38                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 158.93/25.38                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.38                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 158.93/25.38                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.38                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 158.93/25.38                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.38                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 158.93/25.38                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.93/25.38                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 158.93/25.38                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 158.93/25.38                op(e0, e1) = e0)))
% 158.93/25.38    (26)   ~ (e3 = e1)
% 158.93/25.38    (27)   ~ (e2 = e0)
% 158.93/25.38    (28)   ~ (e3 = e0)
% 158.93/25.38  
% 158.93/25.38  Begin of proof
% 158.93/25.38  | 
% 158.93/25.38  | BETA: splitting (20) gives:
% 158.93/25.38  | 
% 158.93/25.38  | Case 1:
% 158.93/25.38  | | 
% 158.93/25.38  | |   (29)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 158.93/25.38  | |           e1)
% 158.93/25.38  | | 
% 158.93/25.38  | | BETA: splitting (29) gives:
% 158.93/25.38  | | 
% 158.93/25.38  | | Case 1:
% 158.93/25.38  | | | 
% 158.93/25.38  | | |   (30)  all_56_0 = e1 & op(e3, e3) = e1
% 158.93/25.38  | | | 
% 158.93/25.38  | | | ALPHA: (30) implies:
% 158.93/25.38  | | |   (31)  op(e3, e3) = e1
% 158.93/25.38  | | | 
% 158.93/25.38  | | | BETA: splitting (25) gives:
% 158.93/25.38  | | | 
% 158.93/25.38  | | | Case 1:
% 158.93/25.38  | | | | 
% 158.93/25.38  | | | |   (32)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12
% 158.93/25.38  | | | |             = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2
% 158.93/25.38  | | | |           & op(e2, e2) = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 158.93/25.38  | | | |           all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3,
% 158.93/25.38  | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 158.93/25.38  | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 &
% 158.93/25.38  | | | |           all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 158.93/25.38  | | | |           op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.93/25.38  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 =
% 158.93/25.38  | | | |           e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 158.93/25.38  | | | |           = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.93/25.38  | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12
% 158.93/25.38  | | | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0,
% 158.93/25.38  | | | |             e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 158.93/25.38  | | | |           & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) &
% 158.93/25.38  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 158.93/25.38  | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_12
% 158.93/25.38  | | | |           = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 158.93/25.38  | | | |         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 158.93/25.38  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 158.93/25.38  | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 158.93/25.38  | | | |           & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.93/25.38  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.93/25.38  | | | |           op(e2, e1) = e2 & $i(all_57_12)) | (all_57_1 = e3 & all_57_6 =
% 158.93/25.38  | | | |           e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.93/25.38  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.93/25.38  | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3
% 158.93/25.38  | | | |             = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) | (all_57_1 = e3
% 158.93/25.38  | | | |           & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 158.93/25.38  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 158.93/25.38  | | | |           op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 =
% 158.93/25.38  | | | |           e3 & all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 158.93/25.38  | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.93/25.38  | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_14 =
% 158.93/25.38  | | | |           e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 158.93/25.38  | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.93/25.38  | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14
% 158.93/25.38  | | | |             = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1
% 158.93/25.38  | | | |           & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 158.93/25.38  | | | |           all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1,
% 158.93/25.38  | | | |             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 158.93/25.38  | | | |             e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.93/25.38  | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 158.93/25.38  | | | |           & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.93/25.38  | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 =
% 158.93/25.38  | | | |             e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.93/25.38  | | | | 
% 158.93/25.38  | | | | BETA: splitting (32) gives:
% 158.93/25.38  | | | | 
% 158.93/25.38  | | | | Case 1:
% 158.93/25.38  | | | | | 
% 158.93/25.38  | | | | |   (33)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.93/25.38  | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.93/25.38  | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12)) |
% 158.93/25.38  | | | | |         (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 158.93/25.38  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 158.93/25.38  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.93/25.38  | | | | |         (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.93/25.38  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 158.93/25.38  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.93/25.38  | | | | |         (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 158.93/25.38  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 158.93/25.38  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.93/25.38  | | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.93/25.38  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 158.93/25.38  | | | | |           & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.93/25.38  | | | | |         (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 158.93/25.38  | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 158.93/25.38  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.93/25.38  | | | | |         (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) =
% 158.93/25.38  | | | | |           e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 158.93/25.38  | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.93/25.38  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.93/25.38  | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 158.93/25.38  | | | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 158.93/25.38  | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 158.93/25.38  | | | | |           $i(all_57_12))
% 158.93/25.38  | | | | | 
% 158.93/25.38  | | | | | BETA: splitting (33) gives:
% 158.93/25.38  | | | | | 
% 158.93/25.38  | | | | | Case 1:
% 158.93/25.38  | | | | | | 
% 158.93/25.38  | | | | | |   (34)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.93/25.38  | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.93/25.38  | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12))
% 158.93/25.38  | | | | | |         | (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 158.93/25.38  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.93/25.38  | | | | | |           e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 158.93/25.38  | | | | | |         (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.93/25.38  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.93/25.38  | | | | | |           all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.93/25.38  | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.93/25.38  | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.93/25.38  | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 158.93/25.38  | | | | | |           = e3 & $i(all_57_10))
% 158.93/25.38  | | | | | | 
% 158.93/25.38  | | | | | | BETA: splitting (34) gives:
% 158.93/25.38  | | | | | | 
% 158.93/25.38  | | | | | | Case 1:
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | |   (35)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 158.93/25.38  | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.93/25.38  | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 158.93/25.38  | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 158.93/25.38  | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 158.93/25.38  | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 158.93/25.38  | | | | | | |             e2) = e3 & $i(all_57_10))
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | | REF_CLOSE: (7), (19), (22), (26), (31), (35) are inconsistent by
% 158.93/25.38  | | | | | | |            sub-proof #494.
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | Case 2:
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | |   (36)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 158.93/25.38  | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.93/25.38  | | | | | | |           all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.93/25.38  | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 158.93/25.38  | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.93/25.38  | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 158.93/25.38  | | | | | | |             e2) = e3 & $i(all_57_10))
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | | REF_CLOSE: (7), (9), (19), (22), (26), (36) are inconsistent by
% 158.93/25.38  | | | | | | |            sub-proof #800.
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | End of split
% 158.93/25.38  | | | | | | 
% 158.93/25.38  | | | | | Case 2:
% 158.93/25.38  | | | | | | 
% 158.93/25.38  | | | | | |   (37)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.93/25.38  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.93/25.38  | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.93/25.38  | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.93/25.38  | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.93/25.38  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 158.93/25.38  | | | | | |           = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 & 
% 158.93/25.38  | | | | | |           ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 158.93/25.38  | | | | | |         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.93/25.38  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.93/25.38  | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.93/25.38  | | | | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 158.93/25.38  | | | | | |           (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.93/25.38  | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.93/25.38  | | | | | | 
% 158.93/25.38  | | | | | | BETA: splitting (37) gives:
% 158.93/25.38  | | | | | | 
% 158.93/25.38  | | | | | | Case 1:
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | |   (38)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.93/25.38  | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.93/25.38  | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.93/25.38  | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 158.93/25.38  | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.93/25.38  | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 158.93/25.38  | | | | | | |             e2) = e3 & $i(all_57_10))
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | | BETA: splitting (38) gives:
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | | Case 1:
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | |   (39)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.93/25.38  | | | | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 158.93/25.38  | | | | | | | |         all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.93/25.38  | | | | | | | |         $i(all_57_12)
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | | ALPHA: (39) implies:
% 158.93/25.38  | | | | | | | |   (40)  op(e0, e0) = e2
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | | REF_CLOSE: (1), (7), (22), (40) are inconsistent by sub-proof
% 158.93/25.38  | | | | | | | |            #875.
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | Case 2:
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | |   (41)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 158.93/25.38  | | | | | | | |         (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 158.93/25.38  | | | | | | | |         e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | | ALPHA: (41) implies:
% 158.93/25.38  | | | | | | | |   (42)  op(e2, e2) = e3
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | | REF_CLOSE: (7), (19), (26), (42) are inconsistent by sub-proof
% 158.93/25.38  | | | | | | | |            #847.
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | End of split
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | Case 2:
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | |   (43)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2,
% 158.93/25.38  | | | | | | |             e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 &
% 158.93/25.38  | | | | | | |           all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 158.93/25.38  | | | | | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) =
% 158.93/25.38  | | | | | | |           e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 158.93/25.38  | | | | | | |           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 158.93/25.38  | | | | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 158.93/25.38  | | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | | BETA: splitting (43) gives:
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | | Case 1:
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | |   (44)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2,
% 158.93/25.38  | | | | | | | |           e3) = e2 & op(e2, e2) = e2
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | | ALPHA: (44) implies:
% 158.93/25.38  | | | | | | | |   (45)  op(e2, e2) = e2
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | | REF_CLOSE: (7), (19), (22), (45) are inconsistent by sub-proof
% 158.93/25.38  | | | | | | | |            #993.
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | Case 2:
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | |   (46)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 158.93/25.38  | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2)
% 158.93/25.38  | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.93/25.38  | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 158.93/25.38  | | | | | | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 158.93/25.38  | | | | | | | |           & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 158.93/25.38  | | | | | | | |             e1) = e2 & $i(all_57_12))
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | | REF_CLOSE: (7), (9), (22), (26), (31), (46) are inconsistent by
% 158.93/25.38  | | | | | | | |            sub-proof #825.
% 158.93/25.38  | | | | | | | | 
% 158.93/25.38  | | | | | | | End of split
% 158.93/25.38  | | | | | | | 
% 158.93/25.38  | | | | | | End of split
% 158.93/25.38  | | | | | | 
% 158.93/25.38  | | | | | End of split
% 158.93/25.38  | | | | | 
% 158.93/25.38  | | | | Case 2:
% 158.93/25.38  | | | | | 
% 158.93/25.38  | | | | |   (47)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.38  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 158.93/25.38  | | | | |           & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.93/25.38  | | | | |         (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) =
% 158.93/25.38  | | | | |           e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 158.93/25.38  | | | | |           all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 &
% 158.93/25.38  | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.93/25.38  | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10
% 158.93/25.38  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 158.93/25.38  | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.93/25.38  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_14
% 158.93/25.38  | | | | |           = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.38  | | | | |             e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.93/25.38  | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12
% 158.93/25.38  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 158.93/25.38  | | | | |           e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.93/25.38  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 & all_57_15
% 158.93/25.38  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 158.93/25.38  | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.38  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14
% 158.93/25.38  | | | | |           = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.38  | | | | |             e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 158.93/25.38  | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 =
% 158.93/25.38  | | | | |             e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.93/25.38  | | | | | 
% 158.93/25.38  | | | | | BETA: splitting (47) gives:
% 158.93/25.38  | | | | | 
% 158.93/25.38  | | | | | Case 1:
% 158.93/25.38  | | | | | | 
% 158.93/25.38  | | | | | |   (48)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.38  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.93/25.38  | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 158.93/25.38  | | | | | |         (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3)
% 158.93/25.38  | | | | | |           = e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2
% 158.93/25.38  | | | | | |           & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 &
% 158.93/25.39  | | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 158.93/25.39  | | | | | |           & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.93/25.39  | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 158.93/25.39  | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 158.93/25.39  | | | | | |           & $i(all_57_14))
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | | BETA: splitting (48) gives:
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | | Case 1:
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | |   (49)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.39  | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.93/25.39  | | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 158.93/25.39  | | | | | | |         | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3,
% 158.93/25.39  | | | | | | |             e3) = e3 & op(e3, e2) = e3)
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | | BETA: splitting (49) gives:
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | | Case 1:
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | |   (50)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.39  | | | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 158.93/25.39  | | | | | | | |         e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | | ALPHA: (50) implies:
% 158.93/25.39  | | | | | | | |   (51)  op(e0, e0) = e3
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | | REF_CLOSE: (1), (7), (26), (51) are inconsistent by sub-proof
% 158.93/25.39  | | | | | | | |            #473.
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | Case 2:
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | |   (52)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3,
% 158.93/25.39  | | | | | | | |           e3) = e3 & op(e3, e2) = e3
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | | ALPHA: (52) implies:
% 158.93/25.39  | | | | | | | |   (53)  op(e3, e3) = e3
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | | REF_CLOSE: (7), (26), (31), (53) are inconsistent by sub-proof
% 158.93/25.39  | | | | | | | |            #995.
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | End of split
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | Case 2:
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | |   (54)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 158.93/25.39  | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 158.93/25.39  | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.93/25.39  | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 158.93/25.39  | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 158.93/25.39  | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 158.93/25.39  | | | | | | |           all_57_14 & $i(all_57_14))
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | | REF_CLOSE: (7), (11), (13), (22), (31), (54) are inconsistent by
% 158.93/25.39  | | | | | | |            sub-proof #823.
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | End of split
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | Case 2:
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | |   (55)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.93/25.39  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 158.93/25.39  | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 158.93/25.39  | | | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.93/25.39  | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.93/25.39  | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.93/25.39  | | | | | |         | (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.93/25.39  | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 158.93/25.39  | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.39  | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.93/25.39  | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.93/25.39  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 158.93/25.39  | | | | | |           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 & 
% 158.93/25.39  | | | | | |           ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | | BETA: splitting (55) gives:
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | | Case 1:
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | |   (56)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 158.93/25.39  | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 158.93/25.39  | | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 158.93/25.39  | | | | | | |         | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.93/25.39  | | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.93/25.39  | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 158.93/25.39  | | | | | | |           $i(all_57_14))
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | | REF_CLOSE: (7), (9), (11), (13), (26), (56) are inconsistent by
% 158.93/25.39  | | | | | | |            sub-proof #791.
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | Case 2:
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | |   (57)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.93/25.39  | | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 158.93/25.39  | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.39  | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 158.93/25.39  | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.93/25.39  | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 158.93/25.39  | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 158.93/25.39  | | | | | | |           = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | | REF_CLOSE: (7), (9), (11), (13), (26), (57) are inconsistent by
% 158.93/25.39  | | | | | | |            sub-proof #354.
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | End of split
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | End of split
% 158.93/25.39  | | | | | 
% 158.93/25.39  | | | | End of split
% 158.93/25.39  | | | | 
% 158.93/25.39  | | | Case 2:
% 158.93/25.39  | | | | 
% 158.93/25.39  | | | |   (58)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14
% 158.93/25.39  | | | |             = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1
% 158.93/25.39  | | | |           & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 158.93/25.39  | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2,
% 158.93/25.39  | | | |             e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.93/25.39  | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.93/25.39  | | | |           all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12
% 158.93/25.39  | | | |           & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 158.93/25.39  | | | |           $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 =
% 158.93/25.39  | | | |           e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.93/25.39  | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 158.93/25.39  | | | |         | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.93/25.39  | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 158.93/25.39  | | | |           op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3
% 158.93/25.39  | | | |           = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 158.93/25.39  | | | |           op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 158.93/25.39  | | | |           = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.39  | | | |             e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.93/25.39  | | | |           $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 =
% 158.93/25.39  | | | |             e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.93/25.39  | | | |           all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 158.93/25.39  | | | |             e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 158.93/25.39  | | | |             e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 &
% 158.93/25.39  | | | |           all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12
% 158.93/25.39  | | | |           & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.93/25.39  | | | |           $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 =
% 158.93/25.39  | | | |             e1) & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 &
% 158.93/25.39  | | | |           all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 158.93/25.39  | | | |             e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 158.93/25.39  | | | |             e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.93/25.39  | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 158.93/25.39  | | | |           & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.93/25.39  | | | |           $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 & all_57_15 =
% 158.93/25.39  | | | |           e2 &  ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0)
% 158.93/25.39  | | | |           = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.93/25.39  | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3
% 158.93/25.39  | | | |           & op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 158.93/25.39  | | | |             = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 158.93/25.39  | | | |           & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0)
% 158.93/25.39  | | | |           = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 =
% 158.93/25.39  | | | |               e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 158.93/25.39  | | | |               & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 158.93/25.39  | | | |             (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.93/25.39  | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.93/25.39  | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 158.93/25.39  | | | |               all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 158.93/25.39  | | | |               op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.93/25.39  | | | |               all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 158.93/25.39  | | | |             (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 158.93/25.39  | | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.93/25.39  | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 158.93/25.39  | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 158.93/25.39  | | | |               op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 158.93/25.39  | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 158.93/25.39  | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 158.93/25.39  | | | |             (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2)
% 158.93/25.39  | | | |               = e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 158.93/25.39  | | | |               ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 158.93/25.39  | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 158.93/25.39  | | | |               all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 158.93/25.39  | | | |               op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.93/25.39  | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.39  | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 158.93/25.39  | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 158.93/25.39  | | | |               (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 158.93/25.39  | | | |               e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 158.93/25.39  | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.93/25.39  | | | | 
% 158.93/25.39  | | | | BETA: splitting (58) gives:
% 158.93/25.39  | | | | 
% 158.93/25.39  | | | | Case 1:
% 158.93/25.39  | | | | | 
% 158.93/25.39  | | | | |   (59)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.93/25.39  | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.93/25.39  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.93/25.39  | | | | |         (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.93/25.39  | | | | |           (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.93/25.39  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 158.93/25.39  | | | | |         (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.93/25.39  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 158.93/25.39  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.93/25.39  | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.93/25.39  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 158.93/25.39  | | | | |           & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 158.93/25.39  | | | | |         (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.93/25.39  | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 158.93/25.39  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.93/25.39  | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) =
% 158.93/25.39  | | | | |           e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.93/25.39  | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.93/25.39  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 158.93/25.39  | | | | |           e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~
% 158.93/25.39  | | | | |           (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 158.93/25.39  | | | | |           e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.93/25.39  | | | | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 158.93/25.39  | | | | |           op(e1, e0) = e1 & $i(all_57_14))
% 158.93/25.39  | | | | | 
% 158.93/25.39  | | | | | BETA: splitting (59) gives:
% 158.93/25.39  | | | | | 
% 158.93/25.39  | | | | | Case 1:
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | |   (60)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.93/25.39  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.93/25.39  | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.93/25.39  | | | | | |         | (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 158.93/25.39  | | | | | |           (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.93/25.39  | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 158.93/25.39  | | | | | |         | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.93/25.39  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 158.93/25.39  | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.93/25.39  | | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.93/25.39  | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.93/25.39  | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.39  | | | | | |           $i(all_57_14))
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | | BETA: splitting (60) gives:
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | | Case 1:
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | |   (61)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 158.93/25.39  | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.93/25.39  | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 158.93/25.39  | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 158.93/25.39  | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 &
% 158.93/25.39  | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 158.93/25.39  | | | | | | |           all_57_14 & $i(all_57_14))
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | | REF_CLOSE: (2), (7), (14), (61) are inconsistent by sub-proof
% 158.93/25.39  | | | | | | |            #492.
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | Case 2:
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | |   (62)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 158.93/25.39  | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 158.93/25.39  | | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 158.93/25.39  | | | | | | |         | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 158.93/25.39  | | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 158.93/25.39  | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 158.93/25.39  | | | | | | |           $i(all_57_14))
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | | REF_CLOSE: (2), (7), (9), (14), (22), (62) are inconsistent by
% 158.93/25.39  | | | | | | |            sub-proof #351.
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | End of split
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | Case 2:
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | |   (63)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.93/25.39  | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 158.93/25.39  | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 158.93/25.39  | | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2)
% 158.93/25.39  | | | | | |           = e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 158.93/25.39  | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 158.93/25.39  | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.93/25.39  | | | | | |           = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 & 
% 158.93/25.39  | | | | | |           ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) |
% 158.93/25.39  | | | | | |         (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 158.93/25.39  | | | | | |           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 158.93/25.39  | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | | BETA: splitting (63) gives:
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | | Case 1:
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | |   (64)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 158.93/25.39  | | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 158.93/25.39  | | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 158.93/25.39  | | | | | | |         | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1,
% 158.93/25.39  | | | | | | |             e2) = e1 & op(e1, e1) = e1)
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | | REF_CLOSE: (2), (7), (9), (14), (22), (64) are inconsistent by
% 158.93/25.39  | | | | | | |            sub-proof #983.
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | Case 2:
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | |   (65)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.39  | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 158.93/25.39  | | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 158.93/25.39  | | | | | | |         | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3,
% 158.93/25.39  | | | | | | |             e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.93/25.39  | | | | | | |           all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 158.93/25.39  | | | | | | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.93/25.39  | | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | | BETA: splitting (65) gives:
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | | Case 1:
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | |   (66)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 158.93/25.39  | | | | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 158.93/25.39  | | | | | | | |         e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | | ALPHA: (66) implies:
% 158.93/25.39  | | | | | | | |   (67)  op(e0, e0) = e3
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | | REF_CLOSE: (1), (7), (26), (67) are inconsistent by sub-proof
% 158.93/25.39  | | | | | | | |            #473.
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | Case 2:
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | |   (68)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3,
% 158.93/25.39  | | | | | | | |             e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 158.93/25.39  | | | | | | | |           all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 158.93/25.39  | | | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 158.93/25.39  | | | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | | REF_CLOSE: (7), (15), (24), (31), (68) are inconsistent by
% 158.93/25.39  | | | | | | | |            sub-proof #839.
% 158.93/25.39  | | | | | | | | 
% 158.93/25.39  | | | | | | | End of split
% 158.93/25.39  | | | | | | | 
% 158.93/25.39  | | | | | | End of split
% 158.93/25.39  | | | | | | 
% 158.93/25.39  | | | | | End of split
% 158.93/25.39  | | | | | 
% 158.93/25.39  | | | | Case 2:
% 158.93/25.39  | | | | | 
% 158.93/25.40  | | | | |   (69)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.93/25.40  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 158.93/25.40  | | | | |           & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.93/25.40  | | | | |         (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) =
% 158.93/25.40  | | | | |           e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 158.93/25.40  | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 &
% 158.93/25.40  | | | | |           op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.93/25.40  | | | | |           $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15
% 158.93/25.40  | | | | |           = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 158.93/25.40  | | | | |             e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 158.93/25.40  | | | | |           $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 & all_57_15
% 158.93/25.40  | | | | |           = e2 &  ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 158.93/25.40  | | | | |             e0) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 158.93/25.40  | | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 =
% 158.93/25.40  | | | | |             e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2
% 158.93/25.40  | | | | |           & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2,
% 158.93/25.40  | | | | |             e0) = e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 =
% 158.93/25.40  | | | | |             e0) & op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 158.93/25.40  | | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3
% 158.93/25.40  | | | | |               & all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0
% 158.93/25.40  | | | | |               & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 158.93/25.40  | | | | |               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 158.93/25.40  | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 158.93/25.40  | | | | |             (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 158.93/25.40  | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 158.93/25.40  | | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 158.93/25.40  | | | | |               (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9
% 158.93/25.40  | | | | |               = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3)
% 158.93/25.40  | | | | |               = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 158.93/25.40  | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 158.93/25.40  | | | | |                 e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 158.93/25.40  | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 158.93/25.40  | | | | |                ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1
% 158.93/25.40  | | | | |               & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 & 
% 158.93/25.40  | | | | |               ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 158.93/25.40  | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 158.93/25.40  | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 158.93/25.40  | | | | |             (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 158.93/25.40  | | | | |               (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 158.93/25.40  | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 158.93/25.40  | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 158.93/25.40  | | | | |               op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 158.93/25.40  | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 158.93/25.40  | | | | |               op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 158.93/25.40  | | | | |               e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 158.93/25.40  | | | | |               ~ (e1 = e0) & op(e0, e1) = e0)))
% 158.93/25.40  | | | | | 
% 158.93/25.40  | | | | | BETA: splitting (69) gives:
% 158.93/25.40  | | | | | 
% 158.93/25.40  | | | | | Case 1:
% 158.93/25.40  | | | | | | 
% 158.93/25.40  | | | | | |   (70)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.93/25.40  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 158.93/25.40  | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 158.93/25.40  | | | | | |         (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2)
% 158.93/25.40  | | | | | |           = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 158.93/25.40  | | | | | |           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 &
% 158.93/25.40  | | | | | |           op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 158.93/25.40  | | | | | |           & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.93/25.40  | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.93/25.40  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 158.93/25.40  | | | | | |           = e3 & $i(all_57_10))
% 158.93/25.40  | | | | | | 
% 158.93/25.40  | | | | | | BETA: splitting (70) gives:
% 158.93/25.40  | | | | | | 
% 158.93/25.40  | | | | | | Case 1:
% 158.93/25.40  | | | | | | | 
% 158.93/25.40  | | | | | | |   (71)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 158.93/25.40  | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 158.93/25.40  | | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 158.93/25.40  | | | | | | |         | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2,
% 158.93/25.40  | | | | | | |             e2) = e2 & op(e2, e1) = e2)
% 158.93/25.40  | | | | | | | 
% 158.93/25.40  | | | | | | | REF_CLOSE: (1), (7), (19), (22), (71) are inconsistent by
% 158.93/25.40  | | | | | | |            sub-proof #337.
% 158.93/25.40  | | | | | | | 
% 158.93/25.40  | | | | | | Case 2:
% 158.93/25.40  | | | | | | | 
% 158.93/25.40  | | | | | | |   (72)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 158.93/25.40  | | | | | | |           (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.93/25.40  | | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 158.93/25.40  | | | | | | |           $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 158.93/25.40  | | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 158.93/25.40  | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 158.93/25.40  | | | | | | |             e0) = e3 & $i(all_57_10))
% 158.93/25.40  | | | | | | | 
% 158.93/25.40  | | | | | | | BETA: splitting (72) gives:
% 158.93/25.40  | | | | | | | 
% 158.93/25.40  | | | | | | | Case 1:
% 158.93/25.40  | | | | | | | | 
% 158.93/25.40  | | | | | | | |   (73)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 158.93/25.40  | | | | | | | |         (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 158.93/25.40  | | | | | | | |         op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)
% 158.93/25.40  | | | | | | | | 
% 158.93/25.40  | | | | | | | | ALPHA: (73) implies:
% 158.93/25.40  | | | | | | | |   (74)  op(e1, e0) = e1
% 158.93/25.40  | | | | | | | | 
% 158.93/25.40  | | | | | | | | REF_CLOSE: (7), (15), (24), (74) are inconsistent by sub-proof
% 158.93/25.40  | | | | | | | |            #974.
% 158.93/25.40  | | | | | | | | 
% 158.93/25.40  | | | | | | | Case 2:
% 158.93/25.40  | | | | | | | | 
% 158.93/25.40  | | | | | | | |   (75)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~
% 158.93/25.40  | | | | | | | |         (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 158.93/25.40  | | | | | | | |         e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)
% 158.93/25.40  | | | | | | | | 
% 158.93/25.40  | | | | | | | | ALPHA: (75) implies:
% 158.93/25.40  | | | | | | | |   (76)  op(e0, e0) = e3
% 158.93/25.40  | | | | | | | | 
% 158.93/25.40  | | | | | | | | REF_CLOSE: (1), (7), (26), (76) are inconsistent by sub-proof
% 158.93/25.40  | | | | | | | |            #473.
% 158.93/25.40  | | | | | | | | 
% 158.93/25.40  | | | | | | | End of split
% 158.93/25.40  | | | | | | | 
% 158.93/25.40  | | | | | | End of split
% 158.93/25.40  | | | | | | 
% 158.93/25.40  | | | | | Case 2:
% 158.93/25.40  | | | | | | 
% 159.08/25.40  | | | | | |   (77)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 159.08/25.40  | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 159.08/25.40  | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.08/25.40  | | | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3)
% 159.08/25.40  | | | | | |           = e3 & op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2
% 159.08/25.40  | | | | | |           &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.08/25.40  | | | | | |         (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1)
% 159.08/25.40  | | | | | |           = e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 159.08/25.40  | | | | | |           $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 159.08/25.40  | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0
% 159.08/25.40  | | | | | |               & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.08/25.40  | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.08/25.40  | | | | | |                 e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3)
% 159.08/25.40  | | | | | |               = e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 159.08/25.40  | | | | | |               e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.08/25.40  | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.08/25.40  | | | | | |               all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.08/25.40  | | | | | |             (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.08/25.40  | | | | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.08/25.40  | | | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.08/25.40  | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 159.08/25.40  | | | | | |               & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0
% 159.08/25.40  | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.08/25.40  | | | | | |                 e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2)
% 159.08/25.40  | | | | | |               = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 159.08/25.40  | | | | | |               & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 159.08/25.40  | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 159.08/25.40  | | | | | |               & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.08/25.40  | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.08/25.40  | | | | | |                 e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 159.08/25.40  | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.08/25.40  | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 159.08/25.40  | | | | | |                 e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.08/25.40  | | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 159.08/25.40  | | | | | |               & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.08/25.40  | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.08/25.40  | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.08/25.40  | | | | | | 
% 159.08/25.40  | | | | | | BETA: splitting (77) gives:
% 159.08/25.40  | | | | | | 
% 159.08/25.40  | | | | | | Case 1:
% 159.08/25.40  | | | | | | | 
% 159.08/25.40  | | | | | | |   (78)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 159.08/25.40  | | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 159.08/25.40  | | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 159.08/25.40  | | | | | | |         | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3,
% 159.08/25.40  | | | | | | |             e3) = e3 & op(e3, e0) = e3)
% 159.08/25.40  | | | | | | | 
% 159.08/25.40  | | | | | | | REF_CLOSE: (1), (7), (22), (26), (31), (78) are inconsistent by
% 159.08/25.40  | | | | | | |            sub-proof #336.
% 159.08/25.40  | | | | | | | 
% 159.08/25.40  | | | | | | Case 2:
% 159.08/25.40  | | | | | | | 
% 159.08/25.40  | | | | | | |   (79)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 159.08/25.40  | | | | | | |             e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 159.08/25.40  | | | | | | |           all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1,
% 159.08/25.40  | | | | | | |             e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.08/25.40  | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.08/25.40  | | | | | | |               (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3
% 159.08/25.40  | | | | | | |               & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2
% 159.08/25.40  | | | | | | |               & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2)
% 159.08/25.40  | | | | | | |               = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.08/25.40  | | | | | | |             (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.08/25.40  | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1
% 159.08/25.40  | | | | | | |               & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0
% 159.08/25.40  | | | | | | |               &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.08/25.40  | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 159.08/25.40  | | | | | | |               & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.08/25.40  | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.08/25.40  | | | | | | |               e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 159.08/25.40  | | | | | | |                 e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.08/25.40  | | | | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.08/25.40  | | | | | | |                 e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.08/25.40  | | | | | | |                 e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~
% 159.08/25.40  | | | | | | |               (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.08/25.40  | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 159.08/25.40  | | | | | | |               & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.08/25.40  | | | | | | |               e0) | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.08/25.40  | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.08/25.40  | | | | | | |                 e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.08/25.40  | | | | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.08/25.40  | | | | | | |                 e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.08/25.40  | | | | | | |                 e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.08/25.40  | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.08/25.40  | | | | | | |               all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.08/25.40  | | | | | | |               $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 159.08/25.40  | | | | | | |               ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.08/25.40  | | | | | | | 
% 159.08/25.40  | | | | | | | BETA: splitting (79) gives:
% 159.08/25.40  | | | | | | | 
% 159.08/25.40  | | | | | | | Case 1:
% 159.08/25.40  | | | | | | | | 
% 159.08/25.40  | | | | | | | |   (80)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 159.08/25.40  | | | | | | | |           e2) = e2 & op(e2, e0) = e2
% 159.08/25.40  | | | | | | | | 
% 159.08/25.40  | | | | | | | | ALPHA: (80) implies:
% 159.08/25.40  | | | | | | | |   (81)  op(e2, e2) = e2
% 159.08/25.40  | | | | | | | | 
% 159.08/25.40  | | | | | | | | REF_CLOSE: (7), (19), (22), (81) are inconsistent by sub-proof
% 159.08/25.40  | | | | | | | |            #993.
% 159.08/25.40  | | | | | | | | 
% 159.08/25.40  | | | | | | | Case 2:
% 159.08/25.40  | | | | | | | | 
% 159.08/25.40  | | | | | | | |   (82)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 159.08/25.40  | | | | | | | |             e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.08/25.40  | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9
% 159.08/25.40  | | | | | | | |               = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.08/25.40  | | | | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 159.08/25.40  | | | | | | | |               e0) | (all_57_6 = e0 & all_57_11 = e2 & all_57_12
% 159.08/25.40  | | | | | | | |               = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 159.08/25.40  | | | | | | | |               op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.08/25.40  | | | | | | | |               e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.08/25.40  | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 159.08/25.40  | | | | | | | |               e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15
% 159.08/25.40  | | | | | | | |               = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 159.08/25.40  | | | | | | | |               = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.08/25.40  | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 159.08/25.40  | | | | | | | |               e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11
% 159.08/25.40  | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.08/25.40  | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.08/25.40  | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14
% 159.08/25.40  | | | | | | | |               = e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 159.08/25.40  | | | | | | | |               op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.08/25.40  | | | | | | | |               e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.08/25.40  | | | | | | | |               e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.08/25.40  | | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.08/25.40  | | | | | | | |               op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.08/25.40  | | | | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.08/25.40  | | | | | | | |               (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 159.08/25.40  | | | | | | | |               e2 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13
% 159.08/25.40  | | | | | | | |               = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.08/25.40  | | | | | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.08/25.40  | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15
% 159.08/25.40  | | | | | | | |               = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.08/25.40  | | | | | | | |               all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.08/25.40  | | | | | | | |               $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &
% 159.08/25.40  | | | | | | | |                ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.08/25.40  | | | | | | | | 
% 159.08/25.40  | | | | | | | | BETA: splitting (82) gives:
% 159.08/25.40  | | | | | | | | 
% 159.08/25.40  | | | | | | | | Case 1:
% 159.08/25.40  | | | | | | | | | 
% 159.08/25.40  | | | | | | | | |   (83)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.08/25.40  | | | | | | | | |         op(e1, e1) = e1 & op(e1, e0) = e1
% 159.08/25.40  | | | | | | | | | 
% 159.08/25.40  | | | | | | | | | ALPHA: (83) implies:
% 159.08/25.40  | | | | | | | | |   (84)  op(e1, e0) = e1
% 159.08/25.40  | | | | | | | | | 
% 159.08/25.40  | | | | | | | | | REF_CLOSE: (7), (15), (24), (84) are inconsistent by sub-proof
% 159.08/25.40  | | | | | | | | |            #974.
% 159.08/25.40  | | | | | | | | | 
% 159.08/25.40  | | | | | | | | Case 2:
% 159.08/25.40  | | | | | | | | | 
% 159.08/25.40  | | | | | | | | |   (85)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 =
% 159.08/25.40  | | | | | | | | |             e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.08/25.40  | | | | | | | | |             (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 159.08/25.40  | | | | | | | | |             e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 159.08/25.40  | | | | | | | | |             = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.08/25.40  | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 159.08/25.40  | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 159.08/25.40  | | | | | | | | |             = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.08/25.40  | | | | | | | | |             op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.08/25.40  | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.08/25.40  | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 159.08/25.40  | | | | | | | | |             e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 159.08/25.40  | | | | | | | | |             op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.08/25.40  | | | | | | | | |             e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.08/25.40  | | | | | | | | |             (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 159.08/25.40  | | | | | | | | |             e2 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_13
% 159.08/25.40  | | | | | | | | |             = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.08/25.40  | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.08/25.40  | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 =
% 159.08/25.40  | | | | | | | | |               e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.08/25.40  | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.08/25.40  | | | | | | | | |               e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.08/25.40  | | | | | | | | |               e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 159.08/25.40  | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2)
% 159.08/25.40  | | | | | | | | |             = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.08/25.40  | | | | | | | | |           (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.08/25.40  | | | | | | | | |             ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 159.08/25.40  | | | | | | | | |             = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.08/25.40  | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.08/25.40  | | | | | | | | |               e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.08/25.40  | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0
% 159.08/25.40  | | | | | | | | |             & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.08/25.40  | | | | | | | | |             e0))
% 159.08/25.40  | | | | | | | | | 
% 159.08/25.40  | | | | | | | | | ALPHA: (85) implies:
% 159.08/25.40  | | | | | | | | |   (86)  op(e0, e0) = all_57_15
% 159.08/25.41  | | | | | | | | |   (87)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.08/25.41  | | | | | | | | |           (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3
% 159.08/25.41  | | | | | | | | |           & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2
% 159.08/25.41  | | | | | | | | |           & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2)
% 159.08/25.41  | | | | | | | | |           = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.08/25.41  | | | | | | | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.08/25.41  | | | | | | | | |           (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1
% 159.08/25.41  | | | | | | | | |           & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0
% 159.08/25.41  | | | | | | | | |           &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.08/25.41  | | | | | | | | |           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 159.08/25.41  | | | | | | | | |           & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.08/25.41  | | | | | | | | |           e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.08/25.41  | | | | | | | | |           e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 159.08/25.41  | | | | | | | | |             e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.08/25.41  | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.08/25.41  | | | | | | | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.08/25.41  | | | | | | | | |             e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~
% 159.08/25.41  | | | | | | | | |           (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.08/25.41  | | | | | | | | |           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 159.08/25.41  | | | | | | | | |           & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.08/25.41  | | | | | | | | |           e0) | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.08/25.41  | | | | | | | | |           e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.08/25.41  | | | | | | | | |             e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.08/25.41  | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.08/25.41  | | | | | | | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.08/25.41  | | | | | | | | |             e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.08/25.41  | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.08/25.41  | | | | | | | | |           all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.08/25.41  | | | | | | | | |           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 159.08/25.41  | | | | | | | | |           ~ (e1 = e0) & op(e0, e1) = e0)
% 159.08/25.41  | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_57_15, e0, e0,
% 159.08/25.41  | | | | | | | | |              simplifying with (1), (86) gives:
% 159.08/25.41  | | | | | | | | |   (88)  all_57_15 = e1
% 159.08/25.41  | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | BETA: splitting (87) gives:
% 159.08/25.41  | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | |   (89)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.08/25.41  | | | | | | | | | |           (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 159.08/25.41  | | | | | | | | | |           e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 159.08/25.41  | | | | | | | | | |           = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.08/25.41  | | | | | | | | | |           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 159.08/25.41  | | | | | | | | | |           e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 159.08/25.41  | | | | | | | | | |           = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.08/25.41  | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.08/25.41  | | | | | | | | | |           e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.08/25.41  | | | | | | | | | |           e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 159.08/25.41  | | | | | | | | | |           e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 159.08/25.41  | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.08/25.41  | | | | | | | | | |           e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.08/25.41  | | | | | | | | | |           (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 159.08/25.41  | | | | | | | | | |           e2 & op(e0, e2) = e0)
% 159.08/25.41  | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | BETA: splitting (89) gives:
% 159.08/25.41  | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | |   (90)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.08/25.41  | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.08/25.41  | | | | | | | | | | |             e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.08/25.41  | | | | | | | | | | |           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.08/25.41  | | | | | | | | | | |             = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.08/25.41  | | | | | | | | | | |           op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.08/25.41  | | | | | | | | | | |           e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.08/25.41  | | | | | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.08/25.41  | | | | | | | | | | |           e0)
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | BETA: splitting (90) gives:
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | |   (91)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.08/25.41  | | | | | | | | | | | |         ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 159.08/25.41  | | | | | | | | | | | |         = e3 & op(e0, e3) = e0
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | ALPHA: (91) implies:
% 159.08/25.41  | | | | | | | | | | | |   (92)  op(e3, e3) = e0
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | REF_CLOSE: (7), (21), (31), (92) are inconsistent by
% 159.08/25.41  | | | | | | | | | | | |            sub-proof #834.
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | |   (93)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.08/25.41  | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.08/25.41  | | | | | | | | | | | |             e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.08/25.41  | | | | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.08/25.41  | | | | | | | | | | | |             = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.08/25.41  | | | | | | | | | | | |           op(e0, e3) = e0)
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | BETA: splitting (93) gives:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | |   (94)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 159.08/25.41  | | | | | | | | | | | | |         ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 159.08/25.41  | | | | | | | | | | | | |         = e2 & op(e0, e3) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | ALPHA: (94) implies:
% 159.08/25.41  | | | | | | | | | | | | |   (95)  op(e2, e2) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | REF_CLOSE: (7), (19), (21), (95) are inconsistent by
% 159.08/25.41  | | | | | | | | | | | | |            sub-proof #960.
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | |   (96)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.08/25.41  | | | | | | | | | | | | |         ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 159.08/25.41  | | | | | | | | | | | | |         = e1 & op(e0, e3) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | ALPHA: (96) implies:
% 159.08/25.41  | | | | | | | | | | | | |   (97)  op(e1, e1) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (10), (11), (13), (15), (18), (21),
% 159.08/25.41  | | | | | | | | | | | | |            (24), (26), (27), (31), (97) are inconsistent by
% 159.08/25.41  | | | | | | | | | | | | |            sub-proof #628.
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | |   (98)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.08/25.41  | | | | | | | | | | |           op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 159.08/25.41  | | | | | | | | | | |           e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.08/25.41  | | | | | | | | | | |           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.08/25.41  | | | | | | | | | | |           e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.08/25.41  | | | | | | | | | | |           all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.08/25.41  | | | | | | | | | | |             e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | BETA: splitting (98) gives:
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | |   (99)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.08/25.41  | | | | | | | | | | | |         op(e0, e3) = e0
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | REF_CLOSE: (21), (88), (99) are inconsistent by sub-proof
% 159.08/25.41  | | | | | | | | | | | |            #372.
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | |   (100)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.08/25.41  | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.08/25.41  | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.08/25.41  | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.08/25.41  | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.08/25.41  | | | | | | | | | | | |            op(e0, e2) = e0)
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | BETA: splitting (100) gives:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | |   (101)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.08/25.41  | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 159.08/25.41  | | | | | | | | | | | | |          = e3 & op(e0, e2) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | ALPHA: (101) implies:
% 159.08/25.41  | | | | | | | | | | | | |   (102)  op(e3, e3) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | REF_CLOSE: (7), (21), (31), (102) are inconsistent by
% 159.08/25.41  | | | | | | | | | | | | |            sub-proof #834.
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | |   (103)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 159.08/25.41  | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 159.08/25.41  | | | | | | | | | | | | |          = e2 & op(e0, e2) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | ALPHA: (103) implies:
% 159.08/25.41  | | | | | | | | | | | | |   (104)  op(e2, e2) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | REF_CLOSE: (7), (19), (21), (104) are inconsistent by
% 159.08/25.41  | | | | | | | | | | | | |            sub-proof #960.
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | |   (105)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.08/25.41  | | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 159.08/25.41  | | | | | | | | | |            = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.08/25.41  | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.08/25.41  | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.08/25.41  | | | | | | | | | |             ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.08/25.41  | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.08/25.41  | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.08/25.41  | | | | | | | | | |              e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.08/25.41  | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.08/25.41  | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.08/25.41  | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.08/25.41  | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15
% 159.08/25.41  | | | | | | | | | |            = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.08/25.41  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.08/25.41  | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 159.08/25.41  | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.08/25.41  | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | BETA: splitting (105) gives:
% 159.08/25.41  | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | |   (106)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.08/25.41  | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.08/25.41  | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.08/25.41  | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.08/25.41  | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.08/25.41  | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.08/25.41  | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | BETA: splitting (106) gives:
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | |   (107)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.08/25.41  | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 159.08/25.41  | | | | | | | | | | | |          = e1 & op(e0, e2) = e0
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | ALPHA: (107) implies:
% 159.08/25.41  | | | | | | | | | | | |   (108)  op(e1, e1) = e0
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (10), (11), (13), (15), (18), (21),
% 159.08/25.41  | | | | | | | | | | | |            (24), (26), (27), (31), (108) are inconsistent by
% 159.08/25.41  | | | | | | | | | | | |            sub-proof #628.
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | |   (109)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 159.08/25.41  | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 159.08/25.41  | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.08/25.41  | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.08/25.41  | | | | | | | | | | | |            e0)
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | BETA: splitting (109) gives:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | |   (110)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 159.08/25.41  | | | | | | | | | | | | |          op(e0, e2) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | REF_CLOSE: (21), (88), (110) are inconsistent by sub-proof
% 159.08/25.41  | | | | | | | | | | | | |            #371.
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | |   (111)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.08/25.41  | | | | | | | | | | | | |          ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0)
% 159.08/25.41  | | | | | | | | | | | | |          = e3 & op(e0, e1) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | ALPHA: (111) implies:
% 159.08/25.41  | | | | | | | | | | | | |   (112)  op(e3, e3) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | REF_CLOSE: (7), (21), (31), (112) are inconsistent by
% 159.08/25.41  | | | | | | | | | | | | |            sub-proof #834.
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | |   (113)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.08/25.41  | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.08/25.41  | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.08/25.41  | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.08/25.41  | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.08/25.41  | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.08/25.41  | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.08/25.41  | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.08/25.41  | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 159.08/25.41  | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 159.08/25.41  | | | | | | | | | | |            = e0)
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | BETA: splitting (113) gives:
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | |   (114)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.08/25.41  | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.08/25.41  | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.08/25.41  | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.08/25.41  | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.08/25.41  | | | | | | | | | | | |            op(e0, e1) = e0)
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | BETA: splitting (114) gives:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | Case 1:
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | |   (115)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 159.08/25.41  | | | | | | | | | | | | |          ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 159.08/25.41  | | | | | | | | | | | | |          = e2 & op(e0, e1) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | ALPHA: (115) implies:
% 159.08/25.41  | | | | | | | | | | | | |   (116)  op(e2, e2) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | REF_CLOSE: (7), (19), (21), (116) are inconsistent by
% 159.08/25.41  | | | | | | | | | | | | |            sub-proof #960.
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | |   (117)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.08/25.41  | | | | | | | | | | | | |          ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 159.08/25.41  | | | | | | | | | | | | |          = e1 & op(e0, e1) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | ALPHA: (117) implies:
% 159.08/25.41  | | | | | | | | | | | | |   (118)  op(e1, e1) = e0
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (10), (11), (13), (15), (18), (21),
% 159.08/25.41  | | | | | | | | | | | | |            (24), (26), (27), (31), (118) are inconsistent by
% 159.08/25.41  | | | | | | | | | | | | |            sub-proof #628.
% 159.08/25.41  | | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | Case 2:
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | |   (119)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 159.08/25.41  | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.08/25.41  | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.08/25.41  | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 159.08/25.41  | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | | REF_CLOSE: (7), (15), (24), (88), (119) are inconsistent by
% 159.08/25.41  | | | | | | | | | | | |            sub-proof #349.
% 159.08/25.41  | | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | | 
% 159.08/25.41  | | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | | 
% 159.08/25.41  | | | | | | | | End of split
% 159.08/25.41  | | | | | | | | 
% 159.08/25.41  | | | | | | | End of split
% 159.08/25.41  | | | | | | | 
% 159.08/25.41  | | | | | | End of split
% 159.08/25.41  | | | | | | 
% 159.08/25.41  | | | | | End of split
% 159.08/25.41  | | | | | 
% 159.08/25.41  | | | | End of split
% 159.08/25.41  | | | | 
% 159.08/25.41  | | | End of split
% 159.08/25.41  | | | 
% 159.08/25.41  | | Case 2:
% 159.08/25.41  | | | 
% 159.08/25.41  | | |   (120)  all_56_1 = e1 & op(e3, e2) = e1
% 159.08/25.41  | | | 
% 159.08/25.41  | | | ALPHA: (120) implies:
% 159.08/25.41  | | |   (121)  all_56_1 = e1
% 159.08/25.41  | | | 
% 159.08/25.41  | | | REF_CLOSE: (4), (6), (7), (12), (17), (19), (21), (22), (26), (27), (28),
% 159.08/25.41  | | |            (121) are inconsistent by sub-proof #332.
% 159.08/25.41  | | | 
% 159.08/25.41  | | End of split
% 159.08/25.41  | | 
% 159.08/25.41  | Case 2:
% 159.08/25.41  | | 
% 159.08/25.41  | |   (122)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 159.08/25.41  | |            e1)
% 159.08/25.41  | | 
% 159.08/25.41  | | BETA: splitting (122) gives:
% 159.08/25.41  | | 
% 159.08/25.41  | | Case 1:
% 159.08/25.41  | | | 
% 159.08/25.41  | | |   (123)  all_56_4 = e1 & op(e3, e1) = e1
% 159.08/25.41  | | | 
% 159.08/25.41  | | | REF_CLOSE: (7), (8), (16), (123) are inconsistent by sub-proof #331.
% 159.08/25.41  | | | 
% 159.08/25.41  | | Case 2:
% 159.08/25.41  | | | 
% 159.08/25.41  | | |   (124)  all_56_9 = e1 & op(e3, e0) = e1
% 159.08/25.41  | | | 
% 159.08/25.41  | | | REF_CLOSE: (3), (7), (23), (124) are inconsistent by sub-proof #851.
% 159.08/25.41  | | | 
% 159.08/25.41  | | End of split
% 159.08/25.41  | | 
% 159.08/25.41  | End of split
% 159.08/25.41  | 
% 159.08/25.41  End of proof
% 159.08/25.41  
% 159.08/25.41  Sub-proof #331 shows that the following formulas are inconsistent:
% 159.08/25.41  ----------------------------------------------------------------
% 159.08/25.41    (1)  all_56_4 = e1 & op(e3, e1) = e1
% 159.08/25.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.41    (3)  op(e3, e1) = all_52_8
% 159.08/25.41    (4)   ~ (all_52_8 = e1)
% 159.08/25.41  
% 159.08/25.41  Begin of proof
% 159.08/25.41  | 
% 159.08/25.41  | ALPHA: (1) implies:
% 159.08/25.41  |   (5)  op(e3, e1) = e1
% 159.08/25.41  | 
% 159.08/25.41  | GROUND_INST: instantiating (2) with all_52_8, e1, e1, e3, simplifying with
% 159.08/25.41  |              (3), (5) gives:
% 159.08/25.41  |   (6)  all_52_8 = e1
% 159.08/25.41  | 
% 159.08/25.41  | REDUCE: (4), (6) imply:
% 159.08/25.41  |   (7)  $false
% 159.08/25.41  | 
% 159.08/25.41  | CLOSE: (7) is inconsistent.
% 159.08/25.41  | 
% 159.08/25.41  End of proof
% 159.08/25.41  
% 159.08/25.41  Sub-proof #332 shows that the following formulas are inconsistent:
% 159.08/25.41  ----------------------------------------------------------------
% 159.08/25.41    (1)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.08/25.41         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 159.08/25.41    (2)   ~ (e3 = e2)
% 159.08/25.41    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.41    (4)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.08/25.41         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.08/25.42    (5)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.08/25.42         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.08/25.42    (6)  all_56_1 = e1
% 159.08/25.42    (7)  op(e2, e2) = e1
% 159.08/25.42    (8)   ~ (e1 = e0)
% 159.08/25.42    (9)   ~ (e2 = e1)
% 159.08/25.42    (10)   ~ (e3 = e1)
% 159.08/25.42    (11)   ~ (e2 = e0)
% 159.08/25.42    (12)   ~ (e3 = e0)
% 159.08/25.42  
% 159.08/25.42  Begin of proof
% 159.08/25.42  | 
% 159.08/25.42  | BETA: splitting (4) gives:
% 159.08/25.42  | 
% 159.08/25.42  | Case 1:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (13)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 159.08/25.42  | |           e2)
% 159.08/25.42  | | 
% 159.08/25.42  | | BETA: splitting (13) gives:
% 159.08/25.42  | | 
% 159.08/25.42  | | Case 1:
% 159.08/25.42  | | | 
% 159.08/25.42  | | |   (14)  all_56_1 = e2 & op(e3, e2) = e2
% 159.08/25.42  | | | 
% 159.08/25.42  | | | ALPHA: (14) implies:
% 159.08/25.42  | | |   (15)  all_56_1 = e2
% 159.08/25.42  | | | 
% 159.08/25.42  | | | REF_CLOSE: (6), (9), (15) are inconsistent by sub-proof #680.
% 159.08/25.42  | | | 
% 159.08/25.42  | | Case 2:
% 159.08/25.42  | | | 
% 159.08/25.42  | | |   (16)  all_56_3 = e2 & op(e2, e2) = e2
% 159.08/25.42  | | | 
% 159.08/25.42  | | | ALPHA: (16) implies:
% 159.08/25.42  | | |   (17)  op(e2, e2) = e2
% 159.08/25.42  | | | 
% 159.08/25.42  | | | REF_CLOSE: (3), (7), (9), (17) are inconsistent by sub-proof #993.
% 159.08/25.42  | | | 
% 159.08/25.42  | | End of split
% 159.08/25.42  | | 
% 159.08/25.42  | Case 2:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (18)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 159.08/25.42  | |           e2)
% 159.08/25.42  | | 
% 159.08/25.42  | | BETA: splitting (18) gives:
% 159.08/25.42  | | 
% 159.08/25.42  | | Case 1:
% 159.08/25.42  | | | 
% 159.08/25.42  | | |   (19)  all_56_7 = e2 & op(e1, e2) = e2
% 159.08/25.42  | | | 
% 159.08/25.42  | | | ALPHA: (19) implies:
% 159.08/25.42  | | |   (20)  all_56_7 = e2
% 159.08/25.42  | | | 
% 159.08/25.42  | | | BETA: splitting (1) gives:
% 159.08/25.42  | | | 
% 159.08/25.42  | | | Case 1:
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | |   (21)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2)
% 159.08/25.42  | | | |           = e0)
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | | REF_CLOSE: (3), (6), (7), (8), (21) are inconsistent by sub-proof #335.
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | Case 2:
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | |   (22)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2)
% 159.08/25.42  | | | |           = e0)
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | | BETA: splitting (22) gives:
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | | Case 1:
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | |   (23)  all_56_7 = e0 & op(e1, e2) = e0
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | ALPHA: (23) implies:
% 159.08/25.42  | | | | |   (24)  all_56_7 = e0
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | COMBINE_EQS: (20), (24) imply:
% 159.08/25.42  | | | | |   (25)  e2 = e0
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | REDUCE: (11), (25) imply:
% 159.08/25.42  | | | | |   (26)  $false
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | CLOSE: (26) is inconsistent.
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | Case 2:
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | |   (27)  all_56_13 = e0 & op(e0, e2) = e0
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | ALPHA: (27) implies:
% 159.08/25.42  | | | | |   (28)  all_56_13 = e0
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | BETA: splitting (5) gives:
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | Case 1:
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | |   (29)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2,
% 159.08/25.42  | | | | | |             e2) = e3)
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | | REF_CLOSE: (3), (6), (7), (10), (29) are inconsistent by sub-proof
% 159.08/25.42  | | | | | |            #334.
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | Case 2:
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | |   (30)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0,
% 159.08/25.42  | | | | | |             e2) = e3)
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | | BETA: splitting (30) gives:
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | | Case 1:
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | |   (31)  all_56_7 = e3 & op(e1, e2) = e3
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | | ALPHA: (31) implies:
% 159.08/25.42  | | | | | | |   (32)  all_56_7 = e3
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | | COMBINE_EQS: (20), (32) imply:
% 159.08/25.42  | | | | | | |   (33)  e3 = e2
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | | REDUCE: (2), (33) imply:
% 159.08/25.42  | | | | | | |   (34)  $false
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | | CLOSE: (34) is inconsistent.
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | Case 2:
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | |   (35)  all_56_13 = e3 & op(e0, e2) = e3
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | | ALPHA: (35) implies:
% 159.08/25.42  | | | | | | |   (36)  all_56_13 = e3
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | | COMBINE_EQS: (28), (36) imply:
% 159.08/25.42  | | | | | | |   (37)  e3 = e0
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | | REDUCE: (12), (37) imply:
% 159.08/25.42  | | | | | | |   (38)  $false
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | | CLOSE: (38) is inconsistent.
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | End of split
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | End of split
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | End of split
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | End of split
% 159.08/25.42  | | | 
% 159.08/25.42  | | Case 2:
% 159.08/25.42  | | | 
% 159.08/25.42  | | |   (39)  all_56_13 = e2 & op(e0, e2) = e2
% 159.08/25.42  | | | 
% 159.08/25.42  | | | ALPHA: (39) implies:
% 159.08/25.42  | | |   (40)  all_56_13 = e2
% 159.08/25.42  | | | 
% 159.08/25.42  | | | BETA: splitting (1) gives:
% 159.08/25.42  | | | 
% 159.08/25.42  | | | Case 1:
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | |   (41)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2)
% 159.08/25.42  | | | |           = e0)
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | | REF_CLOSE: (3), (6), (7), (8), (41) are inconsistent by sub-proof #335.
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | Case 2:
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | |   (42)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2)
% 159.08/25.42  | | | |           = e0)
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | | BETA: splitting (42) gives:
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | | Case 1:
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | |   (43)  all_56_7 = e0 & op(e1, e2) = e0
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | ALPHA: (43) implies:
% 159.08/25.42  | | | | |   (44)  all_56_7 = e0
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | BETA: splitting (5) gives:
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | Case 1:
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | |   (45)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2,
% 159.08/25.42  | | | | | |             e2) = e3)
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | | REF_CLOSE: (3), (6), (7), (10), (45) are inconsistent by sub-proof
% 159.08/25.42  | | | | | |            #334.
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | Case 2:
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | |   (46)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0,
% 159.08/25.42  | | | | | |             e2) = e3)
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | | BETA: splitting (46) gives:
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | | Case 1:
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | |   (47)  all_56_7 = e3 & op(e1, e2) = e3
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | | REF_CLOSE: (12), (44), (47) are inconsistent by sub-proof #333.
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | Case 2:
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | |   (48)  all_56_13 = e3 & op(e0, e2) = e3
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | | REF_CLOSE: (2), (40), (48) are inconsistent by sub-proof #906.
% 159.08/25.42  | | | | | | | 
% 159.08/25.42  | | | | | | End of split
% 159.08/25.42  | | | | | | 
% 159.08/25.42  | | | | | End of split
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | Case 2:
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | |   (49)  all_56_13 = e0 & op(e0, e2) = e0
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | | REF_CLOSE: (11), (40), (49) are inconsistent by sub-proof #908.
% 159.08/25.42  | | | | | 
% 159.08/25.42  | | | | End of split
% 159.08/25.42  | | | | 
% 159.08/25.42  | | | End of split
% 159.08/25.42  | | | 
% 159.08/25.42  | | End of split
% 159.08/25.42  | | 
% 159.08/25.42  | End of split
% 159.08/25.42  | 
% 159.08/25.42  End of proof
% 159.08/25.42  
% 159.08/25.42  Sub-proof #333 shows that the following formulas are inconsistent:
% 159.08/25.42  ----------------------------------------------------------------
% 159.08/25.42    (1)  all_56_7 = e3 & op(e1, e2) = e3
% 159.08/25.42    (2)  all_56_7 = e0
% 159.08/25.42    (3)   ~ (e3 = e0)
% 159.08/25.42  
% 159.08/25.42  Begin of proof
% 159.08/25.42  | 
% 159.08/25.42  | ALPHA: (1) implies:
% 159.08/25.42  |   (4)  all_56_7 = e3
% 159.08/25.42  | 
% 159.08/25.42  | COMBINE_EQS: (2), (4) imply:
% 159.08/25.42  |   (5)  e3 = e0
% 159.08/25.42  | 
% 159.08/25.42  | REDUCE: (3), (5) imply:
% 159.08/25.42  |   (6)  $false
% 159.08/25.42  | 
% 159.08/25.42  | CLOSE: (6) is inconsistent.
% 159.08/25.42  | 
% 159.08/25.42  End of proof
% 159.08/25.42  
% 159.08/25.42  Sub-proof #334 shows that the following formulas are inconsistent:
% 159.08/25.42  ----------------------------------------------------------------
% 159.08/25.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.42    (2)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 159.08/25.42    (3)  all_56_1 = e1
% 159.08/25.42    (4)  op(e2, e2) = e1
% 159.08/25.42    (5)   ~ (e3 = e1)
% 159.08/25.42  
% 159.08/25.42  Begin of proof
% 159.08/25.42  | 
% 159.08/25.42  | BETA: splitting (2) gives:
% 159.08/25.42  | 
% 159.08/25.42  | Case 1:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (6)  all_56_1 = e3 & op(e3, e2) = e3
% 159.08/25.42  | | 
% 159.08/25.42  | | ALPHA: (6) implies:
% 159.08/25.42  | |   (7)  all_56_1 = e3
% 159.08/25.42  | | 
% 159.08/25.42  | | COMBINE_EQS: (3), (7) imply:
% 159.08/25.42  | |   (8)  e3 = e1
% 159.08/25.42  | | 
% 159.08/25.42  | | SIMP: (8) implies:
% 159.08/25.42  | |   (9)  e3 = e1
% 159.08/25.42  | | 
% 159.08/25.42  | | REDUCE: (5), (9) imply:
% 159.08/25.42  | |   (10)  $false
% 159.08/25.42  | | 
% 159.08/25.42  | | CLOSE: (10) is inconsistent.
% 159.08/25.42  | | 
% 159.08/25.42  | Case 2:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (11)  all_56_3 = e3 & op(e2, e2) = e3
% 159.08/25.42  | | 
% 159.08/25.42  | | ALPHA: (11) implies:
% 159.08/25.42  | |   (12)  op(e2, e2) = e3
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (1), (4), (5), (12) are inconsistent by sub-proof #847.
% 159.08/25.42  | | 
% 159.08/25.42  | End of split
% 159.08/25.42  | 
% 159.08/25.42  End of proof
% 159.08/25.42  
% 159.08/25.42  Sub-proof #335 shows that the following formulas are inconsistent:
% 159.08/25.42  ----------------------------------------------------------------
% 159.08/25.42    (1)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 159.08/25.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.42    (3)  all_56_1 = e1
% 159.08/25.42    (4)  op(e2, e2) = e1
% 159.08/25.42    (5)   ~ (e1 = e0)
% 159.08/25.42  
% 159.08/25.42  Begin of proof
% 159.08/25.42  | 
% 159.08/25.42  | BETA: splitting (1) gives:
% 159.08/25.42  | 
% 159.08/25.42  | Case 1:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (6)  all_56_1 = e0 & op(e3, e2) = e0
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #760.
% 159.08/25.42  | | 
% 159.08/25.42  | Case 2:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (7)  all_56_3 = e0 & op(e2, e2) = e0
% 159.08/25.42  | | 
% 159.08/25.42  | | ALPHA: (7) implies:
% 159.08/25.42  | |   (8)  op(e2, e2) = e0
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #960.
% 159.08/25.42  | | 
% 159.08/25.42  | End of split
% 159.08/25.42  | 
% 159.08/25.42  End of proof
% 159.08/25.42  
% 159.08/25.42  Sub-proof #336 shows that the following formulas are inconsistent:
% 159.08/25.42  ----------------------------------------------------------------
% 159.08/25.42    (1)  op(e0, e0) = e1
% 159.08/25.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.42    (3)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.08/25.42           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.08/25.42           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 159.08/25.42           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 159.08/25.42    (4)  op(e3, e3) = e1
% 159.08/25.42    (5)   ~ (e2 = e1)
% 159.08/25.42    (6)   ~ (e3 = e1)
% 159.08/25.42  
% 159.08/25.42  Begin of proof
% 159.08/25.42  | 
% 159.08/25.42  | BETA: splitting (3) gives:
% 159.08/25.42  | 
% 159.08/25.42  | Case 1:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (7)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 159.08/25.42  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.08/25.42  | |          e0) = e2 & $i(all_57_12)
% 159.08/25.42  | | 
% 159.08/25.42  | | ALPHA: (7) implies:
% 159.08/25.42  | |   (8)  op(e0, e0) = e2
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #875.
% 159.08/25.42  | | 
% 159.08/25.42  | Case 2:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (9)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 159.08/25.42  | |        op(e3, e0) = e3
% 159.08/25.42  | | 
% 159.08/25.42  | | ALPHA: (9) implies:
% 159.08/25.42  | |   (10)  op(e3, e3) = e3
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #995.
% 159.08/25.42  | | 
% 159.08/25.42  | End of split
% 159.08/25.42  | 
% 159.08/25.42  End of proof
% 159.08/25.42  
% 159.08/25.42  Sub-proof #337 shows that the following formulas are inconsistent:
% 159.08/25.42  ----------------------------------------------------------------
% 159.08/25.42    (1)  op(e0, e0) = e1
% 159.08/25.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.42    (3)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.08/25.42           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.08/25.42           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 159.08/25.42           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.08/25.42    (4)  op(e2, e2) = e1
% 159.08/25.42    (5)   ~ (e2 = e1)
% 159.08/25.42  
% 159.08/25.42  Begin of proof
% 159.08/25.42  | 
% 159.08/25.42  | BETA: splitting (3) gives:
% 159.08/25.42  | 
% 159.08/25.42  | Case 1:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (6)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 159.08/25.42  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 159.08/25.42  | |          e0) = e2 & $i(all_57_12)
% 159.08/25.42  | | 
% 159.08/25.42  | | ALPHA: (6) implies:
% 159.08/25.42  | |   (7)  op(e0, e0) = e2
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #875.
% 159.08/25.42  | | 
% 159.08/25.42  | Case 2:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (8)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 159.08/25.42  | |        op(e2, e1) = e2
% 159.08/25.42  | | 
% 159.08/25.42  | | ALPHA: (8) implies:
% 159.08/25.42  | |   (9)  op(e2, e2) = e2
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #993.
% 159.08/25.42  | | 
% 159.08/25.42  | End of split
% 159.08/25.42  | 
% 159.08/25.42  End of proof
% 159.08/25.42  
% 159.08/25.42  Sub-proof #338 shows that the following formulas are inconsistent:
% 159.08/25.42  ----------------------------------------------------------------
% 159.08/25.42    (1)   ~ (all_52_6 = e1)
% 159.08/25.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.42    (3)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.08/25.42    (4)  op(e0, e2) = all_52_7
% 159.08/25.42    (5)  op(e1, e2) = all_52_6
% 159.08/25.42    (6)   ~ (all_52_7 = e1)
% 159.08/25.42  
% 159.08/25.42  Begin of proof
% 159.08/25.42  | 
% 159.08/25.42  | BETA: splitting (3) gives:
% 159.08/25.42  | 
% 159.08/25.42  | Case 1:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (7)  all_56_7 = e1 & op(e1, e2) = e1
% 159.08/25.42  | | 
% 159.08/25.42  | | ALPHA: (7) implies:
% 159.08/25.42  | |   (8)  op(e1, e2) = e1
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #984.
% 159.08/25.42  | | 
% 159.08/25.42  | Case 2:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (9)  all_56_13 = e1 & op(e0, e2) = e1
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #712.
% 159.08/25.42  | | 
% 159.08/25.42  | End of split
% 159.08/25.42  | 
% 159.08/25.42  End of proof
% 159.08/25.42  
% 159.08/25.42  Sub-proof #339 shows that the following formulas are inconsistent:
% 159.08/25.42  ----------------------------------------------------------------
% 159.08/25.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.42    (2)  op(e1, e1) = e1
% 159.08/25.42    (3)  all_57_15 = e1
% 159.08/25.42    (4)   ~ (e1 = e0)
% 159.08/25.42    (5)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.08/25.42           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.08/25.42           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 159.08/25.42           & op(e1, e0) = e1 & op(e0, e1) = e0)
% 159.08/25.42  
% 159.08/25.42  Begin of proof
% 159.08/25.42  | 
% 159.08/25.42  | BETA: splitting (5) gives:
% 159.08/25.42  | 
% 159.08/25.42  | Case 1:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (6)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1)
% 159.08/25.42  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 159.08/25.42  | | 
% 159.08/25.42  | | ALPHA: (6) implies:
% 159.08/25.42  | |   (7)   ~ (all_57_15 = e1)
% 159.08/25.42  | | 
% 159.08/25.42  | | REDUCE: (3), (7) imply:
% 159.08/25.42  | |   (8)  $false
% 159.08/25.42  | | 
% 159.08/25.42  | | CLOSE: (8) is inconsistent.
% 159.08/25.42  | | 
% 159.08/25.42  | Case 2:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (9)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1)
% 159.08/25.42  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.08/25.42  | | 
% 159.08/25.42  | | ALPHA: (9) implies:
% 159.08/25.42  | |   (10)  op(e1, e1) = e0
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #903.
% 159.08/25.42  | | 
% 159.08/25.42  | End of split
% 159.08/25.42  | 
% 159.08/25.42  End of proof
% 159.08/25.42  
% 159.08/25.42  Sub-proof #340 shows that the following formulas are inconsistent:
% 159.08/25.42  ----------------------------------------------------------------
% 159.08/25.42    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.08/25.42         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.08/25.42    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.08/25.42         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.08/25.42    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.08/25.42         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.08/25.42    (4)   ~ (e3 = e2)
% 159.08/25.42    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.42    (6)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.08/25.42         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.08/25.42    (7)  op(e0, e2) = all_52_7
% 159.08/25.42    (8)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.08/25.42         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.08/25.42    (9)  op(e3, e3) = e3
% 159.08/25.42    (10)  op(e2, e2) = e0
% 159.08/25.42    (11)  all_56_1 = e0
% 159.08/25.42    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.08/25.42          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.08/25.42    (13)   ~ (e1 = e0)
% 159.08/25.42    (14)   ~ (e2 = e1)
% 159.08/25.42    (15)   ~ (all_52_7 = e1)
% 159.08/25.42    (16)   ~ (e3 = e1)
% 159.08/25.42    (17)   ~ (e2 = e0)
% 159.08/25.42    (18)   ~ (e3 = e0)
% 159.08/25.42  
% 159.08/25.42  Begin of proof
% 159.08/25.42  | 
% 159.08/25.42  | BETA: splitting (1) gives:
% 159.08/25.42  | 
% 159.08/25.42  | Case 1:
% 159.08/25.42  | | 
% 159.08/25.42  | |   (19)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 159.08/25.42  | |           e1)
% 159.08/25.42  | | 
% 159.08/25.42  | | REF_CLOSE: (5), (10), (11), (13), (19) are inconsistent by sub-proof #959.
% 159.08/25.43  | | 
% 159.08/25.43  | Case 2:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (20)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 159.08/25.43  | |           e1)
% 159.08/25.43  | | 
% 159.08/25.43  | | BETA: splitting (20) gives:
% 159.08/25.43  | | 
% 159.08/25.43  | | Case 1:
% 159.08/25.43  | | | 
% 159.08/25.43  | | |   (21)  all_56_7 = e1 & op(e1, e2) = e1
% 159.08/25.43  | | | 
% 159.08/25.43  | | | ALPHA: (21) implies:
% 159.08/25.43  | | |   (22)  op(e1, e2) = e1
% 159.08/25.43  | | | 
% 159.08/25.43  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.08/25.43  | | |            (13), (14), (15), (16), (17), (18), (22) are inconsistent by
% 159.08/25.43  | | |            sub-proof #341.
% 159.08/25.43  | | | 
% 159.08/25.43  | | Case 2:
% 159.08/25.43  | | | 
% 159.08/25.43  | | |   (23)  all_56_13 = e1 & op(e0, e2) = e1
% 159.08/25.43  | | | 
% 159.08/25.43  | | | REF_CLOSE: (5), (7), (15), (23) are inconsistent by sub-proof #712.
% 159.08/25.43  | | | 
% 159.08/25.43  | | End of split
% 159.08/25.43  | | 
% 159.08/25.43  | End of split
% 159.08/25.43  | 
% 159.08/25.43  End of proof
% 159.08/25.43  
% 159.08/25.43  Sub-proof #341 shows that the following formulas are inconsistent:
% 159.08/25.43  ----------------------------------------------------------------
% 159.08/25.43    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.08/25.43         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.08/25.43    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.08/25.43         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.08/25.43    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.08/25.43         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.08/25.43    (4)   ~ (e3 = e2)
% 159.08/25.43    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.43    (6)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.08/25.43         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.08/25.43    (7)  op(e0, e2) = all_52_7
% 159.08/25.43    (8)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.08/25.43         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.08/25.43    (9)  op(e3, e3) = e3
% 159.08/25.43    (10)  op(e2, e2) = e0
% 159.08/25.43    (11)  all_56_1 = e0
% 159.08/25.43    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.08/25.43          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.08/25.43    (13)   ~ (e1 = e0)
% 159.08/25.43    (14)   ~ (e2 = e1)
% 159.08/25.43    (15)   ~ (all_52_7 = e1)
% 159.08/25.43    (16)   ~ (e3 = e1)
% 159.08/25.43    (17)   ~ (e2 = e0)
% 159.08/25.43    (18)  op(e1, e2) = e1
% 159.08/25.43    (19)   ~ (e3 = e0)
% 159.08/25.43  
% 159.08/25.43  Begin of proof
% 159.08/25.43  | 
% 159.08/25.43  | BETA: splitting (6) gives:
% 159.08/25.43  | 
% 159.08/25.43  | Case 1:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (20)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 159.08/25.43  | |           e2)
% 159.08/25.43  | | 
% 159.08/25.43  | | REF_CLOSE: (5), (10), (11), (17), (20) are inconsistent by sub-proof #941.
% 159.08/25.43  | | 
% 159.08/25.43  | Case 2:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (21)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 159.08/25.43  | |           e2)
% 159.08/25.43  | | 
% 159.08/25.43  | | BETA: splitting (21) gives:
% 159.08/25.43  | | 
% 159.08/25.43  | | Case 1:
% 159.08/25.43  | | | 
% 159.08/25.43  | | |   (22)  all_56_7 = e2 & op(e1, e2) = e2
% 159.08/25.43  | | | 
% 159.08/25.43  | | | ALPHA: (22) implies:
% 159.08/25.43  | | |   (23)  all_56_7 = e2
% 159.08/25.43  | | | 
% 159.08/25.43  | | | REF_CLOSE: (1), (5), (7), (10), (11), (13), (14), (15), (23) are
% 159.08/25.43  | | |            inconsistent by sub-proof #603.
% 159.08/25.43  | | | 
% 159.08/25.43  | | Case 2:
% 159.08/25.43  | | | 
% 159.08/25.43  | | |   (24)  all_56_13 = e2 & op(e0, e2) = e2
% 159.08/25.43  | | | 
% 159.08/25.43  | | | ALPHA: (24) implies:
% 159.08/25.43  | | |   (25)  all_56_13 = e2
% 159.08/25.43  | | | 
% 159.08/25.43  | | | BETA: splitting (8) gives:
% 159.08/25.43  | | | 
% 159.08/25.43  | | | Case 1:
% 159.08/25.43  | | | | 
% 159.08/25.43  | | | |   (26)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2)
% 159.08/25.43  | | | |           = e3)
% 159.08/25.43  | | | | 
% 159.08/25.43  | | | | REF_CLOSE: (2), (3), (4), (5), (9), (10), (12), (13), (14), (16), (17),
% 159.08/25.43  | | | |            (19), (26) are inconsistent by sub-proof #944.
% 159.08/25.43  | | | | 
% 159.08/25.43  | | | Case 2:
% 159.08/25.43  | | | | 
% 159.08/25.43  | | | |   (27)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2)
% 159.08/25.43  | | | |           = e3)
% 159.08/25.43  | | | | 
% 159.08/25.43  | | | | BETA: splitting (27) gives:
% 159.08/25.43  | | | | 
% 159.08/25.43  | | | | Case 1:
% 159.08/25.43  | | | | | 
% 159.08/25.43  | | | | |   (28)  all_56_7 = e3 & op(e1, e2) = e3
% 159.08/25.43  | | | | | 
% 159.08/25.43  | | | | | ALPHA: (28) implies:
% 159.08/25.43  | | | | |   (29)  op(e1, e2) = e3
% 159.08/25.43  | | | | | 
% 159.08/25.43  | | | | | REF_CLOSE: (5), (16), (18), (29) are inconsistent by sub-proof #939.
% 159.08/25.43  | | | | | 
% 159.08/25.43  | | | | Case 2:
% 159.08/25.43  | | | | | 
% 159.08/25.43  | | | | |   (30)  all_56_13 = e3 & op(e0, e2) = e3
% 159.08/25.43  | | | | | 
% 159.08/25.43  | | | | | ALPHA: (30) implies:
% 159.08/25.43  | | | | |   (31)  all_56_13 = e3
% 159.08/25.43  | | | | | 
% 159.08/25.43  | | | | | REF_CLOSE: (4), (25), (31) are inconsistent by sub-proof #688.
% 159.08/25.43  | | | | | 
% 159.08/25.43  | | | | End of split
% 159.08/25.43  | | | | 
% 159.08/25.43  | | | End of split
% 159.08/25.43  | | | 
% 159.08/25.43  | | End of split
% 159.08/25.43  | | 
% 159.08/25.43  | End of split
% 159.08/25.43  | 
% 159.08/25.43  End of proof
% 159.08/25.43  
% 159.08/25.43  Sub-proof #342 shows that the following formulas are inconsistent:
% 159.08/25.43  ----------------------------------------------------------------
% 159.08/25.43    (1)  op(e0, e0) = e1
% 159.08/25.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.43    (3)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.08/25.43           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.08/25.43           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 159.08/25.43           & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 159.08/25.43           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 159.08/25.43           e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 159.08/25.43         (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 159.08/25.43           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.08/25.43           = e3 & $i(all_57_10))
% 159.08/25.43    (4)  op(e2, e2) = e0
% 159.08/25.43    (5)   ~ (e1 = e0)
% 159.08/25.43    (6)   ~ (e2 = e1)
% 159.08/25.43    (7)   ~ (e3 = e1)
% 159.08/25.43    (8)   ~ (e2 = e0)
% 159.08/25.43  
% 159.08/25.43  Begin of proof
% 159.08/25.43  | 
% 159.08/25.43  | BETA: splitting (3) gives:
% 159.08/25.43  | 
% 159.08/25.43  | Case 1:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (9)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 159.08/25.43  | |          & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 &
% 159.08/25.43  | |          op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2
% 159.08/25.43  | |          &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.08/25.43  | | 
% 159.08/25.43  | | REF_CLOSE: (1), (2), (4), (6), (8), (9) are inconsistent by sub-proof #343.
% 159.08/25.43  | | 
% 159.08/25.43  | Case 2:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (10)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 159.08/25.43  | |             e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 159.08/25.43  | |           & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 159.08/25.43  | |           e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 159.08/25.43  | |           & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.08/25.43  | |           $i(all_57_10))
% 159.08/25.43  | | 
% 159.08/25.43  | | BETA: splitting (10) gives:
% 159.08/25.43  | | 
% 159.08/25.43  | | Case 1:
% 159.08/25.43  | | | 
% 159.08/25.43  | | |   (11)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 159.08/25.43  | | |           e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 159.08/25.43  | | |         & op(e1, e0) = e1 & $i(all_57_14)
% 159.08/25.43  | | | 
% 159.08/25.43  | | | ALPHA: (11) implies:
% 159.08/25.43  | | |   (12)  op(e2, e2) = e1
% 159.08/25.43  | | | 
% 159.08/25.43  | | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #960.
% 159.08/25.43  | | | 
% 159.08/25.43  | | Case 2:
% 159.08/25.43  | | | 
% 159.08/25.43  | | |   (13)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 159.08/25.43  | | |           e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0
% 159.08/25.43  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 159.08/25.43  | | | 
% 159.08/25.43  | | | ALPHA: (13) implies:
% 159.08/25.43  | | |   (14)  op(e0, e0) = e3
% 159.08/25.43  | | | 
% 159.08/25.43  | | | REF_CLOSE: (1), (2), (7), (14) are inconsistent by sub-proof #473.
% 159.08/25.43  | | | 
% 159.08/25.43  | | End of split
% 159.08/25.43  | | 
% 159.08/25.43  | End of split
% 159.08/25.43  | 
% 159.08/25.43  End of proof
% 159.08/25.43  
% 159.08/25.43  Sub-proof #343 shows that the following formulas are inconsistent:
% 159.08/25.43  ----------------------------------------------------------------
% 159.08/25.43    (1)  op(e0, e0) = e1
% 159.08/25.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.43    (3)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.08/25.43           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.08/25.43           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 159.08/25.43           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.08/25.43    (4)  op(e2, e2) = e0
% 159.08/25.43    (5)   ~ (e2 = e1)
% 159.08/25.43    (6)   ~ (e2 = e0)
% 159.08/25.43  
% 159.08/25.43  Begin of proof
% 159.08/25.43  | 
% 159.08/25.43  | BETA: splitting (3) gives:
% 159.08/25.43  | 
% 159.08/25.43  | Case 1:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (7)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 159.08/25.43  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 159.08/25.43  | |          e0) = e2 & $i(all_57_12)
% 159.08/25.43  | | 
% 159.08/25.43  | | ALPHA: (7) implies:
% 159.08/25.43  | |   (8)  op(e0, e0) = e2
% 159.08/25.43  | | 
% 159.08/25.43  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #875.
% 159.08/25.43  | | 
% 159.08/25.43  | Case 2:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (9)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 159.08/25.43  | |        op(e2, e1) = e2
% 159.08/25.43  | | 
% 159.08/25.43  | | ALPHA: (9) implies:
% 159.08/25.43  | |   (10)  op(e2, e2) = e2
% 159.08/25.43  | | 
% 159.08/25.43  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #942.
% 159.08/25.43  | | 
% 159.08/25.43  | End of split
% 159.08/25.43  | 
% 159.08/25.43  End of proof
% 159.08/25.43  
% 159.08/25.43  Sub-proof #344 shows that the following formulas are inconsistent:
% 159.08/25.43  ----------------------------------------------------------------
% 159.08/25.43    (1)  op(e0, e0) = e1
% 159.08/25.43    (2)  op(e3, e2) = e1
% 159.08/25.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.43    (4)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 159.08/25.43           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.08/25.43           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 159.08/25.43           & op(e3, e3) = e3 & op(e3, e2) = e3)
% 159.08/25.43    (5)   ~ (e3 = e1)
% 159.08/25.43  
% 159.08/25.43  Begin of proof
% 159.08/25.43  | 
% 159.08/25.43  | BETA: splitting (4) gives:
% 159.08/25.43  | 
% 159.08/25.43  | Case 1:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (6)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 159.08/25.43  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 159.08/25.43  | |          e0) = e3 & $i(all_57_10)
% 159.08/25.43  | | 
% 159.08/25.43  | | ALPHA: (6) implies:
% 159.08/25.43  | |   (7)  op(e0, e0) = e3
% 159.08/25.43  | | 
% 159.08/25.43  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #473.
% 159.08/25.43  | | 
% 159.08/25.43  | Case 2:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (8)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 159.08/25.43  | |        op(e3, e2) = e3
% 159.08/25.43  | | 
% 159.08/25.43  | | ALPHA: (8) implies:
% 159.08/25.43  | |   (9)  op(e3, e2) = e3
% 159.08/25.43  | | 
% 159.08/25.43  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #345.
% 159.08/25.43  | | 
% 159.08/25.43  | End of split
% 159.08/25.43  | 
% 159.08/25.43  End of proof
% 159.08/25.43  
% 159.08/25.43  Sub-proof #345 shows that the following formulas are inconsistent:
% 159.08/25.43  ----------------------------------------------------------------
% 159.08/25.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.43    (2)  op(e3, e2) = e3
% 159.08/25.43    (3)  op(e3, e2) = e1
% 159.08/25.43    (4)   ~ (e3 = e1)
% 159.08/25.43  
% 159.08/25.43  Begin of proof
% 159.08/25.43  | 
% 159.08/25.43  | GROUND_INST: instantiating (1) with e1, e3, e2, e3, simplifying with (2), (3)
% 159.08/25.43  |              gives:
% 159.08/25.43  |   (5)  e3 = e1
% 159.08/25.43  | 
% 159.08/25.43  | REDUCE: (4), (5) imply:
% 159.08/25.43  |   (6)  $false
% 159.08/25.43  | 
% 159.08/25.43  | CLOSE: (6) is inconsistent.
% 159.08/25.43  | 
% 159.08/25.43  End of proof
% 159.08/25.43  
% 159.08/25.43  Sub-proof #346 shows that the following formulas are inconsistent:
% 159.08/25.43  ----------------------------------------------------------------
% 159.08/25.43    (1)   ~ (e3 = e2)
% 159.08/25.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.43    (3)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.08/25.43           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.08/25.43           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 159.08/25.43           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.08/25.43           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.08/25.43           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 159.08/25.43           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.08/25.43           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 159.08/25.43           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 159.08/25.43             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.08/25.43           all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 159.08/25.43           & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.08/25.43           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 159.08/25.43           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 159.08/25.43             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.08/25.43           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 159.08/25.43         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.08/25.43           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.08/25.43           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 159.08/25.43           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 159.08/25.43           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.08/25.43    (4)  op(e1, e1) = e1
% 159.08/25.43    (5)  op(e3, e3) = e3
% 159.08/25.43    (6)  op(e2, e3) = e1
% 159.08/25.43    (7)   ~ (e2 = e1)
% 159.08/25.43    (8)   ~ (e3 = e1)
% 159.08/25.43  
% 159.08/25.43  Begin of proof
% 159.08/25.43  | 
% 159.08/25.43  | BETA: splitting (3) gives:
% 159.08/25.43  | 
% 159.08/25.43  | Case 1:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (9)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 159.08/25.43  | |          & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 159.08/25.43  | |          = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.08/25.43  | |          all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.08/25.43  | |          op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.08/25.43  | |          $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 159.08/25.43  | |          ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.08/25.43  | |          op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 159.08/25.43  | |          & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.08/25.43  | |          = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.08/25.43  | |          $i(all_57_10))
% 159.08/25.43  | | 
% 159.08/25.43  | | REF_CLOSE: (2), (6), (7), (9) are inconsistent by sub-proof #348.
% 159.08/25.43  | | 
% 159.08/25.43  | Case 2:
% 159.08/25.43  | | 
% 159.08/25.43  | |   (10)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.08/25.43  | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0
% 159.08/25.43  | |           & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 =
% 159.08/25.43  | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 159.08/25.43  | |           & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.08/25.43  | |           $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.08/25.43  | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 159.08/25.43  | |           e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 159.08/25.43  | |           & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.08/25.43  | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &
% 159.08/25.43  | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2,
% 159.08/25.43  | |             e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.08/25.44  | | 
% 159.08/25.44  | | BETA: splitting (10) gives:
% 159.08/25.44  | | 
% 159.08/25.44  | | Case 1:
% 159.08/25.44  | | | 
% 159.08/25.44  | | |   (11)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.08/25.44  | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) =
% 159.08/25.44  | | |           e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.08/25.44  | | |           all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 159.08/25.44  | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 159.08/25.44  | | |             e2) = e3 & $i(all_57_10))
% 159.08/25.44  | | | 
% 159.08/25.44  | | | REF_CLOSE: (2), (6), (7), (11) are inconsistent by sub-proof #347.
% 159.08/25.44  | | | 
% 159.08/25.44  | | Case 2:
% 159.08/25.44  | | | 
% 159.08/25.44  | | |   (12)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.08/25.44  | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 =
% 159.08/25.44  | | |           e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 159.08/25.44  | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.08/25.44  | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 =
% 159.08/25.44  | | |             e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.08/25.44  | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.08/25.44  | | | 
% 159.08/25.44  | | | BETA: splitting (12) gives:
% 159.08/25.44  | | | 
% 159.08/25.44  | | | Case 1:
% 159.08/25.44  | | | | 
% 159.08/25.44  | | | |   (13)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 159.08/25.44  | | | |         & op(e2, e2) = e2
% 159.08/25.44  | | | | 
% 159.08/25.44  | | | | ALPHA: (13) implies:
% 159.08/25.44  | | | |   (14)  op(e2, e3) = e2
% 159.08/25.44  | | | | 
% 159.08/25.44  | | | | REF_CLOSE: (2), (6), (7), (14) are inconsistent by sub-proof #428.
% 159.08/25.44  | | | | 
% 159.08/25.44  | | | Case 2:
% 159.08/25.44  | | | | 
% 159.08/25.44  | | | |   (15)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 159.08/25.44  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.08/25.44  | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 159.08/25.44  | | | |           & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.08/25.44  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.08/25.44  | | | |           op(e2, e1) = e2 & $i(all_57_12))
% 159.08/25.44  | | | | 
% 159.08/25.44  | | | | REF_CLOSE: (1), (2), (4), (5), (8), (15) are inconsistent by sub-proof
% 159.08/25.44  | | | |            #924.
% 159.08/25.44  | | | | 
% 159.08/25.44  | | | End of split
% 159.08/25.44  | | | 
% 159.08/25.44  | | End of split
% 159.08/25.44  | | 
% 159.08/25.44  | End of split
% 159.08/25.44  | 
% 159.08/25.44  End of proof
% 159.08/25.44  
% 159.08/25.44  Sub-proof #347 shows that the following formulas are inconsistent:
% 159.08/25.44  ----------------------------------------------------------------
% 159.08/25.44    (1)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.08/25.44           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.08/25.44           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 159.08/25.44           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.08/25.44           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.08/25.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.44    (3)  op(e2, e3) = e1
% 159.08/25.44    (4)   ~ (e2 = e1)
% 159.08/25.44  
% 159.08/25.44  Begin of proof
% 159.08/25.44  | 
% 159.08/25.44  | BETA: splitting (1) gives:
% 159.08/25.44  | 
% 159.08/25.44  | Case 1:
% 159.08/25.44  | | 
% 159.08/25.44  | |   (5)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 159.08/25.44  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 159.08/25.44  | |          e0) = e2 & $i(all_57_12)
% 159.08/25.44  | | 
% 159.08/25.44  | | ALPHA: (5) implies:
% 159.08/25.44  | |   (6)  op(e2, e3) = e2
% 159.08/25.44  | | 
% 159.08/25.44  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #428.
% 159.08/25.44  | | 
% 159.08/25.44  | Case 2:
% 159.08/25.44  | | 
% 159.08/25.44  | |   (7)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 159.08/25.44  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 159.08/25.44  | |          e2) = e3 & $i(all_57_10)
% 159.08/25.44  | | 
% 159.08/25.44  | | ALPHA: (7) implies:
% 159.08/25.44  | |   (8)  op(e2, e3) = e2
% 159.08/25.44  | | 
% 159.08/25.44  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #428.
% 159.08/25.44  | | 
% 159.08/25.44  | End of split
% 159.08/25.44  | 
% 159.08/25.44  End of proof
% 159.08/25.44  
% 159.08/25.44  Sub-proof #348 shows that the following formulas are inconsistent:
% 159.08/25.44  ----------------------------------------------------------------
% 159.08/25.44    (1)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.08/25.44           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.08/25.44           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 159.08/25.44           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.08/25.44           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.08/25.44           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 159.08/25.44           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.08/25.44           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 159.08/25.44           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 159.08/25.44             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.08/25.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.44    (3)  op(e2, e3) = e1
% 159.08/25.44    (4)   ~ (e2 = e1)
% 159.08/25.44  
% 159.08/25.44  Begin of proof
% 159.08/25.44  | 
% 159.08/25.44  | BETA: splitting (1) gives:
% 159.08/25.44  | 
% 159.08/25.44  | Case 1:
% 159.08/25.44  | | 
% 159.08/25.44  | |   (5)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 159.08/25.44  | |          & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 159.08/25.44  | |          = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.08/25.44  | |          all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.08/25.44  | |          op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.08/25.44  | |          $i(all_57_10))
% 159.08/25.44  | | 
% 159.08/25.44  | | REF_CLOSE: (2), (3), (4), (5) are inconsistent by sub-proof #359.
% 159.08/25.44  | | 
% 159.08/25.44  | Case 2:
% 159.08/25.44  | | 
% 159.08/25.44  | |   (6)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 159.08/25.44  | |          & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 &
% 159.08/25.44  | |          op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.08/25.44  | |          all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.08/25.44  | |          op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.08/25.44  | |          $i(all_57_10))
% 159.08/25.44  | | 
% 159.08/25.44  | | BETA: splitting (6) gives:
% 159.08/25.44  | | 
% 159.08/25.44  | | Case 1:
% 159.08/25.44  | | | 
% 159.08/25.44  | | |   (7)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.08/25.44  | | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 159.08/25.44  | | |        & op(e1, e1) = e2 & $i(all_57_12)
% 159.08/25.44  | | | 
% 159.08/25.44  | | | ALPHA: (7) implies:
% 159.08/25.44  | | |   (8)  op(e2, e3) = e2
% 159.08/25.44  | | | 
% 159.08/25.44  | | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #428.
% 159.08/25.44  | | | 
% 159.08/25.44  | | Case 2:
% 159.08/25.44  | | | 
% 159.08/25.44  | | |   (9)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.08/25.44  | | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2
% 159.08/25.44  | | |        & op(e2, e2) = e3 & $i(all_57_10)
% 159.08/25.44  | | | 
% 159.08/25.44  | | | ALPHA: (9) implies:
% 159.08/25.44  | | |   (10)  op(e2, e3) = e2
% 159.08/25.44  | | | 
% 159.08/25.44  | | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #428.
% 159.08/25.44  | | | 
% 159.08/25.44  | | End of split
% 159.08/25.44  | | 
% 159.08/25.44  | End of split
% 159.08/25.44  | 
% 159.08/25.44  End of proof
% 159.08/25.44  
% 159.08/25.44  Sub-proof #349 shows that the following formulas are inconsistent:
% 159.08/25.44  ----------------------------------------------------------------
% 159.08/25.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.44    (2)  all_57_15 = e1
% 159.08/25.44    (3)  op(e1, e0) = all_52_14
% 159.08/25.44    (4)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.08/25.44           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.08/25.44           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.08/25.44           op(e0, e1) = e0)
% 159.08/25.44    (5)   ~ (all_52_14 = e1)
% 159.08/25.44  
% 159.08/25.44  Begin of proof
% 159.08/25.44  | 
% 159.08/25.44  | BETA: splitting (4) gives:
% 159.08/25.44  | 
% 159.08/25.44  | Case 1:
% 159.08/25.44  | | 
% 159.08/25.44  | |   (6)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 159.08/25.44  | |        & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.08/25.44  | |        $i(all_57_14)
% 159.08/25.44  | | 
% 159.08/25.44  | | ALPHA: (6) implies:
% 159.08/25.44  | |   (7)  op(e1, e0) = e1
% 159.08/25.44  | | 
% 159.08/25.44  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #974.
% 159.08/25.44  | | 
% 159.08/25.44  | Case 2:
% 159.08/25.44  | | 
% 159.08/25.44  | |   (8)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0
% 159.08/25.44  | | 
% 159.08/25.44  | | ALPHA: (8) implies:
% 159.08/25.44  | |   (9)  all_57_15 = e0
% 159.08/25.44  | |   (10)   ~ (e1 = e0)
% 159.08/25.44  | | 
% 159.08/25.44  | | COMBINE_EQS: (2), (9) imply:
% 159.08/25.44  | |   (11)  e1 = e0
% 159.08/25.44  | | 
% 159.08/25.44  | | REDUCE: (10), (11) imply:
% 159.08/25.44  | |   (12)  $false
% 159.08/25.44  | | 
% 159.08/25.44  | | CLOSE: (12) is inconsistent.
% 159.08/25.44  | | 
% 159.08/25.44  | End of split
% 159.08/25.44  | 
% 159.08/25.44  End of proof
% 159.08/25.44  
% 159.08/25.44  Sub-proof #350 shows that the following formulas are inconsistent:
% 159.08/25.44  ----------------------------------------------------------------
% 159.08/25.44    (1)  op(e0, e0) = e1
% 159.08/25.44    (2)   ~ (e3 = e2)
% 159.08/25.44    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.44    (4)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.08/25.44           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.08/25.44           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 159.08/25.44           & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 159.08/25.44           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 159.08/25.44           e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 159.08/25.44         (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 159.08/25.44           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.08/25.44           = e3 & $i(all_57_10))
% 159.08/25.44    (5)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.08/25.44         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.08/25.44    (6)   ~ (e1 = e0)
% 159.08/25.44    (7)  op(e2, e1) = all_52_9
% 159.08/25.44    (8)  all_56_2 = e1
% 159.08/25.44    (9)   ~ (e2 = e1)
% 159.08/25.44    (10)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.08/25.44          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 159.08/25.44    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.08/25.44          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.08/25.44    (12)   ~ (all_52_9 = e2)
% 159.08/25.44    (13)   ~ (e3 = e1)
% 159.08/25.44    (14)   ~ (e2 = e0)
% 159.08/25.44    (15)   ~ (e3 = e0)
% 159.08/25.44  
% 159.08/25.44  Begin of proof
% 159.08/25.44  | 
% 159.08/25.44  | BETA: splitting (4) gives:
% 159.08/25.44  | 
% 159.08/25.44  | Case 1:
% 159.08/25.44  | | 
% 159.08/25.44  | |   (16)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.08/25.44  | |             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0
% 159.08/25.44  | |           & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 =
% 159.08/25.44  | |           e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.08/25.44  | | 
% 159.08/25.44  | | REF_CLOSE: (1), (3), (7), (9), (12), (16) are inconsistent by sub-proof
% 159.08/25.44  | |            #374.
% 159.08/25.44  | | 
% 159.08/25.44  | Case 2:
% 159.08/25.44  | | 
% 159.08/25.44  | |   (17)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 159.08/25.44  | |             e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 159.08/25.44  | |           & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 159.08/25.44  | |           e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 159.08/25.44  | |           & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.08/25.44  | |           $i(all_57_10))
% 159.08/25.44  | | 
% 159.08/25.44  | | BETA: splitting (17) gives:
% 159.08/25.44  | | 
% 159.08/25.44  | | Case 1:
% 159.08/25.44  | | | 
% 159.08/25.44  | | |   (18)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 159.08/25.44  | | |           e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 159.08/25.44  | | |         & op(e1, e0) = e1 & $i(all_57_14)
% 159.08/25.44  | | | 
% 159.08/25.44  | | | ALPHA: (18) implies:
% 159.08/25.44  | | |   (19)  op(e2, e2) = e1
% 159.08/25.44  | | | 
% 159.08/25.44  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.08/25.44  | | |            (14), (15), (19) are inconsistent by sub-proof #355.
% 159.08/25.44  | | | 
% 159.08/25.44  | | Case 2:
% 159.08/25.44  | | | 
% 159.08/25.44  | | |   (20)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 159.08/25.44  | | |           e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0
% 159.08/25.44  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 159.08/25.44  | | | 
% 159.08/25.44  | | | ALPHA: (20) implies:
% 159.08/25.44  | | |   (21)  op(e0, e0) = e3
% 159.08/25.44  | | | 
% 159.08/25.44  | | | REF_CLOSE: (1), (3), (13), (21) are inconsistent by sub-proof #473.
% 159.08/25.44  | | | 
% 159.08/25.44  | | End of split
% 159.08/25.44  | | 
% 159.08/25.44  | End of split
% 159.08/25.44  | 
% 159.08/25.44  End of proof
% 159.08/25.44  
% 159.08/25.44  Sub-proof #351 shows that the following formulas are inconsistent:
% 159.08/25.44  ----------------------------------------------------------------
% 159.08/25.44    (1)   ~ (all_52_6 = e1)
% 159.08/25.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.44    (3)  op(e1, e1) = e1
% 159.08/25.44    (4)  op(e1, e2) = all_52_6
% 159.08/25.44    (5)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 159.08/25.44           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.08/25.44           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 159.08/25.44           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.08/25.44           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.08/25.44    (6)   ~ (e2 = e1)
% 159.08/25.44  
% 159.08/25.44  Begin of proof
% 159.08/25.44  | 
% 159.08/25.44  | BETA: splitting (5) gives:
% 159.08/25.44  | 
% 159.08/25.44  | Case 1:
% 159.08/25.44  | | 
% 159.08/25.44  | |   (7)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.08/25.44  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.08/25.44  | |          e1) = e2 & $i(all_57_12)
% 159.08/25.44  | | 
% 159.08/25.44  | | ALPHA: (7) implies:
% 159.08/25.44  | |   (8)  op(e1, e1) = e2
% 159.08/25.44  | | 
% 159.08/25.44  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #986.
% 159.08/25.44  | | 
% 159.08/25.44  | Case 2:
% 159.08/25.44  | | 
% 159.08/25.44  | |   (9)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 159.08/25.44  | |        & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.08/25.44  | |          e0) = e1 & $i(all_57_14)
% 159.08/25.44  | | 
% 159.08/25.44  | | ALPHA: (9) implies:
% 159.08/25.44  | |   (10)  op(e1, e2) = e1
% 159.08/25.44  | | 
% 159.08/25.44  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #984.
% 159.08/25.44  | | 
% 159.08/25.44  | End of split
% 159.08/25.44  | 
% 159.08/25.44  End of proof
% 159.08/25.44  
% 159.08/25.44  Sub-proof #352 shows that the following formulas are inconsistent:
% 159.08/25.44  ----------------------------------------------------------------
% 159.08/25.44    (1)   ~ (e3 = e2)
% 159.08/25.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.44    (3)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 159.08/25.44           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.08/25.44           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 159.08/25.44           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 159.08/25.44             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.08/25.44    (4)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.08/25.44         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.08/25.44    (5)  op(e3, e3) = e3
% 159.08/25.44    (6)   ~ (e1 = e0)
% 159.08/25.44    (7)  op(e2, e1) = all_52_9
% 159.08/25.44    (8)  all_56_2 = e1
% 159.08/25.44    (9)   ~ (e2 = e1)
% 159.08/25.44    (10)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.08/25.44          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 159.08/25.44    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.08/25.44          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.08/25.44    (12)   ~ (all_52_9 = e2)
% 159.08/25.44    (13)   ~ (e3 = e1)
% 159.08/25.45    (14)   ~ (e2 = e0)
% 159.08/25.45    (15)   ~ (e3 = e0)
% 159.08/25.45  
% 159.08/25.45  Begin of proof
% 159.08/25.45  | 
% 159.08/25.45  | BETA: splitting (3) gives:
% 159.08/25.45  | 
% 159.08/25.45  | Case 1:
% 159.08/25.45  | | 
% 159.08/25.45  | |   (16)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 159.08/25.45  | |         & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.08/25.45  | |         all_57_14 & $i(all_57_14)
% 159.08/25.45  | | 
% 159.08/25.45  | | ALPHA: (16) implies:
% 159.08/25.45  | |   (17)  op(e3, e3) = e1
% 159.08/25.45  | | 
% 159.08/25.45  | | REF_CLOSE: (2), (5), (13), (17) are inconsistent by sub-proof #995.
% 159.08/25.45  | | 
% 159.08/25.45  | Case 2:
% 159.08/25.45  | | 
% 159.08/25.45  | |   (18)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 159.08/25.45  | |         & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.08/25.45  | |         all_57_14 & $i(all_57_14)
% 159.08/25.45  | | 
% 159.08/25.45  | | ALPHA: (18) implies:
% 159.08/25.45  | |   (19)  op(e2, e2) = e1
% 159.08/25.45  | | 
% 159.08/25.45  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 159.08/25.45  | |            (15), (19) are inconsistent by sub-proof #355.
% 159.08/25.45  | | 
% 159.08/25.45  | End of split
% 159.08/25.45  | 
% 159.08/25.45  End of proof
% 159.08/25.45  
% 159.08/25.45  Sub-proof #353 shows that the following formulas are inconsistent:
% 159.08/25.45  ----------------------------------------------------------------
% 159.08/25.45    (1)   ~ (e3 = e2)
% 159.08/25.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.45    (3)  op(e1, e1) = e1
% 159.08/25.45    (4)  op(e1, e3) = all_52_2
% 159.08/25.45    (5)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.08/25.45         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.08/25.45    (6)   ~ (all_52_2 = e1)
% 159.08/25.45    (7)   ~ (e1 = e0)
% 159.08/25.45    (8)  op(e2, e1) = all_52_9
% 159.08/25.45    (9)  all_56_2 = e1
% 159.08/25.45    (10)   ~ (e2 = e1)
% 159.08/25.45    (11)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.08/25.45          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 159.08/25.45    (12)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.08/25.45          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.08/25.45    (13)   ~ (all_52_9 = e2)
% 159.08/25.45    (14)   ~ (e3 = e1)
% 159.08/25.45    (15)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.08/25.45            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.08/25.45              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 159.08/25.45            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 159.08/25.45            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.08/25.45          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.08/25.45            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.08/25.45              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.08/25.45            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.08/25.45              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.08/25.45          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.08/25.45            op(e1, e1) = e1)
% 159.08/25.45    (16)   ~ (e2 = e0)
% 159.08/25.45    (17)   ~ (e3 = e0)
% 159.08/25.45  
% 159.08/25.45  Begin of proof
% 159.08/25.45  | 
% 159.08/25.45  | BETA: splitting (15) gives:
% 159.08/25.45  | 
% 159.08/25.45  | Case 1:
% 159.08/25.45  | | 
% 159.08/25.45  | |   (18)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.08/25.45  | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1
% 159.08/25.45  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 =
% 159.08/25.45  | |           e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 &
% 159.08/25.45  | |           op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.08/25.45  | |           $i(all_57_14))
% 159.08/25.45  | | 
% 159.08/25.45  | | BETA: splitting (18) gives:
% 159.08/25.45  | | 
% 159.08/25.45  | | Case 1:
% 159.08/25.45  | | | 
% 159.08/25.45  | | |   (19)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.08/25.45  | | |           e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1
% 159.08/25.45  | | |         & op(e1, e1) = e3 & $i(all_57_10)
% 159.08/25.45  | | | 
% 159.08/25.45  | | | ALPHA: (19) implies:
% 159.08/25.45  | | |   (20)  op(e1, e1) = e3
% 159.08/25.45  | | | 
% 159.08/25.45  | | | REF_CLOSE: (2), (3), (14), (20) are inconsistent by sub-proof #1003.
% 159.08/25.45  | | | 
% 159.08/25.45  | | Case 2:
% 159.08/25.45  | | | 
% 159.08/25.45  | | |   (21)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 159.08/25.45  | | |           e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 159.08/25.45  | | |         op(e1, e1) = all_57_14 & $i(all_57_14)
% 159.08/25.45  | | | 
% 159.08/25.45  | | | ALPHA: (21) implies:
% 159.08/25.45  | | |   (22)  op(e2, e2) = e1
% 159.08/25.45  | | | 
% 159.08/25.45  | | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 159.08/25.45  | | |            (16), (17), (22) are inconsistent by sub-proof #355.
% 159.08/25.45  | | | 
% 159.08/25.45  | | End of split
% 159.08/25.45  | | 
% 159.08/25.45  | Case 2:
% 159.08/25.45  | | 
% 159.08/25.45  | |   (23)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.08/25.45  | |             e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0
% 159.08/25.45  | |           & op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 =
% 159.08/25.45  | |           e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 159.08/25.45  | |           & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.08/25.45  | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 159.08/25.45  | |           op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.08/25.45  | | 
% 159.08/25.45  | | REF_CLOSE: (2), (3), (4), (6), (14), (23) are inconsistent by sub-proof
% 159.08/25.45  | |            #354.
% 159.08/25.45  | | 
% 159.08/25.45  | End of split
% 159.08/25.45  | 
% 159.08/25.45  End of proof
% 159.08/25.45  
% 159.08/25.45  Sub-proof #354 shows that the following formulas are inconsistent:
% 159.08/25.45  ----------------------------------------------------------------
% 159.08/25.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.45    (2)  op(e1, e1) = e1
% 159.08/25.45    (3)  op(e1, e3) = all_52_2
% 159.08/25.45    (4)   ~ (all_52_2 = e1)
% 159.08/25.45    (5)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.08/25.45           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.08/25.45           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 159.08/25.45           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.08/25.45           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 159.08/25.45           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.08/25.45    (6)   ~ (e3 = e1)
% 159.08/25.45  
% 159.08/25.45  Begin of proof
% 159.08/25.45  | 
% 159.08/25.45  | BETA: splitting (5) gives:
% 159.08/25.45  | 
% 159.08/25.45  | Case 1:
% 159.08/25.45  | | 
% 159.08/25.45  | |   (7)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 159.08/25.45  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.08/25.45  | |          e0) = e1 & $i(all_57_14)
% 159.08/25.45  | | 
% 159.08/25.45  | | ALPHA: (7) implies:
% 159.08/25.45  | |   (8)  op(e1, e3) = e1
% 159.08/25.45  | | 
% 159.08/25.45  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #990.
% 159.08/25.45  | | 
% 159.08/25.45  | Case 2:
% 159.08/25.45  | | 
% 159.08/25.45  | |   (9)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 159.08/25.45  | |          & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 159.08/25.45  | |          op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.08/25.45  | |          &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.08/25.45  | | 
% 159.08/25.45  | | REF_CLOSE: (1), (2), (3), (4), (6), (9) are inconsistent by sub-proof #989.
% 159.08/25.45  | | 
% 159.08/25.45  | End of split
% 159.08/25.45  | 
% 159.08/25.45  End of proof
% 159.08/25.45  
% 159.08/25.45  Sub-proof #355 shows that the following formulas are inconsistent:
% 159.08/25.45  ----------------------------------------------------------------
% 159.08/25.45    (1)   ~ (e3 = e2)
% 159.08/25.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.08/25.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.08/25.45    (3)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.08/25.45         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.14/25.45    (4)  op(e2, e2) = e1
% 159.14/25.45    (5)   ~ (e1 = e0)
% 159.14/25.45    (6)  op(e2, e1) = all_52_9
% 159.14/25.45    (7)  all_56_2 = e1
% 159.14/25.45    (8)   ~ (e2 = e1)
% 159.14/25.45    (9)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.14/25.45         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 159.14/25.45    (10)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.14/25.45          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.14/25.45    (11)   ~ (all_52_9 = e2)
% 159.14/25.45    (12)   ~ (e3 = e1)
% 159.14/25.45    (13)   ~ (e2 = e0)
% 159.14/25.45    (14)   ~ (e3 = e0)
% 159.14/25.45  
% 159.14/25.45  Begin of proof
% 159.14/25.45  | 
% 159.14/25.45  | BETA: splitting (10) gives:
% 159.14/25.45  | 
% 159.14/25.45  | Case 1:
% 159.14/25.45  | | 
% 159.14/25.45  | |   (15)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 159.14/25.45  | |           e2)
% 159.14/25.45  | | 
% 159.14/25.45  | | BETA: splitting (15) gives:
% 159.14/25.45  | | 
% 159.14/25.45  | | Case 1:
% 159.14/25.45  | | | 
% 159.14/25.45  | | |   (16)  all_56_2 = e2 & op(e2, e3) = e2
% 159.14/25.45  | | | 
% 159.14/25.45  | | | ALPHA: (16) implies:
% 159.14/25.45  | | |   (17)  all_56_2 = e2
% 159.14/25.45  | | | 
% 159.14/25.45  | | | REF_CLOSE: (7), (8), (17) are inconsistent by sub-proof #600.
% 159.14/25.45  | | | 
% 159.14/25.45  | | Case 2:
% 159.14/25.45  | | | 
% 159.14/25.45  | | |   (18)  all_56_3 = e2 & op(e2, e2) = e2
% 159.14/25.45  | | | 
% 159.14/25.45  | | | ALPHA: (18) implies:
% 159.14/25.45  | | |   (19)  op(e2, e2) = e2
% 159.14/25.45  | | | 
% 159.14/25.45  | | | REF_CLOSE: (2), (4), (8), (19) are inconsistent by sub-proof #993.
% 159.14/25.45  | | | 
% 159.14/25.45  | | End of split
% 159.14/25.45  | | 
% 159.14/25.45  | Case 2:
% 159.14/25.45  | | 
% 159.14/25.45  | |   (20)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 159.14/25.45  | |           e2)
% 159.14/25.45  | | 
% 159.14/25.45  | | BETA: splitting (20) gives:
% 159.14/25.45  | | 
% 159.14/25.45  | | Case 1:
% 159.14/25.45  | | | 
% 159.14/25.45  | | |   (21)  all_56_5 = e2 & op(e2, e1) = e2
% 159.14/25.45  | | | 
% 159.14/25.45  | | | ALPHA: (21) implies:
% 159.14/25.45  | | |   (22)  op(e2, e1) = e2
% 159.14/25.45  | | | 
% 159.14/25.45  | | | REF_CLOSE: (2), (6), (11), (22) are inconsistent by sub-proof #1002.
% 159.14/25.45  | | | 
% 159.14/25.45  | | Case 2:
% 159.14/25.45  | | | 
% 159.14/25.45  | | |   (23)  all_56_10 = e2 & op(e2, e0) = e2
% 159.14/25.45  | | | 
% 159.14/25.45  | | | ALPHA: (23) implies:
% 159.14/25.45  | | |   (24)  all_56_10 = e2
% 159.14/25.45  | | | 
% 159.14/25.45  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (12), (13), (14), (24) are
% 159.14/25.45  | | |            inconsistent by sub-proof #356.
% 159.14/25.45  | | | 
% 159.14/25.45  | | End of split
% 159.14/25.45  | | 
% 159.14/25.45  | End of split
% 159.14/25.45  | 
% 159.14/25.45  End of proof
% 159.14/25.45  
% 159.14/25.45  Sub-proof #356 shows that the following formulas are inconsistent:
% 159.14/25.45  ----------------------------------------------------------------
% 159.14/25.45    (1)   ~ (e3 = e2)
% 159.14/25.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.45    (3)  all_56_10 = e2
% 159.14/25.45    (4)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.14/25.45         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.14/25.45    (5)  op(e2, e2) = e1
% 159.14/25.45    (6)   ~ (e1 = e0)
% 159.14/25.45    (7)  all_56_2 = e1
% 159.14/25.45    (8)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.14/25.45         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 159.14/25.45    (9)   ~ (e3 = e1)
% 159.14/25.45    (10)   ~ (e2 = e0)
% 159.14/25.45    (11)   ~ (e3 = e0)
% 159.14/25.45  
% 159.14/25.45  Begin of proof
% 159.14/25.45  | 
% 159.14/25.45  | BETA: splitting (4) gives:
% 159.14/25.45  | 
% 159.14/25.45  | Case 1:
% 159.14/25.45  | | 
% 159.14/25.45  | |   (12)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 159.14/25.45  | |           e3)
% 159.14/25.45  | | 
% 159.14/25.45  | | REF_CLOSE: (2), (5), (7), (9), (12) are inconsistent by sub-proof #358.
% 159.14/25.45  | | 
% 159.14/25.45  | Case 2:
% 159.14/25.45  | | 
% 159.14/25.45  | |   (13)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 159.14/25.45  | |           e3)
% 159.14/25.45  | | 
% 159.14/25.45  | | BETA: splitting (13) gives:
% 159.14/25.45  | | 
% 159.14/25.45  | | Case 1:
% 159.14/25.45  | | | 
% 159.14/25.45  | | |   (14)  all_56_5 = e3 & op(e2, e1) = e3
% 159.14/25.45  | | | 
% 159.14/25.45  | | | ALPHA: (14) implies:
% 159.14/25.45  | | |   (15)  all_56_5 = e3
% 159.14/25.45  | | | 
% 159.14/25.45  | | | BETA: splitting (8) gives:
% 159.14/25.45  | | | 
% 159.14/25.45  | | | Case 1:
% 159.14/25.45  | | | | 
% 159.14/25.45  | | | |   (16)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2)
% 159.14/25.45  | | | |           = e0)
% 159.14/25.45  | | | | 
% 159.14/25.45  | | | | REF_CLOSE: (2), (5), (6), (7), (16) are inconsistent by sub-proof #357.
% 159.14/25.45  | | | | 
% 159.14/25.45  | | | Case 2:
% 159.14/25.45  | | | | 
% 159.14/25.45  | | | |   (17)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0)
% 159.14/25.45  | | | |           = e0)
% 159.14/25.45  | | | | 
% 159.14/25.45  | | | | BETA: splitting (17) gives:
% 159.14/25.45  | | | | 
% 159.14/25.45  | | | | Case 1:
% 159.14/25.45  | | | | | 
% 159.14/25.45  | | | | |   (18)  all_56_5 = e0 & op(e2, e1) = e0
% 159.14/25.45  | | | | | 
% 159.14/25.45  | | | | | ALPHA: (18) implies:
% 159.14/25.45  | | | | |   (19)  all_56_5 = e0
% 159.14/25.45  | | | | | 
% 159.14/25.45  | | | | | REF_CLOSE: (11), (15), (19) are inconsistent by sub-proof #591.
% 159.14/25.45  | | | | | 
% 159.14/25.45  | | | | Case 2:
% 159.14/25.45  | | | | | 
% 159.14/25.45  | | | | |   (20)  all_56_10 = e0 & op(e2, e0) = e0
% 159.14/25.45  | | | | | 
% 159.14/25.45  | | | | | ALPHA: (20) implies:
% 159.14/25.45  | | | | |   (21)  all_56_10 = e0
% 159.14/25.45  | | | | | 
% 159.14/25.45  | | | | | REF_CLOSE: (3), (10), (21) are inconsistent by sub-proof #755.
% 159.14/25.45  | | | | | 
% 159.14/25.45  | | | | End of split
% 159.14/25.45  | | | | 
% 159.14/25.45  | | | End of split
% 159.14/25.45  | | | 
% 159.14/25.45  | | Case 2:
% 159.14/25.45  | | | 
% 159.14/25.45  | | |   (22)  all_56_10 = e3 & op(e2, e0) = e3
% 159.14/25.45  | | | 
% 159.14/25.45  | | | REF_CLOSE: (1), (3), (22) are inconsistent by sub-proof #894.
% 159.14/25.45  | | | 
% 159.14/25.45  | | End of split
% 159.14/25.45  | | 
% 159.14/25.45  | End of split
% 159.14/25.45  | 
% 159.14/25.45  End of proof
% 159.14/25.45  
% 159.14/25.45  Sub-proof #357 shows that the following formulas are inconsistent:
% 159.14/25.45  ----------------------------------------------------------------
% 159.14/25.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.45    (2)  op(e2, e2) = e1
% 159.14/25.45    (3)   ~ (e1 = e0)
% 159.14/25.45    (4)  all_56_2 = e1
% 159.14/25.45    (5)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 159.14/25.45  
% 159.14/25.45  Begin of proof
% 159.14/25.45  | 
% 159.14/25.45  | BETA: splitting (5) gives:
% 159.14/25.45  | 
% 159.14/25.45  | Case 1:
% 159.14/25.45  | | 
% 159.14/25.45  | |   (6)  all_56_2 = e0 & op(e2, e3) = e0
% 159.14/25.45  | | 
% 159.14/25.45  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #486.
% 159.14/25.45  | | 
% 159.14/25.45  | Case 2:
% 159.14/25.45  | | 
% 159.14/25.45  | |   (7)  all_56_3 = e0 & op(e2, e2) = e0
% 159.14/25.45  | | 
% 159.14/25.45  | | ALPHA: (7) implies:
% 159.14/25.45  | |   (8)  op(e2, e2) = e0
% 159.14/25.45  | | 
% 159.14/25.45  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #960.
% 159.14/25.45  | | 
% 159.14/25.45  | End of split
% 159.14/25.45  | 
% 159.14/25.45  End of proof
% 159.14/25.45  
% 159.14/25.45  Sub-proof #358 shows that the following formulas are inconsistent:
% 159.14/25.45  ----------------------------------------------------------------
% 159.14/25.45    (1)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 159.14/25.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.45    (3)  op(e2, e2) = e1
% 159.14/25.45    (4)  all_56_2 = e1
% 159.14/25.45    (5)   ~ (e3 = e1)
% 159.14/25.45  
% 159.14/25.45  Begin of proof
% 159.14/25.45  | 
% 159.14/25.45  | BETA: splitting (1) gives:
% 159.14/25.45  | 
% 159.14/25.45  | Case 1:
% 159.14/25.45  | | 
% 159.14/25.45  | |   (6)  all_56_2 = e3 & op(e2, e3) = e3
% 159.14/25.45  | | 
% 159.14/25.45  | | ALPHA: (6) implies:
% 159.14/25.45  | |   (7)  all_56_2 = e3
% 159.14/25.45  | | 
% 159.14/25.45  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #484.
% 159.14/25.45  | | 
% 159.14/25.45  | Case 2:
% 159.14/25.45  | | 
% 159.14/25.45  | |   (8)  all_56_3 = e3 & op(e2, e2) = e3
% 159.14/25.45  | | 
% 159.14/25.45  | | ALPHA: (8) implies:
% 159.14/25.45  | |   (9)  op(e2, e2) = e3
% 159.14/25.45  | | 
% 159.14/25.45  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #847.
% 159.14/25.45  | | 
% 159.14/25.45  | End of split
% 159.14/25.45  | 
% 159.14/25.45  End of proof
% 159.14/25.45  
% 159.14/25.45  Sub-proof #359 shows that the following formulas are inconsistent:
% 159.14/25.45  ----------------------------------------------------------------
% 159.14/25.45    (1)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.14/25.45           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.14/25.45           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 159.14/25.45           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.14/25.45           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.14/25.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.45    (3)  op(e2, e3) = e1
% 159.14/25.45    (4)   ~ (e2 = e1)
% 159.14/25.45  
% 159.14/25.45  Begin of proof
% 159.14/25.45  | 
% 159.14/25.45  | BETA: splitting (1) gives:
% 159.14/25.45  | 
% 159.14/25.45  | Case 1:
% 159.14/25.45  | | 
% 159.14/25.46  | |   (5)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 159.14/25.46  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.14/25.46  | |        all_57_12 & $i(all_57_12)
% 159.14/25.46  | | 
% 159.14/25.46  | | ALPHA: (5) implies:
% 159.14/25.46  | |   (6)  op(e2, e3) = e2
% 159.14/25.46  | | 
% 159.14/25.46  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #428.
% 159.14/25.46  | | 
% 159.14/25.46  | Case 2:
% 159.14/25.46  | | 
% 159.14/25.46  | |   (7)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2)
% 159.14/25.46  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 159.14/25.46  | |          e2) = e3 & $i(all_57_10)
% 159.14/25.46  | | 
% 159.14/25.46  | | ALPHA: (7) implies:
% 159.14/25.46  | |   (8)  op(e2, e3) = e2
% 159.14/25.46  | | 
% 159.14/25.46  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #428.
% 159.14/25.46  | | 
% 159.14/25.46  | End of split
% 159.14/25.46  | 
% 159.14/25.46  End of proof
% 159.14/25.46  
% 159.14/25.46  Sub-proof #360 shows that the following formulas are inconsistent:
% 159.14/25.46  ----------------------------------------------------------------
% 159.14/25.46    (1)  all_54_10 = all_10_2
% 159.14/25.46    (2)  all_54_10 = e2
% 159.14/25.46    (3)   ~ (all_10_2 = e2)
% 159.14/25.46  
% 159.14/25.46  Begin of proof
% 159.14/25.46  | 
% 159.14/25.46  | COMBINE_EQS: (1), (2) imply:
% 159.14/25.46  |   (4)  all_10_2 = e2
% 159.14/25.46  | 
% 159.14/25.46  | SIMP: (4) implies:
% 159.14/25.46  |   (5)  all_10_2 = e2
% 159.14/25.46  | 
% 159.14/25.46  | REDUCE: (3), (5) imply:
% 159.14/25.46  |   (6)  $false
% 159.14/25.46  | 
% 159.14/25.46  | CLOSE: (6) is inconsistent.
% 159.14/25.46  | 
% 159.14/25.46  End of proof
% 159.14/25.46  
% 159.14/25.46  Sub-proof #361 shows that the following formulas are inconsistent:
% 159.14/25.46  ----------------------------------------------------------------
% 159.14/25.46    (1)  all_54_10 = all_10_2
% 159.14/25.46    (2)  all_54_10 = e3
% 159.14/25.46    (3)   ~ (all_10_2 = e3)
% 159.14/25.46  
% 159.14/25.46  Begin of proof
% 159.14/25.46  | 
% 159.14/25.46  | COMBINE_EQS: (1), (2) imply:
% 159.14/25.46  |   (4)  all_10_2 = e3
% 159.14/25.46  | 
% 159.14/25.46  | SIMP: (4) implies:
% 159.14/25.46  |   (5)  all_10_2 = e3
% 159.14/25.46  | 
% 159.14/25.46  | REDUCE: (3), (5) imply:
% 159.14/25.46  |   (6)  $false
% 159.14/25.46  | 
% 159.14/25.46  | CLOSE: (6) is inconsistent.
% 159.14/25.46  | 
% 159.14/25.46  End of proof
% 159.14/25.46  
% 159.14/25.46  Sub-proof #362 shows that the following formulas are inconsistent:
% 159.14/25.46  ----------------------------------------------------------------
% 159.14/25.46    (1)   ~ (all_22_1 = e3) & op(e0, e0) = all_22_1 & $i(all_22_1)
% 159.14/25.46    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.46    (3)  op(e0, e0) = e3
% 159.14/25.46  
% 159.14/25.46  Begin of proof
% 159.14/25.46  | 
% 159.14/25.46  | ALPHA: (1) implies:
% 159.14/25.46  |   (4)   ~ (all_22_1 = e3)
% 159.14/25.46  |   (5)  op(e0, e0) = all_22_1
% 159.14/25.46  | 
% 159.14/25.46  | GROUND_INST: instantiating (2) with e3, all_22_1, e0, e0, simplifying with
% 159.14/25.46  |              (3), (5) gives:
% 159.14/25.46  |   (6)  all_22_1 = e3
% 159.14/25.46  | 
% 159.14/25.46  | REDUCE: (4), (6) imply:
% 159.14/25.46  |   (7)  $false
% 159.14/25.46  | 
% 159.14/25.46  | CLOSE: (7) is inconsistent.
% 159.14/25.46  | 
% 159.14/25.46  End of proof
% 159.14/25.46  
% 159.14/25.46  Sub-proof #363 shows that the following formulas are inconsistent:
% 159.14/25.46  ----------------------------------------------------------------
% 159.14/25.46    (1)  all_54_14 = all_22_0
% 159.14/25.46    (2)  all_54_14 = e0
% 159.14/25.46    (3)   ~ (all_22_0 = e0)
% 159.14/25.46  
% 159.14/25.46  Begin of proof
% 159.14/25.46  | 
% 159.14/25.46  | COMBINE_EQS: (1), (2) imply:
% 159.14/25.46  |   (4)  all_22_0 = e0
% 159.14/25.46  | 
% 159.14/25.46  | SIMP: (4) implies:
% 159.14/25.46  |   (5)  all_22_0 = e0
% 159.14/25.46  | 
% 159.14/25.46  | REDUCE: (3), (5) imply:
% 159.14/25.46  |   (6)  $false
% 159.14/25.46  | 
% 159.14/25.46  | CLOSE: (6) is inconsistent.
% 159.14/25.46  | 
% 159.14/25.46  End of proof
% 159.14/25.46  
% 159.14/25.46  Sub-proof #364 shows that the following formulas are inconsistent:
% 159.14/25.46  ----------------------------------------------------------------
% 159.14/25.46    (1)  all_54_2 = e1 | all_54_2 = e0
% 159.14/25.46    (2)  all_54_2 = all_52_8
% 159.14/25.46    (3)   ~ (all_52_8 = e1)
% 159.14/25.46    (4)   ~ (all_52_8 = e0)
% 159.14/25.46  
% 159.14/25.46  Begin of proof
% 159.14/25.46  | 
% 159.14/25.46  | BETA: splitting (1) gives:
% 159.14/25.46  | 
% 159.14/25.46  | Case 1:
% 159.14/25.46  | | 
% 159.14/25.46  | |   (5)  all_54_2 = e1
% 159.14/25.46  | | 
% 159.14/25.46  | | COMBINE_EQS: (2), (5) imply:
% 159.14/25.46  | |   (6)  all_52_8 = e1
% 159.14/25.46  | | 
% 159.14/25.46  | | REDUCE: (3), (6) imply:
% 159.14/25.46  | |   (7)  $false
% 159.14/25.46  | | 
% 159.14/25.46  | | CLOSE: (7) is inconsistent.
% 159.14/25.46  | | 
% 159.14/25.46  | Case 2:
% 159.14/25.46  | | 
% 159.14/25.46  | |   (8)  all_54_2 = e0
% 159.14/25.46  | | 
% 159.14/25.46  | | COMBINE_EQS: (2), (8) imply:
% 159.14/25.46  | |   (9)  all_52_8 = e0
% 159.14/25.46  | | 
% 159.14/25.46  | | REDUCE: (4), (9) imply:
% 159.14/25.46  | |   (10)  $false
% 159.14/25.46  | | 
% 159.14/25.46  | | CLOSE: (10) is inconsistent.
% 159.14/25.46  | | 
% 159.14/25.46  | End of split
% 159.14/25.46  | 
% 159.14/25.46  End of proof
% 159.14/25.46  
% 159.14/25.46  Sub-proof #365 shows that the following formulas are inconsistent:
% 159.14/25.46  ----------------------------------------------------------------
% 159.14/25.46    (1)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.14/25.46           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.14/25.46           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 159.14/25.46           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 159.14/25.46           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 159.14/25.46           e1 & op(e0, e3) = e0)
% 159.14/25.46    (2)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 159.14/25.46           all_57_6 & $i(all_57_6))
% 159.14/25.46  
% 159.14/25.46  Begin of proof
% 159.14/25.46  | 
% 159.14/25.46  | BETA: splitting (1) gives:
% 159.14/25.46  | 
% 159.14/25.46  | Case 1:
% 159.14/25.46  | | 
% 159.14/25.46  | |   (3)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 159.14/25.46  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 159.14/25.46  | | 
% 159.14/25.46  | | ALPHA: (3) implies:
% 159.14/25.46  | |   (4)  all_57_6 = e0
% 159.14/25.46  | |   (5)   ~ (all_57_15 = e3)
% 159.14/25.46  | | 
% 159.14/25.46  | | REF_CLOSE: (2), (4), (5) are inconsistent by sub-proof #684.
% 159.14/25.46  | | 
% 159.14/25.46  | Case 2:
% 159.14/25.46  | | 
% 159.14/25.46  | |   (6)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.46  | |            e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.14/25.46  | |        (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.46  | |            e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.14/25.46  | | 
% 159.14/25.46  | | BETA: splitting (6) gives:
% 159.14/25.46  | | 
% 159.14/25.46  | | Case 1:
% 159.14/25.46  | | | 
% 159.14/25.46  | | |   (7)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.46  | | |          e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 159.14/25.46  | | | 
% 159.14/25.46  | | | ALPHA: (7) implies:
% 159.14/25.46  | | |   (8)  all_57_6 = e0
% 159.14/25.46  | | |   (9)   ~ (all_57_15 = e3)
% 159.14/25.46  | | | 
% 159.14/25.46  | | | REF_CLOSE: (2), (8), (9) are inconsistent by sub-proof #684.
% 159.14/25.46  | | | 
% 159.14/25.46  | | Case 2:
% 159.14/25.46  | | | 
% 159.14/25.46  | | |   (10)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.46  | | |           e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 159.14/25.46  | | | 
% 159.14/25.46  | | | ALPHA: (10) implies:
% 159.14/25.46  | | |   (11)  all_57_6 = e0
% 159.14/25.46  | | |   (12)   ~ (all_57_15 = e3)
% 159.14/25.46  | | | 
% 159.14/25.46  | | | REF_CLOSE: (2), (11), (12) are inconsistent by sub-proof #684.
% 159.14/25.46  | | | 
% 159.14/25.46  | | End of split
% 159.14/25.46  | | 
% 159.14/25.46  | End of split
% 159.14/25.46  | 
% 159.14/25.46  End of proof
% 159.14/25.46  
% 159.14/25.46  Sub-proof #366 shows that the following formulas are inconsistent:
% 159.14/25.46  ----------------------------------------------------------------
% 159.14/25.46    (1)  op(e1, e1) = e0
% 159.14/25.46    (2)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.14/25.46           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.14/25.46           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 159.14/25.46           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 159.14/25.46           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.14/25.46    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.46    (4)  op(e2, e2) = e0
% 159.14/25.46    (5)   ~ (e1 = e0)
% 159.14/25.46    (6)   ~ (e3 = e0)
% 159.14/25.46  
% 159.14/25.46  Begin of proof
% 159.14/25.46  | 
% 159.14/25.46  | BETA: splitting (2) gives:
% 159.14/25.46  | 
% 159.14/25.46  | Case 1:
% 159.14/25.46  | | 
% 159.14/25.46  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 159.14/25.46  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.14/25.46  | |          e1) = e3 & $i(all_57_10)
% 159.14/25.46  | | 
% 159.14/25.46  | | ALPHA: (7) implies:
% 159.14/25.46  | |   (8)  op(e1, e1) = e3
% 159.14/25.46  | | 
% 159.14/25.46  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #912.
% 159.14/25.46  | | 
% 159.14/25.46  | Case 2:
% 159.14/25.46  | | 
% 159.14/25.46  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 159.14/25.46  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 159.14/25.46  | |        all_57_14 & $i(all_57_14)
% 159.14/25.46  | | 
% 159.14/25.46  | | ALPHA: (9) implies:
% 159.14/25.46  | |   (10)  op(e2, e2) = e1
% 159.14/25.46  | | 
% 159.14/25.46  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #960.
% 159.14/25.46  | | 
% 159.14/25.46  | End of split
% 159.14/25.46  | 
% 159.14/25.46  End of proof
% 159.14/25.46  
% 159.14/25.46  Sub-proof #367 shows that the following formulas are inconsistent:
% 159.14/25.46  ----------------------------------------------------------------
% 159.14/25.46    (1)  op(e1, e1) = e0
% 159.14/25.46    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.46    (3)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.14/25.46           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 159.14/25.46           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3
% 159.14/25.46           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 159.14/25.46           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.14/25.46    (4)  op(e2, e2) = e0
% 159.14/25.46    (5)   ~ (e2 = e0)
% 159.14/25.46    (6)   ~ (e3 = e0)
% 159.14/25.46  
% 159.14/25.46  Begin of proof
% 159.14/25.46  | 
% 159.14/25.46  | BETA: splitting (3) gives:
% 159.14/25.46  | 
% 159.14/25.46  | Case 1:
% 159.14/25.46  | | 
% 159.14/25.46  | |   (7)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 159.14/25.46  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.14/25.46  | |          e1) = e2 & $i(all_57_12)
% 159.14/25.46  | | 
% 159.14/25.46  | | ALPHA: (7) implies:
% 159.14/25.46  | |   (8)  op(e1, e1) = e2
% 159.14/25.46  | | 
% 159.14/25.46  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #914.
% 159.14/25.46  | | 
% 159.14/25.46  | Case 2:
% 159.14/25.46  | | 
% 159.14/25.46  | |   (9)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1)
% 159.14/25.46  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 159.14/25.46  | |          e2) = e3 & $i(all_57_10)
% 159.14/25.46  | | 
% 159.14/25.46  | | ALPHA: (9) implies:
% 159.14/25.46  | |   (10)  op(e2, e2) = e3
% 159.14/25.46  | | 
% 159.14/25.46  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #945.
% 159.14/25.46  | | 
% 159.14/25.46  | End of split
% 159.14/25.46  | 
% 159.14/25.46  End of proof
% 159.14/25.46  
% 159.14/25.46  Sub-proof #368 shows that the following formulas are inconsistent:
% 159.14/25.46  ----------------------------------------------------------------
% 159.14/25.46    (1)  all_54_7 = all_52_13
% 159.14/25.46    (2)  all_54_7 = e0
% 159.14/25.46    (3)   ~ (all_52_13 = e0)
% 159.14/25.46  
% 159.14/25.46  Begin of proof
% 159.14/25.46  | 
% 159.14/25.46  | COMBINE_EQS: (1), (2) imply:
% 159.14/25.46  |   (4)  all_52_13 = e0
% 159.14/25.46  | 
% 159.14/25.46  | SIMP: (4) implies:
% 159.14/25.46  |   (5)  all_52_13 = e0
% 159.14/25.46  | 
% 159.14/25.46  | REDUCE: (3), (5) imply:
% 159.14/25.46  |   (6)  $false
% 159.14/25.46  | 
% 159.14/25.46  | CLOSE: (6) is inconsistent.
% 159.14/25.46  | 
% 159.14/25.46  End of proof
% 159.14/25.46  
% 159.14/25.46  Sub-proof #369 shows that the following formulas are inconsistent:
% 159.14/25.46  ----------------------------------------------------------------
% 159.14/25.46    (1)  all_54_5 = all_4_2
% 159.14/25.46    (2)  op(e0, e0) = e1
% 159.14/25.46    (3)   ~ (all_52_4 = e3)
% 159.14/25.46    (4)  op(e1, e1) = e0
% 159.14/25.46    (5)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.14/25.46    (6)  op(e0, e1) = all_52_11
% 159.14/25.46    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.46    (8)  op(e3, e1) = all_52_8
% 159.14/25.46    (9)   ~ (all_52_12 = e3)
% 159.14/25.46    (10)   ~ (all_52_9 = all_4_2)
% 159.14/25.46    (11)   ~ (all_4_2 = e3)
% 159.14/25.46    (12)   ~ (all_52_13 = all_4_2)
% 159.14/25.46    (13)  op(e1, e0) = all_52_14
% 159.14/25.46    (14)  op(e2, e2) = all_4_2
% 159.14/25.46    (15)  op(e3, e3) = e3
% 159.14/25.46    (16)  op(e2, e3) = all_52_1
% 159.14/25.46    (17)   ~ (all_4_2 = e1)
% 159.14/25.46    (18)  op(e3, e2) = all_52_4
% 159.14/25.46    (19)   ~ (e1 = e0)
% 159.14/25.46    (20)  op(e2, e1) = all_52_9
% 159.14/25.46    (21)  op(e2, e0) = all_52_13
% 159.14/25.46    (22)   ~ (all_4_2 = e0)
% 159.14/25.46    (23)   ~ (all_52_11 = e0)
% 159.14/25.46    (24)  op(e3, e0) = all_52_12
% 159.14/25.46    (25)   ~ (all_52_14 = e1)
% 159.14/25.47    (26)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.14/25.47            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.14/25.47            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.14/25.47            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.47              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.14/25.47          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.14/25.47            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.14/25.47              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.14/25.47            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.47              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.14/25.47          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.14/25.47            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 159.14/25.47              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.14/25.47            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.47              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.14/25.47          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.14/25.47            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 159.14/25.47            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.14/25.47              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.14/25.47            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 159.14/25.47            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.14/25.47            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.14/25.47            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 159.14/25.47              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.14/25.47            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 159.14/25.47          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.14/25.47            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.14/25.47              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.14/25.47            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 159.14/25.47            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.14/25.47          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.14/25.47            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.14/25.47              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 159.14/25.47            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 159.14/25.47            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.14/25.47          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.14/25.47            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.14/25.47              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.14/25.47            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.47              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.14/25.47          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.14/25.47            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.14/25.47            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 159.14/25.47            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.14/25.47            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 159.14/25.47            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.14/25.47            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.14/25.47            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 159.14/25.47              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.14/25.47            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 159.14/25.47            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.14/25.47            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.14/25.47            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 159.14/25.47              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.14/25.47            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 159.14/25.47          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 159.14/25.47            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 159.14/25.47              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 159.14/25.47              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 159.14/25.47            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 159.14/25.47            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.14/25.47            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.14/25.47            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 159.14/25.47              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 159.14/25.47            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 159.14/25.47          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.14/25.47            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.14/25.47              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.14/25.47            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.47              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.14/25.47          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.14/25.47            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.14/25.47              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 159.14/25.47              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 159.14/25.47            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.14/25.47          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.14/25.47            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.14/25.47            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 159.14/25.47                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 159.14/25.47                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.14/25.47                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.14/25.47                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.14/25.47                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.14/25.47                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 159.14/25.47                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.14/25.47                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.14/25.47                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.14/25.47                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 159.14/25.47                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.14/25.47                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.14/25.47                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 159.14/25.47                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.14/25.47                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.14/25.47                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.14/25.47                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 159.14/25.47                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.14/25.47                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 159.14/25.47                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.14/25.47                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.14/25.47                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.14/25.47                op(e0, e1) = e0)))
% 159.14/25.47    (27)   ~ (e3 = e1)
% 159.14/25.47    (28)   ~ (all_52_1 = all_4_2)
% 159.14/25.47    (29)   ~ (all_52_8 = e3)
% 159.14/25.47    (30)   ~ (e3 = e0)
% 159.14/25.47  
% 159.14/25.47  Begin of proof
% 159.14/25.47  | 
% 159.14/25.47  | BETA: splitting (5) gives:
% 159.14/25.47  | 
% 159.14/25.47  | Case 1:
% 159.14/25.47  | | 
% 159.14/25.47  | |   (31)  all_54_5 = e3
% 159.14/25.47  | | 
% 159.14/25.47  | | COMBINE_EQS: (1), (31) imply:
% 159.14/25.47  | |   (32)  all_4_2 = e3
% 159.14/25.47  | | 
% 159.14/25.47  | | REDUCE: (11), (32) imply:
% 159.14/25.47  | |   (33)  $false
% 159.14/25.47  | | 
% 159.14/25.47  | | CLOSE: (33) is inconsistent.
% 159.14/25.47  | | 
% 159.14/25.47  | Case 2:
% 159.14/25.47  | | 
% 159.14/25.47  | |   (34)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.14/25.47  | | 
% 159.14/25.47  | | BETA: splitting (34) gives:
% 159.14/25.47  | | 
% 159.14/25.47  | | Case 1:
% 159.14/25.47  | | | 
% 159.14/25.47  | | |   (35)  all_54_5 = e2
% 159.14/25.47  | | | 
% 159.14/25.47  | | | COMBINE_EQS: (1), (35) imply:
% 159.14/25.47  | | |   (36)  all_4_2 = e2
% 159.14/25.47  | | | 
% 159.14/25.47  | | | REDUCE: (28), (36) imply:
% 159.14/25.47  | | |   (37)   ~ (all_52_1 = e2)
% 159.14/25.47  | | | 
% 159.14/25.47  | | | REDUCE: (10), (36) imply:
% 159.14/25.47  | | |   (38)   ~ (all_52_9 = e2)
% 159.14/25.47  | | | 
% 159.14/25.47  | | | REDUCE: (17), (36) imply:
% 159.14/25.47  | | |   (39)   ~ (e2 = e1)
% 159.14/25.47  | | | 
% 159.14/25.47  | | | REDUCE: (22), (36) imply:
% 159.14/25.47  | | |   (40)   ~ (e2 = e0)
% 159.14/25.47  | | | 
% 159.14/25.47  | | | REDUCE: (14), (36) imply:
% 159.14/25.47  | | |   (41)  op(e2, e2) = e2
% 159.14/25.47  | | | 
% 159.14/25.47  | | | BETA: splitting (26) gives:
% 159.14/25.47  | | | 
% 159.14/25.47  | | | Case 1:
% 159.14/25.47  | | | | 
% 159.14/25.47  | | | |   (42)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12
% 159.14/25.47  | | | |             = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2
% 159.14/25.47  | | | |           & op(e2, e2) = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.14/25.47  | | | |           all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3,
% 159.14/25.47  | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 159.14/25.47  | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 &
% 159.14/25.47  | | | |           all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 159.14/25.47  | | | |           op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.14/25.47  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 =
% 159.14/25.47  | | | |           e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 159.14/25.47  | | | |           = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.14/25.47  | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12
% 159.14/25.47  | | | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0,
% 159.14/25.47  | | | |             e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 159.14/25.47  | | | |           & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) &
% 159.14/25.47  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 159.14/25.47  | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_12
% 159.14/25.47  | | | |           = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 159.14/25.47  | | | |         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 159.14/25.47  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.14/25.47  | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 159.14/25.47  | | | |           & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.14/25.47  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.14/25.47  | | | |           op(e2, e1) = e2 & $i(all_57_12)) | (all_57_1 = e3 & all_57_6 =
% 159.14/25.47  | | | |           e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.14/25.47  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.14/25.47  | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3
% 159.14/25.47  | | | |             = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) | (all_57_1 = e3
% 159.14/25.47  | | | |           & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.14/25.47  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.14/25.47  | | | |           op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 =
% 159.14/25.47  | | | |           e3 & all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 159.14/25.47  | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.14/25.47  | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_14 =
% 159.14/25.47  | | | |           e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 159.14/25.47  | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.14/25.47  | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14
% 159.14/25.47  | | | |             = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1
% 159.14/25.47  | | | |           & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.14/25.47  | | | |           all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1,
% 159.14/25.47  | | | |             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.14/25.47  | | | |             e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.14/25.47  | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 159.14/25.47  | | | |           & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.14/25.47  | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 =
% 159.14/25.47  | | | |             e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.14/25.47  | | | | 
% 159.14/25.47  | | | | BETA: splitting (42) gives:
% 159.14/25.47  | | | | 
% 159.14/25.47  | | | | Case 1:
% 159.14/25.47  | | | | | 
% 159.14/25.47  | | | | |   (43)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.14/25.47  | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.14/25.47  | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12)) |
% 159.14/25.47  | | | | |         (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 159.14/25.47  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 159.14/25.47  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.14/25.47  | | | | |         (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 159.14/25.47  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 159.14/25.47  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.14/25.47  | | | | |         (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 159.14/25.47  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 159.14/25.47  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.14/25.47  | | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.14/25.47  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 159.14/25.47  | | | | |           & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.14/25.47  | | | | |         (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 159.14/25.47  | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.14/25.47  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.14/25.47  | | | | |         (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) =
% 159.14/25.47  | | | | |           e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 159.14/25.47  | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.14/25.47  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.14/25.47  | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 159.14/25.47  | | | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 159.14/25.47  | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.14/25.47  | | | | |           $i(all_57_12))
% 159.14/25.47  | | | | | 
% 159.14/25.47  | | | | | REF_CLOSE: (4), (7), (16), (20), (30), (37), (38), (43) are
% 159.14/25.47  | | | | |            inconsistent by sub-proof #379.
% 159.14/25.47  | | | | | 
% 159.14/25.47  | | | | Case 2:
% 159.14/25.47  | | | | | 
% 159.14/25.47  | | | | |   (44)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.14/25.47  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 159.14/25.47  | | | | |           & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.14/25.47  | | | | |         (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) =
% 159.14/25.47  | | | | |           e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 159.14/25.47  | | | | |           all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 &
% 159.14/25.47  | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.14/25.47  | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10
% 159.14/25.47  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 159.14/25.47  | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.14/25.47  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_14
% 159.14/25.47  | | | | |           = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.47  | | | | |             e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.14/25.47  | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12
% 159.14/25.47  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 159.14/25.47  | | | | |           e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.14/25.47  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 & all_57_15
% 159.14/25.47  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 159.14/25.47  | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.14/25.47  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14
% 159.14/25.47  | | | | |           = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.47  | | | | |             e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.14/25.47  | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 =
% 159.14/25.47  | | | | |             e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.14/25.47  | | | | | 
% 159.14/25.47  | | | | | BETA: splitting (44) gives:
% 159.14/25.47  | | | | | 
% 159.14/25.47  | | | | | Case 1:
% 159.14/25.47  | | | | | | 
% 159.14/25.47  | | | | | |   (45)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.14/25.47  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 159.14/25.47  | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.14/25.47  | | | | | |         (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3)
% 159.14/25.47  | | | | | |           = e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2
% 159.14/25.47  | | | | | |           & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 &
% 159.14/25.47  | | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 159.14/25.47  | | | | | |           & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.14/25.47  | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 159.14/25.47  | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 159.14/25.47  | | | | | |           & $i(all_57_14))
% 159.14/25.47  | | | | | | 
% 159.14/25.47  | | | | | | BETA: splitting (45) gives:
% 159.14/25.47  | | | | | | 
% 159.14/25.47  | | | | | | Case 1:
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | |   (46)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.14/25.47  | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 159.14/25.47  | | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 159.14/25.47  | | | | | | |         | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3,
% 159.14/25.47  | | | | | | |             e3) = e3 & op(e3, e2) = e3)
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | | REF_CLOSE: (2), (3), (7), (18), (27), (46) are inconsistent by
% 159.14/25.47  | | | | | | |            sub-proof #378.
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | Case 2:
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | |   (47)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 159.14/25.47  | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.14/25.47  | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.14/25.47  | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.14/25.47  | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 159.14/25.47  | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.14/25.47  | | | | | | |           all_57_14 & $i(all_57_14))
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | | REF_CLOSE: (7), (12), (14), (15), (21), (27), (41), (47) are
% 159.14/25.47  | | | | | | |            inconsistent by sub-proof #706.
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | End of split
% 159.14/25.47  | | | | | | 
% 159.14/25.47  | | | | | Case 2:
% 159.14/25.47  | | | | | | 
% 159.14/25.47  | | | | | |   (48)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 159.14/25.47  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 159.14/25.47  | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.14/25.47  | | | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.14/25.47  | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.14/25.47  | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.14/25.47  | | | | | |         | (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.14/25.47  | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 159.14/25.47  | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.14/25.47  | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.14/25.47  | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.14/25.47  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.14/25.47  | | | | | |           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 & 
% 159.14/25.47  | | | | | |           ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.14/25.47  | | | | | | 
% 159.14/25.47  | | | | | | BETA: splitting (48) gives:
% 159.14/25.47  | | | | | | 
% 159.14/25.47  | | | | | | Case 1:
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | |   (49)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 159.14/25.47  | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 159.14/25.47  | | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.14/25.47  | | | | | | |         | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.14/25.47  | | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.14/25.47  | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.14/25.47  | | | | | | |           $i(all_57_14))
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | | REF_CLOSE: (4), (7), (30), (39), (41), (49) are inconsistent by
% 159.14/25.47  | | | | | | |            sub-proof #705.
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | Case 2:
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | |   (50)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.14/25.47  | | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 159.14/25.47  | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.14/25.47  | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.14/25.47  | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.14/25.47  | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 159.14/25.47  | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 159.14/25.47  | | | | | | |           = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | | REF_CLOSE: (4), (6), (7), (19), (23), (30), (50) are inconsistent
% 159.14/25.47  | | | | | | |            by sub-proof #377.
% 159.14/25.47  | | | | | | | 
% 159.14/25.47  | | | | | | End of split
% 159.14/25.47  | | | | | | 
% 159.14/25.47  | | | | | End of split
% 159.14/25.47  | | | | | 
% 159.14/25.47  | | | | End of split
% 159.14/25.47  | | | | 
% 159.14/25.47  | | | Case 2:
% 159.14/25.47  | | | | 
% 159.14/25.48  | | | |   (51)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14
% 159.14/25.48  | | | |             = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1
% 159.14/25.48  | | | |           & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.14/25.48  | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2,
% 159.14/25.48  | | | |             e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.14/25.48  | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.14/25.48  | | | |           all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12
% 159.14/25.48  | | | |           & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.14/25.48  | | | |           $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 =
% 159.14/25.48  | | | |           e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.14/25.48  | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.14/25.48  | | | |         | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.14/25.48  | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.14/25.48  | | | |           op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3
% 159.14/25.48  | | | |           = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 159.14/25.48  | | | |           op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 159.14/25.48  | | | |           = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.48  | | | |             e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.14/25.48  | | | |           $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 =
% 159.14/25.48  | | | |             e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 159.14/25.48  | | | |           all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 159.14/25.48  | | | |             e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 159.14/25.48  | | | |             e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 &
% 159.14/25.48  | | | |           all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12
% 159.14/25.48  | | | |           & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.14/25.48  | | | |           $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 =
% 159.14/25.48  | | | |             e1) & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 &
% 159.14/25.48  | | | |           all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 159.14/25.48  | | | |             e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.14/25.48  | | | |             e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.14/25.48  | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 159.14/25.48  | | | |           & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.14/25.48  | | | |           $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 & all_57_15 =
% 159.14/25.48  | | | |           e2 &  ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.14/25.48  | | | |           = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.14/25.48  | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3
% 159.14/25.48  | | | |           & op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 159.14/25.48  | | | |             = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 159.14/25.48  | | | |           & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0)
% 159.14/25.48  | | | |           = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 =
% 159.14/25.48  | | | |               e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 159.14/25.48  | | | |               & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.14/25.48  | | | |             (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.14/25.48  | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.14/25.48  | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 159.14/25.48  | | | |               all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.14/25.48  | | | |               op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.14/25.48  | | | |               all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.14/25.48  | | | |             (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.14/25.48  | | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.14/25.48  | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.14/25.48  | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 159.14/25.48  | | | |               op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.14/25.48  | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.14/25.48  | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 159.14/25.48  | | | |             (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2)
% 159.14/25.48  | | | |               = e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.14/25.48  | | | |               ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.14/25.48  | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 159.14/25.48  | | | |               all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.14/25.48  | | | |               op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.14/25.48  | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.14/25.48  | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.14/25.48  | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 159.14/25.48  | | | |               (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 159.14/25.48  | | | |               e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.14/25.48  | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.14/25.48  | | | | 
% 159.14/25.48  | | | | BETA: splitting (51) gives:
% 159.14/25.48  | | | | 
% 159.14/25.48  | | | | Case 1:
% 159.14/25.48  | | | | | 
% 159.14/25.48  | | | | |   (52)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.14/25.48  | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.14/25.48  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.14/25.48  | | | | |         (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.14/25.48  | | | | |           (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.14/25.48  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.14/25.48  | | | | |         (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.14/25.48  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 159.14/25.48  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.14/25.48  | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.14/25.48  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 159.14/25.48  | | | | |           & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 159.14/25.48  | | | | |         (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.14/25.48  | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 159.14/25.48  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.14/25.48  | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) =
% 159.14/25.48  | | | | |           e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.14/25.48  | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.14/25.48  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.14/25.48  | | | | |           e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~
% 159.14/25.48  | | | | |           (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 159.14/25.48  | | | | |           e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.14/25.48  | | | | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 159.14/25.48  | | | | |           op(e1, e0) = e1 & $i(all_57_14))
% 159.14/25.48  | | | | | 
% 159.14/25.48  | | | | | BETA: splitting (52) gives:
% 159.14/25.48  | | | | | 
% 159.14/25.48  | | | | | Case 1:
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | |   (53)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.14/25.48  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.14/25.48  | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.14/25.48  | | | | | |         | (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.14/25.48  | | | | | |           (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.14/25.48  | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.14/25.48  | | | | | |         | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.14/25.48  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 159.14/25.48  | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.14/25.48  | | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.14/25.48  | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.14/25.48  | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.14/25.48  | | | | | |           $i(all_57_14))
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | | BETA: splitting (53) gives:
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | | Case 1:
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | |   (54)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.14/25.48  | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.14/25.48  | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.14/25.48  | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.14/25.48  | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 &
% 159.14/25.48  | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.14/25.48  | | | | | | |           all_57_14 & $i(all_57_14))
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | | REF_CLOSE: (7), (15), (27), (39), (41), (54) are inconsistent by
% 159.14/25.48  | | | | | | |            sub-proof #987.
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | Case 2:
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | |   (55)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.14/25.48  | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 159.14/25.48  | | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 159.14/25.48  | | | | | | |         | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.14/25.48  | | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.14/25.48  | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.14/25.48  | | | | | | |           $i(all_57_14))
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | | REF_CLOSE: (4), (6), (7), (23), (40), (55) are inconsistent by
% 159.14/25.48  | | | | | | |            sub-proof #376.
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | End of split
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | Case 2:
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | |   (56)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.14/25.48  | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 159.14/25.48  | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.14/25.48  | | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2)
% 159.14/25.48  | | | | | |           = e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.14/25.48  | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.14/25.48  | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.14/25.48  | | | | | |           = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 & 
% 159.14/25.48  | | | | | |           ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) |
% 159.14/25.48  | | | | | |         (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 159.14/25.48  | | | | | |           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.14/25.48  | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | | BETA: splitting (56) gives:
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | | Case 1:
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | |   (57)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.14/25.48  | | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 159.14/25.48  | | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 159.14/25.48  | | | | | | |         | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1,
% 159.14/25.48  | | | | | | |             e2) = e1 & op(e1, e1) = e1)
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | | REF_CLOSE: (4), (7), (19), (40), (57) are inconsistent by
% 159.14/25.48  | | | | | | |            sub-proof #701.
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | Case 2:
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | |   (58)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.14/25.48  | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 159.14/25.48  | | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 159.14/25.48  | | | | | | |         | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3,
% 159.14/25.48  | | | | | | |             e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 159.14/25.48  | | | | | | |           all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.14/25.48  | | | | | | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.14/25.48  | | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | | REF_CLOSE: (2), (7), (8), (15), (27), (29), (58) are inconsistent
% 159.14/25.48  | | | | | | |            by sub-proof #375.
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | End of split
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | End of split
% 159.14/25.48  | | | | | 
% 159.14/25.48  | | | | Case 2:
% 159.14/25.48  | | | | | 
% 159.14/25.48  | | | | |   (59)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.14/25.48  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 159.14/25.48  | | | | |           & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.14/25.48  | | | | |         (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) =
% 159.14/25.48  | | | | |           e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 159.14/25.48  | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 &
% 159.14/25.48  | | | | |           op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.14/25.48  | | | | |           $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15
% 159.14/25.48  | | | | |           = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.48  | | | | |             e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.14/25.48  | | | | |           $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 & all_57_15
% 159.14/25.48  | | | | |           = e2 &  ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 159.14/25.48  | | | | |             e0) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.14/25.48  | | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 =
% 159.14/25.48  | | | | |             e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2
% 159.14/25.48  | | | | |           & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2,
% 159.14/25.48  | | | | |             e0) = e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 =
% 159.14/25.48  | | | | |             e0) & op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.14/25.48  | | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3
% 159.14/25.48  | | | | |               & all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0
% 159.14/25.48  | | | | |               & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.14/25.48  | | | | |               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.14/25.48  | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.14/25.48  | | | | |             (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.14/25.48  | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.14/25.48  | | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.14/25.48  | | | | |               (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9
% 159.14/25.48  | | | | |               = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3)
% 159.14/25.48  | | | | |               = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.14/25.48  | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.48  | | | | |                 e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.14/25.48  | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.14/25.48  | | | | |                ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1
% 159.14/25.48  | | | | |               & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 & 
% 159.14/25.48  | | | | |               ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.14/25.48  | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.14/25.48  | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.14/25.48  | | | | |             (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.14/25.48  | | | | |               (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.14/25.48  | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.14/25.48  | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.14/25.48  | | | | |               op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.14/25.48  | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.14/25.48  | | | | |               op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.14/25.48  | | | | |               e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 159.14/25.48  | | | | |               ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.14/25.48  | | | | | 
% 159.14/25.48  | | | | | BETA: splitting (59) gives:
% 159.14/25.48  | | | | | 
% 159.14/25.48  | | | | | Case 1:
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | |   (60)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.14/25.48  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 159.14/25.48  | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.14/25.48  | | | | | |         (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2)
% 159.14/25.48  | | | | | |           = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 159.14/25.48  | | | | | |           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 &
% 159.14/25.48  | | | | | |           op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 159.14/25.48  | | | | | |           & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.14/25.48  | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.14/25.48  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.14/25.48  | | | | | |           = e3 & $i(all_57_10))
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | | BETA: splitting (60) gives:
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | | Case 1:
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | |   (61)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.14/25.48  | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 159.14/25.48  | | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 159.14/25.48  | | | | | | |         | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2,
% 159.14/25.48  | | | | | | |             e2) = e2 & op(e2, e1) = e2)
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | | REF_CLOSE: (2), (7), (20), (38), (39), (61) are inconsistent by
% 159.14/25.48  | | | | | | |            sub-proof #374.
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | Case 2:
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | |   (62)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 159.14/25.48  | | | | | | |           (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.14/25.48  | | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.14/25.48  | | | | | | |           $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.14/25.48  | | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.14/25.48  | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 159.14/25.48  | | | | | | |             e0) = e3 & $i(all_57_10))
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | | BETA: splitting (62) gives:
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | | Case 1:
% 159.14/25.48  | | | | | | | | 
% 159.14/25.48  | | | | | | | |   (63)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 159.14/25.48  | | | | | | | |         (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.14/25.48  | | | | | | | |         op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)
% 159.14/25.48  | | | | | | | | 
% 159.14/25.48  | | | | | | | | ALPHA: (63) implies:
% 159.14/25.48  | | | | | | | |   (64)  op(e2, e2) = e1
% 159.14/25.48  | | | | | | | | 
% 159.14/25.48  | | | | | | | | REF_CLOSE: (7), (39), (41), (64) are inconsistent by sub-proof
% 159.14/25.48  | | | | | | | |            #993.
% 159.14/25.48  | | | | | | | | 
% 159.14/25.48  | | | | | | | Case 2:
% 159.14/25.48  | | | | | | | | 
% 159.14/25.48  | | | | | | | |   (65)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~
% 159.14/25.48  | | | | | | | |         (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 159.14/25.48  | | | | | | | |         e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)
% 159.14/25.48  | | | | | | | | 
% 159.14/25.48  | | | | | | | | ALPHA: (65) implies:
% 159.14/25.48  | | | | | | | |   (66)  op(e0, e0) = e3
% 159.14/25.48  | | | | | | | | 
% 159.14/25.48  | | | | | | | | REF_CLOSE: (2), (7), (27), (66) are inconsistent by sub-proof
% 159.14/25.48  | | | | | | | |            #473.
% 159.14/25.48  | | | | | | | | 
% 159.14/25.48  | | | | | | | End of split
% 159.14/25.48  | | | | | | | 
% 159.14/25.48  | | | | | | End of split
% 159.14/25.48  | | | | | | 
% 159.14/25.48  | | | | | Case 2:
% 159.14/25.48  | | | | | | 
% 159.14/25.49  | | | | | |   (67)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 159.14/25.49  | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 159.14/25.49  | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.14/25.49  | | | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3)
% 159.14/25.49  | | | | | |           = e3 & op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2
% 159.14/25.49  | | | | | |           &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.14/25.49  | | | | | |         (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1)
% 159.14/25.49  | | | | | |           = e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 159.14/25.49  | | | | | |           $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 159.14/25.49  | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0
% 159.14/25.49  | | | | | |               & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.14/25.49  | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.49  | | | | | |                 e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3)
% 159.14/25.49  | | | | | |               = e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 159.14/25.49  | | | | | |               e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.14/25.49  | | | | | |                 e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.14/25.49  | | | | | |               all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.14/25.49  | | | | | |             (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.14/25.49  | | | | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.14/25.49  | | | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.14/25.49  | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 159.14/25.49  | | | | | |               & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0
% 159.14/25.49  | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.49  | | | | | |                 e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2)
% 159.14/25.49  | | | | | |               = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 159.14/25.49  | | | | | |               & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 159.14/25.49  | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 159.14/25.49  | | | | | |               & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.14/25.49  | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.49  | | | | | |                 e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 159.14/25.49  | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.14/25.49  | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 159.14/25.49  | | | | | |                 e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.14/25.49  | | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 159.14/25.49  | | | | | |               & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.14/25.49  | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.14/25.49  | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.14/25.49  | | | | | | 
% 159.14/25.49  | | | | | | BETA: splitting (67) gives:
% 159.14/25.49  | | | | | | 
% 159.14/25.49  | | | | | | Case 1:
% 159.14/25.49  | | | | | | | 
% 159.14/25.49  | | | | | | |   (68)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 159.14/25.49  | | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 159.14/25.49  | | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 159.14/25.49  | | | | | | |         | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3,
% 159.14/25.49  | | | | | | |             e3) = e3 & op(e3, e0) = e3)
% 159.14/25.49  | | | | | | | 
% 159.14/25.49  | | | | | | | REF_CLOSE: (2), (7), (9), (24), (39), (68) are inconsistent by
% 159.14/25.49  | | | | | | |            sub-proof #373.
% 159.14/25.49  | | | | | | | 
% 159.14/25.49  | | | | | | Case 2:
% 159.14/25.49  | | | | | | | 
% 159.14/25.49  | | | | | | |   (69)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 159.14/25.49  | | | | | | |             e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 159.14/25.49  | | | | | | |           all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1,
% 159.14/25.49  | | | | | | |             e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.14/25.49  | | | | | | |           ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.14/25.49  | | | | | | |               (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3
% 159.14/25.49  | | | | | | |               & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2
% 159.14/25.49  | | | | | | |               & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2)
% 159.14/25.49  | | | | | | |               = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.14/25.49  | | | | | | |             (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.14/25.49  | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1
% 159.14/25.49  | | | | | | |               & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0
% 159.14/25.49  | | | | | | |               &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.14/25.49  | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 159.14/25.49  | | | | | | |               & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.14/25.49  | | | | | | |               e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.14/25.49  | | | | | | |               e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 159.14/25.49  | | | | | | |                 e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.14/25.49  | | | | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.49  | | | | | | |                 e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.14/25.49  | | | | | | |                 e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~
% 159.14/25.49  | | | | | | |               (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.14/25.49  | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 159.14/25.49  | | | | | | |               & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.14/25.49  | | | | | | |               e0) | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.14/25.49  | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.14/25.49  | | | | | | |                 e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.14/25.49  | | | | | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.49  | | | | | | |                 e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.14/25.49  | | | | | | |                 e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.14/25.49  | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.14/25.49  | | | | | | |               all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.14/25.49  | | | | | | |               $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 159.14/25.49  | | | | | | |               ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.14/25.49  | | | | | | | 
% 159.14/25.49  | | | | | | | BETA: splitting (69) gives:
% 159.14/25.49  | | | | | | | 
% 159.14/25.49  | | | | | | | Case 1:
% 159.14/25.49  | | | | | | | | 
% 159.14/25.49  | | | | | | | |   (70)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 159.14/25.49  | | | | | | | |           e2) = e2 & op(e2, e0) = e2
% 159.14/25.49  | | | | | | | | 
% 159.14/25.49  | | | | | | | | ALPHA: (70) implies:
% 159.14/25.49  | | | | | | | |   (71)  op(e2, e0) = e2
% 159.14/25.49  | | | | | | | | 
% 159.14/25.49  | | | | | | | | REF_CLOSE: (7), (12), (14), (21), (41), (71) are inconsistent by
% 159.14/25.49  | | | | | | | |            sub-proof #972.
% 159.14/25.49  | | | | | | | | 
% 159.14/25.49  | | | | | | | Case 2:
% 159.14/25.49  | | | | | | | | 
% 159.14/25.49  | | | | | | | |   (72)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 159.14/25.49  | | | | | | | |             e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.14/25.49  | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9
% 159.14/25.49  | | | | | | | |               = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.14/25.49  | | | | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 159.14/25.49  | | | | | | | |               e0) | (all_57_6 = e0 & all_57_11 = e2 & all_57_12
% 159.14/25.49  | | | | | | | |               = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 159.14/25.49  | | | | | | | |               op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.14/25.49  | | | | | | | |               e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.14/25.49  | | | | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 159.14/25.49  | | | | | | | |               e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15
% 159.14/25.49  | | | | | | | |               = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 159.14/25.49  | | | | | | | |               = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.14/25.49  | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 159.14/25.49  | | | | | | | |               e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11
% 159.14/25.49  | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.14/25.49  | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.14/25.49  | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14
% 159.14/25.49  | | | | | | | |               = e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 159.14/25.49  | | | | | | | |               op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.14/25.49  | | | | | | | |               e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.14/25.49  | | | | | | | |               e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.14/25.49  | | | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.14/25.49  | | | | | | | |               op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.14/25.49  | | | | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.14/25.49  | | | | | | | |               (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 159.14/25.49  | | | | | | | |               e2 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13
% 159.14/25.49  | | | | | | | |               = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.14/25.49  | | | | | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.14/25.49  | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15
% 159.14/25.49  | | | | | | | |               = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.14/25.49  | | | | | | | |               all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.14/25.49  | | | | | | | |               $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &
% 159.14/25.49  | | | | | | | |                ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.14/25.49  | | | | | | | | 
% 159.14/25.49  | | | | | | | | BETA: splitting (72) gives:
% 159.14/25.49  | | | | | | | | 
% 159.14/25.49  | | | | | | | | Case 1:
% 159.14/25.49  | | | | | | | | | 
% 159.14/25.49  | | | | | | | | |   (73)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.14/25.49  | | | | | | | | |         op(e1, e1) = e1 & op(e1, e0) = e1
% 159.14/25.49  | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | ALPHA: (73) implies:
% 159.14/25.49  | | | | | | | | |   (74)  op(e1, e1) = e1
% 159.14/25.49  | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | REF_CLOSE: (4), (7), (19), (74) are inconsistent by sub-proof
% 159.14/25.49  | | | | | | | | |            #903.
% 159.14/25.49  | | | | | | | | | 
% 159.14/25.49  | | | | | | | | Case 2:
% 159.14/25.49  | | | | | | | | | 
% 159.14/25.49  | | | | | | | | |   (75)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 =
% 159.14/25.49  | | | | | | | | |             e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.14/25.49  | | | | | | | | |             (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 159.14/25.49  | | | | | | | | |             e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 159.14/25.49  | | | | | | | | |             = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.14/25.49  | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 159.14/25.49  | | | | | | | | |             e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 159.14/25.49  | | | | | | | | |             = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.14/25.49  | | | | | | | | |             op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.14/25.49  | | | | | | | | |             e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.14/25.49  | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 159.14/25.49  | | | | | | | | |             e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 159.14/25.49  | | | | | | | | |             op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.14/25.49  | | | | | | | | |             e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.14/25.49  | | | | | | | | |             (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 159.14/25.49  | | | | | | | | |             e2 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_13
% 159.14/25.49  | | | | | | | | |             = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.14/25.49  | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.14/25.49  | | | | | | | | |             e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 =
% 159.14/25.49  | | | | | | | | |               e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.14/25.49  | | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.14/25.49  | | | | | | | | |               e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.14/25.49  | | | | | | | | |               e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 159.14/25.49  | | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2)
% 159.14/25.49  | | | | | | | | |             = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.14/25.49  | | | | | | | | |           (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.14/25.49  | | | | | | | | |             ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 159.14/25.49  | | | | | | | | |             = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.14/25.49  | | | | | | | | |             all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.14/25.49  | | | | | | | | |               e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.14/25.49  | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0
% 159.14/25.49  | | | | | | | | |             & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.14/25.49  | | | | | | | | |             e0))
% 159.14/25.49  | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | ALPHA: (75) implies:
% 159.14/25.49  | | | | | | | | |   (76)  op(e0, e0) = all_57_15
% 159.14/25.49  | | | | | | | | |   (77)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.14/25.49  | | | | | | | | |           (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3
% 159.14/25.49  | | | | | | | | |           & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2
% 159.14/25.49  | | | | | | | | |           & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2)
% 159.14/25.49  | | | | | | | | |           = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.14/25.49  | | | | | | | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.14/25.49  | | | | | | | | |           (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1
% 159.14/25.49  | | | | | | | | |           & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0
% 159.14/25.49  | | | | | | | | |           &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.14/25.49  | | | | | | | | |           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 159.14/25.49  | | | | | | | | |           & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.14/25.49  | | | | | | | | |           e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.14/25.49  | | | | | | | | |           e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 159.14/25.49  | | | | | | | | |             e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.14/25.49  | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.49  | | | | | | | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.14/25.49  | | | | | | | | |             e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~
% 159.14/25.49  | | | | | | | | |           (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.14/25.49  | | | | | | | | |           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 159.14/25.49  | | | | | | | | |           & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.14/25.49  | | | | | | | | |           e0) | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.14/25.49  | | | | | | | | |           e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.14/25.49  | | | | | | | | |             e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.14/25.49  | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.49  | | | | | | | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.14/25.49  | | | | | | | | |             e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.14/25.49  | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.14/25.49  | | | | | | | | |           all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.14/25.49  | | | | | | | | |           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 159.14/25.49  | | | | | | | | |           ~ (e1 = e0) & op(e0, e1) = e0)
% 159.14/25.49  | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_57_15, e0, e0,
% 159.14/25.49  | | | | | | | | |              simplifying with (2), (76) gives:
% 159.14/25.49  | | | | | | | | |   (78)  all_57_15 = e1
% 159.14/25.49  | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | BETA: splitting (77) gives:
% 159.14/25.49  | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | Case 1:
% 159.14/25.49  | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | |   (79)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.14/25.49  | | | | | | | | | |           (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 159.14/25.49  | | | | | | | | | |           e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 159.14/25.49  | | | | | | | | | |           = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.14/25.49  | | | | | | | | | |           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 159.14/25.49  | | | | | | | | | |           e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 159.14/25.49  | | | | | | | | | |           = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.14/25.49  | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.14/25.49  | | | | | | | | | |           e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.14/25.49  | | | | | | | | | |           e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 159.14/25.49  | | | | | | | | | |           e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 159.14/25.49  | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.14/25.49  | | | | | | | | | |           e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.14/25.49  | | | | | | | | | |           (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 159.14/25.49  | | | | | | | | | |           e2 & op(e0, e2) = e0)
% 159.14/25.49  | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | | BETA: splitting (79) gives:
% 159.14/25.49  | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | | Case 1:
% 159.14/25.49  | | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | | |   (80)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.14/25.49  | | | | | | | | | | |           ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.14/25.49  | | | | | | | | | | |             e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.14/25.49  | | | | | | | | | | |           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.14/25.49  | | | | | | | | | | |             = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.14/25.49  | | | | | | | | | | |           op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.14/25.49  | | | | | | | | | | |           e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.14/25.49  | | | | | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.14/25.49  | | | | | | | | | | |           e0)
% 159.14/25.49  | | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | | | BETA: splitting (80) gives:
% 159.14/25.49  | | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | | | Case 1:
% 159.14/25.49  | | | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | | | |   (81)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.14/25.49  | | | | | | | | | | | |         ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 159.14/25.49  | | | | | | | | | | | |         = e3 & op(e0, e3) = e0
% 159.14/25.49  | | | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | | | | ALPHA: (81) implies:
% 159.14/25.49  | | | | | | | | | | | |   (82)  op(e3, e3) = e0
% 159.14/25.49  | | | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | | | | REF_CLOSE: (7), (15), (30), (82) are inconsistent by
% 159.14/25.49  | | | | | | | | | | | |            sub-proof #971.
% 159.14/25.49  | | | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | | | Case 2:
% 159.14/25.49  | | | | | | | | | | | | 
% 159.14/25.49  | | | | | | | | | | | |   (83)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.14/25.49  | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.14/25.49  | | | | | | | | | | | |             e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.14/25.50  | | | | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.14/25.50  | | | | | | | | | | | |             = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.14/25.50  | | | | | | | | | | | |           op(e0, e3) = e0)
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | BETA: splitting (83) gives:
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | Case 1:
% 159.14/25.50  | | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | |   (84)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 159.14/25.50  | | | | | | | | | | | | |         ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 159.14/25.50  | | | | | | | | | | | | |         = e2 & op(e0, e3) = e0
% 159.14/25.50  | | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | | ALPHA: (84) implies:
% 159.14/25.50  | | | | | | | | | | | | |   (85)  op(e2, e0) = e2
% 159.14/25.50  | | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | | REF_CLOSE: (7), (12), (14), (21), (41), (85) are inconsistent
% 159.14/25.50  | | | | | | | | | | | | |            by sub-proof #972.
% 159.14/25.50  | | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | Case 2:
% 159.14/25.50  | | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | |   (86)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.14/25.50  | | | | | | | | | | | | |         ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 159.14/25.50  | | | | | | | | | | | | |         = e1 & op(e0, e3) = e0
% 159.14/25.50  | | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | | ALPHA: (86) implies:
% 159.14/25.50  | | | | | | | | | | | | |   (87)  op(e1, e0) = e1
% 159.14/25.50  | | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | | REF_CLOSE: (7), (13), (25), (87) are inconsistent by
% 159.14/25.50  | | | | | | | | | | | | |            sub-proof #974.
% 159.14/25.50  | | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | End of split
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | End of split
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | Case 2:
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | |   (88)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.14/25.50  | | | | | | | | | | |           op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 159.14/25.50  | | | | | | | | | | |           e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.14/25.50  | | | | | | | | | | |           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.14/25.50  | | | | | | | | | | |           e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.14/25.50  | | | | | | | | | | |           all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.14/25.50  | | | | | | | | | | |             e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | BETA: splitting (88) gives:
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | Case 1:
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | |   (89)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.14/25.50  | | | | | | | | | | | |         op(e0, e3) = e0
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | REF_CLOSE: (19), (78), (89) are inconsistent by sub-proof
% 159.14/25.50  | | | | | | | | | | | |            #372.
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | Case 2:
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | |   (90)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.14/25.50  | | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.14/25.50  | | | | | | | | | | | |             e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.14/25.50  | | | | | | | | | | | |           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.14/25.50  | | | | | | | | | | | |             = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.14/25.50  | | | | | | | | | | | |           op(e0, e2) = e0)
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | REF_CLOSE: (7), (12), (14), (15), (21), (30), (41), (90) are
% 159.14/25.50  | | | | | | | | | | | |            inconsistent by sub-proof #970.
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | End of split
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | End of split
% 159.14/25.50  | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | Case 2:
% 159.14/25.50  | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | |   (91)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.14/25.50  | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 159.14/25.50  | | | | | | | | | |           = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.14/25.50  | | | | | | | | | |           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.14/25.50  | | | | | | | | | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.14/25.50  | | | | | | | | | |           (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) =
% 159.14/25.50  | | | | | | | | | |           e3 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 159.14/25.50  | | | | | | | | | |           = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.14/25.50  | | | | | | | | | |           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) =
% 159.14/25.50  | | | | | | | | | |           e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14
% 159.14/25.50  | | | | | | | | | |           = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.14/25.50  | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 159.14/25.50  | | | | | | | | | |           e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 159.14/25.50  | | | | | | | | | |           (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1,
% 159.14/25.50  | | | | | | | | | |             e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 159.14/25.50  | | | | | | | | | |         (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.14/25.50  | | | | | | | | | |           op(e0, e1) = e0)
% 159.14/25.50  | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | BETA: splitting (91) gives:
% 159.14/25.50  | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | Case 1:
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | |   (92)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.14/25.50  | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.14/25.50  | | | | | | | | | | |             e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.14/25.50  | | | | | | | | | | |           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.14/25.50  | | | | | | | | | | |         | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.14/25.50  | | | | | | | | | | |           &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.14/25.50  | | | | | | | | | | |             e0) = e3 & op(e0, e1) = e0)
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | BETA: splitting (92) gives:
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | Case 1:
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | |   (93)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.14/25.50  | | | | | | | | | | | |         ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 159.14/25.50  | | | | | | | | | | | |         = e1 & op(e0, e2) = e0
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | ALPHA: (93) implies:
% 159.14/25.50  | | | | | | | | | | | |   (94)  op(e1, e0) = e1
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | REF_CLOSE: (7), (13), (25), (94) are inconsistent by
% 159.14/25.50  | | | | | | | | | | | |            sub-proof #974.
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | Case 2:
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | |   (95)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 159.14/25.50  | | | | | | | | | | | |           op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 159.14/25.50  | | | | | | | | | | | |           e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.14/25.50  | | | | | | | | | | | |           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.14/25.50  | | | | | | | | | | | |           e0)
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | | REF_CLOSE: (7), (15), (19), (30), (78), (95) are inconsistent
% 159.14/25.50  | | | | | | | | | | | |            by sub-proof #370.
% 159.14/25.50  | | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | End of split
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | Case 2:
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | |   (96)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.14/25.50  | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.14/25.50  | | | | | | | | | | |             e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.14/25.50  | | | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.14/25.50  | | | | | | | | | | |             = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.14/25.50  | | | | | | | | | | |           op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.14/25.50  | | | | | | | | | | |           e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.14/25.50  | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.14/25.50  | | | | | | | | | | |           op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 159.14/25.50  | | | | | | | | | | |           e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 159.14/25.50  | | | | | | | | | | |           = e0)
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | | REF_CLOSE: (6), (7), (12), (14), (21), (23), (41), (96) are
% 159.14/25.50  | | | | | | | | | | |            inconsistent by sub-proof #964.
% 159.14/25.50  | | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | | End of split
% 159.14/25.50  | | | | | | | | | | 
% 159.14/25.50  | | | | | | | | | End of split
% 159.14/25.50  | | | | | | | | | 
% 159.14/25.50  | | | | | | | | End of split
% 159.14/25.50  | | | | | | | | 
% 159.14/25.50  | | | | | | | End of split
% 159.14/25.50  | | | | | | | 
% 159.14/25.50  | | | | | | End of split
% 159.14/25.50  | | | | | | 
% 159.14/25.50  | | | | | End of split
% 159.14/25.50  | | | | | 
% 159.14/25.50  | | | | End of split
% 159.14/25.50  | | | | 
% 159.14/25.50  | | | End of split
% 159.14/25.50  | | | 
% 159.14/25.50  | | Case 2:
% 159.14/25.50  | | | 
% 159.14/25.50  | | |   (97)  all_54_5 = e1 | all_54_5 = e0
% 159.14/25.50  | | | 
% 159.14/25.50  | | | REF_CLOSE: (1), (17), (22), (97) are inconsistent by sub-proof #962.
% 159.14/25.50  | | | 
% 159.14/25.50  | | End of split
% 159.14/25.50  | | 
% 159.14/25.50  | End of split
% 159.14/25.50  | 
% 159.14/25.50  End of proof
% 159.14/25.50  
% 159.14/25.50  Sub-proof #370 shows that the following formulas are inconsistent:
% 159.14/25.50  ----------------------------------------------------------------
% 159.14/25.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.50    (2)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.14/25.50         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.14/25.50           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.14/25.50    (3)  all_57_15 = e1
% 159.14/25.50    (4)  op(e3, e3) = e3
% 159.14/25.50    (5)   ~ (e1 = e0)
% 159.14/25.50    (6)   ~ (e3 = e0)
% 159.14/25.50  
% 159.14/25.50  Begin of proof
% 159.14/25.50  | 
% 159.14/25.50  | BETA: splitting (2) gives:
% 159.14/25.50  | 
% 159.14/25.50  | Case 1:
% 159.14/25.50  | | 
% 159.14/25.50  | |   (7)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 159.14/25.50  | | 
% 159.14/25.50  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #371.
% 159.14/25.50  | | 
% 159.14/25.50  | Case 2:
% 159.14/25.50  | | 
% 159.14/25.50  | |   (8)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 159.14/25.50  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 159.14/25.50  | | 
% 159.14/25.50  | | ALPHA: (8) implies:
% 159.14/25.50  | |   (9)  op(e3, e3) = e0
% 159.14/25.50  | | 
% 159.14/25.50  | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #971.
% 159.14/25.50  | | 
% 159.14/25.50  | End of split
% 159.14/25.50  | 
% 159.14/25.50  End of proof
% 159.14/25.50  
% 159.14/25.50  Sub-proof #371 shows that the following formulas are inconsistent:
% 159.14/25.50  ----------------------------------------------------------------
% 159.14/25.50    (1)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 159.14/25.50    (2)  all_57_15 = e1
% 159.14/25.50    (3)   ~ (e1 = e0)
% 159.14/25.50  
% 159.14/25.50  Begin of proof
% 159.14/25.50  | 
% 159.14/25.50  | ALPHA: (1) implies:
% 159.14/25.50  |   (4)  all_57_15 = e0
% 159.14/25.50  | 
% 159.14/25.50  | COMBINE_EQS: (2), (4) imply:
% 159.14/25.50  |   (5)  e1 = e0
% 159.14/25.50  | 
% 159.14/25.50  | REDUCE: (3), (5) imply:
% 159.14/25.50  |   (6)  $false
% 159.14/25.50  | 
% 159.14/25.50  | CLOSE: (6) is inconsistent.
% 159.14/25.50  | 
% 159.14/25.50  End of proof
% 159.14/25.50  
% 159.14/25.50  Sub-proof #372 shows that the following formulas are inconsistent:
% 159.14/25.50  ----------------------------------------------------------------
% 159.14/25.50    (1)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 159.14/25.50    (2)  all_57_15 = e1
% 159.14/25.50    (3)   ~ (e1 = e0)
% 159.14/25.50  
% 159.14/25.50  Begin of proof
% 159.14/25.50  | 
% 159.14/25.50  | ALPHA: (1) implies:
% 159.14/25.50  |   (4)  all_57_15 = e0
% 159.14/25.50  | 
% 159.14/25.50  | COMBINE_EQS: (2), (4) imply:
% 159.14/25.50  |   (5)  e1 = e0
% 159.14/25.50  | 
% 159.14/25.50  | REDUCE: (3), (5) imply:
% 159.14/25.50  |   (6)  $false
% 159.14/25.50  | 
% 159.14/25.50  | CLOSE: (6) is inconsistent.
% 159.14/25.50  | 
% 159.14/25.50  End of proof
% 159.14/25.50  
% 159.14/25.50  Sub-proof #373 shows that the following formulas are inconsistent:
% 159.14/25.50  ----------------------------------------------------------------
% 159.14/25.50    (1)  op(e0, e0) = e1
% 159.14/25.50    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.50    (3)   ~ (all_52_12 = e3)
% 159.14/25.50    (4)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.14/25.50           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.14/25.50           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 159.14/25.50           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 159.14/25.50    (5)   ~ (e2 = e1)
% 159.14/25.50    (6)  op(e3, e0) = all_52_12
% 159.14/25.50  
% 159.14/25.50  Begin of proof
% 159.14/25.50  | 
% 159.14/25.50  | BETA: splitting (4) gives:
% 159.14/25.50  | 
% 159.14/25.50  | Case 1:
% 159.14/25.50  | | 
% 159.14/25.50  | |   (7)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 159.14/25.50  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.14/25.50  | |          e0) = e2 & $i(all_57_12)
% 159.14/25.50  | | 
% 159.14/25.50  | | ALPHA: (7) implies:
% 159.14/25.50  | |   (8)  op(e0, e0) = e2
% 159.14/25.50  | | 
% 159.14/25.50  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #875.
% 159.14/25.50  | | 
% 159.14/25.50  | Case 2:
% 159.14/25.50  | | 
% 159.14/25.50  | |   (9)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 159.14/25.50  | |        op(e3, e0) = e3
% 159.14/25.50  | | 
% 159.14/25.50  | | ALPHA: (9) implies:
% 159.14/25.50  | |   (10)  op(e3, e0) = e3
% 159.14/25.50  | | 
% 159.14/25.50  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #976.
% 159.14/25.50  | | 
% 159.14/25.50  | End of split
% 159.14/25.50  | 
% 159.14/25.50  End of proof
% 159.14/25.50  
% 159.14/25.50  Sub-proof #374 shows that the following formulas are inconsistent:
% 159.14/25.50  ----------------------------------------------------------------
% 159.14/25.50    (1)  op(e0, e0) = e1
% 159.14/25.50    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.50    (3)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.14/25.50           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.14/25.50           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 159.14/25.50           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.14/25.50    (4)  op(e2, e1) = all_52_9
% 159.14/25.50    (5)   ~ (e2 = e1)
% 159.14/25.50    (6)   ~ (all_52_9 = e2)
% 159.14/25.50  
% 159.14/25.50  Begin of proof
% 159.14/25.50  | 
% 159.14/25.50  | BETA: splitting (3) gives:
% 159.14/25.50  | 
% 159.14/25.50  | Case 1:
% 159.14/25.50  | | 
% 159.14/25.50  | |   (7)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 159.14/25.50  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 159.14/25.50  | |          e0) = e2 & $i(all_57_12)
% 159.14/25.50  | | 
% 159.14/25.50  | | ALPHA: (7) implies:
% 159.14/25.50  | |   (8)  op(e0, e0) = e2
% 159.14/25.50  | | 
% 159.14/25.50  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #875.
% 159.14/25.50  | | 
% 159.14/25.50  | Case 2:
% 159.14/25.50  | | 
% 159.14/25.50  | |   (9)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 159.14/25.50  | |        op(e2, e1) = e2
% 159.14/25.50  | | 
% 159.14/25.50  | | ALPHA: (9) implies:
% 159.14/25.50  | |   (10)  op(e2, e1) = e2
% 159.14/25.50  | | 
% 159.14/25.50  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1002.
% 159.14/25.50  | | 
% 159.14/25.50  | End of split
% 159.14/25.50  | 
% 159.14/25.50  End of proof
% 159.14/25.50  
% 159.14/25.50  Sub-proof #375 shows that the following formulas are inconsistent:
% 159.14/25.50  ----------------------------------------------------------------
% 159.14/25.50    (1)  op(e0, e0) = e1
% 159.14/25.50    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.50    (3)  op(e3, e1) = all_52_8
% 159.14/25.50    (4)  op(e3, e3) = e3
% 159.14/25.50    (5)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 159.14/25.50           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.14/25.50           = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1)
% 159.14/25.50           & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 159.14/25.50           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 159.14/25.50           e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.14/25.50    (6)   ~ (e3 = e1)
% 159.14/25.50    (7)   ~ (all_52_8 = e3)
% 159.14/25.50  
% 159.14/25.50  Begin of proof
% 159.14/25.50  | 
% 159.14/25.50  | BETA: splitting (5) gives:
% 159.14/25.50  | 
% 159.14/25.50  | Case 1:
% 159.14/25.50  | | 
% 159.14/25.50  | |   (8)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1)
% 159.14/25.50  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 159.14/25.50  | |          e0) = e3 & $i(all_57_10)
% 159.14/25.50  | | 
% 159.14/25.50  | | ALPHA: (8) implies:
% 159.14/25.50  | |   (9)  op(e0, e0) = e3
% 159.14/25.50  | | 
% 159.14/25.50  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #473.
% 159.14/25.50  | | 
% 159.14/25.50  | Case 2:
% 159.14/25.50  | | 
% 159.14/25.50  | |   (10)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 159.14/25.50  | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 =
% 159.14/25.50  | |           e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.14/25.50  | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.14/25.50  | | 
% 159.14/25.50  | | REF_CLOSE: (2), (3), (4), (6), (7), (10) are inconsistent by sub-proof #981.
% 159.14/25.50  | | 
% 159.14/25.50  | End of split
% 159.14/25.50  | 
% 159.14/25.50  End of proof
% 159.14/25.50  
% 159.14/25.50  Sub-proof #376 shows that the following formulas are inconsistent:
% 159.14/25.50  ----------------------------------------------------------------
% 159.14/25.50    (1)  op(e1, e1) = e0
% 159.14/25.50    (2)  op(e0, e1) = all_52_11
% 159.14/25.50    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.50    (4)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 159.14/25.50           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.14/25.50           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 159.14/25.50           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.14/25.50           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.14/25.50    (5)   ~ (all_52_11 = e0)
% 159.14/25.50    (6)   ~ (e2 = e0)
% 159.14/25.50  
% 159.14/25.50  Begin of proof
% 159.14/25.50  | 
% 159.14/25.50  | BETA: splitting (4) gives:
% 159.14/25.50  | 
% 159.14/25.50  | Case 1:
% 159.14/25.50  | | 
% 159.14/25.50  | |   (7)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.14/25.50  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.14/25.50  | |          e1) = e2 & $i(all_57_12)
% 159.14/25.50  | | 
% 159.14/25.50  | | ALPHA: (7) implies:
% 159.14/25.50  | |   (8)  op(e1, e1) = e2
% 159.14/25.50  | | 
% 159.14/25.50  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #914.
% 159.14/25.50  | | 
% 159.14/25.50  | Case 2:
% 159.14/25.50  | | 
% 159.14/25.50  | |   (9)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 159.14/25.50  | |        & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.14/25.50  | |          e0) = e1 & $i(all_57_14)
% 159.14/25.50  | | 
% 159.14/25.50  | | ALPHA: (9) implies:
% 159.14/25.50  | |   (10)  op(e0, e1) = e0
% 159.14/25.50  | | 
% 159.14/25.50  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #966.
% 159.14/25.50  | | 
% 159.14/25.50  | End of split
% 159.14/25.50  | 
% 159.14/25.50  End of proof
% 159.14/25.50  
% 159.14/25.50  Sub-proof #377 shows that the following formulas are inconsistent:
% 159.14/25.50  ----------------------------------------------------------------
% 159.14/25.50    (1)  op(e1, e1) = e0
% 159.14/25.50    (2)  op(e0, e1) = all_52_11
% 159.14/25.50    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.51    (4)   ~ (e1 = e0)
% 159.14/25.51    (5)   ~ (all_52_11 = e0)
% 159.14/25.51    (6)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.14/25.51           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.14/25.51           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 159.14/25.51           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.14/25.51           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 159.14/25.51           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.14/25.51    (7)   ~ (e3 = e0)
% 159.14/25.51  
% 159.14/25.51  Begin of proof
% 159.14/25.51  | 
% 159.14/25.51  | BETA: splitting (6) gives:
% 159.14/25.51  | 
% 159.14/25.51  | Case 1:
% 159.14/25.51  | | 
% 159.14/25.51  | |   (8)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 159.14/25.51  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.14/25.51  | |          e0) = e1 & $i(all_57_14)
% 159.14/25.51  | | 
% 159.14/25.51  | | ALPHA: (8) implies:
% 159.14/25.51  | |   (9)  op(e0, e1) = e0
% 159.14/25.51  | | 
% 159.14/25.51  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #966.
% 159.14/25.51  | | 
% 159.14/25.51  | Case 2:
% 159.14/25.51  | | 
% 159.14/25.51  | |   (10)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.14/25.51  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 159.14/25.51  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 159.14/25.51  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.14/25.51  | | 
% 159.14/25.51  | | REF_CLOSE: (1), (3), (4), (7), (10) are inconsistent by sub-proof #704.
% 159.14/25.51  | | 
% 159.14/25.51  | End of split
% 159.14/25.51  | 
% 159.14/25.51  End of proof
% 159.14/25.51  
% 159.14/25.51  Sub-proof #378 shows that the following formulas are inconsistent:
% 159.14/25.51  ----------------------------------------------------------------
% 159.14/25.51    (1)  op(e0, e0) = e1
% 159.14/25.51    (2)   ~ (all_52_4 = e3)
% 159.14/25.51    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.51    (4)  op(e3, e2) = all_52_4
% 159.14/25.51    (5)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 159.14/25.51           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.14/25.51           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 159.14/25.51           & op(e3, e3) = e3 & op(e3, e2) = e3)
% 159.14/25.51    (6)   ~ (e3 = e1)
% 159.14/25.51  
% 159.14/25.51  Begin of proof
% 159.14/25.51  | 
% 159.14/25.51  | BETA: splitting (5) gives:
% 159.14/25.51  | 
% 159.14/25.51  | Case 1:
% 159.14/25.51  | | 
% 159.14/25.51  | |   (7)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 159.14/25.51  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 159.14/25.51  | |          e0) = e3 & $i(all_57_10)
% 159.14/25.51  | | 
% 159.14/25.51  | | ALPHA: (7) implies:
% 159.14/25.51  | |   (8)  op(e0, e0) = e3
% 159.14/25.51  | | 
% 159.14/25.51  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #473.
% 159.14/25.51  | | 
% 159.14/25.51  | Case 2:
% 159.14/25.51  | | 
% 159.14/25.51  | |   (9)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 159.14/25.51  | |        op(e3, e2) = e3
% 159.14/25.51  | | 
% 159.14/25.51  | | ALPHA: (9) implies:
% 159.14/25.51  | |   (10)  op(e3, e2) = e3
% 159.14/25.51  | | 
% 159.14/25.51  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #998.
% 159.14/25.51  | | 
% 159.14/25.51  | End of split
% 159.14/25.51  | 
% 159.14/25.51  End of proof
% 159.14/25.51  
% 159.14/25.51  Sub-proof #379 shows that the following formulas are inconsistent:
% 159.14/25.51  ----------------------------------------------------------------
% 159.14/25.51    (1)   ~ (all_52_1 = e2)
% 159.14/25.51    (2)  op(e1, e1) = e0
% 159.14/25.51    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.51    (4)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.14/25.51           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.14/25.51           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 159.14/25.51           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.14/25.51           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.14/25.51           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 159.14/25.51           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.14/25.51           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 159.14/25.51           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 159.14/25.51             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.14/25.51           all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 159.14/25.51           & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.14/25.51           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 159.14/25.51           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 159.14/25.51             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.14/25.51           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 159.14/25.51         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.14/25.51           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.14/25.51           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 159.14/25.51           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 159.14/25.51           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.14/25.51    (5)  op(e2, e3) = all_52_1
% 159.14/25.51    (6)  op(e2, e1) = all_52_9
% 159.14/25.51    (7)   ~ (all_52_9 = e2)
% 159.14/25.51    (8)   ~ (e3 = e0)
% 159.14/25.51  
% 159.14/25.51  Begin of proof
% 159.14/25.51  | 
% 159.14/25.51  | BETA: splitting (4) gives:
% 159.14/25.51  | 
% 159.14/25.51  | Case 1:
% 159.14/25.51  | | 
% 159.14/25.51  | |   (9)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 159.14/25.51  | |          & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 159.14/25.51  | |          = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.14/25.51  | |          all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.14/25.51  | |          op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.14/25.51  | |          $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 159.14/25.51  | |          ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.14/25.51  | |          op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 159.14/25.51  | |          & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.14/25.51  | |          = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.14/25.51  | |          $i(all_57_10))
% 159.14/25.51  | | 
% 159.14/25.51  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1005.
% 159.14/25.51  | | 
% 159.14/25.51  | Case 2:
% 159.14/25.51  | | 
% 159.14/25.51  | |   (10)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.14/25.51  | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0
% 159.14/25.51  | |           & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 =
% 159.14/25.51  | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 159.14/25.51  | |           & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.14/25.51  | |           $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.14/25.51  | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 159.14/25.51  | |           e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 159.14/25.51  | |           & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.14/25.51  | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &
% 159.14/25.51  | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2,
% 159.14/25.51  | |             e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.14/25.51  | | 
% 159.14/25.51  | | BETA: splitting (10) gives:
% 159.14/25.51  | | 
% 159.14/25.51  | | Case 1:
% 159.14/25.51  | | | 
% 159.14/25.51  | | |   (11)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.14/25.51  | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) =
% 159.14/25.51  | | |           e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.14/25.51  | | |           all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 159.14/25.51  | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 159.14/25.51  | | |             e2) = e3 & $i(all_57_10))
% 159.14/25.51  | | | 
% 159.14/25.51  | | | REF_CLOSE: (1), (3), (5), (11) are inconsistent by sub-proof #1004.
% 159.14/25.51  | | | 
% 159.14/25.51  | | Case 2:
% 159.14/25.51  | | | 
% 159.14/25.51  | | |   (12)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.14/25.51  | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 =
% 159.14/25.51  | | |           e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 159.14/25.51  | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.14/25.51  | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 =
% 159.14/25.51  | | |             e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.14/25.51  | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.14/25.51  | | | 
% 159.14/25.51  | | | BETA: splitting (12) gives:
% 159.14/25.51  | | | 
% 159.14/25.51  | | | Case 1:
% 159.14/25.51  | | | | 
% 159.14/25.51  | | | |   (13)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 159.14/25.51  | | | |         & op(e2, e2) = e2
% 159.14/25.51  | | | | 
% 159.14/25.51  | | | | ALPHA: (13) implies:
% 159.14/25.51  | | | |   (14)  op(e2, e3) = e2
% 159.14/25.51  | | | | 
% 159.14/25.51  | | | | REF_CLOSE: (1), (3), (5), (14) are inconsistent by sub-proof #1007.
% 159.14/25.51  | | | | 
% 159.14/25.51  | | | Case 2:
% 159.14/25.51  | | | | 
% 159.14/25.51  | | | |   (15)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 159.14/25.51  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.14/25.51  | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 159.14/25.51  | | | |           & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.14/25.51  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.14/25.51  | | | |           op(e2, e1) = e2 & $i(all_57_12))
% 159.14/25.51  | | | | 
% 159.14/25.51  | | | | REF_CLOSE: (2), (3), (6), (7), (8), (15) are inconsistent by sub-proof
% 159.14/25.51  | | | |            #708.
% 159.14/25.51  | | | | 
% 159.14/25.51  | | | End of split
% 159.14/25.51  | | | 
% 159.14/25.51  | | End of split
% 159.14/25.51  | | 
% 159.14/25.51  | End of split
% 159.14/25.51  | 
% 159.14/25.51  End of proof
% 159.14/25.51  
% 159.14/25.51  Sub-proof #380 shows that the following formulas are inconsistent:
% 159.14/25.51  ----------------------------------------------------------------
% 159.14/25.51    (1)  all_54_5 = all_4_2
% 159.14/25.51    (2)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.14/25.51    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.51    (4)   ~ (all_4_2 = e3)
% 159.14/25.51    (5)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.14/25.51           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.14/25.51           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 159.14/25.51           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.14/25.51           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.14/25.51    (6)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 159.14/25.51    (7)  op(e2, e2) = e2
% 159.14/25.51    (8)  op(e2, e2) = all_4_2
% 159.14/25.51    (9)  op(e2, e3) = all_52_1
% 159.14/25.51    (10)   ~ (all_4_2 = e1)
% 159.14/25.51    (11)  all_54_4 = all_52_1
% 159.14/25.51    (12)   ~ (all_52_1 = all_4_2)
% 159.14/25.51  
% 159.14/25.51  Begin of proof
% 159.14/25.51  | 
% 159.14/25.51  | BETA: splitting (5) gives:
% 159.14/25.51  | 
% 159.14/25.51  | Case 1:
% 159.14/25.51  | | 
% 159.14/25.51  | |   (13)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 159.14/25.51  | |         & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 159.14/25.51  | |         op(e0, e0) = e2 & $i(all_57_12)
% 159.14/25.51  | | 
% 159.14/25.51  | | ALPHA: (13) implies:
% 159.14/25.51  | |   (14)  op(e2, e3) = e2
% 159.14/25.51  | | 
% 159.14/25.51  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14)
% 159.14/25.51  | |            are inconsistent by sub-proof #926.
% 159.14/25.51  | | 
% 159.14/25.51  | Case 2:
% 159.14/25.51  | | 
% 159.14/25.51  | |   (15)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 159.14/25.51  | |         & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 159.14/25.51  | |         op(e2, e2) = e3 & $i(all_57_10)
% 159.14/25.51  | | 
% 159.14/25.51  | | ALPHA: (15) implies:
% 159.14/25.51  | |   (16)  op(e2, e3) = e2
% 159.14/25.51  | | 
% 159.14/25.51  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (16)
% 159.14/25.51  | |            are inconsistent by sub-proof #926.
% 159.14/25.51  | | 
% 159.14/25.51  | End of split
% 159.14/25.51  | 
% 159.14/25.51  End of proof
% 159.14/25.51  
% 159.14/25.51  Sub-proof #381 shows that the following formulas are inconsistent:
% 159.14/25.51  ----------------------------------------------------------------
% 159.14/25.51    (1)  all_54_5 = all_4_2
% 159.14/25.51    (2)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.14/25.51    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.51    (4)   ~ (all_4_2 = e3)
% 159.14/25.51    (5)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 159.14/25.51    (6)  op(e2, e2) = e2
% 159.14/25.51    (7)  op(e2, e2) = all_4_2
% 159.14/25.51    (8)  op(e2, e3) = all_52_1
% 159.14/25.51    (9)   ~ (all_4_2 = e1)
% 159.14/25.51    (10)  all_54_4 = all_52_1
% 159.14/25.51    (11)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.14/25.51            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.14/25.51            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.14/25.51            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.51              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.14/25.51          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.14/25.51            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.14/25.51              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.14/25.51            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.14/25.51              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.14/25.51    (12)   ~ (all_52_1 = all_4_2)
% 159.14/25.51  
% 159.14/25.51  Begin of proof
% 159.14/25.51  | 
% 159.14/25.51  | BETA: splitting (11) gives:
% 159.14/25.51  | 
% 159.14/25.51  | Case 1:
% 159.14/25.51  | | 
% 159.14/25.51  | |   (13)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 =
% 159.14/25.51  | |             e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.14/25.51  | |           op(e2, e2) = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.14/25.51  | |           all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 159.14/25.51  | |           = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3
% 159.14/25.51  | |           & $i(all_57_10))
% 159.14/25.51  | | 
% 159.14/25.51  | | BETA: splitting (13) gives:
% 159.14/25.51  | | 
% 159.14/25.51  | | Case 1:
% 159.14/25.51  | | | 
% 159.14/25.51  | | |   (14)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 =
% 159.14/25.51  | | |           e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.14/25.51  | | |         op(e2, e2) = all_57_12 & $i(all_57_12)
% 159.14/25.51  | | | 
% 159.14/25.51  | | | ALPHA: (14) implies:
% 159.14/25.51  | | |   (15)  op(e2, e3) = e2
% 159.14/25.51  | | | 
% 159.14/25.51  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (15)
% 159.14/25.51  | | |            are inconsistent by sub-proof #926.
% 159.14/25.51  | | | 
% 159.14/25.51  | | Case 2:
% 159.14/25.51  | | | 
% 159.14/25.51  | | |   (16)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.14/25.51  | | |           e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2
% 159.14/25.51  | | |         & op(e2, e2) = e3 & $i(all_57_10)
% 159.14/25.51  | | | 
% 159.14/25.51  | | | ALPHA: (16) implies:
% 159.14/25.51  | | |   (17)  op(e2, e3) = e2
% 159.14/25.51  | | | 
% 159.14/25.51  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (17)
% 159.14/25.51  | | |            are inconsistent by sub-proof #926.
% 159.14/25.51  | | | 
% 159.14/25.51  | | End of split
% 159.14/25.51  | | 
% 159.14/25.51  | Case 2:
% 159.14/25.51  | | 
% 159.14/25.51  | |   (18)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.14/25.51  | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 159.14/25.51  | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 =
% 159.14/25.51  | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 159.14/25.51  | |           & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.14/25.51  | |           $i(all_57_10))
% 159.14/25.51  | | 
% 159.14/25.51  | | BETA: splitting (18) gives:
% 159.14/25.51  | | 
% 159.14/25.51  | | Case 1:
% 159.14/25.51  | | | 
% 159.14/25.51  | | |   (19)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.14/25.51  | | |           e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 159.14/25.51  | | |         & op(e1, e1) = e2 & $i(all_57_12)
% 159.14/25.51  | | | 
% 159.14/25.51  | | | ALPHA: (19) implies:
% 159.14/25.51  | | |   (20)  op(e2, e3) = e2
% 159.14/25.51  | | | 
% 159.14/25.51  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (20)
% 159.14/25.51  | | |            are inconsistent by sub-proof #926.
% 159.14/25.51  | | | 
% 159.14/25.51  | | Case 2:
% 159.14/25.51  | | | 
% 159.14/25.52  | | |   (21)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.14/25.52  | | |           e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2
% 159.14/25.52  | | |         & op(e2, e2) = e3 & $i(all_57_10)
% 159.14/25.52  | | | 
% 159.14/25.52  | | | ALPHA: (21) implies:
% 159.14/25.52  | | |   (22)  op(e2, e3) = e2
% 159.14/25.52  | | | 
% 159.14/25.52  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (22)
% 159.14/25.52  | | |            are inconsistent by sub-proof #926.
% 159.14/25.52  | | | 
% 159.14/25.52  | | End of split
% 159.14/25.52  | | 
% 159.14/25.52  | End of split
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #382 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)  all_54_7 = all_52_13
% 159.14/25.52    (2)  all_54_7 = e2
% 159.14/25.52    (3)   ~ (all_52_13 = e2)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | COMBINE_EQS: (1), (2) imply:
% 159.14/25.52  |   (4)  all_52_13 = e2
% 159.14/25.52  | 
% 159.14/25.52  | SIMP: (4) implies:
% 159.14/25.52  |   (5)  all_52_13 = e2
% 159.14/25.52  | 
% 159.14/25.52  | REDUCE: (3), (5) imply:
% 159.14/25.52  |   (6)  $false
% 159.14/25.52  | 
% 159.14/25.52  | CLOSE: (6) is inconsistent.
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #383 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)  all_54_7 = all_52_13
% 159.14/25.52    (2)  all_54_7 = e3
% 159.14/25.52    (3)   ~ (all_52_13 = e3)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | COMBINE_EQS: (1), (2) imply:
% 159.14/25.52  |   (4)  all_52_13 = e3
% 159.14/25.52  | 
% 159.14/25.52  | SIMP: (4) implies:
% 159.14/25.52  |   (5)  all_52_13 = e3
% 159.14/25.52  | 
% 159.14/25.52  | REDUCE: (3), (5) imply:
% 159.14/25.52  |   (6)  $false
% 159.14/25.52  | 
% 159.14/25.52  | CLOSE: (6) is inconsistent.
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #384 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)   ~ (all_52_12 = e2)
% 159.14/25.52    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.52    (3)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.14/25.52    (4)  op(e2, e0) = all_52_13
% 159.14/25.52    (5)  op(e3, e0) = all_52_12
% 159.14/25.52    (6)   ~ (all_52_13 = e2)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | BETA: splitting (3) gives:
% 159.14/25.52  | 
% 159.14/25.52  | Case 1:
% 159.14/25.52  | | 
% 159.14/25.52  | |   (7)  all_56_9 = e2 & op(e3, e0) = e2
% 159.14/25.52  | | 
% 159.14/25.52  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #880.
% 159.14/25.52  | | 
% 159.14/25.52  | Case 2:
% 159.14/25.52  | | 
% 159.14/25.52  | |   (8)  all_56_10 = e2 & op(e2, e0) = e2
% 159.14/25.52  | | 
% 159.14/25.52  | | ALPHA: (8) implies:
% 159.14/25.52  | |   (9)  op(e2, e0) = e2
% 159.14/25.52  | | 
% 159.14/25.52  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #996.
% 159.14/25.52  | | 
% 159.14/25.52  | End of split
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #385 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)  all_54_13 = all_52_7
% 159.14/25.52    (2)  all_54_13 = e3
% 159.14/25.52    (3)   ~ (all_52_7 = e3)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | COMBINE_EQS: (1), (2) imply:
% 159.14/25.52  |   (4)  all_52_7 = e3
% 159.14/25.52  | 
% 159.14/25.52  | SIMP: (4) implies:
% 159.14/25.52  |   (5)  all_52_7 = e3
% 159.14/25.52  | 
% 159.14/25.52  | REDUCE: (3), (5) imply:
% 159.14/25.52  |   (6)  $false
% 159.14/25.52  | 
% 159.14/25.52  | CLOSE: (6) is inconsistent.
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #386 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)  all_54_14 = all_22_0
% 159.14/25.52    (2)  all_54_14 = e2
% 159.14/25.52    (3)   ~ (all_22_0 = e2)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | COMBINE_EQS: (1), (2) imply:
% 159.14/25.52  |   (4)  all_22_0 = e2
% 159.14/25.52  | 
% 159.14/25.52  | SIMP: (4) implies:
% 159.14/25.52  |   (5)  all_22_0 = e2
% 159.14/25.52  | 
% 159.14/25.52  | REDUCE: (3), (5) imply:
% 159.14/25.52  |   (6)  $false
% 159.14/25.52  | 
% 159.14/25.52  | CLOSE: (6) is inconsistent.
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #387 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)  all_54_14 = all_22_0
% 159.14/25.52    (2)  all_54_14 = e3
% 159.14/25.52    (3)   ~ (all_22_0 = e3)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | COMBINE_EQS: (1), (2) imply:
% 159.14/25.52  |   (4)  all_22_0 = e3
% 159.14/25.52  | 
% 159.14/25.52  | SIMP: (4) implies:
% 159.14/25.52  |   (5)  all_22_0 = e3
% 159.14/25.52  | 
% 159.14/25.52  | REDUCE: (3), (5) imply:
% 159.14/25.52  |   (6)  $false
% 159.14/25.52  | 
% 159.14/25.52  | CLOSE: (6) is inconsistent.
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #388 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)  all_56_7 = e3 & op(e1, e2) = e3
% 159.14/25.52    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.52    (3)  op(e1, e2) = all_52_6
% 159.14/25.52    (4)   ~ (all_52_6 = e3)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | ALPHA: (1) implies:
% 159.14/25.52  |   (5)  op(e1, e2) = e3
% 159.14/25.52  | 
% 159.14/25.52  | GROUND_INST: instantiating (2) with all_52_6, e3, e2, e1, simplifying with
% 159.14/25.52  |              (3), (5) gives:
% 159.14/25.52  |   (6)  all_52_6 = e3
% 159.14/25.52  | 
% 159.14/25.52  | REDUCE: (4), (6) imply:
% 159.14/25.52  |   (7)  $false
% 159.14/25.52  | 
% 159.14/25.52  | CLOSE: (7) is inconsistent.
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #389 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)  op(e1, e1) = e3
% 159.14/25.52    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.52    (3)  op(e0, e0) = e3
% 159.14/25.52    (4)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.14/25.52             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.14/25.52           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.14/25.52               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.14/25.52             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.14/25.52         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.14/25.52             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.14/25.52           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.14/25.52               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.14/25.52             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.14/25.52    (5)   ~ (e3 = e1)
% 159.14/25.52    (6)   ~ (e3 = e0)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | BETA: splitting (4) gives:
% 159.14/25.52  | 
% 159.14/25.52  | Case 1:
% 159.14/25.52  | | 
% 159.14/25.52  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.14/25.52  | |            e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.14/25.52  | |            $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.14/25.52  | |            (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.14/25.52  | |        ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.14/25.52  | |              e1) = all_57_8 & $i(all_57_8)))
% 159.14/25.52  | | 
% 159.14/25.52  | | ALPHA: (7) implies:
% 159.14/25.52  | |   (8)  op(e1, e1) = e1
% 159.14/25.52  | | 
% 159.14/25.52  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1003.
% 159.14/25.52  | | 
% 159.14/25.52  | Case 2:
% 159.14/25.52  | | 
% 159.14/25.52  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 159.14/25.52  | |            e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.14/25.52  | |            $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 159.14/25.52  | |            (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 159.14/25.52  | |        ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 159.14/25.52  | |              e0) = all_57_13 & $i(all_57_13)))
% 159.14/25.52  | | 
% 159.14/25.52  | | ALPHA: (9) implies:
% 159.14/25.52  | |   (10)  op(e0, e0) = e0
% 159.14/25.52  | | 
% 159.14/25.52  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #999.
% 159.14/25.52  | | 
% 159.14/25.52  | End of split
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #390 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)  all_54_0 = all_6_2
% 159.14/25.52    (2)  all_54_0 = e3
% 159.14/25.52    (3)   ~ (all_6_2 = e3)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | COMBINE_EQS: (1), (2) imply:
% 159.14/25.52  |   (4)  all_6_2 = e3
% 159.14/25.52  | 
% 159.14/25.52  | SIMP: (4) implies:
% 159.14/25.52  |   (5)  all_6_2 = e3
% 159.14/25.52  | 
% 159.14/25.52  | REDUCE: (3), (5) imply:
% 159.14/25.52  |   (6)  $false
% 159.14/25.52  | 
% 159.14/25.52  | CLOSE: (6) is inconsistent.
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #391 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.52    (2)  op(e0, e0) = e3
% 159.14/25.52    (3)  op(e1, e0) = all_52_14
% 159.14/25.52    (4)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.14/25.52    (5)   ~ (all_52_14 = e1)
% 159.14/25.52    (6)   ~ (e3 = e1)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | BETA: splitting (4) gives:
% 159.14/25.52  | 
% 159.14/25.52  | Case 1:
% 159.14/25.52  | | 
% 159.14/25.52  | |   (7)  all_56_11 = e1 & op(e1, e0) = e1
% 159.14/25.52  | | 
% 159.14/25.52  | | ALPHA: (7) implies:
% 159.14/25.52  | |   (8)  op(e1, e0) = e1
% 159.14/25.52  | | 
% 159.14/25.52  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #974.
% 159.14/25.52  | | 
% 159.14/25.52  | Case 2:
% 159.14/25.52  | | 
% 159.14/25.52  | |   (9)  all_56_15 = e1 & op(e0, e0) = e1
% 159.14/25.52  | | 
% 159.14/25.52  | | ALPHA: (9) implies:
% 159.14/25.52  | |   (10)  op(e0, e0) = e1
% 159.14/25.52  | | 
% 159.14/25.52  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #473.
% 159.14/25.52  | | 
% 159.14/25.52  | End of split
% 159.14/25.52  | 
% 159.14/25.52  End of proof
% 159.14/25.52  
% 159.14/25.52  Sub-proof #392 shows that the following formulas are inconsistent:
% 159.14/25.52  ----------------------------------------------------------------
% 159.14/25.52    (1)   ~ (all_6_2 = e0)
% 159.14/25.52    (2)   ~ (all_52_2 = all_6_2)
% 159.14/25.52    (3)   ~ (all_52_14 = e3)
% 159.14/25.52    (4)  op(e1, e1) = e0
% 159.14/25.52    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.14/25.52             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.14/25.52           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.14/25.52               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.14/25.52             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.14/25.52         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.14/25.52             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.14/25.52           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.14/25.52               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.14/25.52             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.14/25.52         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.14/25.52             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.14/25.52           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.14/25.52               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.14/25.52             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.14/25.52         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.14/25.52             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.14/25.52           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.14/25.52               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.14/25.52             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.14/25.52    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.52    (7)  op(e1, e3) = all_52_2
% 159.14/25.52    (8)  op(e0, e0) = e3
% 159.14/25.52    (9)  op(e1, e2) = all_52_6
% 159.14/25.52    (10)  ( ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 & $i(all_24_0)) | ( ~
% 159.14/25.52            (all_24_1 = e0) & op(e1, e1) = all_24_1 & $i(all_24_1))
% 159.14/25.52    (11)  op(e1, e0) = all_52_14
% 159.14/25.52    (12)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 159.14/25.52          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 159.14/25.52    (13)  op(e2, e2) = e1
% 159.14/25.52    (14)   ~ (e1 = e0)
% 159.14/25.52    (15)   ~ (e2 = e1)
% 159.14/25.52    (16)  op(e3, e3) = all_6_2
% 159.14/25.52    (17)   ~ (e3 = e0)
% 159.14/25.52  
% 159.14/25.52  Begin of proof
% 159.14/25.52  | 
% 159.14/25.52  | BETA: splitting (5) gives:
% 159.14/25.52  | 
% 159.14/25.52  | Case 1:
% 159.14/25.52  | | 
% 159.14/25.52  | |   (18)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.14/25.52  | |               e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.14/25.52  | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.14/25.52  | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.14/25.52  | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.14/25.52  | |                 e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 159.14/25.52  | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 159.14/25.52  | |                 e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 159.14/25.52  | |               e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 159.14/25.52  | |               all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 159.14/25.52  | |               e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 159.14/25.52  | |               $i(all_57_7))))
% 159.14/25.52  | | 
% 159.14/25.52  | | BETA: splitting (18) gives:
% 159.14/25.52  | | 
% 159.14/25.52  | | Case 1:
% 159.14/25.52  | | | 
% 159.14/25.52  | | |   (19)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.14/25.52  | | |             e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.14/25.52  | | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.14/25.52  | | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.14/25.52  | | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.14/25.52  | | |               e3) = all_57_6 & $i(all_57_6)))
% 159.14/25.52  | | | 
% 159.14/25.52  | | | ALPHA: (19) implies:
% 159.14/25.52  | | |   (20)  op(e3, e3) = e3
% 159.14/25.52  | | |   (21)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1,
% 159.14/25.52  | | |             e3) = all_57_2 & $i(all_57_2))
% 159.14/25.52  | | | 
% 159.14/25.52  | | | BETA: splitting (21) gives:
% 159.14/25.52  | | | 
% 159.14/25.52  | | | Case 1:
% 159.14/25.52  | | | | 
% 159.14/25.52  | | | |   (22)  all_57_14 = e3 & op(e1, e1) = e3
% 159.14/25.52  | | | | 
% 159.14/25.52  | | | | ALPHA: (22) implies:
% 159.14/25.52  | | | |   (23)  op(e1, e1) = e3
% 159.14/25.52  | | | | 
% 159.14/25.52  | | | | REF_CLOSE: (4), (6), (17), (23) are inconsistent by sub-proof #912.
% 159.14/25.52  | | | | 
% 159.14/25.52  | | | Case 2:
% 159.14/25.52  | | | | 
% 159.14/25.52  | | | |   (24)   ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)
% 159.14/25.52  | | | | 
% 159.14/25.52  | | | | ALPHA: (24) implies:
% 159.14/25.52  | | | |   (25)  op(e1, e3) = all_57_2
% 159.14/25.52  | | | | 
% 159.14/25.52  | | | | BETA: splitting (10) gives:
% 159.14/25.52  | | | | 
% 159.14/25.52  | | | | Case 1:
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | |   (26)   ~ (all_24_0 = e3) & op(e1, e2) = all_24_0 & $i(all_24_0)
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | | ALPHA: (26) implies:
% 159.14/25.52  | | | | |   (27)   ~ (all_24_0 = e3)
% 159.14/25.52  | | | | |   (28)  op(e1, e2) = all_24_0
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | | GROUND_INST: instantiating (6) with all_52_6, all_24_0, e2, e1,
% 159.14/25.52  | | | | |              simplifying with (9), (28) gives:
% 159.14/25.52  | | | | |   (29)  all_52_6 = all_24_0
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | | GROUND_INST: instantiating (6) with all_52_2, all_57_2, e3, e1,
% 159.14/25.52  | | | | |              simplifying with (7), (25) gives:
% 159.14/25.52  | | | | |   (30)  all_57_2 = all_52_2
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | | GROUND_INST: instantiating (6) with all_6_2, e3, e3, e3, simplifying
% 159.14/25.52  | | | | |              with (16), (20) gives:
% 159.14/25.52  | | | | |   (31)  all_6_2 = e3
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | | REDUCE: (2), (31) imply:
% 159.14/25.52  | | | | |   (32)   ~ (all_52_2 = e3)
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | | BETA: splitting (12) gives:
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | | Case 1:
% 159.14/25.52  | | | | | | 
% 159.14/25.52  | | | | | |   (33)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1,
% 159.14/25.52  | | | | | |             e2) = e3)
% 159.14/25.52  | | | | | | 
% 159.14/25.52  | | | | | | BETA: splitting (33) gives:
% 159.14/25.52  | | | | | | 
% 159.14/25.52  | | | | | | Case 1:
% 159.14/25.52  | | | | | | | 
% 159.14/25.52  | | | | | | |   (34)  all_56_6 = e3 & op(e1, e3) = e3
% 159.14/25.52  | | | | | | | 
% 159.14/25.52  | | | | | | | REF_CLOSE: (6), (7), (32), (34) are inconsistent by sub-proof
% 159.14/25.52  | | | | | | |            #681.
% 159.14/25.52  | | | | | | | 
% 159.14/25.52  | | | | | | Case 2:
% 159.14/25.52  | | | | | | | 
% 159.14/25.52  | | | | | | |   (35)  all_56_7 = e3 & op(e1, e2) = e3
% 159.14/25.52  | | | | | | | 
% 159.14/25.52  | | | | | | | ALPHA: (35) implies:
% 159.14/25.52  | | | | | | |   (36)  op(e1, e2) = e3
% 159.14/25.52  | | | | | | | 
% 159.14/25.52  | | | | | | | REF_CLOSE: (6), (27), (28), (36) are inconsistent by sub-proof
% 159.14/25.52  | | | | | | |            #610.
% 159.14/25.52  | | | | | | | 
% 159.14/25.52  | | | | | | End of split
% 159.14/25.52  | | | | | | 
% 159.14/25.52  | | | | | Case 2:
% 159.14/25.52  | | | | | | 
% 159.14/25.52  | | | | | |   (37)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1,
% 159.14/25.52  | | | | | |             e0) = e3)
% 159.14/25.52  | | | | | | 
% 159.14/25.52  | | | | | | REF_CLOSE: (3), (4), (6), (11), (17), (37) are inconsistent by
% 159.14/25.52  | | | | | |            sub-proof #614.
% 159.14/25.52  | | | | | | 
% 159.14/25.52  | | | | | End of split
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | Case 2:
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | |   (38)   ~ (all_24_1 = e0) & op(e1, e1) = all_24_1 & $i(all_24_1)
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | | REF_CLOSE: (4), (6), (38) are inconsistent by sub-proof #477.
% 159.14/25.52  | | | | | 
% 159.14/25.52  | | | | End of split
% 159.14/25.52  | | | | 
% 159.14/25.53  | | | End of split
% 159.14/25.53  | | | 
% 159.14/25.53  | | Case 2:
% 159.14/25.53  | | | 
% 159.14/25.53  | | |   (39)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 159.14/25.53  | | |             e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 159.14/25.53  | | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 159.14/25.53  | | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 159.14/25.53  | | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 159.14/25.53  | | |               e2) = all_57_7 & $i(all_57_7)))
% 159.14/25.53  | | | 
% 159.14/25.53  | | | ALPHA: (39) implies:
% 159.14/25.53  | | |   (40)  op(e2, e2) = e2
% 159.14/25.53  | | | 
% 159.14/25.53  | | | REF_CLOSE: (6), (13), (15), (40) are inconsistent by sub-proof #993.
% 159.14/25.53  | | | 
% 159.14/25.53  | | End of split
% 159.14/25.53  | | 
% 159.14/25.53  | Case 2:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (41)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.14/25.53  | |               e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.14/25.53  | |               $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.14/25.53  | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.14/25.53  | |           ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.14/25.53  | |                 e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 159.14/25.53  | |             e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 159.14/25.53  | |                 e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 =
% 159.14/25.53  | |               e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 159.14/25.53  | |               all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 159.14/25.53  | |               e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.14/25.53  | |               $i(all_57_13))))
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (4), (6), (8), (14), (17), (41) are inconsistent by sub-proof
% 159.14/25.53  | |            #411.
% 159.14/25.53  | | 
% 159.14/25.53  | End of split
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #393 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (2)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.14/25.53           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 159.14/25.53           = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3
% 159.14/25.53           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.14/25.53           op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 159.14/25.53    (3)  op(e1, e0) = all_52_14
% 159.14/25.53    (4)  op(e0, e3) = e1
% 159.14/25.53    (5)   ~ (e1 = e0)
% 159.14/25.53    (6)   ~ (all_52_14 = e1)
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | BETA: splitting (2) gives:
% 159.14/25.53  | 
% 159.14/25.53  | Case 1:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (7)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 159.14/25.53  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.14/25.53  | |          e0) = e1 & $i(all_57_14)
% 159.14/25.53  | | 
% 159.14/25.53  | | ALPHA: (7) implies:
% 159.14/25.53  | |   (8)  op(e1, e0) = e1
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #974.
% 159.14/25.53  | | 
% 159.14/25.53  | Case 2:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0)
% 159.14/25.53  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 159.14/25.53  | |          e0) = e3 & $i(all_57_10)
% 159.14/25.53  | | 
% 159.14/25.53  | | ALPHA: (9) implies:
% 159.14/25.53  | |   (10)  op(e0, e3) = e0
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #786.
% 159.14/25.53  | | 
% 159.14/25.53  | End of split
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #394 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)   ~ (e3 = e2)
% 159.14/25.53    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (3)  op(e0, e0) = e3
% 159.14/25.53    (4)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.14/25.53           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.14/25.53           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 159.14/25.53           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.14/25.53    (5)  op(e2, e2) = e1
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | BETA: splitting (4) gives:
% 159.14/25.53  | 
% 159.14/25.53  | Case 1:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (6)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 159.14/25.53  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 159.14/25.53  | |          e0) = e2 & $i(all_57_12)
% 159.14/25.53  | | 
% 159.14/25.53  | | ALPHA: (6) implies:
% 159.14/25.53  | |   (7)  op(e0, e0) = e2
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #878.
% 159.14/25.53  | | 
% 159.14/25.53  | Case 2:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (8)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 159.14/25.53  | |        op(e2, e1) = e2
% 159.14/25.53  | | 
% 159.14/25.53  | | ALPHA: (8) implies:
% 159.14/25.53  | |   (9)   ~ (e2 = e1)
% 159.14/25.53  | |   (10)  op(e2, e2) = e2
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (2), (5), (9), (10) are inconsistent by sub-proof #993.
% 159.14/25.53  | | 
% 159.14/25.53  | End of split
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #395 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (2)  op(e3, e0) = all_18_0
% 159.14/25.53    (3)  op(e3, e0) = e1
% 159.14/25.53    (4)   ~ (all_18_0 = e1)
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | GROUND_INST: instantiating (1) with e1, all_18_0, e0, e3, simplifying with
% 159.14/25.53  |              (2), (3) gives:
% 159.14/25.53  |   (5)  all_18_0 = e1
% 159.14/25.53  | 
% 159.14/25.53  | REDUCE: (4), (5) imply:
% 159.14/25.53  |   (6)  $false
% 159.14/25.53  | 
% 159.14/25.53  | CLOSE: (6) is inconsistent.
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #396 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)   ~ (all_48_1 = e1) & op(e3, e3) = all_48_1 & $i(all_48_1)
% 159.14/25.53    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (3)  op(e3, e3) = e1
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | ALPHA: (1) implies:
% 159.14/25.53  |   (4)   ~ (all_48_1 = e1)
% 159.14/25.53  |   (5)  op(e3, e3) = all_48_1
% 159.14/25.53  | 
% 159.14/25.53  | GROUND_INST: instantiating (2) with e1, all_48_1, e3, e3, simplifying with
% 159.14/25.53  |              (3), (5) gives:
% 159.14/25.53  |   (6)  all_48_1 = e1
% 159.14/25.53  | 
% 159.14/25.53  | REDUCE: (4), (6) imply:
% 159.14/25.53  |   (7)  $false
% 159.14/25.53  | 
% 159.14/25.53  | CLOSE: (7) is inconsistent.
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #397 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (2)  op(e1, e0) = e2
% 159.14/25.53    (3)  op(e1, e0) = e0
% 159.14/25.53    (4)   ~ (e2 = e0)
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | GROUND_INST: instantiating (1) with e0, e2, e0, e1, simplifying with (2), (3)
% 159.14/25.53  |              gives:
% 159.14/25.53  |   (5)  e2 = e0
% 159.14/25.53  | 
% 159.14/25.53  | REDUCE: (4), (5) imply:
% 159.14/25.53  |   (6)  $false
% 159.14/25.53  | 
% 159.14/25.53  | CLOSE: (6) is inconsistent.
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #398 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)  all_56_12 = e3 & op(e0, e3) = e3
% 159.14/25.53    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (3)  op(e0, e3) = all_52_3
% 159.14/25.53    (4)   ~ (all_52_3 = e3)
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | ALPHA: (1) implies:
% 159.14/25.53  |   (5)  op(e0, e3) = e3
% 159.14/25.53  | 
% 159.14/25.53  | GROUND_INST: instantiating (2) with all_52_3, e3, e3, e0, simplifying with
% 159.14/25.53  |              (3), (5) gives:
% 159.14/25.53  |   (6)  all_52_3 = e3
% 159.14/25.53  | 
% 159.14/25.53  | REDUCE: (4), (6) imply:
% 159.14/25.53  |   (7)  $false
% 159.14/25.53  | 
% 159.14/25.53  | CLOSE: (7) is inconsistent.
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #399 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)  all_56_5 = e2
% 159.14/25.53    (2)  all_56_2 = e3
% 159.14/25.53    (3)   ~ (e3 = e2)
% 159.14/25.53    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (5)  op(e2, e2) = e0
% 159.14/25.53    (6)  all_56_10 = e1
% 159.14/25.53    (7)   ~ (e2 = e1)
% 159.14/25.53    (8)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.14/25.53         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.14/25.53    (9)   ~ (e2 = e0)
% 159.14/25.53    (10)  e2 = e0
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | COMBINE_EQS: (1), (10) imply:
% 159.14/25.53  |   (11)  all_56_5 = e0
% 159.14/25.53  | 
% 159.14/25.53  | BETA: splitting (8) gives:
% 159.14/25.53  | 
% 159.14/25.53  | Case 1:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (12)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 159.14/25.53  | |           e2)
% 159.14/25.53  | | 
% 159.14/25.53  | | BETA: splitting (12) gives:
% 159.14/25.53  | | 
% 159.14/25.53  | | Case 1:
% 159.14/25.53  | | | 
% 159.14/25.53  | | |   (13)  all_56_2 = e2 & op(e2, e3) = e2
% 159.14/25.53  | | | 
% 159.14/25.53  | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #778.
% 159.14/25.53  | | | 
% 159.14/25.53  | | Case 2:
% 159.14/25.53  | | | 
% 159.14/25.53  | | |   (14)  all_56_3 = e2 & op(e2, e2) = e2
% 159.14/25.53  | | | 
% 159.14/25.53  | | | ALPHA: (14) implies:
% 159.14/25.53  | | |   (15)  op(e2, e2) = e2
% 159.14/25.53  | | | 
% 159.14/25.53  | | | REF_CLOSE: (4), (5), (9), (15) are inconsistent by sub-proof #942.
% 159.14/25.53  | | | 
% 159.14/25.53  | | End of split
% 159.14/25.53  | | 
% 159.14/25.53  | Case 2:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (16)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 159.14/25.53  | |           e2)
% 159.14/25.53  | | 
% 159.14/25.53  | | BETA: splitting (16) gives:
% 159.14/25.53  | | 
% 159.14/25.53  | | Case 1:
% 159.14/25.53  | | | 
% 159.14/25.53  | | |   (17)  all_56_5 = e2 & op(e2, e1) = e2
% 159.14/25.53  | | | 
% 159.14/25.53  | | | REF_CLOSE: (9), (11), (17) are inconsistent by sub-proof #553.
% 159.14/25.53  | | | 
% 159.14/25.53  | | Case 2:
% 159.14/25.53  | | | 
% 159.14/25.53  | | |   (18)  all_56_10 = e2 & op(e2, e0) = e2
% 159.14/25.53  | | | 
% 159.14/25.53  | | | ALPHA: (18) implies:
% 159.14/25.53  | | |   (19)  all_56_10 = e2
% 159.14/25.53  | | | 
% 159.14/25.53  | | | COMBINE_EQS: (6), (19) imply:
% 159.14/25.53  | | |   (20)  e2 = e1
% 159.14/25.53  | | | 
% 159.14/25.53  | | | REDUCE: (7), (20) imply:
% 159.14/25.53  | | |   (21)  $false
% 159.14/25.53  | | | 
% 159.14/25.53  | | | CLOSE: (21) is inconsistent.
% 159.14/25.53  | | | 
% 159.14/25.53  | | End of split
% 159.14/25.53  | | 
% 159.14/25.53  | End of split
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #400 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)  all_56_2 = e3
% 159.14/25.53    (2)   ~ (e3 = e2)
% 159.14/25.53    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 159.14/25.53    (5)  op(e3, e3) = e1
% 159.14/25.53    (6)   ~ (e2 = e1)
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | BETA: splitting (4) gives:
% 159.14/25.53  | 
% 159.14/25.53  | Case 1:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 159.14/25.53  | | 
% 159.14/25.53  | | ALPHA: (7) implies:
% 159.14/25.53  | |   (8)  op(e3, e3) = e2
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #828.
% 159.14/25.53  | | 
% 159.14/25.53  | Case 2:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 159.14/25.53  | | 
% 159.14/25.53  | | ALPHA: (9) implies:
% 159.14/25.53  | |   (10)  all_56_2 = e2
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #848.
% 159.14/25.53  | | 
% 159.14/25.53  | End of split
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #401 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)  op(e0, e1) = all_52_11
% 159.14/25.53    (2)   ~ (e3 = e2)
% 159.14/25.53    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (4)  op(e3, e1) = all_52_8
% 159.14/25.53    (5)  op(e1, e1) = e1
% 159.14/25.53    (6)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 159.14/25.53         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 159.14/25.53    (7)  all_54_1 = all_52_4
% 159.14/25.53    (8)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.14/25.53    (9)  op(e3, e2) = all_52_4
% 159.14/25.53    (10)  op(e2, e1) = e2
% 159.14/25.53    (11)   ~ (all_52_4 = all_52_8)
% 159.14/25.53    (12)   ~ (e3 = e1)
% 159.14/25.53    (13)   ~ (all_52_11 = e3)
% 159.14/25.53    (14)  op(e3, e2) = e3
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | BETA: splitting (6) gives:
% 159.14/25.53  | 
% 159.14/25.53  | Case 1:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (15)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) =
% 159.14/25.53  | |           e3)
% 159.14/25.53  | | 
% 159.14/25.53  | | BETA: splitting (15) gives:
% 159.14/25.53  | | 
% 159.14/25.53  | | Case 1:
% 159.14/25.53  | | | 
% 159.14/25.53  | | |   (16)  all_56_4 = e3 & op(e3, e1) = e3
% 159.14/25.53  | | | 
% 159.14/25.53  | | | ALPHA: (16) implies:
% 159.14/25.53  | | |   (17)  op(e3, e1) = e3
% 159.14/25.53  | | | 
% 159.14/25.53  | | | REF_CLOSE: (3), (4), (7), (8), (9), (11), (14), (17) are inconsistent by
% 159.14/25.53  | | |            sub-proof #403.
% 159.14/25.53  | | | 
% 159.14/25.53  | | Case 2:
% 159.14/25.53  | | | 
% 159.14/25.53  | | |   (18)  all_56_5 = e3 & op(e2, e1) = e3
% 159.14/25.53  | | | 
% 159.14/25.53  | | | ALPHA: (18) implies:
% 159.14/25.53  | | |   (19)  op(e2, e1) = e3
% 159.14/25.53  | | | 
% 159.14/25.53  | | | REF_CLOSE: (2), (3), (10), (19) are inconsistent by sub-proof #456.
% 159.14/25.53  | | | 
% 159.14/25.53  | | End of split
% 159.14/25.53  | | 
% 159.14/25.53  | Case 2:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (20)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 159.14/25.53  | |           e3)
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (1), (3), (5), (12), (13), (20) are inconsistent by sub-proof
% 159.14/25.53  | |            #402.
% 159.14/25.53  | | 
% 159.14/25.53  | End of split
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #402 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)  op(e0, e1) = all_52_11
% 159.14/25.53    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (3)  op(e1, e1) = e1
% 159.14/25.53    (4)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 159.14/25.53    (5)   ~ (e3 = e1)
% 159.14/25.53    (6)   ~ (all_52_11 = e3)
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | BETA: splitting (4) gives:
% 159.14/25.53  | 
% 159.14/25.53  | Case 1:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (7)  all_56_8 = e3 & op(e1, e1) = e3
% 159.14/25.53  | | 
% 159.14/25.53  | | ALPHA: (7) implies:
% 159.14/25.53  | |   (8)  op(e1, e1) = e3
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1003.
% 159.14/25.53  | | 
% 159.14/25.53  | Case 2:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (9)  all_56_14 = e3 & op(e0, e1) = e3
% 159.14/25.53  | | 
% 159.14/25.53  | | ALPHA: (9) implies:
% 159.14/25.53  | |   (10)  op(e0, e1) = e3
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #720.
% 159.14/25.53  | | 
% 159.14/25.53  | End of split
% 159.14/25.53  | 
% 159.14/25.53  End of proof
% 159.14/25.53  
% 159.14/25.53  Sub-proof #403 shows that the following formulas are inconsistent:
% 159.14/25.53  ----------------------------------------------------------------
% 159.14/25.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.53    (2)  op(e3, e1) = all_52_8
% 159.14/25.53    (3)  all_54_1 = all_52_4
% 159.14/25.53    (4)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.14/25.53    (5)  op(e3, e2) = all_52_4
% 159.14/25.53    (6)  op(e3, e1) = e3
% 159.14/25.53    (7)   ~ (all_52_4 = all_52_8)
% 159.14/25.53    (8)  op(e3, e2) = e3
% 159.14/25.53  
% 159.14/25.53  Begin of proof
% 159.14/25.53  | 
% 159.14/25.53  | BETA: splitting (4) gives:
% 159.14/25.53  | 
% 159.14/25.53  | Case 1:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (9)  all_54_1 = e3
% 159.14/25.53  | | 
% 159.14/25.53  | | COMBINE_EQS: (3), (9) imply:
% 159.14/25.53  | |   (10)  all_52_4 = e3
% 159.14/25.53  | | 
% 159.14/25.53  | | REDUCE: (7), (10) imply:
% 159.14/25.53  | |   (11)   ~ (all_52_8 = e3)
% 159.14/25.53  | | 
% 159.14/25.53  | | SIMP: (11) implies:
% 159.14/25.53  | |   (12)   ~ (all_52_8 = e3)
% 159.14/25.53  | | 
% 159.14/25.53  | | REF_CLOSE: (1), (2), (6), (12) are inconsistent by sub-proof #982.
% 159.14/25.53  | | 
% 159.14/25.53  | Case 2:
% 159.14/25.53  | | 
% 159.14/25.53  | |   (13)   ~ (all_54_1 = e3)
% 159.14/25.53  | | 
% 159.14/25.53  | | REDUCE: (3), (13) imply:
% 159.14/25.54  | |   (14)   ~ (all_52_4 = e3)
% 159.14/25.54  | | 
% 159.14/25.54  | | REF_CLOSE: (1), (5), (8), (14) are inconsistent by sub-proof #998.
% 159.14/25.54  | | 
% 159.14/25.54  | End of split
% 159.14/25.54  | 
% 159.14/25.54  End of proof
% 159.14/25.54  
% 159.14/25.54  Sub-proof #404 shows that the following formulas are inconsistent:
% 159.14/25.54  ----------------------------------------------------------------
% 159.14/25.54    (1)  all_56_9 = e2
% 159.14/25.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.54    (3)   ~ (all_48_0 = e1)
% 159.14/25.54    (4)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.14/25.54             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.14/25.54               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.14/25.54               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.14/25.54    (5)  op(e0, e0) = e3
% 159.14/25.54    (6)  op(e1, e0) = all_52_14
% 159.14/25.54    (7)  all_56_10 = e1
% 159.14/25.54    (8)  all_54_3 = all_48_0
% 159.14/25.54    (9)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.14/25.54    (10)   ~ (all_48_0 = e3)
% 159.14/25.54    (11)   ~ (all_52_14 = all_48_0)
% 159.14/25.54    (12)   ~ (all_48_0 = e2)
% 159.14/25.54  
% 159.14/25.54  Begin of proof
% 159.14/25.54  | 
% 159.14/25.54  | BETA: splitting (9) gives:
% 159.14/25.54  | 
% 159.14/25.54  | Case 1:
% 159.14/25.54  | | 
% 159.14/25.54  | |   (13)  all_54_3 = e2
% 159.14/25.54  | | 
% 159.14/25.54  | | COMBINE_EQS: (8), (13) imply:
% 159.14/25.54  | |   (14)  all_48_0 = e2
% 159.14/25.54  | | 
% 159.14/25.54  | | REDUCE: (12), (14) imply:
% 159.14/25.54  | |   (15)  $false
% 159.14/25.54  | | 
% 159.14/25.54  | | CLOSE: (15) is inconsistent.
% 159.14/25.54  | | 
% 159.14/25.54  | Case 2:
% 159.14/25.54  | | 
% 159.14/25.54  | |   (16)   ~ (all_54_3 = e2)
% 159.14/25.54  | |   (17)  all_54_3 = e1 | all_54_3 = e0
% 159.14/25.54  | | 
% 159.14/25.54  | | BETA: splitting (17) gives:
% 159.14/25.54  | | 
% 159.14/25.54  | | Case 1:
% 159.14/25.54  | | | 
% 159.14/25.54  | | |   (18)  all_54_3 = e1
% 159.14/25.54  | | | 
% 159.14/25.54  | | | COMBINE_EQS: (8), (18) imply:
% 159.14/25.54  | | |   (19)  all_48_0 = e1
% 159.14/25.54  | | | 
% 159.14/25.54  | | | REDUCE: (3), (19) imply:
% 159.14/25.54  | | |   (20)  $false
% 159.14/25.54  | | | 
% 159.14/25.54  | | | CLOSE: (20) is inconsistent.
% 159.14/25.54  | | | 
% 159.14/25.54  | | Case 2:
% 159.14/25.54  | | | 
% 159.14/25.54  | | |   (21)  all_54_3 = e0
% 159.14/25.54  | | | 
% 159.14/25.54  | | | COMBINE_EQS: (8), (21) imply:
% 159.14/25.54  | | |   (22)  all_48_0 = e0
% 159.14/25.54  | | | 
% 159.14/25.54  | | | REDUCE: (11), (22) imply:
% 159.14/25.54  | | |   (23)   ~ (all_52_14 = e0)
% 159.14/25.54  | | | 
% 159.14/25.54  | | | REDUCE: (10), (22) imply:
% 159.14/25.54  | | |   (24)   ~ (e3 = e0)
% 159.14/25.54  | | | 
% 159.14/25.54  | | | SIMP: (24) implies:
% 159.14/25.54  | | |   (25)   ~ (e3 = e0)
% 159.14/25.54  | | | 
% 159.14/25.54  | | | REDUCE: (12), (22) imply:
% 159.14/25.54  | | |   (26)   ~ (e2 = e0)
% 159.14/25.54  | | | 
% 159.14/25.54  | | | SIMP: (26) implies:
% 159.14/25.54  | | |   (27)   ~ (e2 = e0)
% 159.14/25.54  | | | 
% 159.14/25.54  | | | REDUCE: (3), (22) imply:
% 159.14/25.54  | | |   (28)   ~ (e1 = e0)
% 159.14/25.54  | | | 
% 159.14/25.54  | | | SIMP: (28) implies:
% 159.14/25.54  | | |   (29)   ~ (e1 = e0)
% 159.14/25.54  | | | 
% 159.14/25.54  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (23), (25), (27), (29) are
% 159.14/25.54  | | |            inconsistent by sub-proof #405.
% 159.14/25.54  | | | 
% 159.14/25.54  | | End of split
% 159.14/25.54  | | 
% 159.14/25.54  | End of split
% 159.14/25.54  | 
% 159.14/25.54  End of proof
% 159.14/25.54  
% 159.14/25.54  Sub-proof #405 shows that the following formulas are inconsistent:
% 159.14/25.54  ----------------------------------------------------------------
% 159.14/25.54    (1)   ~ (all_52_14 = e0)
% 159.14/25.54    (2)  all_56_9 = e2
% 159.14/25.54    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.54    (4)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.14/25.54             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.14/25.54               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.14/25.54               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.14/25.54    (5)  op(e0, e0) = e3
% 159.14/25.54    (6)  op(e1, e0) = all_52_14
% 159.14/25.54    (7)  all_56_10 = e1
% 159.14/25.54    (8)   ~ (e1 = e0)
% 159.14/25.54    (9)   ~ (e2 = e0)
% 159.14/25.54    (10)   ~ (e3 = e0)
% 159.14/25.54  
% 159.14/25.54  Begin of proof
% 159.14/25.54  | 
% 159.14/25.54  | BETA: splitting (4) gives:
% 159.14/25.54  | 
% 159.14/25.54  | Case 1:
% 159.14/25.54  | | 
% 159.14/25.54  | |   (11)  all_56_15 = e0 & op(e0, e0) = e0
% 159.14/25.54  | | 
% 159.14/25.54  | | ALPHA: (11) implies:
% 159.14/25.54  | |   (12)  op(e0, e0) = e0
% 159.14/25.54  | | 
% 159.14/25.54  | | REF_CLOSE: (3), (5), (10), (12) are inconsistent by sub-proof #999.
% 159.14/25.54  | | 
% 159.14/25.54  | Case 2:
% 159.14/25.54  | | 
% 159.14/25.54  | |   (13)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 159.14/25.54  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 159.14/25.54  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 159.14/25.54  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 159.14/25.54  | | 
% 159.14/25.54  | | ALPHA: (13) implies:
% 159.14/25.54  | |   (14)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 159.14/25.54  | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.14/25.54  | | 
% 159.14/25.54  | | BETA: splitting (14) gives:
% 159.14/25.54  | | 
% 159.14/25.54  | | Case 1:
% 159.14/25.54  | | | 
% 159.14/25.54  | | |   (15)  all_56_9 = e0 & op(e3, e0) = e0
% 159.14/25.54  | | | 
% 159.14/25.54  | | | REF_CLOSE: (2), (9), (15) are inconsistent by sub-proof #950.
% 159.14/25.54  | | | 
% 159.14/25.54  | | Case 2:
% 159.14/25.54  | | | 
% 159.14/25.54  | | |   (16)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 159.14/25.54  | | |           = e0)
% 159.14/25.54  | | | 
% 159.14/25.54  | | | BETA: splitting (16) gives:
% 159.14/25.54  | | | 
% 159.14/25.54  | | | Case 1:
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | |   (17)  all_56_10 = e0 & op(e2, e0) = e0
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | | REF_CLOSE: (7), (8), (17) are inconsistent by sub-proof #844.
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | Case 2:
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | |   (18)  all_56_11 = e0 & op(e1, e0) = e0
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | | REF_CLOSE: (1), (3), (6), (18) are inconsistent by sub-proof #406.
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | End of split
% 159.14/25.54  | | | 
% 159.14/25.54  | | End of split
% 159.14/25.54  | | 
% 159.14/25.54  | End of split
% 159.14/25.54  | 
% 159.14/25.54  End of proof
% 159.14/25.54  
% 159.14/25.54  Sub-proof #406 shows that the following formulas are inconsistent:
% 159.14/25.54  ----------------------------------------------------------------
% 159.14/25.54    (1)  all_56_11 = e0 & op(e1, e0) = e0
% 159.14/25.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.54    (3)  op(e1, e0) = all_52_14
% 159.14/25.54    (4)   ~ (all_52_14 = e0)
% 159.14/25.54  
% 159.14/25.54  Begin of proof
% 159.14/25.54  | 
% 159.14/25.54  | ALPHA: (1) implies:
% 159.14/25.54  |   (5)  op(e1, e0) = e0
% 159.14/25.54  | 
% 159.14/25.54  | GROUND_INST: instantiating (2) with all_52_14, e0, e0, e1, simplifying with
% 159.14/25.54  |              (3), (5) gives:
% 159.14/25.54  |   (6)  all_52_14 = e0
% 159.14/25.54  | 
% 159.14/25.54  | REDUCE: (4), (6) imply:
% 159.14/25.54  |   (7)  $false
% 159.14/25.54  | 
% 159.14/25.54  | CLOSE: (7) is inconsistent.
% 159.14/25.54  | 
% 159.14/25.54  End of proof
% 159.14/25.54  
% 159.14/25.54  Sub-proof #407 shows that the following formulas are inconsistent:
% 159.14/25.54  ----------------------------------------------------------------
% 159.14/25.54    (1)   ~ (all_52_12 = e1)
% 159.14/25.54    (2)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.14/25.54             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.14/25.54           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.14/25.54               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.14/25.54             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.14/25.54         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.14/25.54             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.14/25.54           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.14/25.54               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.14/25.54             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.14/25.54         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.14/25.54             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.14/25.54           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.14/25.54               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.14/25.54             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.14/25.54         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.14/25.54             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.14/25.54           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.14/25.54               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.14/25.54             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.14/25.54    (3)   ~ (all_52_4 = all_52_12)
% 159.14/25.54    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.14/25.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.14/25.54    (5)  op(e0, e3) = all_52_3
% 159.14/25.54    (6)   ~ (all_52_12 = e3)
% 159.14/25.54    (7)   ~ (all_52_4 = e1)
% 159.14/25.54    (8)  op(e0, e0) = e3
% 159.14/25.54    (9)  all_54_3 = all_52_12
% 159.14/25.54    (10)  all_54_1 = all_52_4
% 159.14/25.54    (11)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.14/25.54    (12)  op(e1, e0) = all_52_14
% 159.14/25.54    (13)  op(e0, e0) = all_57_15
% 159.14/25.54    (14)  op(e2, e2) = all_4_2
% 159.14/25.54    (15)   ~ (all_52_4 = all_4_2)
% 159.14/25.54    (16)  op(e3, e3) = e1
% 159.14/25.54    (17)  op(e3, e2) = all_52_4
% 159.14/25.54    (18)   ~ (e1 = e0)
% 159.14/25.54    (19)  op(e0, e2) = e1
% 159.14/25.54    (20)  all_56_12 = e2 & op(e0, e3) = e2
% 159.14/25.54    (21)   ~ (e2 = e1)
% 159.14/25.54    (22)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.14/25.54            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.14/25.54            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 159.14/25.54            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.14/25.54            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.14/25.54              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.14/25.54            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 159.14/25.54            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 159.14/25.54            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.14/25.54            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.14/25.54              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.14/25.54            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.14/25.54            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.14/25.54            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.14/25.54              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.14/25.54          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.14/25.54            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.14/25.54            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 159.14/25.54            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.14/25.54            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.14/25.54            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.14/25.54            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.14/25.54    (23)  op(e3, e0) = all_52_12
% 159.14/25.54    (24)  all_48_2 = e3
% 159.14/25.54    (25)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.14/25.54    (26)   ~ (all_52_14 = e1)
% 159.14/25.54    (27)   ~ (e3 = e1)
% 159.14/25.54    (28)   ~ (e2 = e0)
% 159.14/25.54    (29)   ~ (e3 = e0)
% 159.14/25.54    (30)   ~ (all_48_2 = e3) | ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 &
% 159.14/25.54            $i(all_48_0)) | ( ~ (all_48_1 = e1) & op(e3, e3) = all_48_1 &
% 159.14/25.54            $i(all_48_1))
% 159.14/25.54    (31)  op(e2, e0) = e1
% 159.14/25.54  
% 159.14/25.54  Begin of proof
% 159.14/25.54  | 
% 159.14/25.54  | ALPHA: (20) implies:
% 159.14/25.54  |   (32)  op(e0, e3) = e2
% 159.14/25.54  | 
% 159.14/25.54  | BETA: splitting (22) gives:
% 159.14/25.54  | 
% 159.14/25.54  | Case 1:
% 159.14/25.54  | | 
% 159.14/25.54  | |   (33)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.14/25.54  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.14/25.54  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.54  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.14/25.54  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.54  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 159.14/25.54  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.14/25.54  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.14/25.54  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.14/25.54  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.54  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.14/25.54  | | 
% 159.14/25.54  | | BETA: splitting (33) gives:
% 159.14/25.54  | | 
% 159.14/25.54  | | Case 1:
% 159.14/25.54  | | | 
% 159.14/25.54  | | |   (34)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.14/25.54  | | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.14/25.54  | | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.54  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.14/25.54  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.54  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.14/25.54  | | | 
% 159.14/25.54  | | | BETA: splitting (34) gives:
% 159.14/25.54  | | | 
% 159.14/25.54  | | | Case 1:
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | |   (35)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.14/25.54  | | | |           e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | | ALPHA: (35) implies:
% 159.14/25.54  | | | |   (36)  op(e0, e3) = e0
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | | REF_CLOSE: (4), (5), (28), (32), (36) are inconsistent by sub-proof
% 159.14/25.54  | | | |            #689.
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | Case 2:
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | |   (37)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.14/25.54  | | | |             = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0)
% 159.14/25.54  | | | |         | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.14/25.54  | | | |           (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.14/25.54  | | | |             e3) = e0)
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (14),
% 159.14/25.54  | | | |            (15), (16), (17), (18), (21), (23), (24), (25), (27), (29),
% 159.14/25.54  | | | |            (30), (31), (37) are inconsistent by sub-proof #409.
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | End of split
% 159.14/25.54  | | | 
% 159.14/25.54  | | Case 2:
% 159.14/25.54  | | | 
% 159.14/25.54  | | |   (38)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0)
% 159.14/25.54  | | |         | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.14/25.54  | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.14/25.54  | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.54  | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.14/25.54  | | | 
% 159.14/25.54  | | | BETA: splitting (38) gives:
% 159.14/25.54  | | | 
% 159.14/25.54  | | | Case 1:
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | |   (39)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | | ALPHA: (39) implies:
% 159.14/25.54  | | | |   (40)  op(e0, e3) = e0
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | | REF_CLOSE: (4), (5), (28), (32), (40) are inconsistent by sub-proof
% 159.14/25.54  | | | |            #689.
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | Case 2:
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | |   (41)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.14/25.54  | | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0)
% 159.14/25.54  | | | |         | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.14/25.54  | | | |           (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.14/25.54  | | | |             e2) = e0)
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | | REF_CLOSE: (4), (16), (18), (21), (31), (41) are inconsistent by
% 159.14/25.54  | | | |            sub-proof #809.
% 159.14/25.54  | | | | 
% 159.14/25.54  | | | End of split
% 159.14/25.54  | | | 
% 159.14/25.54  | | End of split
% 159.14/25.54  | | 
% 159.14/25.54  | Case 2:
% 159.14/25.54  | | 
% 159.14/25.55  | |   (42)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.55  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 159.14/25.55  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.14/25.55  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.14/25.55  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.14/25.55  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.55  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.14/25.55  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.55  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.14/25.55  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.14/25.55  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.14/25.55  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 159.14/25.55  | |           & op(e0, e1) = e0)
% 159.14/25.55  | | 
% 159.14/25.55  | | BETA: splitting (42) gives:
% 159.14/25.55  | | 
% 159.14/25.55  | | Case 1:
% 159.14/25.55  | | | 
% 159.14/25.55  | | |   (43)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.55  | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 159.14/25.55  | | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.14/25.55  | | |         | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.14/25.55  | | |             = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.14/25.55  | | | 
% 159.14/25.55  | | | BETA: splitting (43) gives:
% 159.14/25.55  | | | 
% 159.14/25.55  | | | Case 1:
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | |   (44)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.14/25.55  | | | |           = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | | ALPHA: (44) implies:
% 159.14/25.55  | | | |   (45)  op(e1, e1) = e0
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (14),
% 159.14/25.55  | | | |            (15), (16), (17), (18), (21), (23), (24), (25), (27), (29),
% 159.14/25.55  | | | |            (30), (45) are inconsistent by sub-proof #410.
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | Case 2:
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | |   (46)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.14/25.55  | | | |           e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.14/25.55  | | | |           (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.14/25.55  | | | |             e1) = e0)
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | | REF_CLOSE: (4), (16), (18), (19), (46) are inconsistent by sub-proof
% 159.14/25.55  | | | |            #831.
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | End of split
% 159.14/25.55  | | | 
% 159.14/25.55  | | Case 2:
% 159.14/25.55  | | | 
% 159.14/25.55  | | |   (47)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.14/25.55  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.14/25.55  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.14/25.55  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.14/25.55  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.14/25.55  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.14/25.55  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 159.14/25.55  | | |             e0) & op(e0, e1) = e0)
% 159.14/25.55  | | | 
% 159.14/25.55  | | | BETA: splitting (47) gives:
% 159.14/25.55  | | | 
% 159.14/25.55  | | | Case 1:
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | |   (48)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.14/25.55  | | | |             = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 159.14/25.55  | | | |         | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.14/25.55  | | | |           (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.14/25.55  | | | |             e1) = e0)
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (14),
% 159.14/25.55  | | | |            (15), (16), (17), (18), (21), (23), (24), (25), (27), (29),
% 159.14/25.55  | | | |            (30), (31), (48) are inconsistent by sub-proof #408.
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | Case 2:
% 159.14/25.55  | | | | 
% 159.14/25.55  | | | |   (49)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 159.14/25.55  | | | |             = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.14/25.55  | | | |             e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 159.23/25.55  | | | |           &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.23/25.55  | | | | 
% 159.23/25.55  | | | | BETA: splitting (49) gives:
% 159.23/25.55  | | | | 
% 159.23/25.55  | | | | Case 1:
% 159.23/25.55  | | | | | 
% 159.23/25.55  | | | | |   (50)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 159.23/25.55  | | | | |         (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.23/25.55  | | | | |         op(e0, e1) = e0 & $i(all_57_14)
% 159.23/25.55  | | | | | 
% 159.23/25.55  | | | | | ALPHA: (50) implies:
% 159.23/25.55  | | | | |   (51)  op(e1, e0) = e1
% 159.23/25.55  | | | | | 
% 159.23/25.55  | | | | | REF_CLOSE: (4), (12), (26), (51) are inconsistent by sub-proof #974.
% 159.23/25.55  | | | | | 
% 159.23/25.55  | | | | Case 2:
% 159.23/25.55  | | | | | 
% 159.23/25.55  | | | | |   (52)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.23/25.55  | | | | |         e0
% 159.23/25.55  | | | | | 
% 159.23/25.55  | | | | | ALPHA: (52) implies:
% 159.23/25.55  | | | | |   (53)  all_57_15 = e0
% 159.23/25.55  | | | | | 
% 159.23/25.55  | | | | | REDUCE: (13), (53) imply:
% 159.23/25.55  | | | | |   (54)  op(e0, e0) = e0
% 159.23/25.55  | | | | | 
% 159.23/25.55  | | | | | REF_CLOSE: (4), (8), (29), (54) are inconsistent by sub-proof #999.
% 159.23/25.55  | | | | | 
% 159.23/25.55  | | | | End of split
% 159.23/25.55  | | | | 
% 159.23/25.55  | | | End of split
% 159.23/25.55  | | | 
% 159.23/25.55  | | End of split
% 159.23/25.55  | | 
% 159.23/25.55  | End of split
% 159.23/25.55  | 
% 159.23/25.55  End of proof
% 159.23/25.55  
% 159.23/25.55  Sub-proof #408 shows that the following formulas are inconsistent:
% 159.23/25.55  ----------------------------------------------------------------
% 159.23/25.55    (1)   ~ (all_52_12 = e1)
% 159.23/25.55    (2)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.23/25.55             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.23/25.55           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.23/25.55               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.23/25.55             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.23/25.55         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.23/25.55             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.23/25.55           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.23/25.55               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.23/25.55             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.23/25.55         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.23/25.55             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.23/25.55           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.23/25.55               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.23/25.55             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.23/25.55         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.23/25.55             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.23/25.55           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.23/25.55               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.23/25.55             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.23/25.55    (3)   ~ (all_52_4 = all_52_12)
% 159.23/25.55    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.55    (5)   ~ (all_52_12 = e3)
% 159.23/25.55    (6)   ~ (all_52_4 = e1)
% 159.23/25.55    (7)  op(e0, e0) = e3
% 159.23/25.55    (8)  all_54_3 = all_52_12
% 159.23/25.55    (9)  all_54_1 = all_52_4
% 159.23/25.55    (10)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.23/25.55    (11)  op(e2, e2) = all_4_2
% 159.23/25.55    (12)   ~ (all_52_4 = all_4_2)
% 159.23/25.55    (13)  op(e3, e3) = e1
% 159.23/25.55    (14)  op(e3, e2) = all_52_4
% 159.23/25.55    (15)   ~ (e1 = e0)
% 159.23/25.55    (16)   ~ (e2 = e1)
% 159.23/25.55    (17)  op(e3, e0) = all_52_12
% 159.23/25.55    (18)  all_48_2 = e3
% 159.23/25.55    (19)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.23/25.55    (20)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.23/25.55            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.23/25.55            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 159.23/25.55            e0 & op(e1, e0) = e1 & op(e0, e1) = e0)
% 159.23/25.55    (21)   ~ (e3 = e1)
% 159.23/25.55    (22)   ~ (e3 = e0)
% 159.23/25.55    (23)   ~ (all_48_2 = e3) | ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 &
% 159.23/25.55            $i(all_48_0)) | ( ~ (all_48_1 = e1) & op(e3, e3) = all_48_1 &
% 159.23/25.55            $i(all_48_1))
% 159.23/25.55    (24)  op(e2, e0) = e1
% 159.23/25.55  
% 159.23/25.55  Begin of proof
% 159.23/25.55  | 
% 159.23/25.55  | BETA: splitting (20) gives:
% 159.23/25.55  | 
% 159.23/25.55  | Case 1:
% 159.23/25.55  | | 
% 159.23/25.55  | |   (25)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.23/25.55  | |           e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 159.23/25.55  | | 
% 159.23/25.55  | | ALPHA: (25) implies:
% 159.23/25.55  | |   (26)  op(e2, e0) = e2
% 159.23/25.55  | | 
% 159.23/25.55  | | REF_CLOSE: (4), (16), (24), (26) are inconsistent by sub-proof #813.
% 159.23/25.55  | | 
% 159.23/25.55  | Case 2:
% 159.23/25.55  | | 
% 159.23/25.55  | |   (27)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.23/25.55  | |           e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.23/25.55  | | 
% 159.23/25.55  | | ALPHA: (27) implies:
% 159.23/25.55  | |   (28)  op(e1, e1) = e0
% 159.23/25.55  | | 
% 159.23/25.55  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.23/25.55  | |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (28)
% 159.23/25.55  | |            are inconsistent by sub-proof #410.
% 159.23/25.55  | | 
% 159.23/25.55  | End of split
% 159.23/25.55  | 
% 159.23/25.55  End of proof
% 159.23/25.55  
% 159.23/25.55  Sub-proof #409 shows that the following formulas are inconsistent:
% 159.23/25.55  ----------------------------------------------------------------
% 159.23/25.55    (1)   ~ (all_52_12 = e1)
% 159.23/25.55    (2)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.23/25.55             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.23/25.55           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.23/25.55               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.23/25.55             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.23/25.55         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.23/25.55             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.23/25.55           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.23/25.55               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.23/25.55             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.23/25.55         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.23/25.55             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.23/25.55           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.23/25.55               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.23/25.55             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.23/25.55         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.23/25.55             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.23/25.55           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.23/25.55               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.23/25.55             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.23/25.55    (3)   ~ (all_52_4 = all_52_12)
% 159.23/25.55    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.55    (5)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.23/25.55           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.23/25.55           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 159.23/25.55           & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.23/25.55    (6)   ~ (all_52_12 = e3)
% 159.23/25.55    (7)   ~ (all_52_4 = e1)
% 159.23/25.55    (8)  op(e0, e0) = e3
% 159.23/25.55    (9)  all_54_3 = all_52_12
% 159.23/25.55    (10)  all_54_1 = all_52_4
% 159.23/25.55    (11)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.23/25.55    (12)  op(e2, e2) = all_4_2
% 159.23/25.55    (13)   ~ (all_52_4 = all_4_2)
% 159.23/25.55    (14)  op(e3, e3) = e1
% 159.23/25.55    (15)  op(e3, e2) = all_52_4
% 159.23/25.55    (16)   ~ (e1 = e0)
% 159.23/25.55    (17)   ~ (e2 = e1)
% 159.23/25.55    (18)  op(e3, e0) = all_52_12
% 159.23/25.55    (19)  all_48_2 = e3
% 159.23/25.55    (20)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.23/25.55    (21)   ~ (e3 = e1)
% 159.23/25.55    (22)   ~ (e3 = e0)
% 159.23/25.55    (23)   ~ (all_48_2 = e3) | ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 &
% 159.23/25.55            $i(all_48_0)) | ( ~ (all_48_1 = e1) & op(e3, e3) = all_48_1 &
% 159.23/25.55            $i(all_48_1))
% 159.23/25.55    (24)  op(e2, e0) = e1
% 159.23/25.55  
% 159.23/25.55  Begin of proof
% 159.23/25.55  | 
% 159.23/25.55  | BETA: splitting (5) gives:
% 159.23/25.55  | 
% 159.23/25.55  | Case 1:
% 159.23/25.55  | | 
% 159.23/25.55  | |   (25)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.23/25.55  | |           e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 159.23/25.55  | | 
% 159.23/25.55  | | ALPHA: (25) implies:
% 159.23/25.55  | |   (26)  op(e2, e0) = e2
% 159.23/25.55  | | 
% 159.23/25.55  | | REF_CLOSE: (4), (17), (24), (26) are inconsistent by sub-proof #813.
% 159.23/25.55  | | 
% 159.23/25.55  | Case 2:
% 159.23/25.55  | | 
% 159.23/25.55  | |   (27)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.23/25.55  | |           e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 159.23/25.55  | | 
% 159.23/25.55  | | ALPHA: (27) implies:
% 159.23/25.55  | |   (28)  op(e1, e1) = e0
% 159.23/25.55  | | 
% 159.23/25.55  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.23/25.55  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (28)
% 159.23/25.55  | |            are inconsistent by sub-proof #410.
% 159.23/25.55  | | 
% 159.23/25.55  | End of split
% 159.23/25.55  | 
% 159.23/25.55  End of proof
% 159.23/25.55  
% 159.23/25.55  Sub-proof #410 shows that the following formulas are inconsistent:
% 159.23/25.55  ----------------------------------------------------------------
% 159.23/25.55    (1)   ~ (all_52_12 = e1)
% 159.23/25.55    (2)  op(e1, e1) = e0
% 159.23/25.55    (3)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.23/25.55             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.23/25.55           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.23/25.55               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.23/25.55             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.23/25.55         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.23/25.55             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.23/25.55           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.23/25.55               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.23/25.55             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.23/25.55         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.23/25.55             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.23/25.55           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.23/25.55               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.23/25.55             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.23/25.55         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.23/25.55             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.23/25.55           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.23/25.55               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.23/25.55             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.23/25.55    (4)   ~ (all_52_4 = all_52_12)
% 159.23/25.55    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.55    (6)   ~ (all_52_12 = e3)
% 159.23/25.55    (7)   ~ (all_52_4 = e1)
% 159.23/25.55    (8)  op(e0, e0) = e3
% 159.23/25.55    (9)  all_54_3 = all_52_12
% 159.23/25.55    (10)  all_54_1 = all_52_4
% 159.23/25.55    (11)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.23/25.55    (12)  op(e2, e2) = all_4_2
% 159.23/25.55    (13)   ~ (all_52_4 = all_4_2)
% 159.23/25.56    (14)  op(e3, e3) = e1
% 159.23/25.56    (15)  op(e3, e2) = all_52_4
% 159.23/25.56    (16)   ~ (e1 = e0)
% 159.23/25.56    (17)   ~ (e2 = e1)
% 159.23/25.56    (18)  op(e3, e0) = all_52_12
% 159.23/25.56    (19)  all_48_2 = e3
% 159.23/25.56    (20)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.23/25.56    (21)   ~ (e3 = e1)
% 159.23/25.56    (22)   ~ (e3 = e0)
% 159.23/25.56    (23)   ~ (all_48_2 = e3) | ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 &
% 159.23/25.56            $i(all_48_0)) | ( ~ (all_48_1 = e1) & op(e3, e3) = all_48_1 &
% 159.23/25.56            $i(all_48_1))
% 159.23/25.56  
% 159.23/25.56  Begin of proof
% 159.23/25.56  | 
% 159.23/25.56  | BETA: splitting (3) gives:
% 159.23/25.56  | 
% 159.23/25.56  | Case 1:
% 159.23/25.56  | | 
% 159.23/25.56  | |   (24)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.23/25.56  | |               e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.23/25.56  | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.23/25.56  | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.23/25.56  | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.23/25.56  | |                 e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 159.23/25.56  | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 159.23/25.56  | |                 e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 159.23/25.56  | |               e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 159.23/25.56  | |               all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 159.23/25.56  | |               e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 159.23/25.56  | |               $i(all_57_7))))
% 159.23/25.56  | | 
% 159.23/25.56  | | BETA: splitting (24) gives:
% 159.23/25.56  | | 
% 159.23/25.56  | | Case 1:
% 159.23/25.56  | | | 
% 159.23/25.56  | | |   (25)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.23/25.56  | | |             e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.23/25.56  | | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.23/25.56  | | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.23/25.56  | | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.23/25.56  | | |               e3) = all_57_6 & $i(all_57_6)))
% 159.23/25.56  | | | 
% 159.23/25.56  | | | ALPHA: (25) implies:
% 159.23/25.56  | | |   (26)  op(e3, e3) = e3
% 159.23/25.56  | | | 
% 159.23/25.56  | | | REF_CLOSE: (5), (14), (21), (26) are inconsistent by sub-proof #995.
% 159.23/25.56  | | | 
% 159.23/25.56  | | Case 2:
% 159.23/25.56  | | | 
% 159.23/25.56  | | |   (27)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 159.23/25.56  | | |             e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 159.23/25.56  | | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 159.23/25.56  | | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 159.23/25.56  | | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 159.23/25.56  | | |               e2) = all_57_7 & $i(all_57_7)))
% 159.23/25.56  | | | 
% 159.23/25.56  | | | ALPHA: (27) implies:
% 159.23/25.56  | | |   (28)  op(e2, e2) = e2
% 159.23/25.56  | | |   (29)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) & op(e3,
% 159.23/25.56  | | |             e2) = all_57_1 & $i(all_57_1))
% 159.23/25.56  | | | 
% 159.23/25.56  | | | BETA: splitting (23) gives:
% 159.23/25.56  | | | 
% 159.23/25.56  | | | Case 1:
% 159.23/25.56  | | | | 
% 159.23/25.56  | | | |   (30)   ~ (all_48_2 = e3)
% 159.23/25.56  | | | | 
% 159.23/25.56  | | | | REDUCE: (19), (30) imply:
% 159.23/25.56  | | | |   (31)  $false
% 159.23/25.56  | | | | 
% 159.23/25.56  | | | | CLOSE: (31) is inconsistent.
% 159.23/25.56  | | | | 
% 159.23/25.56  | | | Case 2:
% 159.23/25.56  | | | | 
% 159.23/25.56  | | | |   (32)  ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 & $i(all_48_0)) | (
% 159.23/25.56  | | | |           ~ (all_48_1 = e1) & op(e3, e3) = all_48_1 & $i(all_48_1))
% 159.23/25.56  | | | | 
% 159.23/25.56  | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 159.23/25.56  | | | |            (15), (17), (18), (20), (28), (29), (32) are inconsistent by
% 159.23/25.56  | | | |            sub-proof #417.
% 159.23/25.56  | | | | 
% 159.23/25.56  | | | End of split
% 159.23/25.56  | | | 
% 159.23/25.56  | | End of split
% 159.23/25.56  | | 
% 159.23/25.56  | Case 2:
% 159.23/25.56  | | 
% 159.23/25.56  | |   (33)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.23/25.56  | |               e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.23/25.56  | |               $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.23/25.56  | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.23/25.56  | |           ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.23/25.56  | |                 e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 159.23/25.56  | |             e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 159.23/25.56  | |                 e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 =
% 159.23/25.56  | |               e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 159.23/25.56  | |               all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 159.23/25.56  | |               e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.23/25.56  | |               $i(all_57_13))))
% 159.23/25.56  | | 
% 159.23/25.56  | | REF_CLOSE: (2), (5), (8), (16), (22), (33) are inconsistent by sub-proof
% 159.23/25.56  | |            #411.
% 159.23/25.56  | | 
% 159.23/25.56  | End of split
% 159.23/25.56  | 
% 159.23/25.56  End of proof
% 159.23/25.56  
% 159.23/25.56  Sub-proof #411 shows that the following formulas are inconsistent:
% 159.23/25.56  ----------------------------------------------------------------
% 159.23/25.56    (1)  op(e1, e1) = e0
% 159.23/25.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.56    (3)  op(e0, e0) = e3
% 159.23/25.56    (4)   ~ (e1 = e0)
% 159.23/25.56    (5)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.23/25.56             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.23/25.56           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.23/25.56               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.23/25.56             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.23/25.56         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.23/25.56             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.23/25.56           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.23/25.56               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.23/25.56             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.23/25.56    (6)   ~ (e3 = e0)
% 159.23/25.56  
% 159.23/25.56  Begin of proof
% 159.23/25.56  | 
% 159.23/25.56  | BETA: splitting (5) gives:
% 159.23/25.56  | 
% 159.23/25.56  | Case 1:
% 159.23/25.56  | | 
% 159.23/25.56  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.23/25.56  | |            e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.23/25.56  | |            $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.23/25.56  | |            (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.23/25.56  | |        ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.23/25.56  | |              e1) = all_57_8 & $i(all_57_8)))
% 159.23/25.56  | | 
% 159.23/25.56  | | ALPHA: (7) implies:
% 159.23/25.56  | |   (8)  op(e1, e1) = e1
% 159.23/25.56  | | 
% 159.23/25.56  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #903.
% 159.23/25.56  | | 
% 159.23/25.56  | Case 2:
% 159.23/25.56  | | 
% 159.23/25.56  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 159.23/25.56  | |            e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.23/25.56  | |            $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 159.23/25.56  | |            (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 159.23/25.56  | |        ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 159.23/25.56  | |              e0) = all_57_13 & $i(all_57_13)))
% 159.23/25.56  | | 
% 159.23/25.56  | | ALPHA: (9) implies:
% 159.23/25.56  | |   (10)  op(e0, e0) = e0
% 159.23/25.56  | | 
% 159.23/25.56  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #999.
% 159.23/25.56  | | 
% 159.23/25.56  | End of split
% 159.23/25.56  | 
% 159.23/25.56  End of proof
% 159.23/25.56  
% 159.23/25.56  Sub-proof #412 shows that the following formulas are inconsistent:
% 159.23/25.56  ----------------------------------------------------------------
% 159.23/25.56    (1)   ~ (e3 = e2)
% 159.23/25.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.56    (3)  op(e0, e0) = e3
% 159.23/25.56    (4)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.23/25.56           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.23/25.56           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 159.23/25.56           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.23/25.56    (5)  op(e2, e1) = all_52_9
% 159.23/25.56    (6)   ~ (all_52_9 = e2)
% 159.23/25.56  
% 159.23/25.56  Begin of proof
% 159.23/25.56  | 
% 159.23/25.56  | BETA: splitting (4) gives:
% 159.23/25.56  | 
% 159.23/25.56  | Case 1:
% 159.23/25.56  | | 
% 159.23/25.56  | |   (7)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 159.23/25.56  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 159.23/25.56  | |          e0) = e2 & $i(all_57_12)
% 159.23/25.56  | | 
% 159.23/25.56  | | ALPHA: (7) implies:
% 159.23/25.56  | |   (8)  op(e0, e0) = e2
% 159.23/25.56  | | 
% 159.23/25.56  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #878.
% 159.23/25.56  | | 
% 159.23/25.56  | Case 2:
% 159.23/25.56  | | 
% 159.23/25.56  | |   (9)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 159.23/25.56  | |        op(e2, e1) = e2
% 159.23/25.56  | | 
% 159.23/25.56  | | ALPHA: (9) implies:
% 159.23/25.56  | |   (10)  op(e2, e1) = e2
% 159.23/25.56  | | 
% 159.23/25.56  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1002.
% 159.23/25.56  | | 
% 159.23/25.56  | End of split
% 159.23/25.56  | 
% 159.23/25.56  End of proof
% 159.23/25.56  
% 159.23/25.56  Sub-proof #413 shows that the following formulas are inconsistent:
% 159.23/25.56  ----------------------------------------------------------------
% 159.23/25.56    (1)   ~ (all_52_6 = e1)
% 159.23/25.56    (2)   ~ (all_52_12 = e1)
% 159.23/25.56    (3)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.23/25.56             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.23/25.56           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.23/25.56               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.23/25.56             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.23/25.56         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.23/25.56             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.23/25.56           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.23/25.56               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.23/25.56             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.23/25.56         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.23/25.56             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.23/25.56           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.23/25.56               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.23/25.56             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.23/25.56         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.23/25.56             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.23/25.56           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.23/25.56               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.23/25.56             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.23/25.56    (4)   ~ (all_52_4 = all_52_12)
% 159.23/25.56    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.56    (6)   ~ (all_52_12 = e3)
% 159.23/25.56    (7)   ~ (all_52_4 = e1)
% 159.23/25.56    (8)  op(e0, e0) = e3
% 159.23/25.56    (9)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 159.23/25.56           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.23/25.56           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1)
% 159.23/25.56           & op(e1, e2) = e1 & op(e1, e1) = e1)
% 159.23/25.56    (10)  all_54_3 = all_52_12
% 159.23/25.56    (11)  all_54_1 = all_52_4
% 159.23/25.56    (12)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.23/25.56    (13)  op(e1, e2) = all_52_6
% 159.23/25.56    (14)  ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 & $i(all_48_0)) | ( ~
% 159.23/25.56            (all_48_1 = e1) & op(e3, e3) = all_48_1 & $i(all_48_1))
% 159.23/25.56    (15)  op(e2, e2) = all_4_2
% 159.23/25.56    (16)   ~ (all_52_4 = all_4_2)
% 159.23/25.56    (17)  op(e3, e3) = e1
% 159.23/25.56    (18)  op(e3, e2) = all_52_4
% 159.23/25.56    (19)   ~ (e2 = e1)
% 159.23/25.56    (20)  op(e3, e0) = all_52_12
% 159.23/25.56    (21)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.23/25.56    (22)   ~ (e3 = e1)
% 159.23/25.56    (23)   ~ (e3 = e0)
% 159.23/25.56  
% 159.23/25.56  Begin of proof
% 159.23/25.56  | 
% 159.23/25.56  | BETA: splitting (9) gives:
% 159.23/25.56  | 
% 159.23/25.56  | Case 1:
% 159.23/25.56  | | 
% 159.23/25.56  | |   (24)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.23/25.56  | |           e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 159.23/25.56  | |         op(e1, e1) = e2 & $i(all_57_12)
% 159.23/25.56  | | 
% 159.23/25.56  | | ALPHA: (24) implies:
% 159.23/25.56  | |   (25)  op(e1, e1) = e2
% 159.23/25.56  | | 
% 159.23/25.56  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14), (15),
% 159.23/25.56  | |            (16), (17), (18), (19), (20), (21), (22), (23), (25) are
% 159.23/25.56  | |            inconsistent by sub-proof #415.
% 159.23/25.56  | | 
% 159.23/25.56  | Case 2:
% 159.23/25.56  | | 
% 159.23/25.56  | |   (26)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 159.23/25.56  | |         op(e1, e1) = e1
% 159.23/25.56  | | 
% 159.23/25.56  | | ALPHA: (26) implies:
% 159.23/25.56  | |   (27)  op(e1, e2) = e1
% 159.23/25.56  | | 
% 159.23/25.56  | | REF_CLOSE: (1), (5), (13), (27) are inconsistent by sub-proof #984.
% 159.23/25.56  | | 
% 159.23/25.56  | End of split
% 159.23/25.56  | 
% 159.23/25.56  End of proof
% 159.23/25.56  
% 159.23/25.56  Sub-proof #414 shows that the following formulas are inconsistent:
% 159.23/25.56  ----------------------------------------------------------------
% 159.23/25.56    (1)   ~ (all_52_12 = e1)
% 159.23/25.56    (2)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.23/25.56             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.23/25.56           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.23/25.56               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.23/25.56             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.23/25.56         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.23/25.56             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.23/25.56           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.23/25.56               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.23/25.56             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.23/25.56         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.23/25.56             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.23/25.56           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.23/25.56               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.23/25.56             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.23/25.56         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.23/25.56             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.23/25.56           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.23/25.56               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.23/25.56             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.23/25.56    (3)   ~ (all_52_4 = all_52_12)
% 159.23/25.56    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.56    (5)   ~ (all_52_12 = e3)
% 159.23/25.56    (6)   ~ (all_52_4 = e1)
% 159.23/25.56    (7)  op(e0, e0) = e3
% 159.23/25.56    (8)  all_54_3 = all_52_12
% 159.23/25.56    (9)  all_54_1 = all_52_4
% 159.23/25.56    (10)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.23/25.56    (11)  ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 & $i(all_48_0)) | ( ~
% 159.23/25.56            (all_48_1 = e1) & op(e3, e3) = all_48_1 & $i(all_48_1))
% 159.23/25.56    (12)  op(e2, e2) = all_4_2
% 159.23/25.56    (13)   ~ (all_52_4 = all_4_2)
% 159.23/25.57    (14)  op(e3, e3) = e1
% 159.23/25.57    (15)  op(e3, e2) = all_52_4
% 159.23/25.57    (16)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 159.23/25.57            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.23/25.57              e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 &
% 159.23/25.57            all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.23/25.57            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.23/25.57    (17)   ~ (e2 = e1)
% 159.23/25.57    (18)  op(e3, e0) = all_52_12
% 159.23/25.57    (19)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.23/25.57    (20)   ~ (e3 = e1)
% 159.23/25.57    (21)   ~ (e3 = e0)
% 159.23/25.57  
% 159.23/25.57  Begin of proof
% 159.23/25.57  | 
% 159.23/25.57  | BETA: splitting (16) gives:
% 159.23/25.57  | 
% 159.23/25.57  | Case 1:
% 159.23/25.57  | | 
% 159.23/25.57  | |   (22)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.23/25.57  | |         & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 &
% 159.23/25.57  | |         op(e1, e1) = e2 & $i(all_57_12)
% 159.23/25.57  | | 
% 159.23/25.57  | | ALPHA: (22) implies:
% 159.23/25.57  | |   (23)  op(e1, e1) = e2
% 159.23/25.57  | | 
% 159.23/25.57  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.23/25.57  | |            (13), (14), (15), (17), (18), (19), (20), (21), (23) are
% 159.23/25.57  | |            inconsistent by sub-proof #415.
% 159.23/25.57  | | 
% 159.23/25.57  | Case 2:
% 159.23/25.57  | | 
% 159.23/25.57  | |   (24)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 159.23/25.57  | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.23/25.57  | |         op(e0, e0) = e1 & $i(all_57_14)
% 159.23/25.57  | | 
% 159.23/25.57  | | ALPHA: (24) implies:
% 159.23/25.57  | |   (25)  op(e0, e0) = e1
% 159.23/25.57  | | 
% 159.23/25.57  | | REF_CLOSE: (4), (7), (20), (25) are inconsistent by sub-proof #473.
% 159.23/25.57  | | 
% 159.23/25.57  | End of split
% 159.23/25.57  | 
% 159.23/25.57  End of proof
% 159.23/25.57  
% 159.23/25.57  Sub-proof #415 shows that the following formulas are inconsistent:
% 159.23/25.57  ----------------------------------------------------------------
% 159.23/25.57    (1)   ~ (all_52_12 = e1)
% 159.23/25.57    (2)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.23/25.57             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.23/25.57           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.23/25.57               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.23/25.57             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.23/25.57         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.23/25.57             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.23/25.57           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.23/25.57               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.23/25.57             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.23/25.57         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.23/25.57             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.23/25.57           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.23/25.57               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.23/25.57             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.23/25.57         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.23/25.57             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.23/25.57           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.23/25.57               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.23/25.57             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.23/25.57    (3)   ~ (all_52_4 = all_52_12)
% 159.23/25.57    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.57    (5)   ~ (all_52_12 = e3)
% 159.23/25.57    (6)  op(e1, e1) = e2
% 159.23/25.57    (7)   ~ (all_52_4 = e1)
% 159.23/25.57    (8)  op(e0, e0) = e3
% 159.23/25.57    (9)  all_54_3 = all_52_12
% 159.23/25.57    (10)  all_54_1 = all_52_4
% 159.23/25.57    (11)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.23/25.57    (12)  ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 & $i(all_48_0)) | ( ~
% 159.23/25.57            (all_48_1 = e1) & op(e3, e3) = all_48_1 & $i(all_48_1))
% 159.23/25.57    (13)  op(e2, e2) = all_4_2
% 159.23/25.57    (14)   ~ (all_52_4 = all_4_2)
% 159.23/25.57    (15)  op(e3, e3) = e1
% 159.23/25.57    (16)  op(e3, e2) = all_52_4
% 159.23/25.57    (17)   ~ (e2 = e1)
% 159.23/25.57    (18)  op(e3, e0) = all_52_12
% 159.23/25.57    (19)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.23/25.57    (20)   ~ (e3 = e1)
% 159.23/25.57    (21)   ~ (e3 = e0)
% 159.23/25.57  
% 159.23/25.57  Begin of proof
% 159.23/25.57  | 
% 159.23/25.57  | BETA: splitting (2) gives:
% 159.23/25.57  | 
% 159.23/25.57  | Case 1:
% 159.23/25.57  | | 
% 159.23/25.57  | |   (22)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.23/25.57  | |               e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.23/25.57  | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.23/25.57  | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.23/25.57  | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.23/25.57  | |                 e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 159.23/25.57  | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 159.23/25.57  | |                 e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 159.23/25.57  | |               e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 159.23/25.57  | |               all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 159.23/25.57  | |               e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 159.23/25.57  | |               $i(all_57_7))))
% 159.23/25.57  | | 
% 159.23/25.57  | | BETA: splitting (22) gives:
% 159.23/25.57  | | 
% 159.23/25.57  | | Case 1:
% 159.23/25.57  | | | 
% 159.23/25.57  | | |   (23)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.23/25.57  | | |             e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.23/25.57  | | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.23/25.57  | | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.23/25.57  | | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.23/25.57  | | |               e3) = all_57_6 & $i(all_57_6)))
% 159.23/25.57  | | | 
% 159.23/25.57  | | | ALPHA: (23) implies:
% 159.23/25.57  | | |   (24)  op(e3, e3) = e3
% 159.23/25.57  | | | 
% 159.23/25.57  | | | REF_CLOSE: (4), (15), (20), (24) are inconsistent by sub-proof #995.
% 159.23/25.57  | | | 
% 159.23/25.57  | | Case 2:
% 159.23/25.57  | | | 
% 159.23/25.57  | | |   (25)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 159.23/25.57  | | |             e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 159.23/25.57  | | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 159.23/25.57  | | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 159.23/25.57  | | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 159.23/25.57  | | |               e2) = all_57_7 & $i(all_57_7)))
% 159.23/25.57  | | | 
% 159.23/25.57  | | | ALPHA: (25) implies:
% 159.23/25.57  | | |   (26)  op(e2, e2) = e2
% 159.23/25.57  | | |   (27)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) & op(e3,
% 159.23/25.57  | | |             e2) = all_57_1 & $i(all_57_1))
% 159.23/25.57  | | | 
% 159.23/25.57  | | | REF_CLOSE: (1), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14),
% 159.23/25.57  | | |            (15), (16), (17), (18), (19), (26), (27) are inconsistent by
% 159.23/25.57  | | |            sub-proof #417.
% 159.23/25.57  | | | 
% 159.23/25.57  | | End of split
% 159.23/25.57  | | 
% 159.23/25.57  | Case 2:
% 159.23/25.57  | | 
% 159.23/25.57  | |   (28)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.23/25.57  | |               e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.23/25.57  | |               $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.23/25.57  | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.23/25.57  | |           ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.23/25.57  | |                 e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 159.23/25.57  | |             e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 159.23/25.57  | |                 e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 =
% 159.23/25.57  | |               e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 159.23/25.57  | |               all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 159.23/25.57  | |               e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.23/25.57  | |               $i(all_57_13))))
% 159.23/25.57  | | 
% 159.23/25.57  | | REF_CLOSE: (4), (6), (8), (17), (21), (28) are inconsistent by sub-proof
% 159.23/25.57  | |            #416.
% 159.23/25.57  | | 
% 159.23/25.57  | End of split
% 159.23/25.57  | 
% 159.23/25.57  End of proof
% 159.23/25.57  
% 159.23/25.57  Sub-proof #416 shows that the following formulas are inconsistent:
% 159.23/25.57  ----------------------------------------------------------------
% 159.23/25.57    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.57    (2)  op(e1, e1) = e2
% 159.23/25.57    (3)  op(e0, e0) = e3
% 159.23/25.57    (4)   ~ (e2 = e1)
% 159.23/25.57    (5)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.23/25.57             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.23/25.57           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.23/25.57               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.23/25.57             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.23/25.57         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.23/25.57             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.23/25.57           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.23/25.57               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.23/25.57             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.23/25.57    (6)   ~ (e3 = e0)
% 159.23/25.57  
% 159.23/25.57  Begin of proof
% 159.23/25.57  | 
% 159.23/25.57  | BETA: splitting (5) gives:
% 159.23/25.57  | 
% 159.23/25.57  | Case 1:
% 159.23/25.57  | | 
% 159.23/25.57  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.23/25.57  | |            e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.23/25.57  | |            $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.23/25.57  | |            (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.23/25.57  | |        ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.23/25.57  | |              e1) = all_57_8 & $i(all_57_8)))
% 159.23/25.57  | | 
% 159.23/25.57  | | ALPHA: (7) implies:
% 159.23/25.57  | |   (8)  op(e1, e1) = e1
% 159.23/25.57  | | 
% 159.23/25.57  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #986.
% 159.23/25.57  | | 
% 159.23/25.57  | Case 2:
% 159.23/25.57  | | 
% 159.23/25.57  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 159.23/25.57  | |            e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.23/25.57  | |            $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 159.23/25.57  | |            (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 159.23/25.57  | |        ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 159.23/25.57  | |              e0) = all_57_13 & $i(all_57_13)))
% 159.23/25.57  | | 
% 159.23/25.57  | | ALPHA: (9) implies:
% 159.23/25.57  | |   (10)  op(e0, e0) = e0
% 159.23/25.57  | | 
% 159.23/25.57  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #999.
% 159.23/25.57  | | 
% 159.23/25.57  | End of split
% 159.23/25.57  | 
% 159.23/25.57  End of proof
% 159.23/25.57  
% 159.23/25.57  Sub-proof #417 shows that the following formulas are inconsistent:
% 159.23/25.57  ----------------------------------------------------------------
% 159.23/25.57    (1)   ~ (all_52_12 = e1)
% 159.23/25.57    (2)   ~ (all_52_4 = all_52_12)
% 159.23/25.57    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.57    (4)   ~ (all_52_12 = e3)
% 159.23/25.57    (5)   ~ (all_52_4 = e1)
% 159.23/25.57    (6)  op(e2, e2) = e2
% 159.23/25.57    (7)  all_54_3 = all_52_12
% 159.23/25.57    (8)  all_54_1 = all_52_4
% 159.23/25.57    (9)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.23/25.57    (10)  ( ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 & $i(all_48_0)) | ( ~
% 159.23/25.57            (all_48_1 = e1) & op(e3, e3) = all_48_1 & $i(all_48_1))
% 159.23/25.57    (11)  op(e2, e2) = all_4_2
% 159.23/25.57    (12)   ~ (all_52_4 = all_4_2)
% 159.23/25.57    (13)  op(e3, e3) = e1
% 159.23/25.57    (14)  op(e3, e2) = all_52_4
% 159.23/25.57    (15)   ~ (e2 = e1)
% 159.23/25.57    (16)  op(e3, e0) = all_52_12
% 159.23/25.57    (17)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.23/25.57    (18)  (all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) & op(e3, e2) =
% 159.23/25.57            all_57_1 & $i(all_57_1))
% 159.23/25.57  
% 159.23/25.57  Begin of proof
% 159.23/25.57  | 
% 159.23/25.57  | BETA: splitting (18) gives:
% 159.23/25.57  | 
% 159.23/25.57  | Case 1:
% 159.23/25.57  | | 
% 159.23/25.57  | |   (19)  all_57_10 = e2 & op(e3, e3) = e2
% 159.23/25.57  | | 
% 159.23/25.57  | | ALPHA: (19) implies:
% 159.23/25.57  | |   (20)  op(e3, e3) = e2
% 159.23/25.57  | | 
% 159.23/25.57  | | REF_CLOSE: (3), (13), (15), (20) are inconsistent by sub-proof #828.
% 159.23/25.57  | | 
% 159.23/25.57  | Case 2:
% 159.23/25.57  | | 
% 159.23/25.57  | |   (21)   ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1)
% 159.23/25.57  | | 
% 159.23/25.57  | | ALPHA: (21) implies:
% 159.23/25.57  | |   (22)   ~ (all_57_1 = e3)
% 159.23/25.57  | |   (23)  op(e3, e2) = all_57_1
% 159.23/25.57  | | 
% 159.23/25.57  | | BETA: splitting (10) gives:
% 159.23/25.57  | | 
% 159.23/25.57  | | Case 1:
% 159.23/25.57  | | | 
% 159.23/25.57  | | |   (24)   ~ (all_48_0 = e2) & op(e3, e0) = all_48_0 & $i(all_48_0)
% 159.23/25.57  | | | 
% 159.23/25.57  | | | ALPHA: (24) implies:
% 159.23/25.57  | | |   (25)   ~ (all_48_0 = e2)
% 159.23/25.57  | | |   (26)  op(e3, e0) = all_48_0
% 159.23/25.57  | | | 
% 159.23/25.57  | | | GROUND_INST: instantiating (3) with all_4_2, e2, e2, e2, simplifying with
% 159.23/25.57  | | |              (6), (11) gives:
% 159.23/25.57  | | |   (27)  all_4_2 = e2
% 159.23/25.57  | | | 
% 159.23/25.57  | | | GROUND_INST: instantiating (3) with all_52_12, all_48_0, e0, e3,
% 159.23/25.57  | | |              simplifying with (16), (26) gives:
% 159.23/25.57  | | |   (28)  all_52_12 = all_48_0
% 159.23/25.57  | | | 
% 159.23/25.57  | | | GROUND_INST: instantiating (3) with all_52_4, all_57_1, e2, e3,
% 159.23/25.57  | | |              simplifying with (14), (23) gives:
% 159.23/25.57  | | |   (29)  all_57_1 = all_52_4
% 159.23/25.57  | | | 
% 159.23/25.57  | | | COMBINE_EQS: (7), (28) imply:
% 159.23/25.57  | | |   (30)  all_54_3 = all_48_0
% 159.23/25.57  | | | 
% 159.23/25.57  | | | REDUCE: (22), (29) imply:
% 159.23/25.57  | | |   (31)   ~ (all_52_4 = e3)
% 159.23/25.57  | | | 
% 159.23/25.57  | | | REDUCE: (2), (28) imply:
% 159.23/25.57  | | |   (32)   ~ (all_52_4 = all_48_0)
% 159.23/25.57  | | | 
% 159.23/25.57  | | | REDUCE: (12), (27) imply:
% 159.23/25.57  | | |   (33)   ~ (all_52_4 = e2)
% 159.23/25.57  | | | 
% 159.23/25.57  | | | REDUCE: (4), (28) imply:
% 159.23/25.57  | | |   (34)   ~ (all_48_0 = e3)
% 159.23/25.57  | | | 
% 159.23/25.57  | | | REDUCE: (1), (28) imply:
% 159.23/25.57  | | |   (35)   ~ (all_48_0 = e1)
% 159.23/25.57  | | | 
% 159.23/25.57  | | | BETA: splitting (17) gives:
% 159.23/25.57  | | | 
% 159.23/25.57  | | | Case 1:
% 159.23/25.57  | | | | 
% 159.23/25.57  | | | |   (36)  all_54_3 = e3
% 159.23/25.57  | | | | 
% 159.23/25.57  | | | | COMBINE_EQS: (30), (36) imply:
% 159.23/25.57  | | | |   (37)  all_48_0 = e3
% 159.23/25.57  | | | | 
% 159.23/25.57  | | | | SIMP: (37) implies:
% 159.23/25.57  | | | |   (38)  all_48_0 = e3
% 159.23/25.57  | | | | 
% 159.23/25.57  | | | | REDUCE: (34), (38) imply:
% 159.23/25.57  | | | |   (39)  $false
% 159.23/25.57  | | | | 
% 159.23/25.57  | | | | CLOSE: (39) is inconsistent.
% 159.23/25.57  | | | | 
% 159.23/25.57  | | | Case 2:
% 159.23/25.57  | | | | 
% 159.23/25.57  | | | |   (40)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.23/25.57  | | | | 
% 159.23/25.57  | | | | BETA: splitting (9) gives:
% 159.23/25.57  | | | | 
% 159.23/25.57  | | | | Case 1:
% 159.23/25.57  | | | | | 
% 159.23/25.57  | | | | |   (41)  all_54_1 = e3
% 159.23/25.57  | | | | | 
% 159.23/25.57  | | | | | COMBINE_EQS: (8), (41) imply:
% 159.23/25.57  | | | | |   (42)  all_52_4 = e3
% 159.23/25.57  | | | | | 
% 159.23/25.57  | | | | | REDUCE: (31), (42) imply:
% 159.23/25.57  | | | | |   (43)  $false
% 159.23/25.57  | | | | | 
% 159.23/25.57  | | | | | CLOSE: (43) is inconsistent.
% 159.23/25.57  | | | | | 
% 159.23/25.57  | | | | Case 2:
% 159.23/25.57  | | | | | 
% 159.23/25.57  | | | | |   (44)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.23/25.57  | | | | | 
% 159.23/25.57  | | | | | BETA: splitting (44) gives:
% 159.23/25.57  | | | | | 
% 159.23/25.57  | | | | | Case 1:
% 159.23/25.57  | | | | | | 
% 159.23/25.57  | | | | | |   (45)  all_54_1 = e2
% 159.23/25.57  | | | | | | 
% 159.23/25.57  | | | | | | COMBINE_EQS: (8), (45) imply:
% 159.23/25.57  | | | | | |   (46)  all_52_4 = e2
% 159.23/25.57  | | | | | | 
% 159.23/25.57  | | | | | | REDUCE: (33), (46) imply:
% 159.23/25.57  | | | | | |   (47)  $false
% 159.23/25.57  | | | | | | 
% 159.23/25.57  | | | | | | CLOSE: (47) is inconsistent.
% 159.23/25.57  | | | | | | 
% 159.23/25.57  | | | | | Case 2:
% 159.23/25.57  | | | | | | 
% 159.23/25.57  | | | | | |   (48)  all_54_1 = e1 | all_54_1 = e0
% 159.23/25.57  | | | | | | 
% 159.23/25.57  | | | | | | BETA: splitting (40) gives:
% 159.23/25.57  | | | | | | 
% 159.23/25.57  | | | | | | Case 1:
% 159.23/25.57  | | | | | | | 
% 159.23/25.57  | | | | | | |   (49)  all_54_3 = e2
% 159.23/25.57  | | | | | | | 
% 159.23/25.57  | | | | | | | COMBINE_EQS: (30), (49) imply:
% 159.23/25.57  | | | | | | |   (50)  all_48_0 = e2
% 159.23/25.57  | | | | | | | 
% 159.23/25.57  | | | | | | | SIMP: (50) implies:
% 159.23/25.58  | | | | | | |   (51)  all_48_0 = e2
% 159.23/25.58  | | | | | | | 
% 159.23/25.58  | | | | | | | REDUCE: (25), (51) imply:
% 159.23/25.58  | | | | | | |   (52)  $false
% 159.23/25.58  | | | | | | | 
% 159.23/25.58  | | | | | | | CLOSE: (52) is inconsistent.
% 159.23/25.58  | | | | | | | 
% 159.23/25.58  | | | | | | Case 2:
% 159.23/25.58  | | | | | | | 
% 159.23/25.58  | | | | | | |   (53)  all_54_3 = e1 | all_54_3 = e0
% 159.23/25.58  | | | | | | | 
% 159.23/25.58  | | | | | | | BETA: splitting (53) gives:
% 159.23/25.58  | | | | | | | 
% 159.23/25.58  | | | | | | | Case 1:
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | |   (54)  all_54_3 = e1
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | | COMBINE_EQS: (30), (54) imply:
% 159.23/25.58  | | | | | | | |   (55)  all_48_0 = e1
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | | SIMP: (55) implies:
% 159.23/25.58  | | | | | | | |   (56)  all_48_0 = e1
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | | REDUCE: (35), (56) imply:
% 159.23/25.58  | | | | | | | |   (57)  $false
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | | CLOSE: (57) is inconsistent.
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | Case 2:
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | |   (58)  all_54_3 = e0
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | | COMBINE_EQS: (30), (58) imply:
% 159.23/25.58  | | | | | | | |   (59)  all_48_0 = e0
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | | SIMP: (59) implies:
% 159.23/25.58  | | | | | | | |   (60)  all_48_0 = e0
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | | REDUCE: (32), (60) imply:
% 159.23/25.58  | | | | | | | |   (61)   ~ (all_52_4 = e0)
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | | BETA: splitting (48) gives:
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | | Case 1:
% 159.23/25.58  | | | | | | | | | 
% 159.23/25.58  | | | | | | | | |   (62)  all_54_1 = e1
% 159.23/25.58  | | | | | | | | | 
% 159.23/25.58  | | | | | | | | | REF_CLOSE: (5), (8), (62) are inconsistent by sub-proof #419.
% 159.23/25.58  | | | | | | | | | 
% 159.23/25.58  | | | | | | | | Case 2:
% 159.23/25.58  | | | | | | | | | 
% 159.23/25.58  | | | | | | | | |   (63)  all_54_1 = e0
% 159.23/25.58  | | | | | | | | | 
% 159.23/25.58  | | | | | | | | | REF_CLOSE: (8), (61), (63) are inconsistent by sub-proof #418.
% 159.23/25.58  | | | | | | | | | 
% 159.23/25.58  | | | | | | | | End of split
% 159.23/25.58  | | | | | | | | 
% 159.23/25.58  | | | | | | | End of split
% 159.23/25.58  | | | | | | | 
% 159.23/25.58  | | | | | | End of split
% 159.23/25.58  | | | | | | 
% 159.23/25.58  | | | | | End of split
% 159.23/25.58  | | | | | 
% 159.23/25.58  | | | | End of split
% 159.23/25.58  | | | | 
% 159.23/25.58  | | | End of split
% 159.23/25.58  | | | 
% 159.23/25.58  | | Case 2:
% 159.23/25.58  | | | 
% 159.23/25.58  | | |   (64)   ~ (all_48_1 = e1) & op(e3, e3) = all_48_1 & $i(all_48_1)
% 159.23/25.58  | | | 
% 159.23/25.58  | | | ALPHA: (64) implies:
% 159.23/25.58  | | |   (65)   ~ (all_48_1 = e1)
% 159.23/25.58  | | |   (66)  op(e3, e3) = all_48_1
% 159.23/25.58  | | | 
% 159.23/25.58  | | | GROUND_INST: instantiating (3) with e1, all_48_1, e3, e3, simplifying with
% 159.23/25.58  | | |              (13), (66) gives:
% 159.23/25.58  | | |   (67)  all_48_1 = e1
% 159.23/25.58  | | | 
% 159.23/25.58  | | | REDUCE: (65), (67) imply:
% 159.23/25.58  | | |   (68)  $false
% 159.23/25.58  | | | 
% 159.23/25.58  | | | CLOSE: (68) is inconsistent.
% 159.23/25.58  | | | 
% 159.23/25.58  | | End of split
% 159.23/25.58  | | 
% 159.23/25.58  | End of split
% 159.23/25.58  | 
% 159.23/25.58  End of proof
% 159.23/25.58  
% 159.23/25.58  Sub-proof #418 shows that the following formulas are inconsistent:
% 159.23/25.58  ----------------------------------------------------------------
% 159.23/25.58    (1)  all_54_1 = all_52_4
% 159.23/25.58    (2)  all_54_1 = e0
% 159.23/25.58    (3)   ~ (all_52_4 = e0)
% 159.23/25.58  
% 159.23/25.58  Begin of proof
% 159.23/25.58  | 
% 159.23/25.58  | COMBINE_EQS: (1), (2) imply:
% 159.23/25.58  |   (4)  all_52_4 = e0
% 159.23/25.58  | 
% 159.23/25.58  | SIMP: (4) implies:
% 159.23/25.58  |   (5)  all_52_4 = e0
% 159.23/25.58  | 
% 159.23/25.58  | REDUCE: (3), (5) imply:
% 159.23/25.58  |   (6)  $false
% 159.23/25.58  | 
% 159.23/25.58  | CLOSE: (6) is inconsistent.
% 159.23/25.58  | 
% 159.23/25.58  End of proof
% 159.23/25.58  
% 159.23/25.58  Sub-proof #419 shows that the following formulas are inconsistent:
% 159.23/25.58  ----------------------------------------------------------------
% 159.23/25.58    (1)  all_54_1 = all_52_4
% 159.23/25.58    (2)  all_54_1 = e1
% 159.23/25.58    (3)   ~ (all_52_4 = e1)
% 159.23/25.58  
% 159.23/25.58  Begin of proof
% 159.23/25.58  | 
% 159.23/25.58  | COMBINE_EQS: (1), (2) imply:
% 159.23/25.58  |   (4)  all_52_4 = e1
% 159.23/25.58  | 
% 159.23/25.58  | SIMP: (4) implies:
% 159.23/25.58  |   (5)  all_52_4 = e1
% 159.23/25.58  | 
% 159.23/25.58  | REDUCE: (3), (5) imply:
% 159.23/25.58  |   (6)  $false
% 159.23/25.58  | 
% 159.23/25.58  | CLOSE: (6) is inconsistent.
% 159.23/25.58  | 
% 159.23/25.58  End of proof
% 159.23/25.58  
% 159.23/25.58  Sub-proof #420 shows that the following formulas are inconsistent:
% 159.23/25.58  ----------------------------------------------------------------
% 159.23/25.58    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.58    (2)  op(e1, e1) = e1
% 159.23/25.58    (3)  op(e1, e3) = all_52_2
% 159.23/25.58    (4)  op(e0, e0) = e3
% 159.23/25.58    (5)   ~ (all_52_2 = e1)
% 159.23/25.58    (6)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.23/25.58           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.23/25.58           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 159.23/25.58           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.23/25.58           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 159.23/25.58           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.23/25.58    (7)   ~ (e3 = e1)
% 159.23/25.58  
% 159.23/25.58  Begin of proof
% 159.23/25.58  | 
% 159.23/25.58  | BETA: splitting (6) gives:
% 159.23/25.58  | 
% 159.23/25.58  | Case 1:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (8)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 159.23/25.58  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.23/25.58  | |          e0) = e1 & $i(all_57_14)
% 159.23/25.58  | | 
% 159.23/25.58  | | ALPHA: (8) implies:
% 159.23/25.58  | |   (9)  op(e0, e0) = e1
% 159.23/25.58  | | 
% 159.23/25.58  | | REF_CLOSE: (1), (4), (7), (9) are inconsistent by sub-proof #473.
% 159.23/25.58  | | 
% 159.23/25.58  | Case 2:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (10)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.23/25.58  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 159.23/25.58  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 159.23/25.58  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.23/25.58  | | 
% 159.23/25.58  | | REF_CLOSE: (1), (2), (3), (5), (7), (10) are inconsistent by sub-proof #989.
% 159.23/25.58  | | 
% 159.23/25.58  | End of split
% 159.23/25.58  | 
% 159.23/25.58  End of proof
% 159.23/25.58  
% 159.23/25.58  Sub-proof #421 shows that the following formulas are inconsistent:
% 159.23/25.58  ----------------------------------------------------------------
% 159.23/25.58    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.23/25.58         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.23/25.58    (2)   ~ (all_52_1 = e2)
% 159.23/25.58    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.58    (4)  op(e0, e3) = all_52_3
% 159.23/25.58    (5)  op(e1, e3) = all_52_2
% 159.23/25.58    (6)   ~ (all_52_2 = e2)
% 159.23/25.58    (7)  op(e0, e3) = e0
% 159.23/25.58    (8)  op(e3, e3) = e1
% 159.23/25.58    (9)  op(e2, e3) = all_52_1
% 159.23/25.58    (10)   ~ (e2 = e1)
% 159.23/25.58    (11)   ~ (e2 = e0)
% 159.23/25.58  
% 159.23/25.58  Begin of proof
% 159.23/25.58  | 
% 159.23/25.58  | BETA: splitting (1) gives:
% 159.23/25.58  | 
% 159.23/25.58  | Case 1:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (12)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 159.23/25.58  | |           e2)
% 159.23/25.58  | | 
% 159.23/25.58  | | REF_CLOSE: (2), (3), (8), (9), (10), (12) are inconsistent by sub-proof
% 159.23/25.58  | |            #422.
% 159.23/25.58  | | 
% 159.23/25.58  | Case 2:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (13)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 159.23/25.58  | |           e2)
% 159.23/25.58  | | 
% 159.23/25.58  | | REF_CLOSE: (3), (4), (5), (6), (7), (11), (13) are inconsistent by sub-proof
% 159.23/25.58  | |            #589.
% 159.23/25.58  | | 
% 159.23/25.58  | End of split
% 159.23/25.58  | 
% 159.23/25.58  End of proof
% 159.23/25.58  
% 159.23/25.58  Sub-proof #422 shows that the following formulas are inconsistent:
% 159.23/25.58  ----------------------------------------------------------------
% 159.23/25.58    (1)   ~ (all_52_1 = e2)
% 159.23/25.58    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.58    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 159.23/25.58    (4)  op(e3, e3) = e1
% 159.23/25.58    (5)  op(e2, e3) = all_52_1
% 159.23/25.58    (6)   ~ (e2 = e1)
% 159.23/25.58  
% 159.23/25.58  Begin of proof
% 159.23/25.58  | 
% 159.23/25.58  | BETA: splitting (3) gives:
% 159.23/25.58  | 
% 159.23/25.58  | Case 1:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 159.23/25.58  | | 
% 159.23/25.58  | | ALPHA: (7) implies:
% 159.23/25.58  | |   (8)  op(e3, e3) = e2
% 159.23/25.58  | | 
% 159.23/25.58  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #828.
% 159.23/25.58  | | 
% 159.23/25.58  | Case 2:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 159.23/25.58  | | 
% 159.23/25.58  | | ALPHA: (9) implies:
% 159.23/25.58  | |   (10)  op(e2, e3) = e2
% 159.23/25.58  | | 
% 159.23/25.58  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1007.
% 159.23/25.58  | | 
% 159.23/25.58  | End of split
% 159.23/25.58  | 
% 159.23/25.58  End of proof
% 159.23/25.58  
% 159.23/25.58  Sub-proof #423 shows that the following formulas are inconsistent:
% 159.23/25.58  ----------------------------------------------------------------
% 159.23/25.58    (1)  all_56_5 = e1 & op(e2, e1) = e1
% 159.23/25.58    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.58    (3)  op(e2, e1) = all_52_9
% 159.23/25.58    (4)   ~ (all_52_9 = e1)
% 159.23/25.58  
% 159.23/25.58  Begin of proof
% 159.23/25.58  | 
% 159.23/25.58  | ALPHA: (1) implies:
% 159.23/25.58  |   (5)  op(e2, e1) = e1
% 159.23/25.58  | 
% 159.23/25.58  | GROUND_INST: instantiating (2) with all_52_9, e1, e1, e2, simplifying with
% 159.23/25.58  |              (3), (5) gives:
% 159.23/25.58  |   (6)  all_52_9 = e1
% 159.23/25.58  | 
% 159.23/25.58  | REDUCE: (4), (6) imply:
% 159.23/25.58  |   (7)  $false
% 159.23/25.58  | 
% 159.23/25.58  | CLOSE: (7) is inconsistent.
% 159.23/25.58  | 
% 159.23/25.58  End of proof
% 159.23/25.58  
% 159.23/25.58  Sub-proof #424 shows that the following formulas are inconsistent:
% 159.23/25.58  ----------------------------------------------------------------
% 159.23/25.58    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.23/25.58         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.23/25.58    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 159.23/25.58         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 159.23/25.58    (3)   ~ (e3 = e2)
% 159.23/25.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.58    (5)  op(e0, e3) = all_52_3
% 159.23/25.58    (6)  op(e3, e3) = e1
% 159.23/25.58    (7)   ~ (e1 = e0)
% 159.23/25.58    (8)  all_56_2 = e1
% 159.23/25.58    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.23/25.58         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.23/25.58    (10)  op(e2, e3) = e1
% 159.23/25.58    (11)   ~ (e2 = e1)
% 159.23/25.58    (12)   ~ (e3 = e1)
% 159.23/25.58    (13)   ~ (e2 = e0)
% 159.23/25.58    (14)   ~ (e3 = e0)
% 159.23/25.58  
% 159.23/25.58  Begin of proof
% 159.23/25.58  | 
% 159.23/25.58  | BETA: splitting (1) gives:
% 159.23/25.58  | 
% 159.23/25.58  | Case 1:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (15)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 159.23/25.58  | |           e2)
% 159.23/25.58  | | 
% 159.23/25.58  | | REF_CLOSE: (4), (6), (10), (11), (15) are inconsistent by sub-proof #427.
% 159.23/25.58  | | 
% 159.23/25.58  | Case 2:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (16)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 159.23/25.58  | |           e2)
% 159.23/25.58  | | 
% 159.23/25.58  | | BETA: splitting (16) gives:
% 159.23/25.58  | | 
% 159.23/25.58  | | Case 1:
% 159.23/25.58  | | | 
% 159.23/25.58  | | |   (17)  all_56_6 = e2 & op(e1, e3) = e2
% 159.23/25.58  | | | 
% 159.23/25.58  | | | ALPHA: (17) implies:
% 159.23/25.58  | | |   (18)  all_56_6 = e2
% 159.23/25.58  | | | 
% 159.23/25.58  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.23/25.58  | | |            (14), (18) are inconsistent by sub-proof #425.
% 159.23/25.58  | | | 
% 159.23/25.58  | | Case 2:
% 159.23/25.58  | | | 
% 159.23/25.58  | | |   (19)  all_56_12 = e2 & op(e0, e3) = e2
% 159.23/25.58  | | | 
% 159.23/25.58  | | | ALPHA: (19) implies:
% 159.23/25.58  | | |   (20)  all_56_12 = e2
% 159.23/25.58  | | |   (21)  op(e0, e3) = e2
% 159.23/25.58  | | | 
% 159.23/25.58  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14), (20),
% 159.23/25.58  | | |            (21) are inconsistent by sub-proof #481.
% 159.23/25.58  | | | 
% 159.23/25.58  | | End of split
% 159.23/25.58  | | 
% 159.23/25.58  | End of split
% 159.23/25.58  | 
% 159.23/25.58  End of proof
% 159.23/25.58  
% 159.23/25.58  Sub-proof #425 shows that the following formulas are inconsistent:
% 159.23/25.58  ----------------------------------------------------------------
% 159.23/25.58    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.23/25.58         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.23/25.58    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 159.23/25.58         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 159.23/25.58    (3)   ~ (e3 = e2)
% 159.23/25.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.58    (5)  all_56_6 = e2
% 159.23/25.58    (6)  op(e3, e3) = e1
% 159.23/25.58    (7)   ~ (e1 = e0)
% 159.23/25.58    (8)  all_56_2 = e1
% 159.23/25.58    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.23/25.58         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.23/25.58    (10)  op(e2, e3) = e1
% 159.23/25.58    (11)   ~ (e2 = e1)
% 159.23/25.58    (12)   ~ (e3 = e1)
% 159.23/25.58    (13)   ~ (e2 = e0)
% 159.23/25.58    (14)   ~ (e3 = e0)
% 159.23/25.58  
% 159.23/25.58  Begin of proof
% 159.23/25.58  | 
% 159.23/25.58  | BETA: splitting (2) gives:
% 159.23/25.58  | 
% 159.23/25.58  | Case 1:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (15)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 159.23/25.58  | |           e3)
% 159.23/25.58  | | 
% 159.23/25.58  | | REF_CLOSE: (4), (6), (8), (12), (15) are inconsistent by sub-proof #483.
% 159.23/25.58  | | 
% 159.23/25.58  | Case 2:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (16)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 159.23/25.58  | |           e3)
% 159.23/25.58  | | 
% 159.23/25.58  | | BETA: splitting (16) gives:
% 159.23/25.58  | | 
% 159.23/25.58  | | Case 1:
% 159.23/25.58  | | | 
% 159.23/25.58  | | |   (17)  all_56_6 = e3 & op(e1, e3) = e3
% 159.23/25.58  | | | 
% 159.23/25.58  | | | ALPHA: (17) implies:
% 159.23/25.58  | | |   (18)  all_56_6 = e3
% 159.23/25.58  | | | 
% 159.23/25.58  | | | COMBINE_EQS: (5), (18) imply:
% 159.23/25.58  | | |   (19)  e3 = e2
% 159.23/25.58  | | | 
% 159.23/25.58  | | | SIMP: (19) implies:
% 159.23/25.58  | | |   (20)  e3 = e2
% 159.23/25.58  | | | 
% 159.23/25.58  | | | REDUCE: (3), (20) imply:
% 159.23/25.58  | | |   (21)  $false
% 159.23/25.58  | | | 
% 159.23/25.58  | | | CLOSE: (21) is inconsistent.
% 159.23/25.58  | | | 
% 159.23/25.58  | | Case 2:
% 159.23/25.58  | | | 
% 159.23/25.58  | | |   (22)  all_56_12 = e3 & op(e0, e3) = e3
% 159.23/25.58  | | | 
% 159.23/25.58  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.23/25.58  | | |            (14), (22) are inconsistent by sub-proof #426.
% 159.23/25.58  | | | 
% 159.23/25.58  | | End of split
% 159.23/25.58  | | 
% 159.23/25.58  | End of split
% 159.23/25.58  | 
% 159.23/25.58  End of proof
% 159.23/25.58  
% 159.23/25.58  Sub-proof #426 shows that the following formulas are inconsistent:
% 159.23/25.58  ----------------------------------------------------------------
% 159.23/25.58    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.23/25.58         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.23/25.58    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 159.23/25.58         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 159.23/25.58    (3)  all_56_12 = e3 & op(e0, e3) = e3
% 159.23/25.58    (4)   ~ (e3 = e2)
% 159.23/25.58    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.58    (6)  op(e3, e3) = e1
% 159.23/25.58    (7)   ~ (e1 = e0)
% 159.23/25.58    (8)  all_56_2 = e1
% 159.23/25.58    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.23/25.58         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.23/25.58    (10)  op(e2, e3) = e1
% 159.23/25.58    (11)   ~ (e2 = e1)
% 159.23/25.58    (12)   ~ (e3 = e1)
% 159.23/25.58    (13)   ~ (e2 = e0)
% 159.23/25.58    (14)   ~ (e3 = e0)
% 159.23/25.58  
% 159.23/25.58  Begin of proof
% 159.23/25.58  | 
% 159.23/25.58  | ALPHA: (3) implies:
% 159.23/25.58  |   (15)  all_56_12 = e3
% 159.23/25.58  | 
% 159.23/25.58  | BETA: splitting (9) gives:
% 159.23/25.58  | 
% 159.23/25.58  | Case 1:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (16)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 159.23/25.58  | |           e0)
% 159.23/25.58  | | 
% 159.23/25.58  | | REF_CLOSE: (5), (6), (7), (8), (16) are inconsistent by sub-proof #485.
% 159.23/25.58  | | 
% 159.23/25.58  | Case 2:
% 159.23/25.58  | | 
% 159.23/25.58  | |   (17)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 159.23/25.58  | |           e0)
% 159.23/25.58  | | 
% 159.23/25.58  | | BETA: splitting (17) gives:
% 159.23/25.58  | | 
% 159.23/25.58  | | Case 1:
% 159.23/25.58  | | | 
% 159.23/25.58  | | |   (18)  all_56_6 = e0 & op(e1, e3) = e0
% 159.23/25.58  | | | 
% 159.23/25.58  | | | ALPHA: (18) implies:
% 159.23/25.58  | | |   (19)  all_56_6 = e0
% 159.23/25.58  | | |   (20)  op(e1, e3) = e0
% 159.23/25.58  | | | 
% 159.23/25.58  | | | BETA: splitting (1) gives:
% 159.23/25.58  | | | 
% 159.23/25.58  | | | Case 1:
% 159.23/25.58  | | | | 
% 159.23/25.58  | | | |   (21)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3)
% 159.23/25.58  | | | |           = e2)
% 159.23/25.58  | | | | 
% 159.23/25.59  | | | | REF_CLOSE: (5), (6), (10), (11), (21) are inconsistent by sub-proof
% 159.23/25.59  | | | |            #427.
% 159.23/25.59  | | | | 
% 159.23/25.59  | | | Case 2:
% 159.23/25.59  | | | | 
% 159.23/25.59  | | | |   (22)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3)
% 159.23/25.59  | | | |           = e2)
% 159.23/25.59  | | | | 
% 159.23/25.59  | | | | BETA: splitting (22) gives:
% 159.23/25.59  | | | | 
% 159.23/25.59  | | | | Case 1:
% 159.23/25.59  | | | | | 
% 159.23/25.59  | | | | |   (23)  all_56_6 = e2 & op(e1, e3) = e2
% 159.23/25.59  | | | | | 
% 159.23/25.59  | | | | | ALPHA: (23) implies:
% 159.23/25.59  | | | | |   (24)  all_56_6 = e2
% 159.23/25.59  | | | | | 
% 159.23/25.59  | | | | | COMBINE_EQS: (19), (24) imply:
% 159.23/25.59  | | | | |   (25)  e2 = e0
% 159.23/25.59  | | | | | 
% 159.23/25.59  | | | | | REDUCE: (13), (25) imply:
% 159.23/25.59  | | | | |   (26)  $false
% 159.23/25.59  | | | | | 
% 159.23/25.59  | | | | | CLOSE: (26) is inconsistent.
% 159.23/25.59  | | | | | 
% 159.23/25.59  | | | | Case 2:
% 159.23/25.59  | | | | | 
% 159.23/25.59  | | | | |   (27)  all_56_12 = e2 & op(e0, e3) = e2
% 159.23/25.59  | | | | | 
% 159.23/25.59  | | | | | ALPHA: (27) implies:
% 159.23/25.59  | | | | |   (28)  all_56_12 = e2
% 159.23/25.59  | | | | | 
% 159.23/25.59  | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (12), (14), (20), (28) are
% 159.23/25.59  | | | | |            inconsistent by sub-proof #482.
% 159.23/25.59  | | | | | 
% 159.23/25.59  | | | | End of split
% 159.23/25.59  | | | | 
% 159.23/25.59  | | | End of split
% 159.23/25.59  | | | 
% 159.23/25.59  | | Case 2:
% 159.23/25.59  | | | 
% 159.23/25.59  | | |   (29)  all_56_12 = e0 & op(e0, e3) = e0
% 159.23/25.59  | | | 
% 159.23/25.59  | | | REF_CLOSE: (14), (15), (29) are inconsistent by sub-proof #735.
% 159.23/25.59  | | | 
% 159.23/25.59  | | End of split
% 159.23/25.59  | | 
% 159.23/25.59  | End of split
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #427 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.59    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 159.23/25.59    (3)  op(e3, e3) = e1
% 159.23/25.59    (4)  op(e2, e3) = e1
% 159.23/25.59    (5)   ~ (e2 = e1)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | BETA: splitting (2) gives:
% 159.23/25.59  | 
% 159.23/25.59  | Case 1:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (6)  all_56_0 = e2 & op(e3, e3) = e2
% 159.23/25.59  | | 
% 159.23/25.59  | | ALPHA: (6) implies:
% 159.23/25.59  | |   (7)  op(e3, e3) = e2
% 159.23/25.59  | | 
% 159.23/25.59  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #828.
% 159.23/25.59  | | 
% 159.23/25.59  | Case 2:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (8)  all_56_2 = e2 & op(e2, e3) = e2
% 159.23/25.59  | | 
% 159.23/25.59  | | ALPHA: (8) implies:
% 159.23/25.59  | |   (9)  op(e2, e3) = e2
% 159.23/25.59  | | 
% 159.23/25.59  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #428.
% 159.23/25.59  | | 
% 159.23/25.59  | End of split
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #428 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.59    (2)  op(e2, e3) = e2
% 159.23/25.59    (3)  op(e2, e3) = e1
% 159.23/25.59    (4)   ~ (e2 = e1)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | GROUND_INST: instantiating (1) with e1, e2, e3, e2, simplifying with (2), (3)
% 159.23/25.59  |              gives:
% 159.23/25.59  |   (5)  e2 = e1
% 159.23/25.59  | 
% 159.23/25.59  | REDUCE: (4), (5) imply:
% 159.23/25.59  |   (6)  $false
% 159.23/25.59  | 
% 159.23/25.59  | CLOSE: (6) is inconsistent.
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #429 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)  all_56_13 = e3 & op(e0, e2) = e3
% 159.23/25.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.59    (3)  op(e0, e2) = all_52_7
% 159.23/25.59    (4)   ~ (all_52_7 = e3)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | ALPHA: (1) implies:
% 159.23/25.59  |   (5)  op(e0, e2) = e3
% 159.23/25.59  | 
% 159.23/25.59  | GROUND_INST: instantiating (2) with all_52_7, e3, e2, e0, simplifying with
% 159.23/25.59  |              (3), (5) gives:
% 159.23/25.59  |   (6)  all_52_7 = e3
% 159.23/25.59  | 
% 159.23/25.59  | REDUCE: (4), (6) imply:
% 159.23/25.59  |   (7)  $false
% 159.23/25.59  | 
% 159.23/25.59  | CLOSE: (7) is inconsistent.
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #430 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.59    (2)  op(e0, e0) = e3
% 159.23/25.59    (3)  all_57_8 = e0
% 159.23/25.59    (4)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 159.23/25.59           all_57_8 & $i(all_57_8))
% 159.23/25.59    (5)   ~ (e3 = e1)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | BETA: splitting (4) gives:
% 159.23/25.59  | 
% 159.23/25.59  | Case 1:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (6)  all_57_15 = e1 & op(e0, e0) = e1
% 159.23/25.59  | | 
% 159.23/25.59  | | ALPHA: (6) implies:
% 159.23/25.59  | |   (7)  op(e0, e0) = e1
% 159.23/25.59  | | 
% 159.23/25.59  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #473.
% 159.23/25.59  | | 
% 159.23/25.59  | Case 2:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (8)   ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)
% 159.23/25.59  | | 
% 159.23/25.59  | | ALPHA: (8) implies:
% 159.23/25.59  | |   (9)   ~ (all_57_8 = e0)
% 159.23/25.59  | | 
% 159.23/25.59  | | REDUCE: (3), (9) imply:
% 159.23/25.59  | |   (10)  $false
% 159.23/25.59  | | 
% 159.23/25.59  | | CLOSE: (10) is inconsistent.
% 159.23/25.59  | | 
% 159.23/25.59  | End of split
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #431 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)  op(e0, e1) = all_52_11
% 159.23/25.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.59    (3)  op(e0, e0) = e3
% 159.23/25.59    (4)   ~ (all_52_11 = e1)
% 159.23/25.59    (5)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.23/25.59    (6)   ~ (e3 = e1)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | BETA: splitting (5) gives:
% 159.23/25.59  | 
% 159.23/25.59  | Case 1:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (7)  all_56_14 = e1 & op(e0, e1) = e1
% 159.23/25.59  | | 
% 159.23/25.59  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #803.
% 159.23/25.59  | | 
% 159.23/25.59  | Case 2:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (8)  all_56_15 = e1 & op(e0, e0) = e1
% 159.23/25.59  | | 
% 159.23/25.59  | | ALPHA: (8) implies:
% 159.23/25.59  | |   (9)  op(e0, e0) = e1
% 159.23/25.59  | | 
% 159.23/25.59  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #473.
% 159.23/25.59  | | 
% 159.23/25.59  | End of split
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #432 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)   ~ (e3 = e2)
% 159.23/25.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.59    (3)   ~ (all_4_2 = e3)
% 159.23/25.59    (4)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 159.23/25.59    (5)  op(e2, e2) = all_4_2
% 159.23/25.59    (6)  op(e3, e2) = e2
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | BETA: splitting (4) gives:
% 159.23/25.59  | 
% 159.23/25.59  | Case 1:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (7)  all_56_1 = e3 & op(e3, e2) = e3
% 159.23/25.59  | | 
% 159.23/25.59  | | ALPHA: (7) implies:
% 159.23/25.59  | |   (8)  op(e3, e2) = e3
% 159.23/25.59  | | 
% 159.23/25.59  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #433.
% 159.23/25.59  | | 
% 159.23/25.59  | Case 2:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (9)  all_56_3 = e3 & op(e2, e2) = e3
% 159.23/25.59  | | 
% 159.23/25.59  | | ALPHA: (9) implies:
% 159.23/25.59  | |   (10)  op(e2, e2) = e3
% 159.23/25.59  | | 
% 159.23/25.59  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #711.
% 159.23/25.59  | | 
% 159.23/25.59  | End of split
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #433 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.59    (2)  op(e3, e2) = e3
% 159.23/25.59    (3)  op(e3, e2) = e2
% 159.23/25.59    (4)   ~ (e3 = e2)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | GROUND_INST: instantiating (1) with e2, e3, e2, e3, simplifying with (2), (3)
% 159.23/25.59  |              gives:
% 159.23/25.59  |   (5)  e3 = e2
% 159.23/25.59  | 
% 159.23/25.59  | REDUCE: (4), (5) imply:
% 159.23/25.59  |   (6)  $false
% 159.23/25.59  | 
% 159.23/25.59  | CLOSE: (6) is inconsistent.
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #434 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)  all_56_10 = e1 & op(e2, e0) = e1
% 159.23/25.59    (2)  all_56_10 = e0
% 159.23/25.59    (3)   ~ (e1 = e0)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | ALPHA: (1) implies:
% 159.23/25.59  |   (4)  all_56_10 = e1
% 159.23/25.59  | 
% 159.23/25.59  | COMBINE_EQS: (2), (4) imply:
% 159.23/25.59  |   (5)  e1 = e0
% 159.23/25.59  | 
% 159.23/25.59  | REDUCE: (3), (5) imply:
% 159.23/25.59  |   (6)  $false
% 159.23/25.59  | 
% 159.23/25.59  | CLOSE: (6) is inconsistent.
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #435 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.59    (2)  all_56_10 = e2
% 159.23/25.59    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 159.23/25.59    (4)  op(e3, e3) = e3
% 159.23/25.59    (5)  op(e2, e2) = e0
% 159.23/25.59    (6)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.23/25.59         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.23/25.59    (7)   ~ (e1 = e0)
% 159.23/25.59    (8)   ~ (e2 = e1)
% 159.23/25.59    (9)  all_56_5 = e3
% 159.23/25.59    (10)   ~ (e3 = e1)
% 159.23/25.59    (11)   ~ (e3 = e0)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | BETA: splitting (3) gives:
% 159.23/25.59  | 
% 159.23/25.59  | Case 1:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (12)  all_56_0 = e0 & op(e3, e3) = e0
% 159.23/25.59  | | 
% 159.23/25.59  | | ALPHA: (12) implies:
% 159.23/25.59  | |   (13)  op(e3, e3) = e0
% 159.23/25.59  | | 
% 159.23/25.59  | | REF_CLOSE: (1), (4), (11), (13) are inconsistent by sub-proof #971.
% 159.23/25.59  | | 
% 159.23/25.59  | Case 2:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (14)  all_56_2 = e0 & op(e2, e3) = e0
% 159.23/25.59  | | 
% 159.23/25.59  | | ALPHA: (14) implies:
% 159.23/25.59  | |   (15)  all_56_2 = e0
% 159.23/25.59  | | 
% 159.23/25.59  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (15) are inconsistent by
% 159.23/25.59  | |            sub-proof #436.
% 159.23/25.59  | | 
% 159.23/25.59  | End of split
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #436 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)  all_56_2 = e0
% 159.23/25.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.59    (3)  all_56_10 = e2
% 159.23/25.59    (4)  op(e2, e2) = e0
% 159.23/25.59    (5)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.23/25.59         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.23/25.59    (6)   ~ (e1 = e0)
% 159.23/25.59    (7)   ~ (e2 = e1)
% 159.23/25.59    (8)  all_56_5 = e3
% 159.23/25.59    (9)   ~ (e3 = e1)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | BETA: splitting (5) gives:
% 159.23/25.59  | 
% 159.23/25.59  | Case 1:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (10)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 159.23/25.59  | |           e1)
% 159.23/25.59  | | 
% 159.23/25.59  | | BETA: splitting (10) gives:
% 159.23/25.59  | | 
% 159.23/25.59  | | Case 1:
% 159.23/25.59  | | | 
% 159.23/25.59  | | |   (11)  all_56_2 = e1 & op(e2, e3) = e1
% 159.23/25.59  | | | 
% 159.23/25.59  | | | ALPHA: (11) implies:
% 159.23/25.59  | | |   (12)  all_56_2 = e1
% 159.23/25.59  | | | 
% 159.23/25.59  | | | COMBINE_EQS: (1), (12) imply:
% 159.23/25.59  | | |   (13)  e1 = e0
% 159.23/25.59  | | | 
% 159.23/25.59  | | | REDUCE: (6), (13) imply:
% 159.23/25.59  | | |   (14)  $false
% 159.23/25.59  | | | 
% 159.23/25.59  | | | CLOSE: (14) is inconsistent.
% 159.23/25.59  | | | 
% 159.23/25.59  | | Case 2:
% 159.23/25.59  | | | 
% 159.23/25.59  | | |   (15)  all_56_3 = e1 & op(e2, e2) = e1
% 159.23/25.59  | | | 
% 159.23/25.59  | | | ALPHA: (15) implies:
% 159.23/25.59  | | |   (16)  op(e2, e2) = e1
% 159.23/25.59  | | | 
% 159.23/25.59  | | | REF_CLOSE: (2), (4), (6), (16) are inconsistent by sub-proof #960.
% 159.23/25.59  | | | 
% 159.23/25.59  | | End of split
% 159.23/25.59  | | 
% 159.23/25.59  | Case 2:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (17)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 159.23/25.59  | |           e1)
% 159.23/25.59  | | 
% 159.23/25.59  | | BETA: splitting (17) gives:
% 159.23/25.59  | | 
% 159.23/25.59  | | Case 1:
% 159.23/25.59  | | | 
% 159.23/25.59  | | |   (18)  all_56_5 = e1 & op(e2, e1) = e1
% 159.23/25.59  | | | 
% 159.23/25.59  | | | REF_CLOSE: (8), (9), (18) are inconsistent by sub-proof #437.
% 159.23/25.59  | | | 
% 159.23/25.59  | | Case 2:
% 159.23/25.59  | | | 
% 159.23/25.59  | | |   (19)  all_56_10 = e1 & op(e2, e0) = e1
% 159.23/25.59  | | | 
% 159.23/25.59  | | | ALPHA: (19) implies:
% 159.23/25.59  | | |   (20)  all_56_10 = e1
% 159.23/25.59  | | | 
% 159.23/25.59  | | | REF_CLOSE: (3), (7), (20) are inconsistent by sub-proof #886.
% 159.23/25.59  | | | 
% 159.23/25.59  | | End of split
% 159.23/25.59  | | 
% 159.23/25.59  | End of split
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #437 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)  all_56_5 = e1 & op(e2, e1) = e1
% 159.23/25.59    (2)  all_56_5 = e3
% 159.23/25.59    (3)   ~ (e3 = e1)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | ALPHA: (1) implies:
% 159.23/25.59  |   (4)  all_56_5 = e1
% 159.23/25.59  | 
% 159.23/25.59  | COMBINE_EQS: (2), (4) imply:
% 159.23/25.59  |   (5)  e3 = e1
% 159.23/25.59  | 
% 159.23/25.59  | REDUCE: (3), (5) imply:
% 159.23/25.59  |   (6)  $false
% 159.23/25.59  | 
% 159.23/25.59  | CLOSE: (6) is inconsistent.
% 159.23/25.59  | 
% 159.23/25.59  End of proof
% 159.23/25.59  
% 159.23/25.59  Sub-proof #438 shows that the following formulas are inconsistent:
% 159.23/25.59  ----------------------------------------------------------------
% 159.23/25.59    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.23/25.59         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.23/25.59    (2)   ~ (all_52_7 = e0)
% 159.23/25.59    (3)   ~ (e3 = e2)
% 159.23/25.59    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.23/25.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.23/25.59    (5)  op(e0, e2) = all_52_7
% 159.23/25.59    (6)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.23/25.59         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.23/25.59    (7)  all_57_15 = e3
% 159.23/25.59    (8)  op(e3, e3) = e3
% 159.23/25.59    (9)  op(e2, e2) = e0
% 159.23/25.59    (10)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.23/25.59          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.23/25.59    (11)   ~ (e1 = e0)
% 159.23/25.59    (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.23/25.59          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.23/25.59    (13)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.23/25.59          (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.23/25.59            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 159.23/25.59            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) =
% 159.23/25.59            e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.23/25.59    (14)   ~ (e2 = e1)
% 159.23/25.59    (15)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.23/25.59          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.23/25.59    (16)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.23/25.59          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.23/25.59    (17)  all_56_5 = e3
% 159.23/25.59    (18)   ~ (e3 = e1)
% 159.23/25.59    (19)   ~ (e2 = e0)
% 159.23/25.59    (20)   ~ (e3 = e0)
% 159.23/25.59  
% 159.23/25.59  Begin of proof
% 159.23/25.59  | 
% 159.23/25.59  | BETA: splitting (13) gives:
% 159.23/25.59  | 
% 159.23/25.59  | Case 1:
% 159.23/25.59  | | 
% 159.23/25.59  | |   (21)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 159.23/25.59  | | 
% 159.23/25.59  | | ALPHA: (21) implies:
% 159.23/25.59  | |   (22)  all_57_15 = e0
% 159.23/25.59  | | 
% 159.23/25.59  | | COMBINE_EQS: (7), (22) imply:
% 159.23/25.59  | |   (23)  e3 = e0
% 159.23/25.59  | | 
% 159.23/25.59  | | COMBINE_EQS: (17), (23) imply:
% 159.23/25.59  | |   (24)  all_56_5 = e0
% 159.23/25.59  | | 
% 159.23/25.59  | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (11), (12), (14), (15), (16),
% 159.23/25.59  | |            (18), (19), (20), (24) are inconsistent by sub-proof #439.
% 159.23/25.59  | | 
% 159.23/25.59  | Case 2:
% 159.23/25.59  | | 
% 159.28/25.59  | |   (25)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.28/25.59  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.28/25.59  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.28/25.59  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.28/25.59  | | 
% 159.28/25.60  | | REF_CLOSE: (2), (4), (5), (8), (20), (25) are inconsistent by sub-proof
% 159.28/25.60  | |            #900.
% 159.28/25.60  | | 
% 159.28/25.60  | End of split
% 159.28/25.60  | 
% 159.28/25.60  End of proof
% 159.28/25.60  
% 159.28/25.60  Sub-proof #439 shows that the following formulas are inconsistent:
% 159.28/25.60  ----------------------------------------------------------------
% 159.28/25.60    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.28/25.60         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.28/25.60    (2)   ~ (e3 = e2)
% 159.28/25.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.60    (4)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.28/25.60         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.28/25.60    (5)  op(e3, e3) = e3
% 159.28/25.60    (6)  op(e2, e2) = e0
% 159.28/25.60    (7)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.28/25.60         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.28/25.60    (8)   ~ (e1 = e0)
% 159.28/25.60    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.28/25.60         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.28/25.60    (10)   ~ (e2 = e1)
% 159.28/25.60    (11)  all_56_5 = e0
% 159.28/25.60    (12)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.28/25.60          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.28/25.60    (13)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.28/25.60          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.28/25.60    (14)   ~ (e3 = e1)
% 159.28/25.60    (15)   ~ (e2 = e0)
% 159.28/25.60    (16)   ~ (e3 = e0)
% 159.28/25.60  
% 159.28/25.60  Begin of proof
% 159.28/25.60  | 
% 159.28/25.60  | BETA: splitting (4) gives:
% 159.28/25.60  | 
% 159.28/25.60  | Case 1:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (17)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 159.28/25.60  | |           e3)
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (13), (14), (15), (16),
% 159.28/25.60  | |            (17) are inconsistent by sub-proof #441.
% 159.28/25.60  | | 
% 159.28/25.60  | Case 2:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (18)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 159.28/25.60  | |           e3)
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (2), (3), (6), (7), (8), (10), (11), (12), (14), (15), (16), (18)
% 159.28/25.60  | |            are inconsistent by sub-proof #440.
% 159.28/25.60  | | 
% 159.28/25.60  | End of split
% 159.28/25.60  | 
% 159.28/25.60  End of proof
% 159.28/25.60  
% 159.28/25.60  Sub-proof #440 shows that the following formulas are inconsistent:
% 159.28/25.60  ----------------------------------------------------------------
% 159.28/25.60    (1)   ~ (e3 = e2)
% 159.28/25.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.60    (3)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.28/25.60    (4)  op(e2, e2) = e0
% 159.28/25.60    (5)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.28/25.60         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.28/25.60    (6)   ~ (e1 = e0)
% 159.28/25.60    (7)   ~ (e2 = e1)
% 159.28/25.60    (8)  all_56_5 = e0
% 159.28/25.60    (9)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.28/25.60         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.28/25.60    (10)   ~ (e3 = e1)
% 159.28/25.60    (11)   ~ (e2 = e0)
% 159.28/25.60    (12)   ~ (e3 = e0)
% 159.28/25.60  
% 159.28/25.60  Begin of proof
% 159.28/25.60  | 
% 159.28/25.60  | BETA: splitting (3) gives:
% 159.28/25.60  | 
% 159.28/25.60  | Case 1:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (13)  all_56_5 = e3 & op(e2, e1) = e3
% 159.28/25.60  | | 
% 159.28/25.60  | | ALPHA: (13) implies:
% 159.28/25.60  | |   (14)  all_56_5 = e3
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (8), (12), (14) are inconsistent by sub-proof #591.
% 159.28/25.60  | | 
% 159.28/25.60  | Case 2:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (15)  all_56_10 = e3 & op(e2, e0) = e3
% 159.28/25.60  | | 
% 159.28/25.60  | | ALPHA: (15) implies:
% 159.28/25.60  | |   (16)  all_56_10 = e3
% 159.28/25.60  | |   (17)  op(e2, e0) = e3
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (16), (17)
% 159.28/25.60  | |            are inconsistent by sub-proof #552.
% 159.28/25.60  | | 
% 159.28/25.60  | End of split
% 159.28/25.60  | 
% 159.28/25.60  End of proof
% 159.28/25.60  
% 159.28/25.60  Sub-proof #441 shows that the following formulas are inconsistent:
% 159.28/25.60  ----------------------------------------------------------------
% 159.28/25.60    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.28/25.60         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.28/25.60    (2)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 159.28/25.60    (3)   ~ (e3 = e2)
% 159.28/25.60    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.60    (5)  op(e3, e3) = e3
% 159.28/25.60    (6)  op(e2, e2) = e0
% 159.28/25.60    (7)   ~ (e1 = e0)
% 159.28/25.60    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.28/25.60         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.28/25.60    (9)   ~ (e2 = e1)
% 159.28/25.60    (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.28/25.60          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.28/25.60    (11)   ~ (e3 = e1)
% 159.28/25.60    (12)   ~ (e2 = e0)
% 159.28/25.60    (13)   ~ (e3 = e0)
% 159.28/25.60  
% 159.28/25.60  Begin of proof
% 159.28/25.60  | 
% 159.28/25.60  | BETA: splitting (2) gives:
% 159.28/25.60  | 
% 159.28/25.60  | Case 1:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (14)  all_56_2 = e3 & op(e2, e3) = e3
% 159.28/25.60  | | 
% 159.28/25.60  | | ALPHA: (14) implies:
% 159.28/25.60  | |   (15)  all_56_2 = e3
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (15)
% 159.28/25.60  | |            are inconsistent by sub-proof #765.
% 159.28/25.60  | | 
% 159.28/25.60  | Case 2:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (16)  all_56_3 = e3 & op(e2, e2) = e3
% 159.28/25.60  | | 
% 159.28/25.60  | | ALPHA: (16) implies:
% 159.28/25.60  | |   (17)  op(e2, e2) = e3
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (4), (6), (13), (17) are inconsistent by sub-proof #945.
% 159.28/25.60  | | 
% 159.28/25.60  | End of split
% 159.28/25.60  | 
% 159.28/25.60  End of proof
% 159.28/25.60  
% 159.28/25.60  Sub-proof #442 shows that the following formulas are inconsistent:
% 159.28/25.60  ----------------------------------------------------------------
% 159.28/25.60    (1)   ~ (e3 = e2)
% 159.28/25.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.60    (3)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.28/25.60           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.28/25.60           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 159.28/25.60           & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 159.28/25.60           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 159.28/25.60           e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 159.28/25.60         (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 159.28/25.60           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.28/25.60           = e3 & $i(all_57_10))
% 159.28/25.60    (4)   ~ (all_52_12 = e3)
% 159.28/25.60    (5)  op(e0, e0) = e3
% 159.28/25.60    (6)  op(e2, e2) = e0
% 159.28/25.60    (7)   ~ (e1 = e0)
% 159.28/25.60    (8)  op(e3, e0) = all_52_12
% 159.28/25.60    (9)   ~ (e2 = e0)
% 159.28/25.60  
% 159.28/25.60  Begin of proof
% 159.28/25.60  | 
% 159.28/25.60  | BETA: splitting (3) gives:
% 159.28/25.60  | 
% 159.28/25.60  | Case 1:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (10)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.28/25.60  | |             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0
% 159.28/25.60  | |           & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 =
% 159.28/25.60  | |           e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.28/25.60  | | 
% 159.28/25.60  | | BETA: splitting (10) gives:
% 159.28/25.60  | | 
% 159.28/25.60  | | Case 1:
% 159.28/25.60  | | | 
% 159.28/25.60  | | |   (11)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.28/25.60  | | |           e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0
% 159.28/25.60  | | |         & op(e0, e0) = e2 & $i(all_57_12)
% 159.28/25.60  | | | 
% 159.28/25.60  | | | ALPHA: (11) implies:
% 159.28/25.60  | | |   (12)  op(e0, e0) = e2
% 159.28/25.60  | | | 
% 159.28/25.60  | | | REF_CLOSE: (1), (2), (5), (12) are inconsistent by sub-proof #878.
% 159.28/25.60  | | | 
% 159.28/25.60  | | Case 2:
% 159.28/25.60  | | | 
% 159.28/25.60  | | |   (13)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 159.28/25.60  | | |         op(e2, e1) = e2
% 159.28/25.60  | | | 
% 159.28/25.60  | | | ALPHA: (13) implies:
% 159.28/25.60  | | |   (14)  op(e2, e2) = e2
% 159.28/25.60  | | | 
% 159.28/25.60  | | | REF_CLOSE: (2), (6), (9), (14) are inconsistent by sub-proof #942.
% 159.28/25.60  | | | 
% 159.28/25.60  | | End of split
% 159.28/25.60  | | 
% 159.28/25.60  | Case 2:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (15)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 159.28/25.60  | |             e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 159.28/25.60  | |           & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 159.28/25.60  | |           e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 159.28/25.60  | |           & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.28/25.60  | |           $i(all_57_10))
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (2), (4), (6), (7), (8), (15) are inconsistent by sub-proof #443.
% 159.28/25.60  | | 
% 159.28/25.60  | End of split
% 159.28/25.60  | 
% 159.28/25.60  End of proof
% 159.28/25.60  
% 159.28/25.60  Sub-proof #443 shows that the following formulas are inconsistent:
% 159.28/25.60  ----------------------------------------------------------------
% 159.28/25.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.60    (2)   ~ (all_52_12 = e3)
% 159.28/25.60    (3)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.28/25.60           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 159.28/25.60           = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3
% 159.28/25.60           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.28/25.60           op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 159.28/25.60    (4)  op(e2, e2) = e0
% 159.28/25.60    (5)   ~ (e1 = e0)
% 159.28/25.60    (6)  op(e3, e0) = all_52_12
% 159.28/25.60  
% 159.28/25.60  Begin of proof
% 159.28/25.60  | 
% 159.28/25.60  | BETA: splitting (3) gives:
% 159.28/25.60  | 
% 159.28/25.60  | Case 1:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (7)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 159.28/25.60  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.28/25.60  | |          e0) = e1 & $i(all_57_14)
% 159.28/25.60  | | 
% 159.28/25.60  | | ALPHA: (7) implies:
% 159.28/25.60  | |   (8)  op(e2, e2) = e1
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #960.
% 159.28/25.60  | | 
% 159.28/25.60  | Case 2:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0)
% 159.28/25.60  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 159.28/25.60  | |          e0) = e3 & $i(all_57_10)
% 159.28/25.60  | | 
% 159.28/25.60  | | ALPHA: (9) implies:
% 159.28/25.60  | |   (10)  op(e3, e0) = e3
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #976.
% 159.28/25.60  | | 
% 159.28/25.60  | End of split
% 159.28/25.60  | 
% 159.28/25.60  End of proof
% 159.28/25.60  
% 159.28/25.60  Sub-proof #444 shows that the following formulas are inconsistent:
% 159.28/25.60  ----------------------------------------------------------------
% 159.28/25.60    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.28/25.60           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.28/25.60           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 159.28/25.60           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 159.28/25.60           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.28/25.60    (2)   ~ (e3 = e2)
% 159.28/25.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.60    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.28/25.60         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.28/25.60    (5)  op(e1, e0) = all_52_14
% 159.28/25.60    (6)  op(e2, e2) = e0
% 159.28/25.60    (7)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 159.28/25.60         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.28/25.60    (8)  op(e1, e2) = e3
% 159.28/25.60    (9)  all_56_7 = e3
% 159.28/25.60    (10)   ~ (e1 = e0)
% 159.28/25.60    (11)   ~ (e2 = e1)
% 159.28/25.60    (12)   ~ (all_52_14 = e1)
% 159.28/25.60    (13)   ~ (e3 = e1)
% 159.28/25.60    (14)   ~ (e2 = e0)
% 159.28/25.60    (15)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 159.28/25.60          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 159.28/25.60    (16)   ~ (e3 = e0)
% 159.28/25.60  
% 159.28/25.60  Begin of proof
% 159.28/25.60  | 
% 159.28/25.60  | BETA: splitting (1) gives:
% 159.28/25.60  | 
% 159.28/25.60  | Case 1:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (17)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 159.28/25.60  | |         & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 159.28/25.60  | |         op(e1, e1) = e3 & $i(all_57_10)
% 159.28/25.60  | | 
% 159.28/25.60  | | ALPHA: (17) implies:
% 159.28/25.60  | |   (18)  op(e1, e1) = e3
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 159.28/25.60  | |            (15), (16), (18) are inconsistent by sub-proof #457.
% 159.28/25.60  | | 
% 159.28/25.60  | Case 2:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (19)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 159.28/25.60  | |         & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 159.28/25.60  | |         all_57_14 & $i(all_57_14)
% 159.28/25.60  | | 
% 159.28/25.60  | | ALPHA: (19) implies:
% 159.28/25.60  | |   (20)  op(e2, e2) = e1
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (3), (6), (10), (20) are inconsistent by sub-proof #960.
% 159.28/25.60  | | 
% 159.28/25.60  | End of split
% 159.28/25.60  | 
% 159.28/25.60  End of proof
% 159.28/25.60  
% 159.28/25.60  Sub-proof #445 shows that the following formulas are inconsistent:
% 159.28/25.60  ----------------------------------------------------------------
% 159.28/25.60    (1)   ~ (e3 = e2)
% 159.28/25.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.60    (3)   ~ (all_52_12 = e3)
% 159.28/25.60    (4)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.28/25.60           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.28/25.60           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 159.28/25.60           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.28/25.60           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.28/25.60    (5)  op(e0, e0) = e3
% 159.28/25.60    (6)  op(e3, e0) = all_52_12
% 159.28/25.60  
% 159.28/25.60  Begin of proof
% 159.28/25.60  | 
% 159.28/25.60  | BETA: splitting (4) gives:
% 159.28/25.60  | 
% 159.28/25.60  | Case 1:
% 159.28/25.60  | | 
% 159.28/25.60  | |   (7)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 159.28/25.60  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 159.28/25.60  | |          e0) = e2 & $i(all_57_12)
% 159.28/25.60  | | 
% 159.28/25.60  | | ALPHA: (7) implies:
% 159.28/25.60  | |   (8)  op(e0, e0) = e2
% 159.28/25.60  | | 
% 159.28/25.60  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #878.
% 159.28/25.60  | | 
% 159.28/25.60  | Case 2:
% 159.28/25.60  | | 
% 159.28/25.61  | |   (9)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 159.28/25.61  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 159.28/25.61  | |          e2) = e3 & $i(all_57_10)
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (9) implies:
% 159.28/25.61  | |   (10)  op(e3, e0) = e3
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #976.
% 159.28/25.61  | | 
% 159.28/25.61  | End of split
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #446 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.61    (2)  op(e1, e0) = all_52_14
% 159.28/25.61    (3)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.28/25.61           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.28/25.61           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.28/25.61           op(e0, e1) = e0)
% 159.28/25.61    (4)  all_57_15 = e3
% 159.28/25.61    (5)   ~ (all_52_14 = e1)
% 159.28/25.61    (6)   ~ (e3 = e0)
% 159.28/25.61  
% 159.28/25.61  Begin of proof
% 159.28/25.61  | 
% 159.28/25.61  | BETA: splitting (3) gives:
% 159.28/25.61  | 
% 159.28/25.61  | Case 1:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (7)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 159.28/25.61  | |        & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.28/25.61  | |        $i(all_57_14)
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (7) implies:
% 159.28/25.61  | |   (8)  op(e1, e0) = e1
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #974.
% 159.28/25.61  | | 
% 159.28/25.61  | Case 2:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (9)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #447.
% 159.28/25.61  | | 
% 159.28/25.61  | End of split
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #447 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.61    (1)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0
% 159.28/25.61    (2)  all_57_15 = e3
% 159.28/25.61    (3)   ~ (e3 = e0)
% 159.28/25.61  
% 159.28/25.61  Begin of proof
% 159.28/25.61  | 
% 159.28/25.61  | ALPHA: (1) implies:
% 159.28/25.61  |   (4)  all_57_15 = e0
% 159.28/25.61  | 
% 159.28/25.61  | COMBINE_EQS: (2), (4) imply:
% 159.28/25.61  |   (5)  e3 = e0
% 159.28/25.61  | 
% 159.28/25.61  | REDUCE: (3), (5) imply:
% 159.28/25.61  |   (6)  $false
% 159.28/25.61  | 
% 159.28/25.61  | CLOSE: (6) is inconsistent.
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #448 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.61    (2)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.28/25.61         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.28/25.61           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.28/25.61    (3)  all_57_15 = e3
% 159.28/25.61    (4)  op(e3, e3) = e3
% 159.28/25.61    (5)   ~ (e3 = e0)
% 159.28/25.61  
% 159.28/25.61  Begin of proof
% 159.28/25.61  | 
% 159.28/25.61  | BETA: splitting (2) gives:
% 159.28/25.61  | 
% 159.28/25.61  | Case 1:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (6)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #449.
% 159.28/25.61  | | 
% 159.28/25.61  | Case 2:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (7)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 159.28/25.61  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (7) implies:
% 159.28/25.61  | |   (8)  op(e3, e3) = e0
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #971.
% 159.28/25.61  | | 
% 159.28/25.61  | End of split
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #449 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.61    (1)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 159.28/25.61    (2)  all_57_15 = e3
% 159.28/25.61    (3)   ~ (e3 = e0)
% 159.28/25.61  
% 159.28/25.61  Begin of proof
% 159.28/25.61  | 
% 159.28/25.61  | ALPHA: (1) implies:
% 159.28/25.61  |   (4)  all_57_15 = e0
% 159.28/25.61  | 
% 159.28/25.61  | COMBINE_EQS: (2), (4) imply:
% 159.28/25.61  |   (5)  e3 = e0
% 159.28/25.61  | 
% 159.28/25.61  | REDUCE: (3), (5) imply:
% 159.28/25.61  |   (6)  $false
% 159.28/25.61  | 
% 159.28/25.61  | CLOSE: (6) is inconsistent.
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #450 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.61    (1)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 159.28/25.61    (2)  all_57_15 = e3
% 159.28/25.61  
% 159.28/25.61  Begin of proof
% 159.28/25.61  | 
% 159.28/25.61  | ALPHA: (1) implies:
% 159.28/25.61  |   (3)  all_57_15 = e0
% 159.28/25.61  |   (4)   ~ (e3 = e0)
% 159.28/25.61  | 
% 159.28/25.61  | COMBINE_EQS: (2), (3) imply:
% 159.28/25.61  |   (5)  e3 = e0
% 159.28/25.61  | 
% 159.28/25.61  | REDUCE: (4), (5) imply:
% 159.28/25.61  |   (6)  $false
% 159.28/25.61  | 
% 159.28/25.61  | CLOSE: (6) is inconsistent.
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #451 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.61    (1)   ~ (e3 = e2)
% 159.28/25.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.61    (3)   ~ (all_52_12 = e3)
% 159.28/25.61    (4)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.28/25.61           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.28/25.61           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 159.28/25.61           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 159.28/25.61    (5)  op(e0, e0) = e3
% 159.28/25.61    (6)  op(e3, e0) = all_52_12
% 159.28/25.61  
% 159.28/25.61  Begin of proof
% 159.28/25.61  | 
% 159.28/25.61  | BETA: splitting (4) gives:
% 159.28/25.61  | 
% 159.28/25.61  | Case 1:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (7)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 159.28/25.61  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.28/25.61  | |          e0) = e2 & $i(all_57_12)
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (7) implies:
% 159.28/25.61  | |   (8)  op(e0, e0) = e2
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #878.
% 159.28/25.61  | | 
% 159.28/25.61  | Case 2:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (9)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 159.28/25.61  | |        op(e3, e0) = e3
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (9) implies:
% 159.28/25.61  | |   (10)  op(e3, e0) = e3
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #976.
% 159.28/25.61  | | 
% 159.28/25.61  | End of split
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #452 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.61    (2)   ~ (all_52_12 = e3)
% 159.28/25.61    (3)  op(e2, e2) = e2
% 159.28/25.61    (4)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.28/25.61           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 159.28/25.61           = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3
% 159.28/25.61           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.28/25.61           op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 159.28/25.61    (5)   ~ (e2 = e1)
% 159.28/25.61    (6)  op(e3, e0) = all_52_12
% 159.28/25.61  
% 159.28/25.61  Begin of proof
% 159.28/25.61  | 
% 159.28/25.61  | BETA: splitting (4) gives:
% 159.28/25.61  | 
% 159.28/25.61  | Case 1:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (7)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 159.28/25.61  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.28/25.61  | |          e0) = e1 & $i(all_57_14)
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (7) implies:
% 159.28/25.61  | |   (8)  op(e2, e2) = e1
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #993.
% 159.28/25.61  | | 
% 159.28/25.61  | Case 2:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0)
% 159.28/25.61  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 159.28/25.61  | |          e0) = e3 & $i(all_57_10)
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (9) implies:
% 159.28/25.61  | |   (10)  op(e3, e0) = e3
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #976.
% 159.28/25.61  | | 
% 159.28/25.61  | End of split
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #453 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.61    (2)  op(e1, e1) = e1
% 159.28/25.61    (3)  op(e0, e0) = e3
% 159.28/25.61    (4)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 159.28/25.61           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.28/25.61           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 159.28/25.61           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.28/25.61           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.28/25.61    (5)   ~ (e2 = e1)
% 159.28/25.61    (6)   ~ (e3 = e1)
% 159.28/25.61  
% 159.28/25.61  Begin of proof
% 159.28/25.61  | 
% 159.28/25.61  | BETA: splitting (4) gives:
% 159.28/25.61  | 
% 159.28/25.61  | Case 1:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (7)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.28/25.61  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.28/25.61  | |          e1) = e2 & $i(all_57_12)
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (7) implies:
% 159.28/25.61  | |   (8)  op(e1, e1) = e2
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #986.
% 159.28/25.61  | | 
% 159.28/25.61  | Case 2:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (9)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 159.28/25.61  | |        & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.28/25.61  | |          e0) = e1 & $i(all_57_14)
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (9) implies:
% 159.28/25.61  | |   (10)  op(e0, e0) = e1
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #473.
% 159.28/25.61  | | 
% 159.28/25.61  | End of split
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #454 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.61    (1)   ~ (e3 = e2)
% 159.28/25.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.61    (3)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.28/25.61         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.28/25.61    (4)  op(e1, e3) = all_52_2
% 159.28/25.61    (5)  op(e0, e0) = e3
% 159.28/25.61    (6)   ~ (all_52_2 = e1)
% 159.28/25.61    (7)  op(e1, e0) = all_52_14
% 159.28/25.61    (8)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 159.28/25.61         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.28/25.61    (9)  op(e1, e2) = e3
% 159.28/25.61    (10)  all_56_7 = e3
% 159.28/25.61    (11)   ~ (e1 = e0)
% 159.28/25.61    (12)   ~ (e2 = e1)
% 159.28/25.61    (13)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.28/25.61            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.28/25.61              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.28/25.61            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.28/25.61              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.28/25.61          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.28/25.61            op(e1, e1) = e1)
% 159.28/25.61    (14)   ~ (all_52_14 = e1)
% 159.28/25.61    (15)   ~ (e3 = e1)
% 159.28/25.61    (16)   ~ (e2 = e0)
% 159.28/25.61    (17)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 159.28/25.61          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 159.28/25.61    (18)   ~ (e3 = e0)
% 159.28/25.61  
% 159.28/25.61  Begin of proof
% 159.28/25.61  | 
% 159.28/25.61  | BETA: splitting (13) gives:
% 159.28/25.61  | 
% 159.28/25.61  | Case 1:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (19)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 159.28/25.61  | |         & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.28/25.61  | |         op(e0, e0) = e1 & $i(all_57_14)
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (19) implies:
% 159.28/25.61  | |   (20)  op(e0, e0) = e1
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (2), (5), (15), (20) are inconsistent by sub-proof #473.
% 159.28/25.61  | | 
% 159.28/25.61  | Case 2:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (21)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.28/25.61  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 159.28/25.61  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 159.28/25.61  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 159.28/25.61  | |            (15), (16), (17), (18), (21) are inconsistent by sub-proof #455.
% 159.28/25.61  | | 
% 159.28/25.61  | End of split
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #455 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.61    (1)   ~ (e3 = e2)
% 159.28/25.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.61    (3)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.28/25.61         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.28/25.61    (4)  op(e1, e3) = all_52_2
% 159.28/25.61    (5)   ~ (all_52_2 = e1)
% 159.28/25.61    (6)  op(e1, e0) = all_52_14
% 159.28/25.61    (7)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) &
% 159.28/25.61           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.28/25.61           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1)
% 159.28/25.61           & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.28/25.61    (8)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 159.28/25.61         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.28/25.61    (9)  op(e1, e2) = e3
% 159.28/25.61    (10)  all_56_7 = e3
% 159.28/25.61    (11)   ~ (e1 = e0)
% 159.28/25.61    (12)   ~ (e2 = e1)
% 159.28/25.61    (13)   ~ (all_52_14 = e1)
% 159.28/25.61    (14)   ~ (e3 = e1)
% 159.28/25.61    (15)   ~ (e2 = e0)
% 159.28/25.61    (16)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 159.28/25.61          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 159.28/25.61    (17)   ~ (e3 = e0)
% 159.28/25.61  
% 159.28/25.61  Begin of proof
% 159.28/25.61  | 
% 159.28/25.61  | BETA: splitting (7) gives:
% 159.28/25.61  | 
% 159.28/25.61  | Case 1:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (18)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 159.28/25.61  | |         & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 159.28/25.61  | |         op(e1, e1) = e3 & $i(all_57_10)
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (18) implies:
% 159.28/25.61  | |   (19)  op(e1, e1) = e3
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (11), (12), (13), (14), (15),
% 159.28/25.61  | |            (16), (17), (19) are inconsistent by sub-proof #457.
% 159.28/25.61  | | 
% 159.28/25.61  | Case 2:
% 159.28/25.61  | | 
% 159.28/25.61  | |   (20)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.28/25.61  | |         op(e1, e1) = e1
% 159.28/25.61  | | 
% 159.28/25.61  | | ALPHA: (20) implies:
% 159.28/25.61  | |   (21)  op(e1, e3) = e1
% 159.28/25.61  | | 
% 159.28/25.61  | | REF_CLOSE: (2), (4), (5), (21) are inconsistent by sub-proof #990.
% 159.28/25.61  | | 
% 159.28/25.61  | End of split
% 159.28/25.61  | 
% 159.28/25.61  End of proof
% 159.28/25.61  
% 159.28/25.61  Sub-proof #456 shows that the following formulas are inconsistent:
% 159.28/25.61  ----------------------------------------------------------------
% 159.28/25.62    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.62    (2)  op(e2, e1) = e3
% 159.28/25.62    (3)  op(e2, e1) = e2
% 159.28/25.62    (4)   ~ (e3 = e2)
% 159.28/25.62  
% 159.28/25.62  Begin of proof
% 159.28/25.62  | 
% 159.28/25.62  | GROUND_INST: instantiating (1) with e3, e2, e1, e2, simplifying with (2), (3)
% 159.28/25.62  |              gives:
% 159.28/25.62  |   (5)  e3 = e2
% 159.28/25.62  | 
% 159.28/25.62  | REDUCE: (4), (5) imply:
% 159.28/25.62  |   (6)  $false
% 159.28/25.62  | 
% 159.28/25.62  | CLOSE: (6) is inconsistent.
% 159.28/25.62  | 
% 159.28/25.62  End of proof
% 159.28/25.62  
% 159.28/25.62  Sub-proof #457 shows that the following formulas are inconsistent:
% 159.28/25.62  ----------------------------------------------------------------
% 159.28/25.62    (1)  op(e1, e1) = e3
% 159.28/25.62    (2)   ~ (e3 = e2)
% 159.28/25.62    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.62    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.28/25.62         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.28/25.62    (5)  op(e1, e0) = all_52_14
% 159.28/25.62    (6)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 159.28/25.62         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.28/25.62    (7)  op(e1, e2) = e3
% 159.28/25.62    (8)  all_56_7 = e3
% 159.28/25.62    (9)   ~ (e1 = e0)
% 159.28/25.62    (10)   ~ (e2 = e1)
% 159.28/25.62    (11)   ~ (all_52_14 = e1)
% 159.28/25.62    (12)   ~ (e3 = e1)
% 159.28/25.62    (13)   ~ (e2 = e0)
% 159.28/25.62    (14)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 159.28/25.62          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 159.28/25.62    (15)   ~ (e3 = e0)
% 159.28/25.62  
% 159.28/25.62  Begin of proof
% 159.28/25.62  | 
% 159.28/25.62  | BETA: splitting (4) gives:
% 159.28/25.62  | 
% 159.28/25.62  | Case 1:
% 159.28/25.62  | | 
% 159.28/25.62  | |   (16)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 159.28/25.62  | |           e1)
% 159.28/25.62  | | 
% 159.28/25.62  | | BETA: splitting (16) gives:
% 159.28/25.62  | | 
% 159.28/25.62  | | Case 1:
% 159.28/25.62  | | | 
% 159.28/25.62  | | |   (17)  all_56_6 = e1 & op(e1, e3) = e1
% 159.28/25.62  | | | 
% 159.28/25.62  | | | ALPHA: (17) implies:
% 159.28/25.62  | | |   (18)  all_56_6 = e1
% 159.28/25.62  | | | 
% 159.28/25.62  | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (13), (14), (15), (18) are
% 159.28/25.62  | | |            inconsistent by sub-proof #458.
% 159.28/25.62  | | | 
% 159.28/25.62  | | Case 2:
% 159.28/25.62  | | | 
% 159.28/25.62  | | |   (19)  all_56_7 = e1 & op(e1, e2) = e1
% 159.28/25.62  | | | 
% 159.28/25.62  | | | ALPHA: (19) implies:
% 159.28/25.62  | | |   (20)  op(e1, e2) = e1
% 159.28/25.62  | | | 
% 159.28/25.62  | | | REF_CLOSE: (3), (7), (12), (20) are inconsistent by sub-proof #939.
% 159.28/25.62  | | | 
% 159.28/25.62  | | End of split
% 159.28/25.62  | | 
% 159.28/25.62  | Case 2:
% 159.28/25.62  | | 
% 159.28/25.62  | |   (21)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 159.28/25.62  | |           e1)
% 159.28/25.62  | | 
% 159.28/25.62  | | BETA: splitting (21) gives:
% 159.28/25.62  | | 
% 159.28/25.62  | | Case 1:
% 159.28/25.62  | | | 
% 159.28/25.62  | | |   (22)  all_56_8 = e1 & op(e1, e1) = e1
% 159.28/25.62  | | | 
% 159.28/25.62  | | | ALPHA: (22) implies:
% 159.28/25.62  | | |   (23)  op(e1, e1) = e1
% 159.28/25.62  | | | 
% 159.28/25.62  | | | GROUND_INST: instantiating (3) with e1, e3, e1, e1, simplifying with (1),
% 159.28/25.62  | | |              (23) gives:
% 159.28/25.62  | | |   (24)  e3 = e1
% 159.28/25.62  | | | 
% 159.28/25.62  | | | REDUCE: (12), (24) imply:
% 159.28/25.62  | | |   (25)  $false
% 159.28/25.62  | | | 
% 159.28/25.62  | | | CLOSE: (25) is inconsistent.
% 159.28/25.62  | | | 
% 159.28/25.62  | | Case 2:
% 159.28/25.62  | | | 
% 159.28/25.62  | | |   (26)  all_56_11 = e1 & op(e1, e0) = e1
% 159.28/25.62  | | | 
% 159.28/25.62  | | | ALPHA: (26) implies:
% 159.28/25.62  | | |   (27)  op(e1, e0) = e1
% 159.28/25.62  | | | 
% 159.28/25.62  | | | REF_CLOSE: (3), (5), (11), (27) are inconsistent by sub-proof #974.
% 159.28/25.62  | | | 
% 159.28/25.62  | | End of split
% 159.28/25.62  | | 
% 159.28/25.62  | End of split
% 159.28/25.62  | 
% 159.28/25.62  End of proof
% 159.28/25.62  
% 159.28/25.62  Sub-proof #458 shows that the following formulas are inconsistent:
% 159.28/25.62  ----------------------------------------------------------------
% 159.28/25.62    (1)  op(e1, e1) = e3
% 159.28/25.62    (2)   ~ (e3 = e2)
% 159.28/25.62    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.62    (4)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 159.28/25.62         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.28/25.62    (5)  all_56_7 = e3
% 159.28/25.62    (6)   ~ (e1 = e0)
% 159.28/25.62    (7)   ~ (e2 = e1)
% 159.28/25.62    (8)  all_56_6 = e1
% 159.28/25.62    (9)   ~ (e2 = e0)
% 159.28/25.62    (10)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 159.28/25.62          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 159.28/25.62    (11)   ~ (e3 = e0)
% 159.28/25.62  
% 159.28/25.62  Begin of proof
% 159.28/25.62  | 
% 159.28/25.62  | BETA: splitting (10) gives:
% 159.28/25.62  | 
% 159.28/25.62  | Case 1:
% 159.28/25.62  | | 
% 159.28/25.62  | |   (12)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 159.28/25.62  | |           e2)
% 159.28/25.62  | | 
% 159.28/25.62  | | BETA: splitting (12) gives:
% 159.28/25.62  | | 
% 159.28/25.62  | | Case 1:
% 159.28/25.62  | | | 
% 159.28/25.62  | | |   (13)  all_56_6 = e2 & op(e1, e3) = e2
% 159.28/25.62  | | | 
% 159.28/25.62  | | | ALPHA: (13) implies:
% 159.28/25.62  | | |   (14)  all_56_6 = e2
% 159.28/25.62  | | | 
% 159.28/25.62  | | | REF_CLOSE: (7), (8), (14) are inconsistent by sub-proof #533.
% 159.28/25.62  | | | 
% 159.28/25.62  | | Case 2:
% 159.28/25.62  | | | 
% 159.28/25.62  | | |   (15)  all_56_7 = e2 & op(e1, e2) = e2
% 159.28/25.62  | | | 
% 159.28/25.62  | | | REF_CLOSE: (2), (5), (15) are inconsistent by sub-proof #940.
% 159.28/25.62  | | | 
% 159.28/25.62  | | End of split
% 159.28/25.62  | | 
% 159.28/25.62  | Case 2:
% 159.28/25.62  | | 
% 159.28/25.62  | |   (16)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 159.28/25.62  | |           e2)
% 159.28/25.62  | | 
% 159.28/25.62  | | BETA: splitting (16) gives:
% 159.28/25.62  | | 
% 159.28/25.62  | | Case 1:
% 159.28/25.62  | | | 
% 159.28/25.62  | | |   (17)  all_56_8 = e2 & op(e1, e1) = e2
% 159.28/25.62  | | | 
% 159.28/25.62  | | | ALPHA: (17) implies:
% 159.28/25.62  | | |   (18)  op(e1, e1) = e2
% 159.28/25.62  | | | 
% 159.28/25.62  | | | REF_CLOSE: (1), (2), (3), (18) are inconsistent by sub-proof #646.
% 159.28/25.62  | | | 
% 159.28/25.62  | | Case 2:
% 159.28/25.62  | | | 
% 159.28/25.62  | | |   (19)  all_56_11 = e2 & op(e1, e0) = e2
% 159.28/25.62  | | | 
% 159.28/25.62  | | | ALPHA: (19) implies:
% 159.28/25.62  | | |   (20)  all_56_11 = e2
% 159.28/25.62  | | | 
% 159.28/25.62  | | | BETA: splitting (4) gives:
% 159.28/25.62  | | | 
% 159.28/25.62  | | | Case 1:
% 159.28/25.62  | | | | 
% 159.28/25.62  | | | |   (21)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2)
% 159.28/25.62  | | | |           = e0)
% 159.28/25.62  | | | | 
% 159.28/25.62  | | | | BETA: splitting (21) gives:
% 159.28/25.62  | | | | 
% 159.28/25.62  | | | | Case 1:
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | |   (22)  all_56_6 = e0 & op(e1, e3) = e0
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | | REF_CLOSE: (6), (8), (22) are inconsistent by sub-proof #459.
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | Case 2:
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | |   (23)  all_56_7 = e0 & op(e1, e2) = e0
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | | REF_CLOSE: (5), (11), (23) are inconsistent by sub-proof #909.
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | End of split
% 159.28/25.62  | | | | 
% 159.28/25.62  | | | Case 2:
% 159.28/25.62  | | | | 
% 159.28/25.62  | | | |   (24)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0)
% 159.28/25.62  | | | |           = e0)
% 159.28/25.62  | | | | 
% 159.28/25.62  | | | | BETA: splitting (24) gives:
% 159.28/25.62  | | | | 
% 159.28/25.62  | | | | Case 1:
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | |   (25)  all_56_8 = e0 & op(e1, e1) = e0
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | | ALPHA: (25) implies:
% 159.28/25.62  | | | | |   (26)  op(e1, e1) = e0
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | | GROUND_INST: instantiating (3) with e0, e3, e1, e1, simplifying with
% 159.28/25.62  | | | | |              (1), (26) gives:
% 159.28/25.62  | | | | |   (27)  e3 = e0
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | | REDUCE: (11), (27) imply:
% 159.28/25.62  | | | | |   (28)  $false
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | | CLOSE: (28) is inconsistent.
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | Case 2:
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | |   (29)  all_56_11 = e0 & op(e1, e0) = e0
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | | ALPHA: (29) implies:
% 159.28/25.62  | | | | |   (30)  all_56_11 = e0
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | | REF_CLOSE: (9), (20), (30) are inconsistent by sub-proof #890.
% 159.28/25.62  | | | | | 
% 159.28/25.62  | | | | End of split
% 159.28/25.62  | | | | 
% 159.28/25.62  | | | End of split
% 159.28/25.62  | | | 
% 159.28/25.62  | | End of split
% 159.28/25.62  | | 
% 159.28/25.62  | End of split
% 159.28/25.62  | 
% 159.28/25.62  End of proof
% 159.28/25.62  
% 159.28/25.62  Sub-proof #459 shows that the following formulas are inconsistent:
% 159.28/25.62  ----------------------------------------------------------------
% 159.28/25.62    (1)  all_56_6 = e0 & op(e1, e3) = e0
% 159.28/25.62    (2)  all_56_6 = e1
% 159.28/25.62    (3)   ~ (e1 = e0)
% 159.28/25.62  
% 159.28/25.62  Begin of proof
% 159.28/25.62  | 
% 159.28/25.62  | ALPHA: (1) implies:
% 159.28/25.62  |   (4)  all_56_6 = e0
% 159.28/25.62  | 
% 159.28/25.62  | COMBINE_EQS: (2), (4) imply:
% 159.28/25.62  |   (5)  e1 = e0
% 159.28/25.62  | 
% 159.28/25.62  | REDUCE: (3), (5) imply:
% 159.28/25.62  |   (6)  $false
% 159.28/25.62  | 
% 159.28/25.62  | CLOSE: (6) is inconsistent.
% 159.28/25.62  | 
% 159.28/25.62  End of proof
% 159.28/25.62  
% 159.28/25.62  Sub-proof #460 shows that the following formulas are inconsistent:
% 159.28/25.62  ----------------------------------------------------------------
% 159.28/25.62    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.28/25.62         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.28/25.62    (2)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.28/25.62         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.28/25.62    (3)   ~ (e3 = e2)
% 159.28/25.62    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.62    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.28/25.62             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.28/25.62               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.28/25.62               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.28/25.62    (6)  op(e0, e0) = e3
% 159.28/25.62    (7)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.28/25.62         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.28/25.62    (8)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 159.28/25.62         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 159.28/25.62    (9)  op(e3, e3) = e3
% 159.28/25.62    (10)  op(e2, e2) = e1
% 159.28/25.62    (11)   ~ (e1 = e0)
% 159.28/25.62    (12)  op(e2, e1) = all_52_9
% 159.28/25.62    (13)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.28/25.62          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.28/25.62    (14)   ~ (all_52_9 = e3)
% 159.28/25.62    (15)   ~ (e2 = e1)
% 159.28/25.62    (16)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.28/25.62          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.28/25.62    (17)   ~ (e3 = e1)
% 159.28/25.62    (18)   ~ (e2 = e0)
% 159.28/25.62    (19)   ~ (e3 = e0)
% 159.28/25.62  
% 159.28/25.62  Begin of proof
% 159.28/25.62  | 
% 159.28/25.62  | BETA: splitting (7) gives:
% 159.28/25.62  | 
% 159.28/25.62  | Case 1:
% 159.28/25.62  | | 
% 159.28/25.62  | |   (20)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 159.28/25.62  | |           e3)
% 159.28/25.62  | | 
% 159.28/25.62  | | REF_CLOSE: (1), (3), (4), (9), (10), (11), (13), (15), (16), (17), (18),
% 159.28/25.62  | |            (19), (20) are inconsistent by sub-proof #764.
% 159.28/25.62  | | 
% 159.28/25.62  | Case 2:
% 159.28/25.62  | | 
% 159.28/25.62  | |   (21)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 159.28/25.62  | |           e3)
% 159.28/25.62  | | 
% 159.28/25.62  | | BETA: splitting (21) gives:
% 159.28/25.62  | | 
% 159.28/25.62  | | Case 1:
% 159.28/25.62  | | | 
% 159.28/25.62  | | |   (22)  all_56_5 = e3 & op(e2, e1) = e3
% 159.28/25.62  | | | 
% 159.28/25.62  | | | ALPHA: (22) implies:
% 159.28/25.62  | | |   (23)  op(e2, e1) = e3
% 159.28/25.62  | | | 
% 159.28/25.62  | | | REF_CLOSE: (4), (12), (14), (23) are inconsistent by sub-proof #763.
% 159.28/25.62  | | | 
% 159.28/25.62  | | Case 2:
% 159.28/25.62  | | | 
% 159.28/25.62  | | |   (24)  all_56_10 = e3 & op(e2, e0) = e3
% 159.28/25.62  | | | 
% 159.28/25.62  | | | ALPHA: (24) implies:
% 159.28/25.62  | | |   (25)  all_56_10 = e3
% 159.28/25.62  | | | 
% 159.28/25.62  | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (11), (15), (17), (18), (19),
% 159.28/25.62  | | |            (25) are inconsistent by sub-proof #466.
% 159.28/25.62  | | | 
% 159.28/25.62  | | End of split
% 159.28/25.62  | | 
% 159.28/25.62  | End of split
% 159.28/25.62  | 
% 159.28/25.62  End of proof
% 159.28/25.62  
% 159.28/25.62  Sub-proof #461 shows that the following formulas are inconsistent:
% 159.28/25.62  ----------------------------------------------------------------
% 159.28/25.62    (1)  op(e1, e1) = e3
% 159.28/25.62    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.62    (3)  op(e2, e2) = e2
% 159.28/25.62    (4)   ~ (all_52_13 = all_4_2)
% 159.28/25.62    (5)  op(e2, e2) = all_4_2
% 159.28/25.62    (6)  op(e2, e0) = all_52_13
% 159.28/25.62    (7)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.28/25.62           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.28/25.62           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 159.28/25.62           & op(e1, e0) = e1 & op(e0, e1) = e0)
% 159.28/25.62    (8)   ~ (e3 = e0)
% 159.28/25.62  
% 159.28/25.62  Begin of proof
% 159.28/25.62  | 
% 159.28/25.62  | BETA: splitting (7) gives:
% 159.28/25.62  | 
% 159.28/25.62  | Case 1:
% 159.28/25.62  | | 
% 159.28/25.62  | |   (9)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1)
% 159.28/25.62  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 159.28/25.62  | | 
% 159.28/25.62  | | ALPHA: (9) implies:
% 159.28/25.62  | |   (10)  op(e2, e0) = e2
% 159.28/25.62  | | 
% 159.28/25.62  | | REF_CLOSE: (2), (3), (4), (5), (6), (10) are inconsistent by sub-proof #972.
% 159.28/25.62  | | 
% 159.28/25.62  | Case 2:
% 159.28/25.62  | | 
% 159.28/25.62  | |   (11)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.28/25.62  | |           e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.28/25.62  | | 
% 159.28/25.62  | | ALPHA: (11) implies:
% 159.28/25.62  | |   (12)  op(e1, e1) = e0
% 159.28/25.62  | | 
% 159.28/25.62  | | REF_CLOSE: (1), (2), (8), (12) are inconsistent by sub-proof #912.
% 159.28/25.62  | | 
% 159.28/25.62  | End of split
% 159.28/25.62  | 
% 159.28/25.62  End of proof
% 159.28/25.62  
% 159.28/25.62  Sub-proof #462 shows that the following formulas are inconsistent:
% 159.28/25.62  ----------------------------------------------------------------
% 159.28/25.62    (1)  op(e1, e1) = e3
% 159.28/25.62    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.62    (3)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.28/25.62           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.28/25.62           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 159.28/25.62           & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.28/25.62    (4)  op(e2, e2) = e2
% 159.28/25.62    (5)   ~ (all_52_13 = all_4_2)
% 159.28/25.62    (6)  op(e2, e2) = all_4_2
% 159.28/25.62    (7)  op(e2, e0) = all_52_13
% 159.28/25.62    (8)   ~ (e3 = e0)
% 159.28/25.62  
% 159.28/25.62  Begin of proof
% 159.28/25.62  | 
% 159.28/25.62  | BETA: splitting (3) gives:
% 159.28/25.62  | 
% 159.28/25.62  | Case 1:
% 159.28/25.62  | | 
% 159.28/25.62  | |   (9)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3)
% 159.28/25.62  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 159.28/25.62  | | 
% 159.28/25.62  | | ALPHA: (9) implies:
% 159.28/25.62  | |   (10)  op(e2, e0) = e2
% 159.28/25.62  | | 
% 159.28/25.62  | | REF_CLOSE: (2), (4), (5), (6), (7), (10) are inconsistent by sub-proof #972.
% 159.28/25.62  | | 
% 159.28/25.62  | Case 2:
% 159.28/25.62  | | 
% 159.28/25.62  | |   (11)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.28/25.62  | |           e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 159.28/25.62  | | 
% 159.28/25.62  | | ALPHA: (11) implies:
% 159.28/25.62  | |   (12)  op(e1, e1) = e0
% 159.28/25.62  | | 
% 159.28/25.62  | | REF_CLOSE: (1), (2), (8), (12) are inconsistent by sub-proof #912.
% 159.28/25.62  | | 
% 159.28/25.62  | End of split
% 159.28/25.62  | 
% 159.28/25.62  End of proof
% 159.28/25.62  
% 159.28/25.62  Sub-proof #463 shows that the following formulas are inconsistent:
% 159.28/25.62  ----------------------------------------------------------------
% 159.28/25.63    (1)  op(e1, e1) = e3
% 159.28/25.63    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.63    (3)   ~ (all_52_12 = e3)
% 159.28/25.63    (4)  op(e0, e0) = e0
% 159.28/25.63    (5)  op(e0, e0) = all_14_2
% 159.28/25.63    (6)   ~ (e1 = e0)
% 159.28/25.63    (7)  op(e3, e0) = all_52_12
% 159.28/25.63    (8)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.28/25.63           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.28/25.63           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 159.28/25.63           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.28/25.63           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 159.28/25.63           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.28/25.63  
% 159.28/25.63  Begin of proof
% 159.28/25.63  | 
% 159.28/25.63  | BETA: splitting (8) gives:
% 159.28/25.63  | 
% 159.28/25.63  | Case 1:
% 159.28/25.63  | | 
% 159.28/25.63  | |   (9)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 159.28/25.63  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.28/25.63  | |          e0) = e1 & $i(all_57_14)
% 159.28/25.63  | | 
% 159.28/25.63  | | ALPHA: (9) implies:
% 159.28/25.63  | |   (10)  op(e0, e0) = e1
% 159.28/25.63  | | 
% 159.28/25.63  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #991.
% 159.28/25.63  | | 
% 159.28/25.63  | Case 2:
% 159.28/25.63  | | 
% 159.28/25.63  | |   (11)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.28/25.63  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 159.28/25.63  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 159.28/25.63  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.28/25.63  | | 
% 159.28/25.63  | | REF_CLOSE: (1), (2), (3), (7), (11) are inconsistent by sub-proof #578.
% 159.28/25.63  | | 
% 159.28/25.63  | End of split
% 159.28/25.63  | 
% 159.28/25.63  End of proof
% 159.28/25.63  
% 159.28/25.63  Sub-proof #464 shows that the following formulas are inconsistent:
% 159.28/25.63  ----------------------------------------------------------------
% 159.28/25.63    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.28/25.63         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.28/25.63    (2)  all_54_5 = all_4_2
% 159.28/25.63    (3)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.28/25.63         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.28/25.63    (4)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.28/25.63         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.28/25.63    (5)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.28/25.63         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 159.28/25.63    (6)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.28/25.63    (7)  op(e0, e1) = all_52_11
% 159.28/25.63    (8)   ~ (e3 = e2)
% 159.28/25.63    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.63    (10)   ~ (all_4_2 = e3)
% 159.28/25.63    (11)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.28/25.63              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 159.28/25.63                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.28/25.63                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.28/25.63    (12)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.28/25.63          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.28/25.63    (13)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.28/25.63          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.28/25.63    (14)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 159.28/25.63          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 159.28/25.63    (15)  op(e2, e2) = all_4_2
% 159.28/25.63    (16)  op(e3, e3) = e3
% 159.28/25.63    (17)  op(e1, e2) = e3
% 159.28/25.63    (18)  all_56_7 = e3
% 159.28/25.63    (19)   ~ (all_4_2 = e1)
% 159.28/25.63    (20)   ~ (e1 = e0)
% 159.28/25.63    (21)  op(e2, e1) = all_52_9
% 159.28/25.63    (22)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.28/25.63          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.28/25.63    (23)   ~ (all_52_9 = e3)
% 159.28/25.63    (24)   ~ (e2 = e1)
% 159.28/25.63    (25)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.28/25.63          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 159.28/25.63            e3)
% 159.28/25.63    (26)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.28/25.63          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.28/25.63    (27)   ~ (e3 = e1)
% 159.28/25.63    (28)   ~ (e2 = e0)
% 159.28/25.63    (29)   ~ (all_52_11 = e3)
% 159.28/25.63    (30)   ~ (e3 = e0)
% 159.28/25.63  
% 159.28/25.63  Begin of proof
% 159.28/25.63  | 
% 159.28/25.63  | BETA: splitting (13) gives:
% 159.28/25.63  | 
% 159.28/25.63  | Case 1:
% 159.28/25.63  | | 
% 159.28/25.63  | |   (31)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 159.28/25.63  | |           e3)
% 159.28/25.63  | | 
% 159.28/25.63  | | REF_CLOSE: (1), (8), (9), (10), (15), (16), (20), (22), (24), (26), (27),
% 159.28/25.63  | |            (28), (30), (31) are inconsistent by sub-proof #475.
% 159.28/25.63  | | 
% 159.28/25.63  | Case 2:
% 159.28/25.63  | | 
% 159.28/25.63  | |   (32)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 159.28/25.63  | |           e3)
% 159.28/25.63  | | 
% 159.28/25.63  | | BETA: splitting (32) gives:
% 159.28/25.63  | | 
% 159.28/25.63  | | Case 1:
% 159.28/25.63  | | | 
% 159.28/25.63  | | |   (33)  all_56_5 = e3 & op(e2, e1) = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | ALPHA: (33) implies:
% 159.28/25.63  | | |   (34)  op(e2, e1) = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | REF_CLOSE: (9), (21), (23), (34) are inconsistent by sub-proof #763.
% 159.28/25.63  | | | 
% 159.28/25.63  | | Case 2:
% 159.28/25.63  | | | 
% 159.28/25.63  | | |   (35)  all_56_10 = e3 & op(e2, e0) = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.28/25.63  | | |            (14), (15), (16), (17), (18), (19), (20), (22), (24), (25),
% 159.28/25.63  | | |            (26), (27), (28), (29), (30), (35) are inconsistent by
% 159.28/25.63  | | |            sub-proof #465.
% 159.28/25.63  | | | 
% 159.28/25.63  | | End of split
% 159.28/25.63  | | 
% 159.28/25.63  | End of split
% 159.28/25.63  | 
% 159.28/25.63  End of proof
% 159.28/25.63  
% 159.28/25.63  Sub-proof #465 shows that the following formulas are inconsistent:
% 159.28/25.63  ----------------------------------------------------------------
% 159.28/25.63    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.28/25.63         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.28/25.63    (2)  all_54_5 = all_4_2
% 159.28/25.63    (3)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.28/25.63         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.28/25.63    (4)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.28/25.63         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.28/25.63    (5)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.28/25.63         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 159.28/25.63    (6)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.28/25.63    (7)  op(e0, e1) = all_52_11
% 159.28/25.63    (8)   ~ (e3 = e2)
% 159.28/25.63    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.63    (10)   ~ (all_4_2 = e3)
% 159.28/25.63    (11)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.28/25.63              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 159.28/25.63                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.28/25.63                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.28/25.63    (12)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.28/25.63          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.28/25.63    (13)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 159.28/25.63          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 159.28/25.63    (14)  op(e2, e2) = all_4_2
% 159.28/25.63    (15)  op(e3, e3) = e3
% 159.28/25.63    (16)  op(e1, e2) = e3
% 159.28/25.63    (17)  all_56_7 = e3
% 159.28/25.63    (18)   ~ (all_4_2 = e1)
% 159.28/25.63    (19)   ~ (e1 = e0)
% 159.28/25.63    (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.28/25.63          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.28/25.63    (21)   ~ (e2 = e1)
% 159.28/25.63    (22)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.28/25.63          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 159.28/25.63            e3)
% 159.28/25.63    (23)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.28/25.63          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.28/25.63    (24)   ~ (e3 = e1)
% 159.28/25.63    (25)   ~ (e2 = e0)
% 159.28/25.63    (26)   ~ (all_52_11 = e3)
% 159.28/25.63    (27)  all_56_10 = e3 & op(e2, e0) = e3
% 159.28/25.63    (28)   ~ (e3 = e0)
% 159.28/25.63  
% 159.28/25.63  Begin of proof
% 159.28/25.63  | 
% 159.28/25.63  | ALPHA: (27) implies:
% 159.28/25.63  |   (29)  all_56_10 = e3
% 159.28/25.63  | 
% 159.28/25.63  | BETA: splitting (22) gives:
% 159.28/25.63  | 
% 159.28/25.63  | Case 1:
% 159.28/25.63  | | 
% 159.28/25.63  | |   (30)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 159.28/25.63  | |           e3)
% 159.28/25.63  | | 
% 159.28/25.63  | | BETA: splitting (30) gives:
% 159.28/25.63  | | 
% 159.28/25.63  | | Case 1:
% 159.28/25.63  | | | 
% 159.28/25.63  | | |   (31)  all_56_12 = e3 & op(e0, e3) = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | ALPHA: (31) implies:
% 159.28/25.63  | | |   (32)  all_56_12 = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | REF_CLOSE: (1), (8), (9), (15), (19), (20), (21), (23), (24), (25), (28),
% 159.28/25.63  | | |            (32) are inconsistent by sub-proof #729.
% 159.28/25.63  | | | 
% 159.28/25.63  | | Case 2:
% 159.28/25.63  | | | 
% 159.28/25.63  | | |   (33)  all_56_13 = e3 & op(e0, e2) = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | ALPHA: (33) implies:
% 159.28/25.63  | | |   (34)  all_56_13 = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (12), (14), (16), (17),
% 159.28/25.63  | | |            (18), (19), (21), (24), (25), (28), (34) are inconsistent by
% 159.28/25.63  | | |            sub-proof #678.
% 159.28/25.63  | | | 
% 159.28/25.63  | | End of split
% 159.28/25.63  | | 
% 159.28/25.63  | Case 2:
% 159.28/25.63  | | 
% 159.28/25.63  | |   (35)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 159.28/25.63  | |           e3)
% 159.28/25.63  | | 
% 159.28/25.63  | | BETA: splitting (35) gives:
% 159.28/25.63  | | 
% 159.28/25.63  | | Case 1:
% 159.28/25.63  | | | 
% 159.28/25.63  | | |   (36)  all_56_14 = e3 & op(e0, e1) = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | ALPHA: (36) implies:
% 159.28/25.63  | | |   (37)  op(e0, e1) = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | REF_CLOSE: (7), (9), (26), (37) are inconsistent by sub-proof #720.
% 159.28/25.63  | | | 
% 159.28/25.63  | | Case 2:
% 159.28/25.63  | | | 
% 159.28/25.63  | | |   (38)  all_56_15 = e3 & op(e0, e0) = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | ALPHA: (38) implies:
% 159.28/25.63  | | |   (39)  op(e0, e0) = e3
% 159.28/25.63  | | | 
% 159.28/25.63  | | | REF_CLOSE: (4), (8), (9), (11), (13), (19), (21), (24), (25), (28), (29),
% 159.28/25.63  | | |            (39) are inconsistent by sub-proof #466.
% 159.28/25.63  | | | 
% 159.28/25.63  | | End of split
% 159.28/25.63  | | 
% 159.28/25.63  | End of split
% 159.28/25.63  | 
% 159.28/25.63  End of proof
% 159.28/25.63  
% 159.28/25.63  Sub-proof #466 shows that the following formulas are inconsistent:
% 159.28/25.63  ----------------------------------------------------------------
% 159.28/25.63    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.28/25.63         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.28/25.63    (2)   ~ (e3 = e2)
% 159.28/25.63    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.63    (4)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.28/25.63             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.28/25.63               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.28/25.63               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.28/25.63    (5)  op(e0, e0) = e3
% 159.28/25.63    (6)  all_56_10 = e3
% 159.28/25.63    (7)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 159.28/25.63         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 159.28/25.63    (8)   ~ (e1 = e0)
% 159.28/25.63    (9)   ~ (e2 = e1)
% 159.28/25.63    (10)   ~ (e3 = e1)
% 159.28/25.63    (11)   ~ (e2 = e0)
% 159.28/25.63    (12)   ~ (e3 = e0)
% 159.28/25.63  
% 159.28/25.63  Begin of proof
% 159.28/25.63  | 
% 159.28/25.63  | BETA: splitting (7) gives:
% 159.28/25.63  | 
% 159.28/25.63  | Case 1:
% 159.28/25.63  | | 
% 159.28/25.63  | |   (13)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 159.28/25.63  | |           e2)
% 159.28/25.63  | | 
% 159.28/25.63  | | BETA: splitting (13) gives:
% 159.28/25.63  | | 
% 159.28/25.63  | | Case 1:
% 159.28/25.63  | | | 
% 159.28/25.63  | | |   (14)  all_56_9 = e2 & op(e3, e0) = e2
% 159.28/25.63  | | | 
% 159.28/25.63  | | | ALPHA: (14) implies:
% 159.28/25.63  | | |   (15)  all_56_9 = e2
% 159.28/25.63  | | | 
% 159.28/25.63  | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (15) are
% 159.28/25.63  | | |            inconsistent by sub-proof #471.
% 159.28/25.63  | | | 
% 159.28/25.63  | | Case 2:
% 159.28/25.63  | | | 
% 159.28/25.63  | | |   (16)  all_56_10 = e2 & op(e2, e0) = e2
% 159.28/25.63  | | | 
% 159.28/25.63  | | | REF_CLOSE: (2), (6), (16) are inconsistent by sub-proof #470.
% 159.28/25.63  | | | 
% 159.28/25.63  | | End of split
% 159.28/25.63  | | 
% 159.28/25.63  | Case 2:
% 159.28/25.63  | | 
% 159.28/25.63  | |   (17)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 159.28/25.63  | |           e2)
% 159.28/25.63  | | 
% 159.28/25.63  | | BETA: splitting (17) gives:
% 159.28/25.63  | | 
% 159.28/25.63  | | Case 1:
% 159.28/25.63  | | | 
% 159.28/25.63  | | |   (18)  all_56_11 = e2 & op(e1, e0) = e2
% 159.28/25.63  | | | 
% 159.28/25.63  | | | ALPHA: (18) implies:
% 159.28/25.63  | | |   (19)  all_56_11 = e2
% 159.28/25.63  | | | 
% 159.28/25.63  | | | BETA: splitting (4) gives:
% 159.28/25.63  | | | 
% 159.28/25.63  | | | Case 1:
% 159.28/25.63  | | | | 
% 159.28/25.63  | | | |   (20)  all_56_15 = e0 & op(e0, e0) = e0
% 159.28/25.63  | | | | 
% 159.28/25.63  | | | | ALPHA: (20) implies:
% 159.28/25.63  | | | |   (21)  op(e0, e0) = e0
% 159.28/25.63  | | | | 
% 159.28/25.63  | | | | REF_CLOSE: (3), (5), (12), (21) are inconsistent by sub-proof #999.
% 159.28/25.63  | | | | 
% 159.28/25.63  | | | Case 2:
% 159.28/25.63  | | | | 
% 159.28/25.63  | | | |   (22)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 159.28/25.63  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 159.28/25.63  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 159.28/25.63  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 159.28/25.63  | | | | 
% 159.28/25.63  | | | | ALPHA: (22) implies:
% 159.28/25.64  | | | |   (23)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0)
% 159.28/25.64  | | | |           = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.28/25.64  | | | | 
% 159.28/25.64  | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (12), (19), (23)
% 159.28/25.64  | | | |            are inconsistent by sub-proof #467.
% 159.28/25.64  | | | | 
% 159.28/25.64  | | | End of split
% 159.28/25.64  | | | 
% 159.28/25.64  | | Case 2:
% 159.28/25.64  | | | 
% 159.28/25.64  | | |   (24)  all_56_15 = e2 & op(e0, e0) = e2
% 159.28/25.64  | | | 
% 159.28/25.64  | | | ALPHA: (24) implies:
% 159.28/25.64  | | |   (25)  op(e0, e0) = e2
% 159.28/25.64  | | | 
% 159.28/25.64  | | | REF_CLOSE: (2), (3), (5), (25) are inconsistent by sub-proof #878.
% 159.28/25.64  | | | 
% 159.28/25.64  | | End of split
% 159.28/25.64  | | 
% 159.28/25.64  | End of split
% 159.28/25.64  | 
% 159.28/25.64  End of proof
% 159.28/25.64  
% 159.28/25.64  Sub-proof #467 shows that the following formulas are inconsistent:
% 159.28/25.64  ----------------------------------------------------------------
% 159.28/25.64    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.28/25.64         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.28/25.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.64    (3)  op(e0, e0) = e3
% 159.28/25.64    (4)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 159.28/25.64         (all_56_11 = e0 & op(e1, e0) = e0)
% 159.28/25.64    (5)  all_56_10 = e3
% 159.28/25.64    (6)  all_56_11 = e2
% 159.28/25.64    (7)   ~ (e1 = e0)
% 159.28/25.64    (8)   ~ (e2 = e1)
% 159.28/25.64    (9)   ~ (e3 = e1)
% 159.28/25.64    (10)   ~ (e2 = e0)
% 159.28/25.64    (11)   ~ (e3 = e0)
% 159.28/25.64  
% 159.28/25.64  Begin of proof
% 159.28/25.64  | 
% 159.28/25.64  | BETA: splitting (1) gives:
% 159.28/25.64  | 
% 159.28/25.64  | Case 1:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (12)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 159.28/25.64  | |           e1)
% 159.28/25.64  | | 
% 159.28/25.64  | | BETA: splitting (12) gives:
% 159.28/25.64  | | 
% 159.28/25.64  | | Case 1:
% 159.28/25.64  | | | 
% 159.28/25.64  | | |   (13)  all_56_9 = e1 & op(e3, e0) = e1
% 159.28/25.64  | | | 
% 159.28/25.64  | | | ALPHA: (13) implies:
% 159.28/25.64  | | |   (14)  all_56_9 = e1
% 159.28/25.64  | | | 
% 159.28/25.64  | | | REF_CLOSE: (4), (5), (6), (7), (10), (11), (14) are inconsistent by
% 159.28/25.64  | | |            sub-proof #738.
% 159.28/25.64  | | | 
% 159.28/25.64  | | Case 2:
% 159.28/25.64  | | | 
% 159.28/25.64  | | |   (15)  all_56_10 = e1 & op(e2, e0) = e1
% 159.28/25.64  | | | 
% 159.28/25.64  | | | REF_CLOSE: (5), (9), (15) are inconsistent by sub-proof #556.
% 159.28/25.64  | | | 
% 159.28/25.64  | | End of split
% 159.28/25.64  | | 
% 159.28/25.64  | Case 2:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (16)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.28/25.64  | |           e1)
% 159.28/25.64  | | 
% 159.28/25.64  | | REF_CLOSE: (2), (3), (6), (8), (9), (16) are inconsistent by sub-proof #468.
% 159.28/25.64  | | 
% 159.28/25.64  | End of split
% 159.28/25.64  | 
% 159.28/25.64  End of proof
% 159.28/25.64  
% 159.28/25.64  Sub-proof #468 shows that the following formulas are inconsistent:
% 159.28/25.64  ----------------------------------------------------------------
% 159.28/25.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.64    (2)  op(e0, e0) = e3
% 159.28/25.64    (3)  all_56_11 = e2
% 159.28/25.64    (4)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.28/25.64    (5)   ~ (e2 = e1)
% 159.28/25.64    (6)   ~ (e3 = e1)
% 159.28/25.64  
% 159.28/25.64  Begin of proof
% 159.28/25.64  | 
% 159.28/25.64  | BETA: splitting (4) gives:
% 159.28/25.64  | 
% 159.28/25.64  | Case 1:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (7)  all_56_11 = e1 & op(e1, e0) = e1
% 159.28/25.64  | | 
% 159.28/25.64  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #469.
% 159.28/25.64  | | 
% 159.28/25.64  | Case 2:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (8)  all_56_15 = e1 & op(e0, e0) = e1
% 159.28/25.64  | | 
% 159.28/25.64  | | ALPHA: (8) implies:
% 159.28/25.64  | |   (9)  op(e0, e0) = e1
% 159.28/25.64  | | 
% 159.28/25.64  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #473.
% 159.28/25.64  | | 
% 159.28/25.64  | End of split
% 159.28/25.64  | 
% 159.28/25.64  End of proof
% 159.28/25.64  
% 159.28/25.64  Sub-proof #469 shows that the following formulas are inconsistent:
% 159.28/25.64  ----------------------------------------------------------------
% 159.28/25.64    (1)  all_56_11 = e1 & op(e1, e0) = e1
% 159.28/25.64    (2)  all_56_11 = e2
% 159.28/25.64    (3)   ~ (e2 = e1)
% 159.28/25.64  
% 159.28/25.64  Begin of proof
% 159.28/25.64  | 
% 159.28/25.64  | ALPHA: (1) implies:
% 159.28/25.64  |   (4)  all_56_11 = e1
% 159.28/25.64  | 
% 159.28/25.64  | COMBINE_EQS: (2), (4) imply:
% 159.28/25.64  |   (5)  e2 = e1
% 159.28/25.64  | 
% 159.28/25.64  | REDUCE: (3), (5) imply:
% 159.28/25.64  |   (6)  $false
% 159.28/25.64  | 
% 159.28/25.64  | CLOSE: (6) is inconsistent.
% 159.28/25.64  | 
% 159.28/25.64  End of proof
% 159.28/25.64  
% 159.28/25.64  Sub-proof #470 shows that the following formulas are inconsistent:
% 159.28/25.64  ----------------------------------------------------------------
% 159.28/25.64    (1)  all_56_10 = e2 & op(e2, e0) = e2
% 159.28/25.64    (2)  all_56_10 = e3
% 159.28/25.64    (3)   ~ (e3 = e2)
% 159.28/25.64  
% 159.28/25.64  Begin of proof
% 159.28/25.64  | 
% 159.28/25.64  | ALPHA: (1) implies:
% 159.28/25.64  |   (4)  all_56_10 = e2
% 159.28/25.64  | 
% 159.28/25.64  | COMBINE_EQS: (2), (4) imply:
% 159.28/25.64  |   (5)  e3 = e2
% 159.28/25.64  | 
% 159.28/25.64  | REDUCE: (3), (5) imply:
% 159.28/25.64  |   (6)  $false
% 159.28/25.64  | 
% 159.28/25.64  | CLOSE: (6) is inconsistent.
% 159.28/25.64  | 
% 159.28/25.64  End of proof
% 159.28/25.64  
% 159.28/25.64  Sub-proof #471 shows that the following formulas are inconsistent:
% 159.28/25.64  ----------------------------------------------------------------
% 159.28/25.64    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.28/25.64         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.28/25.64    (2)  all_56_9 = e2
% 159.28/25.64    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.64    (4)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.28/25.64             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.28/25.64               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.28/25.64               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.28/25.64    (5)  op(e0, e0) = e3
% 159.28/25.64    (6)  all_56_10 = e3
% 159.28/25.64    (7)   ~ (e1 = e0)
% 159.28/25.64    (8)   ~ (e2 = e1)
% 159.28/25.64    (9)   ~ (e3 = e1)
% 159.28/25.64    (10)   ~ (e2 = e0)
% 159.28/25.64    (11)   ~ (e3 = e0)
% 159.28/25.64  
% 159.28/25.64  Begin of proof
% 159.28/25.64  | 
% 159.28/25.64  | BETA: splitting (4) gives:
% 159.28/25.64  | 
% 159.28/25.64  | Case 1:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (12)  all_56_15 = e0 & op(e0, e0) = e0
% 159.28/25.64  | | 
% 159.28/25.64  | | ALPHA: (12) implies:
% 159.28/25.64  | |   (13)  op(e0, e0) = e0
% 159.28/25.64  | | 
% 159.28/25.64  | | REF_CLOSE: (3), (5), (11), (13) are inconsistent by sub-proof #999.
% 159.28/25.64  | | 
% 159.28/25.64  | Case 2:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (14)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 159.28/25.64  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 159.28/25.64  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 159.28/25.64  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 159.28/25.64  | | 
% 159.28/25.64  | | ALPHA: (14) implies:
% 159.28/25.64  | |   (15)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 159.28/25.64  | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.28/25.64  | | 
% 159.28/25.64  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (15) are
% 159.28/25.64  | |            inconsistent by sub-proof #472.
% 159.28/25.64  | | 
% 159.28/25.64  | End of split
% 159.28/25.64  | 
% 159.28/25.64  End of proof
% 159.28/25.64  
% 159.28/25.64  Sub-proof #472 shows that the following formulas are inconsistent:
% 159.28/25.64  ----------------------------------------------------------------
% 159.28/25.64    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.28/25.64         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.28/25.64    (2)  all_56_9 = e2
% 159.28/25.64    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.64    (4)  op(e0, e0) = e3
% 159.28/25.64    (5)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 159.28/25.64         (all_56_11 = e0 & op(e1, e0) = e0)
% 159.28/25.64    (6)  all_56_10 = e3
% 159.28/25.64    (7)   ~ (e1 = e0)
% 159.28/25.64    (8)   ~ (e2 = e1)
% 159.28/25.64    (9)   ~ (e3 = e1)
% 159.28/25.64    (10)   ~ (e2 = e0)
% 159.28/25.64    (11)   ~ (e3 = e0)
% 159.28/25.64  
% 159.28/25.64  Begin of proof
% 159.28/25.64  | 
% 159.28/25.64  | BETA: splitting (1) gives:
% 159.28/25.64  | 
% 159.28/25.64  | Case 1:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (12)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 159.28/25.64  | |           e1)
% 159.28/25.64  | | 
% 159.28/25.64  | | BETA: splitting (12) gives:
% 159.28/25.64  | | 
% 159.28/25.64  | | Case 1:
% 159.28/25.64  | | | 
% 159.28/25.64  | | |   (13)  all_56_9 = e1 & op(e3, e0) = e1
% 159.28/25.64  | | | 
% 159.28/25.64  | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #948.
% 159.28/25.64  | | | 
% 159.28/25.64  | | Case 2:
% 159.28/25.64  | | | 
% 159.28/25.64  | | |   (14)  all_56_10 = e1 & op(e2, e0) = e1
% 159.28/25.64  | | | 
% 159.28/25.64  | | | REF_CLOSE: (6), (9), (14) are inconsistent by sub-proof #556.
% 159.28/25.64  | | | 
% 159.28/25.64  | | End of split
% 159.28/25.64  | | 
% 159.28/25.64  | Case 2:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (15)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.28/25.64  | |           e1)
% 159.28/25.64  | | 
% 159.28/25.64  | | BETA: splitting (15) gives:
% 159.28/25.64  | | 
% 159.28/25.64  | | Case 1:
% 159.28/25.64  | | | 
% 159.28/25.64  | | |   (16)  all_56_11 = e1 & op(e1, e0) = e1
% 159.28/25.64  | | | 
% 159.28/25.64  | | | ALPHA: (16) implies:
% 159.28/25.64  | | |   (17)  all_56_11 = e1
% 159.28/25.64  | | | 
% 159.28/25.64  | | | REF_CLOSE: (2), (5), (6), (7), (10), (11), (17) are inconsistent by
% 159.28/25.64  | | |            sub-proof #474.
% 159.28/25.64  | | | 
% 159.28/25.64  | | Case 2:
% 159.28/25.64  | | | 
% 159.28/25.64  | | |   (18)  all_56_15 = e1 & op(e0, e0) = e1
% 159.28/25.64  | | | 
% 159.28/25.64  | | | ALPHA: (18) implies:
% 159.28/25.64  | | |   (19)  op(e0, e0) = e1
% 159.28/25.64  | | | 
% 159.28/25.64  | | | REF_CLOSE: (3), (4), (9), (19) are inconsistent by sub-proof #473.
% 159.28/25.64  | | | 
% 159.28/25.64  | | End of split
% 159.28/25.64  | | 
% 159.28/25.64  | End of split
% 159.28/25.64  | 
% 159.28/25.64  End of proof
% 159.28/25.64  
% 159.28/25.64  Sub-proof #473 shows that the following formulas are inconsistent:
% 159.28/25.64  ----------------------------------------------------------------
% 159.28/25.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.64    (2)  op(e0, e0) = e3
% 159.28/25.64    (3)  op(e0, e0) = e1
% 159.28/25.64    (4)   ~ (e3 = e1)
% 159.28/25.64  
% 159.28/25.64  Begin of proof
% 159.28/25.64  | 
% 159.28/25.64  | GROUND_INST: instantiating (1) with e1, e3, e0, e0, simplifying with (2), (3)
% 159.28/25.64  |              gives:
% 159.28/25.64  |   (5)  e3 = e1
% 159.28/25.64  | 
% 159.28/25.64  | REDUCE: (4), (5) imply:
% 159.28/25.64  |   (6)  $false
% 159.28/25.64  | 
% 159.28/25.64  | CLOSE: (6) is inconsistent.
% 159.28/25.64  | 
% 159.28/25.64  End of proof
% 159.28/25.64  
% 159.28/25.64  Sub-proof #474 shows that the following formulas are inconsistent:
% 159.28/25.64  ----------------------------------------------------------------
% 159.28/25.64    (1)  all_56_9 = e2
% 159.28/25.64    (2)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 159.28/25.64         (all_56_11 = e0 & op(e1, e0) = e0)
% 159.28/25.64    (3)  all_56_10 = e3
% 159.28/25.64    (4)  all_56_11 = e1
% 159.28/25.64    (5)   ~ (e1 = e0)
% 159.28/25.64    (6)   ~ (e2 = e0)
% 159.28/25.64    (7)   ~ (e3 = e0)
% 159.28/25.64  
% 159.28/25.64  Begin of proof
% 159.28/25.64  | 
% 159.28/25.64  | BETA: splitting (2) gives:
% 159.28/25.64  | 
% 159.28/25.64  | Case 1:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (8)  all_56_9 = e0 & op(e3, e0) = e0
% 159.28/25.64  | | 
% 159.28/25.64  | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #950.
% 159.28/25.64  | | 
% 159.28/25.64  | Case 2:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (9)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.28/25.64  | |          e0)
% 159.28/25.64  | | 
% 159.28/25.64  | | BETA: splitting (9) gives:
% 159.28/25.64  | | 
% 159.28/25.64  | | Case 1:
% 159.28/25.64  | | | 
% 159.28/25.64  | | |   (10)  all_56_10 = e0 & op(e2, e0) = e0
% 159.28/25.64  | | | 
% 159.28/25.64  | | | ALPHA: (10) implies:
% 159.28/25.64  | | |   (11)  all_56_10 = e0
% 159.28/25.64  | | | 
% 159.28/25.64  | | | REF_CLOSE: (3), (7), (11) are inconsistent by sub-proof #740.
% 159.28/25.64  | | | 
% 159.28/25.64  | | Case 2:
% 159.28/25.64  | | | 
% 159.28/25.64  | | |   (12)  all_56_11 = e0 & op(e1, e0) = e0
% 159.28/25.64  | | | 
% 159.28/25.64  | | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #660.
% 159.28/25.64  | | | 
% 159.28/25.64  | | End of split
% 159.28/25.64  | | 
% 159.28/25.64  | End of split
% 159.28/25.64  | 
% 159.28/25.64  End of proof
% 159.28/25.64  
% 159.28/25.64  Sub-proof #475 shows that the following formulas are inconsistent:
% 159.28/25.64  ----------------------------------------------------------------
% 159.28/25.64    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.28/25.64         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.28/25.64    (2)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 159.28/25.64    (3)   ~ (e3 = e2)
% 159.28/25.64    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.64    (5)   ~ (all_4_2 = e3)
% 159.28/25.64    (6)  op(e2, e2) = all_4_2
% 159.28/25.64    (7)  op(e3, e3) = e3
% 159.28/25.64    (8)   ~ (e1 = e0)
% 159.28/25.64    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.28/25.64         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.28/25.64    (10)   ~ (e2 = e1)
% 159.28/25.64    (11)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.28/25.64          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.28/25.64    (12)   ~ (e3 = e1)
% 159.28/25.64    (13)   ~ (e2 = e0)
% 159.28/25.64    (14)   ~ (e3 = e0)
% 159.28/25.64  
% 159.28/25.64  Begin of proof
% 159.28/25.64  | 
% 159.28/25.64  | BETA: splitting (2) gives:
% 159.28/25.64  | 
% 159.28/25.64  | Case 1:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (15)  all_56_2 = e3 & op(e2, e3) = e3
% 159.28/25.64  | | 
% 159.28/25.64  | | ALPHA: (15) implies:
% 159.28/25.64  | |   (16)  all_56_2 = e3
% 159.28/25.64  | | 
% 159.28/25.64  | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), (16)
% 159.28/25.64  | |            are inconsistent by sub-proof #765.
% 159.28/25.64  | | 
% 159.28/25.64  | Case 2:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (17)  all_56_3 = e3 & op(e2, e2) = e3
% 159.28/25.64  | | 
% 159.28/25.64  | | ALPHA: (17) implies:
% 159.28/25.64  | |   (18)  op(e2, e2) = e3
% 159.28/25.64  | | 
% 159.28/25.64  | | REF_CLOSE: (4), (5), (6), (18) are inconsistent by sub-proof #711.
% 159.28/25.64  | | 
% 159.28/25.64  | End of split
% 159.28/25.64  | 
% 159.28/25.64  End of proof
% 159.28/25.64  
% 159.28/25.64  Sub-proof #476 shows that the following formulas are inconsistent:
% 159.28/25.64  ----------------------------------------------------------------
% 159.28/25.64    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.28/25.64         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.28/25.64    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.28/25.64         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.28/25.64    (3)   ~ (e3 = e2)
% 159.28/25.64    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.28/25.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.28/25.64    (5)   ~ (all_4_2 = e3)
% 159.28/25.64    (6)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 159.28/25.64    (7)  op(e2, e2) = all_4_2
% 159.28/25.64    (8)  op(e3, e3) = e3
% 159.28/25.64    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.28/25.64         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.28/25.64    (10)   ~ (e1 = e0)
% 159.28/25.64    (11)   ~ (e2 = e1)
% 159.28/25.64    (12)   ~ (e3 = e1)
% 159.28/25.64    (13)   ~ (e2 = e0)
% 159.28/25.64    (14)   ~ (e3 = e0)
% 159.28/25.64  
% 159.28/25.64  Begin of proof
% 159.28/25.64  | 
% 159.28/25.64  | BETA: splitting (6) gives:
% 159.28/25.64  | 
% 159.28/25.64  | Case 1:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (15)  all_56_1 = e3 & op(e3, e2) = e3
% 159.28/25.64  | | 
% 159.28/25.64  | | ALPHA: (15) implies:
% 159.28/25.64  | |   (16)  all_56_1 = e3
% 159.28/25.64  | | 
% 159.28/25.64  | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (12), (13), (14), (16)
% 159.28/25.64  | |            are inconsistent by sub-proof #946.
% 159.28/25.64  | | 
% 159.28/25.64  | Case 2:
% 159.28/25.64  | | 
% 159.28/25.64  | |   (17)  all_56_3 = e3 & op(e2, e2) = e3
% 159.28/25.64  | | 
% 159.28/25.64  | | ALPHA: (17) implies:
% 159.28/25.64  | |   (18)  op(e2, e2) = e3
% 159.28/25.64  | | 
% 159.34/25.64  | | REF_CLOSE: (4), (5), (7), (18) are inconsistent by sub-proof #711.
% 159.34/25.64  | | 
% 159.34/25.64  | End of split
% 159.34/25.64  | 
% 159.34/25.64  End of proof
% 159.34/25.64  
% 159.34/25.64  Sub-proof #477 shows that the following formulas are inconsistent:
% 159.34/25.64  ----------------------------------------------------------------
% 159.34/25.64    (1)   ~ (all_24_1 = e0) & op(e1, e1) = all_24_1 & $i(all_24_1)
% 159.34/25.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.64    (3)  op(e1, e1) = e0
% 159.34/25.64  
% 159.34/25.64  Begin of proof
% 159.34/25.64  | 
% 159.34/25.64  | ALPHA: (1) implies:
% 159.34/25.64  |   (4)   ~ (all_24_1 = e0)
% 159.34/25.64  |   (5)  op(e1, e1) = all_24_1
% 159.34/25.64  | 
% 159.34/25.64  | GROUND_INST: instantiating (2) with e0, all_24_1, e1, e1, simplifying with
% 159.34/25.64  |              (3), (5) gives:
% 159.34/25.64  |   (6)  all_24_1 = e0
% 159.34/25.64  | 
% 159.34/25.64  | REDUCE: (4), (6) imply:
% 159.34/25.64  |   (7)  $false
% 159.34/25.64  | 
% 159.34/25.64  | CLOSE: (7) is inconsistent.
% 159.34/25.64  | 
% 159.34/25.64  End of proof
% 159.34/25.64  
% 159.34/25.64  Sub-proof #478 shows that the following formulas are inconsistent:
% 159.34/25.64  ----------------------------------------------------------------
% 159.34/25.64    (1)  all_54_9 = e1 | all_54_9 = e0
% 159.34/25.65    (2)  all_54_9 = all_52_6
% 159.34/25.65    (3)   ~ (all_52_6 = e1)
% 159.34/25.65    (4)   ~ (all_52_6 = e0)
% 159.34/25.65  
% 159.34/25.65  Begin of proof
% 159.34/25.65  | 
% 159.34/25.65  | BETA: splitting (1) gives:
% 159.34/25.65  | 
% 159.34/25.65  | Case 1:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (5)  all_54_9 = e1
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #675.
% 159.34/25.65  | | 
% 159.34/25.65  | Case 2:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (6)  all_54_9 = e0
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #674.
% 159.34/25.65  | | 
% 159.34/25.65  | End of split
% 159.34/25.65  | 
% 159.34/25.65  End of proof
% 159.34/25.65  
% 159.34/25.65  Sub-proof #479 shows that the following formulas are inconsistent:
% 159.34/25.65  ----------------------------------------------------------------
% 159.34/25.65    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.34/25.65         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.34/25.65    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 159.34/25.65         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 159.34/25.65    (3)   ~ (e3 = e2)
% 159.34/25.65    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.65    (5)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.34/25.65    (6)  op(e1, e3) = all_52_2
% 159.34/25.65    (7)   ~ (all_52_2 = e2)
% 159.34/25.65    (8)   ~ (all_52_2 = e1)
% 159.34/25.65    (9)  op(e3, e3) = e1
% 159.34/25.65    (10)   ~ (e1 = e0)
% 159.34/25.65    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.34/25.65          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.34/25.65    (12)   ~ (e2 = e1)
% 159.34/25.65    (13)   ~ (e3 = e1)
% 159.34/25.65    (14)   ~ (e2 = e0)
% 159.34/25.65    (15)   ~ (e3 = e0)
% 159.34/25.65  
% 159.34/25.65  Begin of proof
% 159.34/25.65  | 
% 159.34/25.65  | BETA: splitting (5) gives:
% 159.34/25.65  | 
% 159.34/25.65  | Case 1:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (16)  all_56_6 = e1 & op(e1, e3) = e1
% 159.34/25.65  | | 
% 159.34/25.65  | | ALPHA: (16) implies:
% 159.34/25.65  | |   (17)  op(e1, e3) = e1
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (4), (6), (8), (17) are inconsistent by sub-proof #990.
% 159.34/25.65  | | 
% 159.34/25.65  | Case 2:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (18)  all_56_12 = e1 & op(e0, e3) = e1
% 159.34/25.65  | | 
% 159.34/25.65  | | ALPHA: (18) implies:
% 159.34/25.65  | |   (19)  all_56_12 = e1
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 159.34/25.65  | |            (15), (19) are inconsistent by sub-proof #495.
% 159.34/25.65  | | 
% 159.34/25.65  | End of split
% 159.34/25.65  | 
% 159.34/25.65  End of proof
% 159.34/25.65  
% 159.34/25.65  Sub-proof #480 shows that the following formulas are inconsistent:
% 159.34/25.65  ----------------------------------------------------------------
% 159.34/25.65    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.34/25.65         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.34/25.65    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 159.34/25.65         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 159.34/25.65    (3)  all_56_2 = e1 & op(e2, e3) = e1
% 159.34/25.65    (4)   ~ (e3 = e2)
% 159.34/25.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.65    (6)  op(e0, e3) = all_52_3
% 159.34/25.65    (7)  op(e1, e3) = all_52_2
% 159.34/25.65    (8)   ~ (all_52_2 = e2)
% 159.34/25.65    (9)  op(e3, e3) = e1
% 159.34/25.65    (10)   ~ (e1 = e0)
% 159.34/25.65    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.34/25.65          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.34/25.65    (12)   ~ (e2 = e1)
% 159.34/25.65    (13)   ~ (e3 = e1)
% 159.34/25.65    (14)   ~ (e2 = e0)
% 159.34/25.65    (15)   ~ (e3 = e0)
% 159.34/25.65  
% 159.34/25.65  Begin of proof
% 159.34/25.65  | 
% 159.34/25.65  | ALPHA: (3) implies:
% 159.34/25.65  |   (16)  all_56_2 = e1
% 159.34/25.65  | 
% 159.34/25.65  | BETA: splitting (1) gives:
% 159.34/25.65  | 
% 159.34/25.65  | Case 1:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (17)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 159.34/25.65  | |           e2)
% 159.34/25.65  | | 
% 159.34/25.65  | | BETA: splitting (17) gives:
% 159.34/25.65  | | 
% 159.34/25.65  | | Case 1:
% 159.34/25.65  | | | 
% 159.34/25.65  | | |   (18)  all_56_0 = e2 & op(e3, e3) = e2
% 159.34/25.65  | | | 
% 159.34/25.65  | | | ALPHA: (18) implies:
% 159.34/25.65  | | |   (19)  op(e3, e3) = e2
% 159.34/25.65  | | | 
% 159.34/25.65  | | | REF_CLOSE: (5), (9), (12), (19) are inconsistent by sub-proof #828.
% 159.34/25.65  | | | 
% 159.34/25.65  | | Case 2:
% 159.34/25.65  | | | 
% 159.34/25.65  | | |   (20)  all_56_2 = e2 & op(e2, e3) = e2
% 159.34/25.65  | | | 
% 159.34/25.65  | | | ALPHA: (20) implies:
% 159.34/25.65  | | |   (21)  all_56_2 = e2
% 159.34/25.65  | | | 
% 159.34/25.65  | | | REF_CLOSE: (12), (16), (21) are inconsistent by sub-proof #600.
% 159.34/25.65  | | | 
% 159.34/25.65  | | End of split
% 159.34/25.65  | | 
% 159.34/25.65  | Case 2:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (22)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 159.34/25.65  | |           e2)
% 159.34/25.65  | | 
% 159.34/25.65  | | BETA: splitting (22) gives:
% 159.34/25.65  | | 
% 159.34/25.65  | | Case 1:
% 159.34/25.65  | | | 
% 159.34/25.65  | | |   (23)  all_56_6 = e2 & op(e1, e3) = e2
% 159.34/25.65  | | | 
% 159.34/25.65  | | | REF_CLOSE: (5), (7), (8), (23) are inconsistent by sub-proof #761.
% 159.34/25.65  | | | 
% 159.34/25.65  | | Case 2:
% 159.34/25.65  | | | 
% 159.34/25.65  | | |   (24)  all_56_12 = e2 & op(e0, e3) = e2
% 159.34/25.65  | | | 
% 159.34/25.65  | | | ALPHA: (24) implies:
% 159.34/25.65  | | |   (25)  all_56_12 = e2
% 159.34/25.65  | | |   (26)  op(e0, e3) = e2
% 159.34/25.65  | | | 
% 159.34/25.65  | | | REF_CLOSE: (2), (4), (5), (6), (9), (10), (11), (13), (14), (15), (16),
% 159.34/25.65  | | |            (25), (26) are inconsistent by sub-proof #481.
% 159.34/25.65  | | | 
% 159.34/25.65  | | End of split
% 159.34/25.65  | | 
% 159.34/25.65  | End of split
% 159.34/25.65  | 
% 159.34/25.65  End of proof
% 159.34/25.65  
% 159.34/25.65  Sub-proof #481 shows that the following formulas are inconsistent:
% 159.34/25.65  ----------------------------------------------------------------
% 159.34/25.65    (1)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 159.34/25.65         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 159.34/25.65    (2)  op(e0, e3) = e2
% 159.34/25.65    (3)   ~ (e3 = e2)
% 159.34/25.65    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.65    (5)  op(e0, e3) = all_52_3
% 159.34/25.65    (6)  all_56_12 = e2
% 159.34/25.65    (7)  op(e3, e3) = e1
% 159.34/25.65    (8)   ~ (e1 = e0)
% 159.34/25.65    (9)  all_56_2 = e1
% 159.34/25.65    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.34/25.65          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.34/25.65    (11)   ~ (e3 = e1)
% 159.34/25.65    (12)   ~ (e2 = e0)
% 159.34/25.65    (13)   ~ (e3 = e0)
% 159.34/25.65  
% 159.34/25.65  Begin of proof
% 159.34/25.65  | 
% 159.34/25.65  | BETA: splitting (10) gives:
% 159.34/25.65  | 
% 159.34/25.65  | Case 1:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (14)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 159.34/25.65  | |           e0)
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (4), (7), (8), (9), (14) are inconsistent by sub-proof #485.
% 159.34/25.65  | | 
% 159.34/25.65  | Case 2:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (15)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 159.34/25.65  | |           e0)
% 159.34/25.65  | | 
% 159.34/25.65  | | BETA: splitting (15) gives:
% 159.34/25.65  | | 
% 159.34/25.65  | | Case 1:
% 159.34/25.65  | | | 
% 159.34/25.65  | | |   (16)  all_56_6 = e0 & op(e1, e3) = e0
% 159.34/25.65  | | | 
% 159.34/25.65  | | | ALPHA: (16) implies:
% 159.34/25.65  | | |   (17)  op(e1, e3) = e0
% 159.34/25.65  | | | 
% 159.34/25.65  | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11), (13), (17) are inconsistent
% 159.34/25.65  | | |            by sub-proof #482.
% 159.34/25.65  | | | 
% 159.34/25.65  | | Case 2:
% 159.34/25.65  | | | 
% 159.34/25.65  | | |   (18)  all_56_12 = e0 & op(e0, e3) = e0
% 159.34/25.65  | | | 
% 159.34/25.65  | | | ALPHA: (18) implies:
% 159.34/25.65  | | |   (19)  op(e0, e3) = e0
% 159.34/25.65  | | | 
% 159.34/25.65  | | | REF_CLOSE: (2), (4), (5), (12), (19) are inconsistent by sub-proof #689.
% 159.34/25.65  | | | 
% 159.34/25.65  | | End of split
% 159.34/25.65  | | 
% 159.34/25.65  | End of split
% 159.34/25.65  | 
% 159.34/25.65  End of proof
% 159.34/25.65  
% 159.34/25.65  Sub-proof #482 shows that the following formulas are inconsistent:
% 159.34/25.65  ----------------------------------------------------------------
% 159.34/25.65    (1)  op(e1, e3) = e0
% 159.34/25.65    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 159.34/25.65         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 159.34/25.65    (3)   ~ (e3 = e2)
% 159.34/25.65    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.65    (5)  all_56_12 = e2
% 159.34/25.65    (6)  op(e3, e3) = e1
% 159.34/25.65    (7)  all_56_2 = e1
% 159.34/25.65    (8)   ~ (e3 = e1)
% 159.34/25.65    (9)   ~ (e3 = e0)
% 159.34/25.65  
% 159.34/25.65  Begin of proof
% 159.34/25.65  | 
% 159.34/25.65  | BETA: splitting (2) gives:
% 159.34/25.65  | 
% 159.34/25.65  | Case 1:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 159.34/25.65  | |           e3)
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (4), (6), (7), (8), (10) are inconsistent by sub-proof #483.
% 159.34/25.65  | | 
% 159.34/25.65  | Case 2:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (11)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 159.34/25.65  | |           e3)
% 159.34/25.65  | | 
% 159.34/25.65  | | BETA: splitting (11) gives:
% 159.34/25.65  | | 
% 159.34/25.65  | | Case 1:
% 159.34/25.65  | | | 
% 159.34/25.65  | | |   (12)  all_56_6 = e3 & op(e1, e3) = e3
% 159.34/25.65  | | | 
% 159.34/25.65  | | | ALPHA: (12) implies:
% 159.34/25.65  | | |   (13)  op(e1, e3) = e3
% 159.34/25.65  | | | 
% 159.34/25.65  | | | REF_CLOSE: (1), (4), (9), (13) are inconsistent by sub-proof #913.
% 159.34/25.65  | | | 
% 159.34/25.65  | | Case 2:
% 159.34/25.65  | | | 
% 159.34/25.65  | | |   (14)  all_56_12 = e3 & op(e0, e3) = e3
% 159.34/25.65  | | | 
% 159.34/25.65  | | | ALPHA: (14) implies:
% 159.34/25.65  | | |   (15)  all_56_12 = e3
% 159.34/25.65  | | | 
% 159.34/25.65  | | | REF_CLOSE: (3), (5), (15) are inconsistent by sub-proof #616.
% 159.34/25.65  | | | 
% 159.34/25.65  | | End of split
% 159.34/25.65  | | 
% 159.34/25.65  | End of split
% 159.34/25.65  | 
% 159.34/25.65  End of proof
% 159.34/25.65  
% 159.34/25.65  Sub-proof #483 shows that the following formulas are inconsistent:
% 159.34/25.65  ----------------------------------------------------------------
% 159.34/25.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.65    (2)  op(e3, e3) = e1
% 159.34/25.65    (3)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 159.34/25.65    (4)  all_56_2 = e1
% 159.34/25.65    (5)   ~ (e3 = e1)
% 159.34/25.65  
% 159.34/25.65  Begin of proof
% 159.34/25.65  | 
% 159.34/25.65  | BETA: splitting (3) gives:
% 159.34/25.65  | 
% 159.34/25.65  | Case 1:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (6)  all_56_0 = e3 & op(e3, e3) = e3
% 159.34/25.65  | | 
% 159.34/25.65  | | ALPHA: (6) implies:
% 159.34/25.65  | |   (7)  op(e3, e3) = e3
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #995.
% 159.34/25.65  | | 
% 159.34/25.65  | Case 2:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (8)  all_56_2 = e3 & op(e2, e3) = e3
% 159.34/25.65  | | 
% 159.34/25.65  | | ALPHA: (8) implies:
% 159.34/25.65  | |   (9)  all_56_2 = e3
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #484.
% 159.34/25.65  | | 
% 159.34/25.65  | End of split
% 159.34/25.65  | 
% 159.34/25.65  End of proof
% 159.34/25.65  
% 159.34/25.65  Sub-proof #484 shows that the following formulas are inconsistent:
% 159.34/25.65  ----------------------------------------------------------------
% 159.34/25.65    (1)  all_56_2 = e3
% 159.34/25.65    (2)  all_56_2 = e1
% 159.34/25.65    (3)   ~ (e3 = e1)
% 159.34/25.65  
% 159.34/25.65  Begin of proof
% 159.34/25.65  | 
% 159.34/25.65  | COMBINE_EQS: (1), (2) imply:
% 159.34/25.65  |   (4)  e3 = e1
% 159.34/25.65  | 
% 159.34/25.65  | SIMP: (4) implies:
% 159.34/25.65  |   (5)  e3 = e1
% 159.34/25.65  | 
% 159.34/25.65  | REDUCE: (3), (5) imply:
% 159.34/25.65  |   (6)  $false
% 159.34/25.65  | 
% 159.34/25.65  | CLOSE: (6) is inconsistent.
% 159.34/25.65  | 
% 159.34/25.65  End of proof
% 159.34/25.65  
% 159.34/25.65  Sub-proof #485 shows that the following formulas are inconsistent:
% 159.34/25.65  ----------------------------------------------------------------
% 159.34/25.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.65    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 159.34/25.65    (3)  op(e3, e3) = e1
% 159.34/25.65    (4)   ~ (e1 = e0)
% 159.34/25.65    (5)  all_56_2 = e1
% 159.34/25.65  
% 159.34/25.65  Begin of proof
% 159.34/25.65  | 
% 159.34/25.65  | BETA: splitting (2) gives:
% 159.34/25.65  | 
% 159.34/25.65  | Case 1:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (6)  all_56_0 = e0 & op(e3, e3) = e0
% 159.34/25.65  | | 
% 159.34/25.65  | | ALPHA: (6) implies:
% 159.34/25.65  | |   (7)  op(e3, e3) = e0
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #834.
% 159.34/25.65  | | 
% 159.34/25.65  | Case 2:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (8)  all_56_2 = e0 & op(e2, e3) = e0
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #486.
% 159.34/25.65  | | 
% 159.34/25.65  | End of split
% 159.34/25.65  | 
% 159.34/25.65  End of proof
% 159.34/25.65  
% 159.34/25.65  Sub-proof #486 shows that the following formulas are inconsistent:
% 159.34/25.65  ----------------------------------------------------------------
% 159.34/25.65    (1)  all_56_2 = e0 & op(e2, e3) = e0
% 159.34/25.65    (2)  all_56_2 = e1
% 159.34/25.65    (3)   ~ (e1 = e0)
% 159.34/25.65  
% 159.34/25.65  Begin of proof
% 159.34/25.65  | 
% 159.34/25.65  | ALPHA: (1) implies:
% 159.34/25.65  |   (4)  all_56_2 = e0
% 159.34/25.65  | 
% 159.34/25.65  | COMBINE_EQS: (2), (4) imply:
% 159.34/25.65  |   (5)  e1 = e0
% 159.34/25.65  | 
% 159.34/25.65  | REDUCE: (3), (5) imply:
% 159.34/25.65  |   (6)  $false
% 159.34/25.65  | 
% 159.34/25.65  | CLOSE: (6) is inconsistent.
% 159.34/25.65  | 
% 159.34/25.65  End of proof
% 159.34/25.65  
% 159.34/25.65  Sub-proof #487 shows that the following formulas are inconsistent:
% 159.34/25.65  ----------------------------------------------------------------
% 159.34/25.65    (1)  op(e1, e1) = e3
% 159.34/25.65    (2)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.34/25.65             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.34/25.65           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.34/25.65               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.34/25.65             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.34/25.65         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.34/25.65             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.34/25.65           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.34/25.65               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.34/25.65             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.34/25.65         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.34/25.65             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.34/25.65           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.34/25.65               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.34/25.65             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.34/25.65         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.34/25.65             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.34/25.65           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.34/25.65               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.34/25.65             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.34/25.65    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.65    (4)  op(e1, e0) = all_52_14
% 159.34/25.65    (5)  op(e3, e3) = e1
% 159.34/25.65    (6)  op(e2, e2) = e1
% 159.34/25.65    (7)  op(e1, e0) = e1
% 159.34/25.65    (8)   ~ (e2 = e1)
% 159.34/25.65    (9)   ~ (e3 = e1)
% 159.34/25.65    (10)   ~ (e3 = e0)
% 159.34/25.65  
% 159.34/25.65  Begin of proof
% 159.34/25.65  | 
% 159.34/25.65  | BETA: splitting (2) gives:
% 159.34/25.65  | 
% 159.34/25.65  | Case 1:
% 159.34/25.65  | | 
% 159.34/25.65  | |   (11)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.34/25.65  | |               e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.34/25.65  | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.34/25.65  | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.34/25.65  | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.34/25.65  | |                 e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 159.34/25.65  | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 159.34/25.65  | |                 e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 159.34/25.65  | |               e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 159.34/25.65  | |               all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 159.34/25.65  | |               e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 159.34/25.65  | |               $i(all_57_7))))
% 159.34/25.65  | | 
% 159.34/25.65  | | REF_CLOSE: (3), (5), (6), (8), (9), (11) are inconsistent by sub-proof #499.
% 159.34/25.65  | | 
% 159.34/25.65  | Case 2:
% 159.34/25.65  | | 
% 159.34/25.66  | |   (12)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.34/25.66  | |               e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.34/25.66  | |               $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.34/25.66  | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.34/25.66  | |           ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.34/25.66  | |                 e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 159.34/25.66  | |             e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 159.34/25.66  | |                 e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 =
% 159.34/25.66  | |               e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 159.34/25.66  | |               all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 159.34/25.66  | |               e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.34/25.66  | |               $i(all_57_13))))
% 159.34/25.66  | | 
% 159.34/25.66  | | BETA: splitting (12) gives:
% 159.34/25.66  | | 
% 159.34/25.66  | | Case 1:
% 159.34/25.66  | | | 
% 159.34/25.66  | | |   (13)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.34/25.66  | | |             e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.34/25.66  | | |             $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.34/25.66  | | |             (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.34/25.66  | | |         ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.34/25.66  | | |               e1) = all_57_8 & $i(all_57_8)))
% 159.34/25.66  | | | 
% 159.34/25.66  | | | ALPHA: (13) implies:
% 159.34/25.66  | | |   (14)  op(e1, e1) = e1
% 159.34/25.66  | | | 
% 159.34/25.66  | | | REF_CLOSE: (1), (3), (9), (14) are inconsistent by sub-proof #1003.
% 159.34/25.66  | | | 
% 159.34/25.66  | | Case 2:
% 159.34/25.66  | | | 
% 159.34/25.66  | | |   (15)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 159.34/25.66  | | |             e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.34/25.66  | | |             $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 159.34/25.66  | | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 159.34/25.66  | | |         ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) &
% 159.34/25.66  | | |             op(e1, e0) = all_57_13 & $i(all_57_13)))
% 159.34/25.66  | | | 
% 159.34/25.66  | | | ALPHA: (15) implies:
% 159.34/25.66  | | |   (16)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 159.34/25.66  | | |             e0) = all_57_13 & $i(all_57_13))
% 159.34/25.66  | | | 
% 159.34/25.66  | | | REF_CLOSE: (1), (3), (4), (7), (10), (16) are inconsistent by sub-proof
% 159.34/25.66  | | |            #493.
% 159.34/25.66  | | | 
% 159.34/25.66  | | End of split
% 159.34/25.66  | | 
% 159.34/25.66  | End of split
% 159.34/25.66  | 
% 159.34/25.66  End of proof
% 159.34/25.66  
% 159.34/25.66  Sub-proof #488 shows that the following formulas are inconsistent:
% 159.34/25.66  ----------------------------------------------------------------
% 159.34/25.66    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.34/25.66         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.34/25.66    (2)   ~ (e3 = e2)
% 159.34/25.66    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.66    (4)  op(e0, e3) = all_52_3
% 159.34/25.66    (5)  all_56_6 = e3
% 159.34/25.66    (6)   ~ (all_52_3 = e0)
% 159.34/25.66    (7)  op(e0, e0) = e0
% 159.34/25.66    (8)  all_56_2 = e2
% 159.34/25.66    (9)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 159.34/25.66         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.34/25.66    (10)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 159.34/25.66          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 159.34/25.66    (11)  all_56_11 = e1
% 159.34/25.66    (12)  all_56_0 = e1
% 159.34/25.66    (13)   ~ (e1 = e0)
% 159.34/25.66    (14)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.34/25.66          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.34/25.66    (15)   ~ (e2 = e1)
% 159.34/25.66    (16)  all_56_15 = e0
% 159.34/25.66    (17)   ~ (e3 = e1)
% 159.34/25.66    (18)   ~ (e2 = e0)
% 159.34/25.66    (19)   ~ (e3 = e0)
% 159.34/25.66  
% 159.34/25.66  Begin of proof
% 159.34/25.66  | 
% 159.34/25.66  | BETA: splitting (14) gives:
% 159.34/25.66  | 
% 159.34/25.66  | Case 1:
% 159.34/25.66  | | 
% 159.34/25.66  | |   (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 159.34/25.66  | |           e0)
% 159.34/25.66  | | 
% 159.34/25.66  | | BETA: splitting (20) gives:
% 159.34/25.66  | | 
% 159.34/25.66  | | Case 1:
% 159.34/25.66  | | | 
% 159.34/25.66  | | |   (21)  all_56_0 = e0 & op(e3, e3) = e0
% 159.34/25.66  | | | 
% 159.34/25.66  | | | REF_CLOSE: (1), (2), (3), (7), (9), (10), (11), (12), (13), (15), (16),
% 159.34/25.66  | | |            (17), (18), (19), (21) are inconsistent by sub-proof #489.
% 159.34/25.66  | | | 
% 159.34/25.66  | | Case 2:
% 159.34/25.66  | | | 
% 159.34/25.66  | | |   (22)  all_56_2 = e0 & op(e2, e3) = e0
% 159.34/25.66  | | | 
% 159.34/25.66  | | | ALPHA: (22) implies:
% 159.34/25.66  | | |   (23)  all_56_2 = e0
% 159.34/25.66  | | | 
% 159.34/25.66  | | | REF_CLOSE: (8), (18), (23) are inconsistent by sub-proof #602.
% 159.34/25.66  | | | 
% 159.34/25.66  | | End of split
% 159.34/25.66  | | 
% 159.34/25.66  | Case 2:
% 159.34/25.66  | | 
% 159.34/25.66  | |   (24)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 159.34/25.66  | |           e0)
% 159.34/25.66  | | 
% 159.34/25.66  | | BETA: splitting (24) gives:
% 159.34/25.66  | | 
% 159.34/25.66  | | Case 1:
% 159.34/25.66  | | | 
% 159.34/25.66  | | |   (25)  all_56_6 = e0 & op(e1, e3) = e0
% 159.34/25.66  | | | 
% 159.34/25.66  | | | ALPHA: (25) implies:
% 159.34/25.66  | | |   (26)  all_56_6 = e0
% 159.34/25.66  | | | 
% 159.34/25.66  | | | COMBINE_EQS: (5), (26) imply:
% 159.34/25.66  | | |   (27)  e3 = e0
% 159.34/25.66  | | | 
% 159.34/25.66  | | | SIMP: (27) implies:
% 159.34/25.66  | | |   (28)  e3 = e0
% 159.34/25.66  | | | 
% 159.34/25.66  | | | REDUCE: (19), (28) imply:
% 159.34/25.66  | | |   (29)  $false
% 159.34/25.66  | | | 
% 159.34/25.66  | | | CLOSE: (29) is inconsistent.
% 159.34/25.66  | | | 
% 159.34/25.66  | | Case 2:
% 159.34/25.66  | | | 
% 159.34/25.66  | | |   (30)  all_56_12 = e0 & op(e0, e3) = e0
% 159.34/25.66  | | | 
% 159.34/25.66  | | | ALPHA: (30) implies:
% 159.34/25.66  | | |   (31)  op(e0, e3) = e0
% 159.34/25.66  | | | 
% 159.34/25.66  | | | REF_CLOSE: (3), (4), (6), (31) are inconsistent by sub-proof #973.
% 159.34/25.66  | | | 
% 159.34/25.66  | | End of split
% 159.34/25.66  | | 
% 159.34/25.66  | End of split
% 159.34/25.66  | 
% 159.34/25.66  End of proof
% 159.34/25.66  
% 159.34/25.66  Sub-proof #489 shows that the following formulas are inconsistent:
% 159.34/25.66  ----------------------------------------------------------------
% 159.34/25.66    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.34/25.66         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.34/25.66    (2)  all_56_0 = e0 & op(e3, e3) = e0
% 159.34/25.66    (3)   ~ (e3 = e2)
% 159.34/25.66    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.66    (5)  op(e0, e0) = e0
% 159.34/25.66    (6)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 159.34/25.66         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.34/25.66    (7)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 159.34/25.66         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 159.34/25.66    (8)  all_56_11 = e1
% 159.34/25.66    (9)  all_56_0 = e1
% 159.34/25.66    (10)   ~ (e1 = e0)
% 159.34/25.66    (11)   ~ (e2 = e1)
% 159.34/25.66    (12)  all_56_15 = e0
% 159.34/25.66    (13)   ~ (e3 = e1)
% 159.34/25.66    (14)   ~ (e2 = e0)
% 159.34/25.66    (15)   ~ (e3 = e0)
% 159.34/25.66  
% 159.34/25.66  Begin of proof
% 159.34/25.66  | 
% 159.34/25.66  | ALPHA: (2) implies:
% 159.34/25.66  |   (16)  all_56_0 = e0
% 159.34/25.66  | 
% 159.34/25.66  | COMBINE_EQS: (9), (16) imply:
% 159.34/25.66  |   (17)  e1 = e0
% 159.34/25.66  | 
% 159.34/25.66  | COMBINE_EQS: (8), (17) imply:
% 159.34/25.66  |   (18)  all_56_11 = e0
% 159.34/25.66  | 
% 159.34/25.66  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14), (15),
% 159.34/25.66  |            (18) are inconsistent by sub-proof #883.
% 159.34/25.66  | 
% 159.34/25.66  End of proof
% 159.34/25.66  
% 159.34/25.66  Sub-proof #490 shows that the following formulas are inconsistent:
% 159.34/25.66  ----------------------------------------------------------------
% 159.34/25.66    (1)  all_56_0 = e2 & op(e3, e3) = e2
% 159.34/25.66    (2)  all_56_0 = e1
% 159.34/25.66    (3)   ~ (e2 = e1)
% 159.34/25.66  
% 159.34/25.66  Begin of proof
% 159.34/25.66  | 
% 159.34/25.66  | ALPHA: (1) implies:
% 159.34/25.66  |   (4)  all_56_0 = e2
% 159.34/25.66  | 
% 159.34/25.66  | COMBINE_EQS: (2), (4) imply:
% 159.34/25.66  |   (5)  e2 = e1
% 159.34/25.66  | 
% 159.34/25.66  | SIMP: (5) implies:
% 159.34/25.66  |   (6)  e2 = e1
% 159.34/25.66  | 
% 159.34/25.66  | REDUCE: (3), (6) imply:
% 159.34/25.66  |   (7)  $false
% 159.34/25.66  | 
% 159.34/25.66  | CLOSE: (7) is inconsistent.
% 159.34/25.66  | 
% 159.34/25.66  End of proof
% 159.34/25.66  
% 159.34/25.66  Sub-proof #491 shows that the following formulas are inconsistent:
% 159.34/25.66  ----------------------------------------------------------------
% 159.34/25.66    (1)  op(e1, e1) = e0
% 159.34/25.66    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.66    (3)  op(e0, e0) = e0
% 159.34/25.66    (4)  op(e0, e0) = all_14_2
% 159.34/25.66    (5)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 159.34/25.66           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.34/25.66           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 159.34/25.66           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.34/25.66           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.34/25.66    (6)   ~ (e1 = e0)
% 159.34/25.66    (7)   ~ (e2 = e0)
% 159.34/25.66  
% 159.34/25.66  Begin of proof
% 159.34/25.66  | 
% 159.34/25.66  | BETA: splitting (5) gives:
% 159.34/25.66  | 
% 159.34/25.66  | Case 1:
% 159.34/25.66  | | 
% 159.34/25.66  | |   (8)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.34/25.66  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.34/25.66  | |          e1) = e2 & $i(all_57_12)
% 159.34/25.66  | | 
% 159.34/25.66  | | ALPHA: (8) implies:
% 159.34/25.66  | |   (9)  op(e1, e1) = e2
% 159.34/25.66  | | 
% 159.34/25.66  | | REF_CLOSE: (1), (2), (7), (9) are inconsistent by sub-proof #914.
% 159.34/25.66  | | 
% 159.34/25.66  | Case 2:
% 159.34/25.66  | | 
% 159.34/25.66  | |   (10)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 159.34/25.66  | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.34/25.66  | |         op(e0, e0) = e1 & $i(all_57_14)
% 159.34/25.66  | | 
% 159.34/25.66  | | ALPHA: (10) implies:
% 159.34/25.66  | |   (11)  op(e0, e0) = e1
% 159.34/25.66  | | 
% 159.34/25.66  | | REF_CLOSE: (2), (3), (4), (6), (11) are inconsistent by sub-proof #991.
% 159.34/25.66  | | 
% 159.34/25.66  | End of split
% 159.34/25.66  | 
% 159.34/25.66  End of proof
% 159.34/25.66  
% 159.34/25.66  Sub-proof #492 shows that the following formulas are inconsistent:
% 159.34/25.66  ----------------------------------------------------------------
% 159.34/25.66    (1)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 159.34/25.66           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.34/25.66           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 159.34/25.66           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 159.34/25.66             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.34/25.66    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.66    (3)  op(e1, e2) = all_52_6
% 159.34/25.66    (4)   ~ (all_52_6 = e1)
% 159.34/25.66  
% 159.34/25.66  Begin of proof
% 159.34/25.66  | 
% 159.34/25.66  | BETA: splitting (1) gives:
% 159.34/25.66  | 
% 159.34/25.66  | Case 1:
% 159.34/25.66  | | 
% 159.34/25.66  | |   (5)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 159.34/25.66  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.34/25.66  | |        all_57_14 & $i(all_57_14)
% 159.34/25.66  | | 
% 159.34/25.66  | | ALPHA: (5) implies:
% 159.34/25.66  | |   (6)  op(e1, e2) = e1
% 159.34/25.66  | | 
% 159.34/25.66  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #984.
% 159.34/25.66  | | 
% 159.34/25.66  | Case 2:
% 159.34/25.66  | | 
% 159.34/25.66  | |   (7)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 159.34/25.66  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.34/25.66  | |        all_57_14 & $i(all_57_14)
% 159.34/25.66  | | 
% 159.34/25.66  | | ALPHA: (7) implies:
% 159.34/25.66  | |   (8)  op(e1, e2) = e1
% 159.34/25.66  | | 
% 159.34/25.66  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #984.
% 159.34/25.66  | | 
% 159.34/25.66  | End of split
% 159.34/25.66  | 
% 159.34/25.66  End of proof
% 159.34/25.66  
% 159.34/25.66  Sub-proof #493 shows that the following formulas are inconsistent:
% 159.34/25.66  ----------------------------------------------------------------
% 159.34/25.66    (1)  op(e1, e1) = e3
% 159.34/25.66    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.66    (3)  op(e1, e0) = all_52_14
% 159.34/25.66    (4)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) =
% 159.34/25.66           all_57_13 & $i(all_57_13))
% 159.34/25.66    (5)  op(e1, e0) = e1
% 159.34/25.66    (6)   ~ (e3 = e0)
% 159.34/25.66  
% 159.34/25.66  Begin of proof
% 159.34/25.66  | 
% 159.34/25.66  | BETA: splitting (4) gives:
% 159.34/25.66  | 
% 159.34/25.66  | Case 1:
% 159.34/25.66  | | 
% 159.34/25.66  | |   (7)  all_57_14 = e0 & op(e1, e1) = e0
% 159.34/25.66  | | 
% 159.34/25.66  | | ALPHA: (7) implies:
% 159.34/25.66  | |   (8)  op(e1, e1) = e0
% 159.34/25.66  | | 
% 159.34/25.66  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #912.
% 159.34/25.66  | | 
% 159.34/25.66  | Case 2:
% 159.34/25.66  | | 
% 159.34/25.66  | |   (9)   ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13)
% 159.34/25.66  | | 
% 159.34/25.66  | | ALPHA: (9) implies:
% 159.34/25.66  | |   (10)   ~ (all_57_13 = e1)
% 159.34/25.66  | |   (11)  op(e1, e0) = all_57_13
% 159.34/25.66  | | 
% 159.34/25.66  | | REF_CLOSE: (2), (3), (5), (10), (11) are inconsistent by sub-proof #637.
% 159.34/25.66  | | 
% 159.34/25.66  | End of split
% 159.34/25.66  | 
% 159.34/25.66  End of proof
% 159.34/25.66  
% 159.34/25.66  Sub-proof #494 shows that the following formulas are inconsistent:
% 159.34/25.66  ----------------------------------------------------------------
% 159.34/25.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.66    (2)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.34/25.66           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.34/25.66           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 159.34/25.66           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.34/25.66           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.34/25.66    (3)  op(e3, e3) = e1
% 159.34/25.66    (4)  op(e2, e2) = e1
% 159.34/25.66    (5)   ~ (e2 = e1)
% 159.34/25.66    (6)   ~ (e3 = e1)
% 159.34/25.66  
% 159.34/25.66  Begin of proof
% 159.34/25.66  | 
% 159.34/25.66  | BETA: splitting (2) gives:
% 159.34/25.66  | 
% 159.34/25.66  | Case 1:
% 159.34/25.66  | | 
% 159.34/25.66  | |   (7)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 159.34/25.66  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.34/25.66  | |        all_57_12 & $i(all_57_12)
% 159.34/25.66  | | 
% 159.34/25.66  | | ALPHA: (7) implies:
% 159.34/25.66  | |   (8)  op(e3, e3) = e2
% 159.34/25.66  | | 
% 159.34/25.66  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #828.
% 159.34/25.66  | | 
% 159.34/25.66  | Case 2:
% 159.34/25.66  | | 
% 159.34/25.66  | |   (9)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2)
% 159.34/25.66  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 159.34/25.66  | |          e2) = e3 & $i(all_57_10)
% 159.34/25.66  | | 
% 159.34/25.66  | | ALPHA: (9) implies:
% 159.34/25.66  | |   (10)  op(e2, e2) = e3
% 159.34/25.66  | | 
% 159.34/25.66  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #847.
% 159.34/25.66  | | 
% 159.34/25.66  | End of split
% 159.34/25.66  | 
% 159.34/25.66  End of proof
% 159.34/25.66  
% 159.34/25.66  Sub-proof #495 shows that the following formulas are inconsistent:
% 159.34/25.66  ----------------------------------------------------------------
% 159.34/25.66    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.34/25.66         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.34/25.66    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 159.34/25.66         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 159.34/25.66    (3)  all_56_12 = e1
% 159.34/25.66    (4)   ~ (e3 = e2)
% 159.34/25.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.66    (6)  op(e1, e3) = all_52_2
% 159.34/25.66    (7)   ~ (all_52_2 = e2)
% 159.34/25.66    (8)  op(e3, e3) = e1
% 159.34/25.66    (9)   ~ (e1 = e0)
% 159.34/25.67    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.34/25.67          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.34/25.67    (11)   ~ (e2 = e1)
% 159.34/25.67    (12)   ~ (e3 = e1)
% 159.34/25.67    (13)   ~ (e2 = e0)
% 159.34/25.67    (14)   ~ (e3 = e0)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | BETA: splitting (1) gives:
% 159.34/25.67  | 
% 159.34/25.67  | Case 1:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (15)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 159.34/25.67  | |           e2)
% 159.34/25.67  | | 
% 159.34/25.67  | | BETA: splitting (15) gives:
% 159.34/25.67  | | 
% 159.34/25.67  | | Case 1:
% 159.34/25.67  | | | 
% 159.34/25.67  | | |   (16)  all_56_0 = e2 & op(e3, e3) = e2
% 159.34/25.67  | | | 
% 159.34/25.67  | | | ALPHA: (16) implies:
% 159.34/25.67  | | |   (17)  op(e3, e3) = e2
% 159.34/25.67  | | | 
% 159.34/25.67  | | | REF_CLOSE: (5), (8), (11), (17) are inconsistent by sub-proof #828.
% 159.34/25.67  | | | 
% 159.34/25.67  | | Case 2:
% 159.34/25.67  | | | 
% 159.34/25.67  | | |   (18)  all_56_2 = e2 & op(e2, e3) = e2
% 159.34/25.67  | | | 
% 159.34/25.67  | | | ALPHA: (18) implies:
% 159.34/25.67  | | |   (19)  all_56_2 = e2
% 159.34/25.67  | | | 
% 159.34/25.67  | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (12), (13), (14), (19) are
% 159.34/25.67  | | |            inconsistent by sub-proof #496.
% 159.34/25.67  | | | 
% 159.34/25.67  | | End of split
% 159.34/25.67  | | 
% 159.34/25.67  | Case 2:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (20)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 159.34/25.67  | |           e2)
% 159.34/25.67  | | 
% 159.34/25.67  | | REF_CLOSE: (3), (5), (6), (7), (11), (20) are inconsistent by sub-proof
% 159.34/25.67  | |            #717.
% 159.34/25.67  | | 
% 159.34/25.67  | End of split
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #496 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 159.34/25.67         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 159.34/25.67    (2)  all_56_12 = e1
% 159.34/25.67    (3)   ~ (e3 = e2)
% 159.34/25.67    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.67    (5)  all_56_2 = e2
% 159.34/25.67    (6)  op(e3, e3) = e1
% 159.34/25.67    (7)   ~ (e1 = e0)
% 159.34/25.67    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.34/25.67         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.34/25.67    (9)   ~ (e3 = e1)
% 159.34/25.67    (10)   ~ (e2 = e0)
% 159.34/25.67    (11)   ~ (e3 = e0)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | BETA: splitting (8) gives:
% 159.34/25.67  | 
% 159.34/25.67  | Case 1:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 159.34/25.67  | |           e0)
% 159.34/25.67  | | 
% 159.34/25.67  | | BETA: splitting (12) gives:
% 159.34/25.67  | | 
% 159.34/25.67  | | Case 1:
% 159.34/25.67  | | | 
% 159.34/25.67  | | |   (13)  all_56_0 = e0 & op(e3, e3) = e0
% 159.34/25.67  | | | 
% 159.34/25.67  | | | ALPHA: (13) implies:
% 159.34/25.67  | | |   (14)  op(e3, e3) = e0
% 159.34/25.67  | | | 
% 159.34/25.67  | | | REF_CLOSE: (4), (6), (7), (14) are inconsistent by sub-proof #834.
% 159.34/25.67  | | | 
% 159.34/25.67  | | Case 2:
% 159.34/25.67  | | | 
% 159.34/25.67  | | |   (15)  all_56_2 = e0 & op(e2, e3) = e0
% 159.34/25.67  | | | 
% 159.34/25.67  | | | REF_CLOSE: (5), (10), (15) are inconsistent by sub-proof #846.
% 159.34/25.67  | | | 
% 159.34/25.67  | | End of split
% 159.34/25.67  | | 
% 159.34/25.67  | Case 2:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 159.34/25.67  | |           e0)
% 159.34/25.67  | | 
% 159.34/25.67  | | BETA: splitting (16) gives:
% 159.34/25.67  | | 
% 159.34/25.67  | | Case 1:
% 159.34/25.67  | | | 
% 159.34/25.67  | | |   (17)  all_56_6 = e0 & op(e1, e3) = e0
% 159.34/25.67  | | | 
% 159.34/25.67  | | | ALPHA: (17) implies:
% 159.34/25.67  | | |   (18)  op(e1, e3) = e0
% 159.34/25.67  | | | 
% 159.34/25.67  | | | BETA: splitting (1) gives:
% 159.34/25.67  | | | 
% 159.34/25.67  | | | Case 1:
% 159.34/25.67  | | | | 
% 159.34/25.67  | | | |   (19)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3)
% 159.34/25.67  | | | |           = e3)
% 159.34/25.67  | | | | 
% 159.34/25.67  | | | | BETA: splitting (19) gives:
% 159.34/25.67  | | | | 
% 159.34/25.67  | | | | Case 1:
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | |   (20)  all_56_0 = e3 & op(e3, e3) = e3
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | | ALPHA: (20) implies:
% 159.34/25.67  | | | | |   (21)  op(e3, e3) = e3
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | | REF_CLOSE: (4), (6), (9), (21) are inconsistent by sub-proof #995.
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | Case 2:
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | |   (22)  all_56_2 = e3 & op(e2, e3) = e3
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | | ALPHA: (22) implies:
% 159.34/25.67  | | | | |   (23)  all_56_2 = e3
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | | REF_CLOSE: (3), (5), (23) are inconsistent by sub-proof #848.
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | End of split
% 159.34/25.67  | | | | 
% 159.34/25.67  | | | Case 2:
% 159.34/25.67  | | | | 
% 159.34/25.67  | | | |   (24)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3)
% 159.34/25.67  | | | |           = e3)
% 159.34/25.67  | | | | 
% 159.34/25.67  | | | | BETA: splitting (24) gives:
% 159.34/25.67  | | | | 
% 159.34/25.67  | | | | Case 1:
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | |   (25)  all_56_6 = e3 & op(e1, e3) = e3
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | | ALPHA: (25) implies:
% 159.34/25.67  | | | | |   (26)  op(e1, e3) = e3
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | | REF_CLOSE: (4), (11), (18), (26) are inconsistent by sub-proof #913.
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | Case 2:
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | |   (27)  all_56_12 = e3 & op(e0, e3) = e3
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | | ALPHA: (27) implies:
% 159.34/25.67  | | | | |   (28)  all_56_12 = e3
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | | REF_CLOSE: (2), (9), (28) are inconsistent by sub-proof #498.
% 159.34/25.67  | | | | | 
% 159.34/25.67  | | | | End of split
% 159.34/25.67  | | | | 
% 159.34/25.67  | | | End of split
% 159.34/25.67  | | | 
% 159.34/25.67  | | Case 2:
% 159.34/25.67  | | | 
% 159.34/25.67  | | |   (29)  all_56_12 = e0 & op(e0, e3) = e0
% 159.34/25.67  | | | 
% 159.34/25.67  | | | REF_CLOSE: (2), (7), (29) are inconsistent by sub-proof #497.
% 159.34/25.67  | | | 
% 159.34/25.67  | | End of split
% 159.34/25.67  | | 
% 159.34/25.67  | End of split
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #497 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)  all_56_12 = e0 & op(e0, e3) = e0
% 159.34/25.67    (2)  all_56_12 = e1
% 159.34/25.67    (3)   ~ (e1 = e0)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | ALPHA: (1) implies:
% 159.34/25.67  |   (4)  all_56_12 = e0
% 159.34/25.67  | 
% 159.34/25.67  | COMBINE_EQS: (2), (4) imply:
% 159.34/25.67  |   (5)  e1 = e0
% 159.34/25.67  | 
% 159.34/25.67  | REDUCE: (3), (5) imply:
% 159.34/25.67  |   (6)  $false
% 159.34/25.67  | 
% 159.34/25.67  | CLOSE: (6) is inconsistent.
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #498 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)  all_56_12 = e3
% 159.34/25.67    (2)  all_56_12 = e1
% 159.34/25.67    (3)   ~ (e3 = e1)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | COMBINE_EQS: (1), (2) imply:
% 159.34/25.67  |   (4)  e3 = e1
% 159.34/25.67  | 
% 159.34/25.67  | SIMP: (4) implies:
% 159.34/25.67  |   (5)  e3 = e1
% 159.34/25.67  | 
% 159.34/25.67  | REDUCE: (3), (5) imply:
% 159.34/25.67  |   (6)  $false
% 159.34/25.67  | 
% 159.34/25.67  | CLOSE: (6) is inconsistent.
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #499 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.67    (2)  op(e3, e3) = e1
% 159.34/25.67    (3)  op(e2, e2) = e1
% 159.34/25.67    (4)   ~ (e2 = e1)
% 159.34/25.67    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.34/25.67             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.34/25.67           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.34/25.67               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.34/25.67             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.34/25.67         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.34/25.67             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.34/25.67           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.34/25.67               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.34/25.67             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 159.34/25.67    (6)   ~ (e3 = e1)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | BETA: splitting (5) gives:
% 159.34/25.67  | 
% 159.34/25.67  | Case 1:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.34/25.67  | |            e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.34/25.67  | |            $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.34/25.67  | |            (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.34/25.67  | |        ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.34/25.67  | |              e3) = all_57_6 & $i(all_57_6)))
% 159.34/25.67  | | 
% 159.34/25.67  | | ALPHA: (7) implies:
% 159.34/25.67  | |   (8)  op(e3, e3) = e3
% 159.34/25.67  | | 
% 159.34/25.67  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #995.
% 159.34/25.67  | | 
% 159.34/25.67  | Case 2:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 159.34/25.67  | |            e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 159.34/25.67  | |            $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 159.34/25.67  | |            (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 159.34/25.67  | |        ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 159.34/25.67  | |              e2) = all_57_7 & $i(all_57_7)))
% 159.34/25.67  | | 
% 159.34/25.67  | | ALPHA: (9) implies:
% 159.34/25.67  | |   (10)  op(e2, e2) = e2
% 159.34/25.67  | | 
% 159.34/25.67  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #993.
% 159.34/25.67  | | 
% 159.34/25.67  | End of split
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #500 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)   ~ (all_52_6 = e1)
% 159.34/25.67    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.67    (3)  op(e1, e3) = all_52_2
% 159.34/25.67    (4)   ~ (all_52_2 = e1)
% 159.34/25.67    (5)  op(e1, e2) = all_52_6
% 159.34/25.67    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | BETA: splitting (6) gives:
% 159.34/25.67  | 
% 159.34/25.67  | Case 1:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (7)  all_56_6 = e1 & op(e1, e3) = e1
% 159.34/25.67  | | 
% 159.34/25.67  | | ALPHA: (7) implies:
% 159.34/25.67  | |   (8)  op(e1, e3) = e1
% 159.34/25.67  | | 
% 159.34/25.67  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #990.
% 159.34/25.67  | | 
% 159.34/25.67  | Case 2:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (9)  all_56_7 = e1 & op(e1, e2) = e1
% 159.34/25.67  | | 
% 159.34/25.67  | | ALPHA: (9) implies:
% 159.34/25.67  | |   (10)  op(e1, e2) = e1
% 159.34/25.67  | | 
% 159.34/25.67  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #984.
% 159.34/25.67  | | 
% 159.34/25.67  | End of split
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #501 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.67    (2)   ~ (all_52_6 = e0)
% 159.34/25.67    (3)  op(e1, e2) = all_52_6
% 159.34/25.67    (4)  op(e0, e2) = e3
% 159.34/25.67    (5)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 159.34/25.67    (6)   ~ (e3 = e0)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | BETA: splitting (5) gives:
% 159.34/25.67  | 
% 159.34/25.67  | Case 1:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (7)  all_56_7 = e0 & op(e1, e2) = e0
% 159.34/25.67  | | 
% 159.34/25.67  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #898.
% 159.34/25.67  | | 
% 159.34/25.67  | Case 2:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (8)  all_56_13 = e0 & op(e0, e2) = e0
% 159.34/25.67  | | 
% 159.34/25.67  | | ALPHA: (8) implies:
% 159.34/25.67  | |   (9)  op(e0, e2) = e0
% 159.34/25.67  | | 
% 159.34/25.67  | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #726.
% 159.34/25.67  | | 
% 159.34/25.67  | End of split
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #502 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)   ~ (all_52_7 = e0)
% 159.34/25.67    (2)  all_54_13 = all_52_7
% 159.34/25.67    (3)   ~ (all_52_7 = e2)
% 159.34/25.67    (4)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.34/25.67    (5)   ~ (all_52_7 = e1)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | BETA: splitting (4) gives:
% 159.34/25.67  | 
% 159.34/25.67  | Case 1:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (6)  all_54_13 = e2
% 159.34/25.67  | | 
% 159.34/25.67  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #505.
% 159.34/25.67  | | 
% 159.34/25.67  | Case 2:
% 159.34/25.67  | | 
% 159.34/25.67  | |   (7)  all_54_13 = e1 | all_54_13 = e0
% 159.34/25.67  | | 
% 159.34/25.67  | | BETA: splitting (7) gives:
% 159.34/25.67  | | 
% 159.34/25.67  | | Case 1:
% 159.34/25.67  | | | 
% 159.34/25.67  | | |   (8)  all_54_13 = e1
% 159.34/25.67  | | | 
% 159.34/25.67  | | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #504.
% 159.34/25.67  | | | 
% 159.34/25.67  | | Case 2:
% 159.34/25.67  | | | 
% 159.34/25.67  | | |   (9)  all_54_13 = e0
% 159.34/25.67  | | | 
% 159.34/25.67  | | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #503.
% 159.34/25.67  | | | 
% 159.34/25.67  | | End of split
% 159.34/25.67  | | 
% 159.34/25.67  | End of split
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #503 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)  all_54_13 = all_52_7
% 159.34/25.67    (2)  all_54_13 = e0
% 159.34/25.67    (3)   ~ (all_52_7 = e0)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | COMBINE_EQS: (1), (2) imply:
% 159.34/25.67  |   (4)  all_52_7 = e0
% 159.34/25.67  | 
% 159.34/25.67  | SIMP: (4) implies:
% 159.34/25.67  |   (5)  all_52_7 = e0
% 159.34/25.67  | 
% 159.34/25.67  | REDUCE: (3), (5) imply:
% 159.34/25.67  |   (6)  $false
% 159.34/25.67  | 
% 159.34/25.67  | CLOSE: (6) is inconsistent.
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #504 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)  all_54_13 = all_52_7
% 159.34/25.67    (2)  all_54_13 = e1
% 159.34/25.67    (3)   ~ (all_52_7 = e1)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | COMBINE_EQS: (1), (2) imply:
% 159.34/25.67  |   (4)  all_52_7 = e1
% 159.34/25.67  | 
% 159.34/25.67  | SIMP: (4) implies:
% 159.34/25.67  |   (5)  all_52_7 = e1
% 159.34/25.67  | 
% 159.34/25.67  | REDUCE: (3), (5) imply:
% 159.34/25.67  |   (6)  $false
% 159.34/25.67  | 
% 159.34/25.67  | CLOSE: (6) is inconsistent.
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #505 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)  all_54_13 = all_52_7
% 159.34/25.67    (2)  all_54_13 = e2
% 159.34/25.67    (3)   ~ (all_52_7 = e2)
% 159.34/25.67  
% 159.34/25.67  Begin of proof
% 159.34/25.67  | 
% 159.34/25.67  | COMBINE_EQS: (1), (2) imply:
% 159.34/25.67  |   (4)  all_52_7 = e2
% 159.34/25.67  | 
% 159.34/25.67  | SIMP: (4) implies:
% 159.34/25.67  |   (5)  all_52_7 = e2
% 159.34/25.67  | 
% 159.34/25.67  | REDUCE: (3), (5) imply:
% 159.34/25.67  |   (6)  $false
% 159.34/25.67  | 
% 159.34/25.67  | CLOSE: (6) is inconsistent.
% 159.34/25.67  | 
% 159.34/25.67  End of proof
% 159.34/25.67  
% 159.34/25.67  Sub-proof #506 shows that the following formulas are inconsistent:
% 159.34/25.67  ----------------------------------------------------------------
% 159.34/25.67    (1)   ~ (all_52_13 = e1)
% 159.34/25.67    (2)  all_54_2 = all_52_8
% 159.34/25.67    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.34/25.67         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.34/25.67    (4)   ~ (all_52_1 = all_52_3)
% 159.34/25.67    (5)  all_54_5 = all_4_2
% 159.34/25.67    (6)   ~ (all_52_3 = all_14_2)
% 159.34/25.67    (7)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.34/25.67         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.34/25.67    (8)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.34/25.67         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.34/25.67    (9)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 159.34/25.67         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 159.34/25.67    (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.34/25.67          (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.34/25.67    (11)   ~ (all_52_9 = all_52_11)
% 159.34/25.67    (12)   ~ (all_52_4 = e3)
% 159.34/25.67    (13)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.34/25.67    (14)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.34/25.67          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 159.34/25.67    (15)  all_54_12 = all_52_3
% 159.34/25.67    (16)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.34/25.67    (17)  op(e1, e1) = e3
% 159.34/25.67    (18)   ~ (all_50_2 = e2) | ( ~ (all_50_0 = e3) & op(e2, e0) = all_50_0 &
% 159.34/25.67            $i(all_50_0)) | ( ~ (all_50_1 = e1) & op(e2, e2) = all_50_1 &
% 159.34/25.67            $i(all_50_1))
% 159.34/25.68    (19)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 159.34/25.68              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.34/25.68            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.34/25.68                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 159.34/25.68              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.34/25.68          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 159.34/25.68              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.34/25.68            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.34/25.68                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 159.34/25.68              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.34/25.68          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 159.34/25.68              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.34/25.68            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.34/25.68                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 159.34/25.68              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.34/25.68          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 159.34/25.68              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.34/25.68            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 159.34/25.68                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 159.34/25.68                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.34/25.68                $i(all_57_13))))
% 159.34/25.68    (20)   ~ (all_52_13 = all_14_2)
% 159.34/25.68    (21)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.34/25.68          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.34/25.68    (22)  op(e0, e1) = all_52_11
% 159.34/25.68    (23)   ~ (e3 = e2)
% 159.34/25.68    (24)  all_50_2 = all_14_2
% 159.34/25.68    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.34/25.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.34/25.68    (26)  op(e0, e3) = all_52_3
% 159.34/25.68    (27)  op(e3, e1) = all_52_8
% 159.34/25.68    (28)   ~ (all_52_9 = all_4_2)
% 159.34/25.68    (29)   ~ (all_4_2 = e3)
% 159.34/25.68    (30)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.34/25.68    (31)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.34/25.68    (32)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.34/25.68              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 159.34/25.68                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.34/25.68                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.34/25.68    (33)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.34/25.68          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.34/25.68    (34)   ~ (all_52_11 = all_14_2)
% 159.34/25.68    (35)   ~ (all_52_12 = all_14_2)
% 159.34/25.68    (36)   ~ (all_52_12 = all_52_14)
% 159.34/25.68    (37)  op(e1, e3) = all_52_2
% 159.34/25.68    (38)  all_54_15 = all_14_2
% 159.34/25.68    (39)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.34/25.68          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.34/25.68    (40)   ~ (all_52_8 = e0)
% 159.34/25.68    (41)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.34/25.68          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.34/25.68    (42)   ~ (all_52_8 = all_52_12)
% 159.34/25.68    (43)   ~ (all_52_13 = all_4_2)
% 159.34/25.68    (44)   ~ (all_52_14 = all_14_2)
% 159.34/25.68    (45)  all_54_3 = all_52_12
% 159.34/25.68    (46)   ~ (all_32_2 = e0) | ( ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 &
% 159.34/25.68            $i(all_32_0)) | ( ~ (all_32_1 = e1) & op(e0, e0) = all_32_1 &
% 159.34/25.68            $i(all_32_1))
% 159.34/25.68    (47)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 159.34/25.68    (48)   ~ (all_52_9 = all_52_13)
% 159.34/25.68    (49)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 159.34/25.68    (50)  all_56_10 = e3
% 159.34/25.68    (51)   ~ (all_52_12 = all_52_13)
% 159.34/25.68    (52)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.34/25.68    (53)  op(e1, e0) = all_52_14
% 159.34/25.68    (54)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.34/25.68          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.34/25.68    (55)   ~ (all_52_13 = all_52_14)
% 159.34/25.68    (56)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 159.34/25.68          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.34/25.68    (57)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 159.34/25.68          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 159.34/25.68    (58)  op(e2, e2) = all_4_2
% 159.34/25.68    (59)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.34/25.68    (60)   ~ (all_52_14 = e2)
% 159.34/25.68    (61)   ~ (all_52_1 = all_52_2)
% 159.34/25.68    (62)   ~ (all_52_8 = all_52_11)
% 159.34/25.68    (63)  op(e3, e3) = e3
% 159.34/25.68    (64)  op(e2, e0) = e3
% 159.34/25.68    (65)  all_32_2 = all_4_2
% 159.34/25.68    (66)  op(e0, e0) = all_14_2
% 159.34/25.68    (67)  op(e2, e3) = all_52_1
% 159.34/25.68    (68)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 159.34/25.68          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.34/25.68    (69)   ~ (all_14_2 = e1)
% 159.34/25.68    (70)  op(e3, e2) = all_52_4
% 159.34/25.68    (71)  op(e2, e2) = e1
% 159.34/25.68    (72)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.34/25.68          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.34/25.68    (73)   ~ (all_52_1 = all_52_9)
% 159.34/25.68    (74)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.34/25.68          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.34/25.68    (75)   ~ (e1 = e0)
% 159.34/25.68    (76)  op(e2, e1) = all_52_9
% 159.34/25.68    (77)  all_54_4 = all_52_1
% 159.34/25.68    (78)   ~ (all_52_3 = e3)
% 159.34/25.68    (79)  all_54_14 = all_52_11
% 159.34/25.68    (80)   ~ (all_52_8 = all_52_9)
% 159.34/25.68    (81)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.34/25.68          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.34/25.68    (82)  op(e2, e0) = all_52_13
% 159.34/25.68    (83)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 159.34/25.68          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 159.34/25.68    (84)  op(e0, e2) = e3
% 159.34/25.68    (85)   ~ (e2 = e1)
% 159.34/25.68    (86)  op(e3, e0) = all_52_12
% 159.34/25.68    (87)  all_56_13 = e3
% 159.34/25.68    (88)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.34/25.68          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.34/25.68    (89)   ~ (all_52_3 = all_52_11)
% 159.34/25.68    (90)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.34/25.68          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.34/25.68    (91)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.34/25.68    (92)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.34/25.68            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.34/25.68            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.34/25.68            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.34/25.68              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.34/25.68          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.34/25.68            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.34/25.68              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.34/25.68            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.34/25.68              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.34/25.68          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.34/25.68            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 159.34/25.68              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.34/25.68            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.34/25.68              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.34/25.68          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.34/25.68            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 159.34/25.68            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.34/25.68              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.34/25.68            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 159.34/25.68            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.34/25.68            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.34/25.68            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 159.34/25.68              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.34/25.68            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 159.34/25.68          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.34/25.68            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.34/25.68              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.34/25.68            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 159.34/25.68            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.34/25.68          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.34/25.68            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.34/25.68              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 159.34/25.68            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 159.34/25.68            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.34/25.68          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.34/25.68            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.34/25.68              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.34/25.68            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.34/25.68              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.34/25.68          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.34/25.68            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.34/25.68            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 159.34/25.68            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.34/25.68            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 159.34/25.68            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.34/25.68            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.34/25.68            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 159.34/25.68              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.34/25.68            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 159.34/25.68            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.34/25.68            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.34/25.68            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 159.34/25.68              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.34/25.68            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 159.34/25.68          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 159.34/25.68            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 159.34/25.68              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 159.34/25.68              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 159.34/25.68            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 159.34/25.68            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.34/25.68            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.34/25.68            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 159.34/25.68              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 159.34/25.68            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 159.34/25.68          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.34/25.68            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.34/25.68              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.34/25.68            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.34/25.68              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.34/25.68          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.34/25.68            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.34/25.68              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 159.34/25.68              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 159.34/25.68            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.34/25.68          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.34/25.68            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.34/25.68            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 159.34/25.68                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 159.34/25.68                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.34/25.68                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.34/25.68                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.34/25.68                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.34/25.68                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 159.34/25.68                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.34/25.68                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.34/25.68                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.34/25.68                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 159.34/25.68                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.34/25.68                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.34/25.68                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 159.34/25.68                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.34/25.68                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.34/25.68                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.34/25.68                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 159.34/25.68                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.34/25.68                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 159.34/25.68                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.34/25.68                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.34/25.68                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.34/25.68                op(e0, e1) = e0)))
% 159.34/25.68    (93)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.34/25.68          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.34/25.68            e1)
% 159.34/25.68    (94)  all_54_11 = all_52_14
% 159.34/25.68    (95)   ~ (all_52_1 = all_4_2)
% 159.34/25.68    (96)  all_54_6 = all_52_9
% 159.34/25.68    (97)   ~ (e2 = e0)
% 159.34/25.68    (98)   ~ (all_52_11 = e3)
% 159.34/25.68    (99)   ~ (all_52_1 = all_52_13)
% 159.34/25.68    (100)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 159.34/25.68           (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 159.34/25.68    (101)   ~ (all_52_8 = e3)
% 159.34/25.68    (102)   ~ (e3 = e0)
% 159.34/25.69  
% 159.34/25.69  Begin of proof
% 159.34/25.69  | 
% 159.34/25.69  | GROUND_INST: instantiating (25) with all_52_13, e3, e0, e2, simplifying with
% 159.34/25.69  |              (64), (82) gives:
% 159.34/25.69  |   (103)  all_52_13 = e3
% 159.34/25.69  | 
% 159.34/25.69  | REDUCE: (99), (103) imply:
% 159.34/25.69  |   (104)   ~ (all_52_1 = e3)
% 159.34/25.69  | 
% 159.34/25.69  | REDUCE: (48), (103) imply:
% 159.34/25.69  |   (105)   ~ (all_52_9 = e3)
% 159.34/25.69  | 
% 159.34/25.69  | REDUCE: (51), (103) imply:
% 159.34/25.69  |   (106)   ~ (all_52_12 = e3)
% 159.34/25.69  | 
% 159.34/25.69  | REDUCE: (55), (103) imply:
% 159.34/25.69  |   (107)   ~ (all_52_14 = e3)
% 159.34/25.69  | 
% 159.34/25.69  | SIMP: (107) implies:
% 159.34/25.69  |   (108)   ~ (all_52_14 = e3)
% 159.34/25.69  | 
% 159.34/25.69  | REDUCE: (20), (103) imply:
% 159.34/25.69  |   (109)   ~ (all_14_2 = e3)
% 159.34/25.69  | 
% 159.34/25.69  | SIMP: (109) implies:
% 159.34/25.69  |   (110)   ~ (all_14_2 = e3)
% 159.34/25.69  | 
% 159.34/25.69  | REDUCE: (1), (103) imply:
% 159.34/25.69  |   (111)   ~ (e3 = e1)
% 159.34/25.69  | 
% 159.34/25.69  | BETA: splitting (18) gives:
% 159.34/25.69  | 
% 159.34/25.69  | Case 1:
% 159.34/25.69  | | 
% 159.34/25.69  | |   (112)   ~ (all_50_2 = e2)
% 159.34/25.69  | | 
% 159.34/25.69  | | REDUCE: (24), (112) imply:
% 159.34/25.69  | |   (113)   ~ (all_14_2 = e2)
% 159.34/25.69  | | 
% 159.34/25.69  | | BETA: splitting (30) gives:
% 159.34/25.69  | | 
% 159.34/25.69  | | Case 1:
% 159.34/25.69  | | | 
% 159.34/25.69  | | |   (114)  all_54_15 = e3
% 159.34/25.69  | | | 
% 159.34/25.69  | | | REF_CLOSE: (38), (110), (114) are inconsistent by sub-proof #1010.
% 159.34/25.69  | | | 
% 159.34/25.69  | | Case 2:
% 159.34/25.69  | | | 
% 159.34/25.69  | | |   (115)   ~ (all_54_15 = e3)
% 159.34/25.69  | | |   (116)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.34/25.69  | | | 
% 159.34/25.69  | | | BETA: splitting (116) gives:
% 159.34/25.69  | | | 
% 159.34/25.69  | | | Case 1:
% 159.34/25.69  | | | | 
% 159.34/25.69  | | | |   (117)  all_54_15 = e2
% 159.34/25.69  | | | | 
% 159.34/25.69  | | | | REF_CLOSE: (38), (113), (117) are inconsistent by sub-proof #1009.
% 159.34/25.69  | | | | 
% 159.34/25.69  | | | Case 2:
% 159.34/25.69  | | | | 
% 159.34/25.69  | | | |   (118)   ~ (all_54_15 = e2)
% 159.34/25.69  | | | |   (119)  all_54_15 = e1 | all_54_15 = e0
% 159.34/25.69  | | | | 
% 159.34/25.69  | | | | BETA: splitting (119) gives:
% 159.34/25.69  | | | | 
% 159.34/25.69  | | | | Case 1:
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | |   (120)  all_54_15 = e1
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | REF_CLOSE: (38), (69), (120) are inconsistent by sub-proof #1008.
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | Case 2:
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | |   (121)  all_54_15 = e0
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | COMBINE_EQS: (38), (121) imply:
% 159.34/25.69  | | | | |   (122)  all_14_2 = e0
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | SIMP: (122) implies:
% 159.34/25.69  | | | | |   (123)  all_14_2 = e0
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | REDUCE: (6), (123) imply:
% 159.34/25.69  | | | | |   (124)   ~ (all_52_3 = e0)
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | REDUCE: (34), (123) imply:
% 159.34/25.69  | | | | |   (125)   ~ (all_52_11 = e0)
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | REDUCE: (35), (123) imply:
% 159.34/25.69  | | | | |   (126)   ~ (all_52_12 = e0)
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | REDUCE: (44), (123) imply:
% 159.34/25.69  | | | | |   (127)   ~ (all_52_14 = e0)
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | REDUCE: (110), (123) imply:
% 159.34/25.69  | | | | |   (128)   ~ (e3 = e0)
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | REDUCE: (113), (123) imply:
% 159.34/25.69  | | | | |   (129)   ~ (e2 = e0)
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | REDUCE: (66), (123) imply:
% 159.34/25.69  | | | | |   (130)  op(e0, e0) = e0
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | BETA: splitting (52) gives:
% 159.34/25.69  | | | | | 
% 159.34/25.69  | | | | | Case 1:
% 159.34/25.69  | | | | | | 
% 159.34/25.69  | | | | | |   (131)  all_54_11 = e3
% 159.34/25.69  | | | | | | 
% 159.34/25.69  | | | | | | REF_CLOSE: (94), (108), (131) are inconsistent by sub-proof #655.
% 159.34/25.69  | | | | | | 
% 159.34/25.69  | | | | | Case 2:
% 159.34/25.69  | | | | | | 
% 159.34/25.69  | | | | | |   (132)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.34/25.69  | | | | | | 
% 159.34/25.69  | | | | | | BETA: splitting (132) gives:
% 159.34/25.69  | | | | | | 
% 159.34/25.69  | | | | | | Case 1:
% 159.34/25.69  | | | | | | | 
% 159.34/25.69  | | | | | | |   (133)  all_54_11 = e2
% 159.34/25.69  | | | | | | | 
% 159.34/25.69  | | | | | | | REF_CLOSE: (60), (94), (133) are inconsistent by sub-proof #588.
% 159.34/25.69  | | | | | | | 
% 159.34/25.69  | | | | | | Case 2:
% 159.34/25.69  | | | | | | | 
% 159.34/25.69  | | | | | | |   (134)  all_54_11 = e1 | all_54_11 = e0
% 159.34/25.69  | | | | | | | 
% 159.34/25.69  | | | | | | | BETA: splitting (92) gives:
% 159.34/25.69  | | | | | | | 
% 159.34/25.69  | | | | | | | Case 1:
% 159.34/25.69  | | | | | | | | 
% 159.34/25.69  | | | | | | | |   (135)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.34/25.69  | | | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3
% 159.34/25.69  | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.34/25.69  | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.34/25.69  | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.34/25.69  | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.34/25.69  | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.34/25.69  | | | | | | | |            all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 159.34/25.69  | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1,
% 159.34/25.69  | | | | | | | |              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.34/25.69  | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 159.34/25.69  | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.34/25.69  | | | | | | | |              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.34/25.69  | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 159.34/25.69  | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 159.34/25.69  | | | | | | | |            e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 159.34/25.69  | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.34/25.69  | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 159.34/25.69  | | | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 159.34/25.69  | | | | | | | |              e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.34/25.69  | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2,
% 159.34/25.69  | | | | | | | |              e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 &
% 159.34/25.69  | | | | | | | |            all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 159.34/25.69  | | | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.34/25.69  | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.34/25.69  | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 159.34/25.69  | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3
% 159.34/25.69  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.34/25.69  | | | | | | | |            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 &
% 159.34/25.69  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.34/25.69  | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 159.34/25.69  | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.34/25.69  | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 159.34/25.69  | | | | | | | |            op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 159.34/25.69  | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) =
% 159.34/25.69  | | | | | | | |            e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.34/25.69  | | | | | | | |            op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 159.34/25.69  | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 159.34/25.69  | | | | | | | |            & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1
% 159.34/25.69  | | | | | | | |            & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2
% 159.34/25.69  | | | | | | | |            = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10
% 159.34/25.69  | | | | | | | |              = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 159.34/25.69  | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.34/25.69  | | | | | | | |          (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.34/25.69  | | | | | | | |            (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2
% 159.34/25.69  | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.34/25.69  | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 159.34/25.69  | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 159.34/25.69  | | | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.34/25.69  | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.34/25.69  | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 159.34/25.69  | | | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1,
% 159.34/25.69  | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.34/25.69  | | | | | | | |          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1,
% 159.34/25.69  | | | | | | | |              e3) = e1 & op(e1, e1) = e1)
% 159.34/25.69  | | | | | | | | 
% 159.34/25.69  | | | | | | | | BETA: splitting (135) gives:
% 159.34/25.69  | | | | | | | | 
% 159.34/25.69  | | | | | | | | Case 1:
% 159.34/25.69  | | | | | | | | | 
% 159.34/25.69  | | | | | | | | |   (136)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.34/25.69  | | | | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) =
% 159.34/25.69  | | | | | | | | |            e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.34/25.69  | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.34/25.69  | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.34/25.69  | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.34/25.69  | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.34/25.69  | | | | | | | | |            all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.34/25.69  | | | | | | | | |              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.34/25.69  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 159.34/25.69  | | | | | | | | |          | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 159.34/25.69  | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.34/25.69  | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3
% 159.34/25.69  | | | | | | | | |            & $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 159.34/25.69  | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 159.34/25.69  | | | | | | | | |            e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 159.34/25.69  | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.34/25.69  | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.34/25.69  | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.34/25.69  | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.34/25.69  | | | | | | | | |          | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.34/25.69  | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3
% 159.34/25.69  | | | | | | | | |            & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.34/25.69  | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.34/25.69  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.34/25.69  | | | | | | | | |          | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 159.34/25.69  | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) =
% 159.34/25.69  | | | | | | | | |            e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.34/25.69  | | | | | | | | |            $i(all_57_12))
% 159.34/25.69  | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | BETA: splitting (136) gives:
% 159.34/25.69  | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | Case 1:
% 159.34/25.69  | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | |   (137)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 159.34/25.69  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 159.34/25.69  | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.34/25.69  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.34/25.69  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 159.34/25.69  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.34/25.69  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 159.34/25.69  | | | | | | | | | |            & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12
% 159.34/25.69  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.34/25.69  | | | | | | | | | |            all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.34/25.69  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.34/25.69  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.34/25.69  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 &
% 159.34/25.69  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10))
% 159.34/25.69  | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | BETA: splitting (137) gives:
% 159.34/25.69  | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | Case 1:
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | |   (138)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 159.34/25.69  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 159.34/25.69  | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.34/25.69  | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.34/25.69  | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.34/25.69  | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 159.34/25.69  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.34/25.69  | | | | | | | | | | |            $i(all_57_10))
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | REF_CLOSE: (23), (25), (63), (71), (111), (138) are
% 159.34/25.69  | | | | | | | | | | |            inconsistent by sub-proof #801.
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | Case 2:
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | |   (139)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 159.34/25.69  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 159.34/25.69  | | | | | | | | | | |              e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 159.34/25.69  | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.34/25.69  | | | | | | | | | | |            all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.34/25.69  | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 159.34/25.69  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.34/25.69  | | | | | | | | | | |            $i(all_57_10))
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | BETA: splitting (139) gives:
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | Case 1:
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | |   (140)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 159.34/25.69  | | | | | | | | | | | |          ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 159.34/25.69  | | | | | | | | | | | |          = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.34/25.69  | | | | | | | | | | | |          $i(all_57_12)
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | ALPHA: (140) implies:
% 159.34/25.69  | | | | | | | | | | | |   (141)  op(e1, e1) = e2
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | REF_CLOSE: (17), (23), (25), (141) are inconsistent by
% 159.34/25.69  | | | | | | | | | | | |            sub-proof #646.
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | Case 2:
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | |   (142)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 159.34/25.69  | | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.34/25.69  | | | | | | | | | | | |          op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.34/25.69  | | | | | | | | | | | |          e3 & $i(all_57_10)
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | ALPHA: (142) implies:
% 159.34/25.69  | | | | | | | | | | | |   (143)  op(e2, e2) = e3
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | REF_CLOSE: (25), (71), (111), (143) are inconsistent by
% 159.34/25.69  | | | | | | | | | | | |            sub-proof #847.
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | End of split
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | End of split
% 159.34/25.69  | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | Case 2:
% 159.34/25.69  | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | |   (144)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.34/25.69  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 159.34/25.69  | | | | | | | | | |            = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.34/25.69  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.34/25.69  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 159.34/25.69  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 159.34/25.69  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 159.34/25.69  | | | | | | | | | |            & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 159.34/25.69  | | | | | | | | | |            & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 159.34/25.69  | | | | | | | | | |            e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.34/25.69  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.34/25.69  | | | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.34/25.69  | | | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 159.34/25.69  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 159.34/25.69  | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.34/25.69  | | | | | | | | | |            $i(all_57_12))
% 159.34/25.69  | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | BETA: splitting (144) gives:
% 159.34/25.69  | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | Case 1:
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | |   (145)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.34/25.69  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 159.34/25.69  | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.34/25.69  | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.34/25.69  | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.34/25.69  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.34/25.69  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.34/25.69  | | | | | | | | | | |            $i(all_57_10))
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | REF_CLOSE: (25), (86), (97), (106), (130), (145) are
% 159.34/25.69  | | | | | | | | | | |            inconsistent by sub-proof #932.
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | Case 2:
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | |   (146)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.34/25.69  | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 159.34/25.69  | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 159.34/25.69  | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.34/25.69  | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.34/25.69  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 159.34/25.69  | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.34/25.69  | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.34/25.69  | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | BETA: splitting (146) gives:
% 159.34/25.69  | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | Case 1:
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | |   (147)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.34/25.69  | | | | | | | | | | | |          op(e2, e3) = e2 & op(e2, e2) = e2
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | ALPHA: (147) implies:
% 159.34/25.69  | | | | | | | | | | | |   (148)  op(e2, e2) = e2
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | REF_CLOSE: (25), (71), (85), (148) are inconsistent by
% 159.34/25.69  | | | | | | | | | | | |            sub-proof #993.
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | Case 2:
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | |   (149)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 159.34/25.69  | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.34/25.69  | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.34/25.69  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 159.34/25.69  | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.34/25.69  | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.34/25.69  | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | BETA: splitting (149) gives:
% 159.34/25.69  | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | Case 1:
% 159.34/25.69  | | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | |   (150)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 159.34/25.69  | | | | | | | | | | | | |          ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.34/25.69  | | | | | | | | | | | | |          op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.34/25.69  | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 159.34/25.69  | | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | | ALPHA: (150) implies:
% 159.34/25.69  | | | | | | | | | | | | |   (151)  op(e3, e2) = e3
% 159.34/25.69  | | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | | REF_CLOSE: (12), (25), (70), (151) are inconsistent by
% 159.34/25.69  | | | | | | | | | | | | |            sub-proof #998.
% 159.34/25.69  | | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | Case 2:
% 159.34/25.69  | | | | | | | | | | | | | 
% 159.34/25.69  | | | | | | | | | | | | |   (152)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 159.34/25.69  | | | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 159.34/25.69  | | | | | | | | | | | | |          = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.34/25.69  | | | | | | | | | | | | |          $i(all_57_12)
% 159.34/25.70  | | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | | | ALPHA: (152) implies:
% 159.34/25.70  | | | | | | | | | | | | |   (153)  op(e2, e1) = e2
% 159.34/25.70  | | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | | | REF_CLOSE: (2), (11), (13), (25), (31), (36), (40), (42),
% 159.34/25.70  | | | | | | | | | | | | |            (45), (62), (76), (79), (91), (94), (98), (101),
% 159.34/25.70  | | | | | | | | | | | | |            (106), (125), (126), (127), (134), (153) are
% 159.34/25.70  | | | | | | | | | | | | |            inconsistent by sub-proof #581.
% 159.34/25.70  | | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | | End of split
% 159.34/25.70  | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | End of split
% 159.34/25.70  | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | End of split
% 159.34/25.70  | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | End of split
% 159.34/25.70  | | | | | | | | | 
% 159.34/25.70  | | | | | | | | Case 2:
% 159.34/25.70  | | | | | | | | | 
% 159.34/25.70  | | | | | | | | |   (154)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.34/25.70  | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.34/25.70  | | | | | | | | |              e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.34/25.70  | | | | | | | | |            $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 & 
% 159.34/25.70  | | | | | | | | |            ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 159.34/25.70  | | | | | | | | |          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 159.34/25.70  | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 159.34/25.70  | | | | | | | | |            e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.34/25.70  | | | | | | | | |            $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.34/25.70  | | | | | | | | |            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) =
% 159.34/25.70  | | | | | | | | |            e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.34/25.70  | | | | | | | | |            = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.34/25.70  | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.34/25.70  | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 159.34/25.70  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.34/25.70  | | | | | | | | |          | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 159.34/25.70  | | | | | | | | |            ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 159.34/25.70  | | | | | | | | |            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.34/25.70  | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 159.34/25.70  | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 159.34/25.70  | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.34/25.70  | | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.34/25.70  | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.34/25.70  | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.34/25.70  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.34/25.70  | | | | | | | | |          | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 159.34/25.70  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.34/25.70  | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | BETA: splitting (154) gives:
% 159.34/25.70  | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | Case 1:
% 159.34/25.70  | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | |   (155)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.34/25.70  | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.34/25.70  | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.34/25.70  | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.34/25.70  | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.34/25.70  | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 159.34/25.70  | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3)
% 159.34/25.70  | | | | | | | | | |            = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.34/25.70  | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1
% 159.34/25.70  | | | | | | | | | |            & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14
% 159.34/25.70  | | | | | | | | | |              = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.34/25.70  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.34/25.70  | | | | | | | | | |            $i(all_57_14))
% 159.34/25.70  | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | BETA: splitting (155) gives:
% 159.34/25.70  | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | Case 1:
% 159.34/25.70  | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | |   (156)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.34/25.70  | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.34/25.70  | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.34/25.70  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.34/25.70  | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.34/25.70  | | | | | | | | | | |              e2) = e3)
% 159.34/25.70  | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | REF_CLOSE: (12), (25), (70), (102), (130), (156) are
% 159.34/25.70  | | | | | | | | | | |            inconsistent by sub-proof #997.
% 159.34/25.70  | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | Case 2:
% 159.34/25.70  | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | |   (157)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 159.34/25.70  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 159.34/25.70  | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.34/25.70  | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 159.34/25.70  | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 159.34/25.70  | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.34/25.70  | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.34/25.70  | | | | | | | | | | |            $i(all_57_14))
% 159.34/25.70  | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | REF_CLOSE: (23), (25), (63), (64), (111), (157) are
% 159.34/25.70  | | | | | | | | | | |            inconsistent by sub-proof #579.
% 159.34/25.70  | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | End of split
% 159.34/25.70  | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | Case 2:
% 159.34/25.70  | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | |   (158)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.34/25.70  | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.34/25.70  | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.34/25.70  | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 =
% 159.34/25.70  | | | | | | | | | |            e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 159.34/25.70  | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 159.34/25.70  | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.34/25.70  | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.34/25.70  | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 159.34/25.70  | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.34/25.70  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.34/25.70  | | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 159.34/25.70  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 159.34/25.70  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 159.34/25.70  | | | | | | | | | |            & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1
% 159.34/25.70  | | | | | | | | | |            & op(e1, e1) = e1)
% 159.34/25.70  | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | BETA: splitting (158) gives:
% 159.34/25.70  | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | Case 1:
% 159.34/25.70  | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | |   (159)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.34/25.70  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.34/25.70  | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.34/25.70  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 159.34/25.70  | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 159.34/25.70  | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 159.34/25.70  | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.34/25.70  | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | BETA: splitting (159) gives:
% 159.34/25.70  | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | Case 1:
% 159.34/25.70  | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | |   (160)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.34/25.70  | | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.34/25.70  | | | | | | | | | | | |          op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.34/25.70  | | | | | | | | | | | |          e3 & $i(all_57_10)
% 159.34/25.70  | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | | ALPHA: (160) implies:
% 159.34/25.70  | | | | | | | | | | | |   (161)  op(e3, e1) = e3
% 159.34/25.70  | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | | REF_CLOSE: (25), (27), (101), (161) are inconsistent by
% 159.34/25.70  | | | | | | | | | | | |            sub-proof #982.
% 159.34/25.70  | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | Case 2:
% 159.34/25.70  | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | |   (162)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 159.34/25.70  | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 159.34/25.70  | | | | | | | | | | | |          = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.34/25.70  | | | | | | | | | | | |          $i(all_57_14)
% 159.34/25.70  | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | | ALPHA: (162) implies:
% 159.34/25.70  | | | | | | | | | | | |   (163)  op(e2, e1) = e2
% 159.34/25.70  | | | | | | | | | | | | 
% 159.34/25.70  | | | | | | | | | | | | REF_CLOSE: (2), (11), (13), (25), (31), (36), (40), (42),
% 159.34/25.70  | | | | | | | | | | | |            (45), (62), (76), (79), (91), (94), (98), (101),
% 159.34/25.70  | | | | | | | | | | | |            (106), (125), (126), (127), (134), (163) are
% 159.39/25.70  | | | | | | | | | | | |            inconsistent by sub-proof #581.
% 159.39/25.70  | | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | | End of split
% 159.39/25.70  | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | Case 2:
% 159.39/25.70  | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | |   (164)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.39/25.70  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 159.39/25.70  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.39/25.70  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.39/25.70  | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.39/25.70  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.39/25.70  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.39/25.70  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.39/25.70  | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 159.39/25.70  | | | | | | | | | | |            e1)
% 159.39/25.70  | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | | BETA: splitting (164) gives:
% 159.39/25.70  | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | | Case 1:
% 159.39/25.70  | | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | | |   (165)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.39/25.70  | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 159.39/25.70  | | | | | | | | | | | |          = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.39/25.70  | | | | | | | | | | | |          $i(all_57_14)
% 159.39/25.70  | | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | | | ALPHA: (165) implies:
% 159.39/25.70  | | | | | | | | | | | |   (166)  op(e0, e0) = e1
% 159.39/25.70  | | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | | | REF_CLOSE: (25), (38), (66), (69), (119), (166) are
% 159.39/25.70  | | | | | | | | | | | |            inconsistent by sub-proof #790.
% 159.39/25.70  | | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | | Case 2:
% 159.39/25.70  | | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | | |   (167)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 & 
% 159.39/25.70  | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 159.39/25.70  | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.39/25.70  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 159.39/25.70  | | | | | | | | | | | |            = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1,
% 159.39/25.70  | | | | | | | | | | | |              e1) = e1)
% 159.39/25.70  | | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | | | REF_CLOSE: (17), (25), (86), (106), (167) are inconsistent by
% 159.39/25.70  | | | | | | | | | | | |            sub-proof #578.
% 159.39/25.70  | | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | | End of split
% 159.39/25.70  | | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | | End of split
% 159.39/25.70  | | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | End of split
% 159.39/25.70  | | | | | | | | | 
% 159.39/25.70  | | | | | | | | End of split
% 159.39/25.70  | | | | | | | | 
% 159.39/25.70  | | | | | | | Case 2:
% 159.39/25.70  | | | | | | | | 
% 159.39/25.70  | | | | | | | |   (168)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.39/25.70  | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3
% 159.39/25.70  | | | | | | | |            & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.70  | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.39/25.70  | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 159.39/25.70  | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.70  | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.39/25.70  | | | | | | | |            all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.39/25.70  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 159.39/25.70  | | | | | | | |              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.39/25.70  | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.39/25.70  | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.70  | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.39/25.70  | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 159.39/25.70  | | | | | | | |            all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 159.39/25.70  | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 159.39/25.70  | | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.39/25.70  | | | | | | | |            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 159.39/25.70  | | | | | | | |            op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.39/25.70  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.39/25.70  | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.39/25.70  | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 159.39/25.70  | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 159.39/25.70  | | | | | | | |            op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 159.39/25.70  | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 159.39/25.70  | | | | | | | |            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 159.39/25.70  | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 &
% 159.39/25.70  | | | | | | | |            all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 159.39/25.70  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 159.39/25.70  | | | | | | | |              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.39/25.70  | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2,
% 159.39/25.70  | | | | | | | |              e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 &
% 159.39/25.70  | | | | | | | |            all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 159.39/25.70  | | | | | | | |            & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 159.39/25.70  | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 159.39/25.70  | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~
% 159.39/25.70  | | | | | | | |            (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.39/25.70  | | | | | | | |              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.39/25.70  | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.39/25.70  | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 159.39/25.70  | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 &
% 159.39/25.70  | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 &
% 159.39/25.70  | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 159.39/25.70  | | | | | | | |            op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 159.39/25.70  | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.39/25.70  | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.39/25.70  | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.39/25.70  | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.39/25.70  | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.39/25.70  | | | | | | | |                  e3) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.39/25.70  | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 159.39/25.70  | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.39/25.70  | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 159.39/25.70  | | | | | | | |                e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 159.39/25.70  | | | | | | | |                = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.39/25.70  | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.70  | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.39/25.70  | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10
% 159.39/25.70  | | | | | | | |                = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 159.39/25.70  | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.39/25.70  | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.39/25.70  | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 159.39/25.70  | | | | | | | |                e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.39/25.70  | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.39/25.70  | | | | | | | |                  e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.39/25.70  | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.39/25.70  | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 159.39/25.70  | | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.39/25.70  | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) =
% 159.39/25.70  | | | | | | | |                e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.39/25.70  | | | | | | | |                all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.39/25.70  | | | | | | | |                  e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.39/25.70  | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.39/25.70  | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.39/25.70  | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.39/25.70  | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15
% 159.39/25.70  | | | | | | | |                = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.39/25.70  | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.39/25.70  | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 159.39/25.70  | | | | | | | |                &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.39/25.70  | | | | | | | | 
% 159.39/25.70  | | | | | | | | BETA: splitting (168) gives:
% 159.39/25.70  | | | | | | | | 
% 159.39/25.70  | | | | | | | | Case 1:
% 159.39/25.70  | | | | | | | | | 
% 159.39/25.70  | | | | | | | | |   (169)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.39/25.70  | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) =
% 159.39/25.70  | | | | | | | | |            e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.70  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.39/25.70  | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 159.39/25.70  | | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.39/25.70  | | | | | | | | |            = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.39/25.70  | | | | | | | | |            all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.39/25.70  | | | | | | | | |              e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.39/25.70  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 159.39/25.70  | | | | | | | | |          | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.39/25.70  | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.70  | | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.39/25.70  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 159.39/25.70  | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 159.39/25.70  | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 159.39/25.70  | | | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.39/25.70  | | | | | | | | |            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 159.39/25.70  | | | | | | | | |            op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.39/25.70  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.39/25.70  | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.39/25.70  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 159.39/25.70  | | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 159.39/25.70  | | | | | | | | |            op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 159.39/25.70  | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3)
% 159.39/25.70  | | | | | | | | |            = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 159.39/25.70  | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14))
% 159.39/25.70  | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | BETA: splitting (169) gives:
% 159.39/25.70  | | | | | | | | | 
% 159.39/25.70  | | | | | | | | | Case 1:
% 159.39/25.70  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | |   (170)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.39/25.71  | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 159.39/25.71  | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.71  | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.39/25.71  | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 159.39/25.71  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.39/25.71  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 159.39/25.71  | | | | | | | | | |            e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.39/25.71  | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.39/25.71  | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.71  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 =
% 159.39/25.71  | | | | | | | | | |            e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 159.39/25.71  | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 159.39/25.71  | | | | | | | | | |              e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | BETA: splitting (170) gives:
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | Case 1:
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | |   (171)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.39/25.71  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 159.39/25.71  | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.71  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.39/25.71  | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 159.39/25.71  | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.39/25.71  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.71  | | | | | | | | | | |            $i(all_57_14))
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | BETA: splitting (171) gives:
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | Case 1:
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | |   (172)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.39/25.71  | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 159.39/25.71  | | | | | | | | | | | |          = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.71  | | | | | | | | | | | |          $i(all_57_14)
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | | ALPHA: (172) implies:
% 159.39/25.71  | | | | | | | | | | | |   (173)  op(e3, e3) = e1
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | | REF_CLOSE: (25), (63), (111), (173) are inconsistent by
% 159.39/25.71  | | | | | | | | | | | |            sub-proof #995.
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | Case 2:
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | |   (174)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 159.39/25.71  | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 159.39/25.71  | | | | | | | | | | | |          = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.71  | | | | | | | | | | | |          $i(all_57_14)
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | | ALPHA: (174) implies:
% 159.39/25.71  | | | | | | | | | | | |   (175)  op(e2, e1) = e2
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | | REF_CLOSE: (2), (11), (13), (25), (31), (36), (40), (42),
% 159.39/25.71  | | | | | | | | | | | |            (45), (62), (76), (79), (91), (94), (98), (101),
% 159.39/25.71  | | | | | | | | | | | |            (106), (125), (126), (127), (134), (175) are
% 159.39/25.71  | | | | | | | | | | | |            inconsistent by sub-proof #581.
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | End of split
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | Case 2:
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | |   (176)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 159.39/25.71  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.39/25.71  | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.71  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 159.39/25.71  | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 159.39/25.71  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.71  | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.39/25.71  | | | | | | | | | | |            $i(all_57_14))
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | REF_CLOSE: (17), (23), (25), (38), (66), (69), (119), (176)
% 159.39/25.71  | | | | | | | | | | |            are inconsistent by sub-proof #577.
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | End of split
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | Case 2:
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | |   (177)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 159.39/25.71  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.39/25.71  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.71  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.39/25.71  | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.39/25.71  | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.39/25.71  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.39/25.71  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.39/25.71  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3
% 159.39/25.71  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3
% 159.39/25.71  | | | | | | | | | |            & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 =
% 159.39/25.71  | | | | | | | | | |            e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.39/25.71  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.39/25.71  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | BETA: splitting (177) gives:
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | Case 1:
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | |   (178)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 159.39/25.71  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.39/25.71  | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.71  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.39/25.71  | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.39/25.71  | | | | | | | | | | |              e1) = e1)
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | REF_CLOSE: (17), (23), (25), (111), (178) are inconsistent by
% 159.39/25.71  | | | | | | | | | | |            sub-proof #644.
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | Case 2:
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | |   (179)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.39/25.71  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.39/25.71  | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.39/25.71  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 159.39/25.71  | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 159.39/25.71  | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 159.39/25.71  | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 159.39/25.71  | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.39/25.71  | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | REF_CLOSE: (25), (27), (63), (101), (102), (111), (130),
% 159.39/25.71  | | | | | | | | | | |            (179) are inconsistent by sub-proof #980.
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | End of split
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | End of split
% 159.39/25.71  | | | | | | | | | 
% 159.39/25.71  | | | | | | | | Case 2:
% 159.39/25.71  | | | | | | | | | 
% 159.39/25.71  | | | | | | | | |   (180)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.39/25.71  | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 159.39/25.71  | | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.39/25.71  | | | | | | | | |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 & 
% 159.39/25.71  | | | | | | | | |            ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 159.39/25.71  | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 159.39/25.71  | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 159.39/25.71  | | | | | | | | |            e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.39/25.71  | | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.39/25.71  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.39/25.71  | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 159.39/25.71  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 &
% 159.39/25.71  | | | | | | | | |            all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.39/25.71  | | | | | | | | |              e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.39/25.71  | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 159.39/25.71  | | | | | | | | |          | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 159.39/25.71  | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 159.39/25.71  | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 159.39/25.71  | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14
% 159.39/25.71  | | | | | | | | |            = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0)
% 159.39/25.71  | | | | | | | | |            = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.39/25.71  | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.39/25.71  | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.39/25.71  | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.39/25.71  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.39/25.71  | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 159.39/25.71  | | | | | | | | |                = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.39/25.71  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.39/25.71  | | | | | | | | |                  = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.39/25.71  | | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 159.39/25.71  | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.39/25.71  | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.39/25.71  | | | | | | | | |                 ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.39/25.71  | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 159.39/25.71  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.39/25.71  | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 159.39/25.71  | | | | | | | | |                = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.39/25.71  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.39/25.71  | | | | | | | | |                  = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.39/25.71  | | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.39/25.71  | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.39/25.71  | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.39/25.71  | | | | | | | | |                 ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.39/25.71  | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.39/25.71  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.39/25.71  | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 159.39/25.71  | | | | | | | | |                = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.39/25.71  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.39/25.71  | | | | | | | | |                  = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.39/25.71  | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.39/25.71  | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.39/25.71  | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.39/25.71  | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 159.39/25.71  | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 159.39/25.71  | | | | | | | | |                = e0)))
% 159.39/25.71  | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | BETA: splitting (180) gives:
% 159.39/25.71  | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | Case 1:
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | |   (181)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.39/25.71  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.39/25.71  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.39/25.71  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 159.39/25.71  | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 159.39/25.71  | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 159.39/25.71  | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2)
% 159.39/25.71  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 &
% 159.39/25.71  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0
% 159.39/25.71  | | | | | | | | | |            & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10
% 159.39/25.71  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 159.39/25.71  | | | | | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.39/25.71  | | | | | | | | | |            $i(all_57_10))
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | BETA: splitting (181) gives:
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | Case 1:
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | |   (182)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.39/25.71  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.39/25.71  | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.39/25.71  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 159.39/25.71  | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 159.39/25.71  | | | | | | | | | | |              e1) = e2)
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | REF_CLOSE: (25), (71), (97), (130), (182) are inconsistent by
% 159.39/25.71  | | | | | | | | | | |            sub-proof #576.
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | Case 2:
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | |   (183)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 159.39/25.71  | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 159.39/25.71  | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 159.39/25.71  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 159.39/25.71  | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 159.39/25.71  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.39/25.71  | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.39/25.71  | | | | | | | | | | |            $i(all_57_10))
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | BETA: splitting (183) gives:
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | Case 1:
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | |   (184)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 & 
% 159.39/25.71  | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 159.39/25.71  | | | | | | | | | | | |          = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.39/25.71  | | | | | | | | | | | |          $i(all_57_14)
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | | ALPHA: (184) implies:
% 159.39/25.71  | | | | | | | | | | | |   (185)  op(e2, e1) = e2
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | | REF_CLOSE: (2), (11), (13), (25), (31), (36), (40), (42),
% 159.39/25.71  | | | | | | | | | | | |            (45), (62), (76), (79), (91), (94), (98), (101),
% 159.39/25.71  | | | | | | | | | | | |            (106), (125), (126), (127), (134), (185) are
% 159.39/25.71  | | | | | | | | | | | |            inconsistent by sub-proof #581.
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | Case 2:
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | |   (186)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 159.39/25.71  | | | | | | | | | | | |          ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 159.39/25.71  | | | | | | | | | | | |          op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.39/25.71  | | | | | | | | | | | |          e3 & $i(all_57_10)
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | | ALPHA: (186) implies:
% 159.39/25.71  | | | | | | | | | | | |   (187)  op(e0, e0) = e3
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | | REF_CLOSE: (25), (102), (130), (187) are inconsistent by
% 159.39/25.71  | | | | | | | | | | | |            sub-proof #999.
% 159.39/25.71  | | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | End of split
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | End of split
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | Case 2:
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | |   (188)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 159.39/25.71  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.39/25.71  | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.39/25.71  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 159.39/25.71  | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 159.39/25.71  | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 & 
% 159.39/25.71  | | | | | | | | | |            ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2)
% 159.39/25.71  | | | | | | | | | |          | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.39/25.71  | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 159.39/25.71  | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.39/25.71  | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.39/25.71  | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.39/25.71  | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.71  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.39/25.71  | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.39/25.71  | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.71  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.39/25.71  | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.39/25.71  | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.71  | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.39/25.71  | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.39/25.71  | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.71  | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.39/25.71  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 = e2
% 159.39/25.71  | | | | | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.71  | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.39/25.71  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 = e1
% 159.39/25.71  | | | | | | | | | |                & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.71  | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.39/25.71  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 = e0
% 159.39/25.71  | | | | | | | | | |                &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 159.39/25.71  | | | | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.39/25.71  | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.39/25.71  | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.39/25.71  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.39/25.71  | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.39/25.71  | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 159.39/25.71  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.39/25.71  | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 159.39/25.71  | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 159.39/25.71  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 159.39/25.71  | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.39/25.71  | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.39/25.71  | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 =
% 159.39/25.71  | | | | | | | | | |                e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | BETA: splitting (188) gives:
% 159.39/25.71  | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | Case 1:
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | |   (189)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 159.39/25.71  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.39/25.71  | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.39/25.71  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 159.39/25.71  | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 159.39/25.71  | | | | | | | | | | |              e0) = e3)
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | | REF_CLOSE: (25), (86), (97), (106), (130), (189) are
% 159.39/25.71  | | | | | | | | | | |            inconsistent by sub-proof #975.
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.71  | | | | | | | | | | Case 2:
% 159.39/25.71  | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | |   (190)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.39/25.72  | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 159.39/25.72  | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 159.39/25.72  | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.39/25.72  | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.39/25.72  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.39/25.72  | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.39/25.72  | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.72  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.39/25.72  | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.39/25.72  | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.72  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.39/25.72  | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.39/25.72  | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.72  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.39/25.72  | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.39/25.72  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.72  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.39/25.72  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.39/25.72  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.72  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.39/25.72  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.39/25.72  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.72  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.39/25.72  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.39/25.72  | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.39/25.72  | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.39/25.72  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.39/25.72  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.39/25.72  | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.39/25.72  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.39/25.72  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.39/25.72  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.39/25.72  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.39/25.72  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.39/25.72  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.39/25.72  | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.39/25.72  | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.39/25.72  | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.39/25.72  | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.39/25.72  | | | | | | | | | | |                e0)))
% 159.39/25.72  | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | | BETA: splitting (190) gives:
% 159.39/25.72  | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | | Case 1:
% 159.39/25.72  | | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | | |   (191)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.39/25.72  | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 159.39/25.72  | | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | | | ALPHA: (191) implies:
% 159.39/25.72  | | | | | | | | | | | |   (192)  op(e2, e2) = e2
% 159.39/25.72  | | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | | | REF_CLOSE: (25), (71), (85), (192) are inconsistent by
% 159.39/25.72  | | | | | | | | | | | |            sub-proof #993.
% 159.39/25.72  | | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | | Case 2:
% 159.39/25.72  | | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | | |   (193)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.39/25.72  | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 159.39/25.72  | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.39/25.72  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.39/25.72  | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.39/25.72  | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.72  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.39/25.72  | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.39/25.72  | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.72  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.39/25.72  | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.39/25.72  | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.72  | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.39/25.72  | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.39/25.72  | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.72  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.39/25.72  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.39/25.72  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.72  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.39/25.72  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.39/25.72  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.72  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.39/25.72  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.39/25.72  | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.39/25.72  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.39/25.72  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.39/25.72  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.39/25.72  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.39/25.72  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.39/25.72  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.39/25.72  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.39/25.72  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.39/25.72  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.39/25.72  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.39/25.72  | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.39/25.72  | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.39/25.72  | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.39/25.72  | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.39/25.72  | | | | | | | | | | | |                e0)))
% 159.39/25.72  | | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | | | REF_CLOSE: (17), (22), (23), (25), (26), (63), (64), (84),
% 159.39/25.72  | | | | | | | | | | | |            (102), (111), (124), (125), (193) are inconsistent
% 159.39/25.72  | | | | | | | | | | | |            by sub-proof #569.
% 159.39/25.72  | | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | | End of split
% 159.39/25.72  | | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | | End of split
% 159.39/25.72  | | | | | | | | | | 
% 159.39/25.72  | | | | | | | | | End of split
% 159.39/25.72  | | | | | | | | | 
% 159.39/25.72  | | | | | | | | End of split
% 159.39/25.72  | | | | | | | | 
% 159.39/25.72  | | | | | | | End of split
% 159.39/25.72  | | | | | | | 
% 159.39/25.72  | | | | | | End of split
% 159.39/25.72  | | | | | | 
% 159.39/25.72  | | | | | End of split
% 159.39/25.72  | | | | | 
% 159.39/25.72  | | | | End of split
% 159.39/25.72  | | | | 
% 159.39/25.72  | | | End of split
% 159.39/25.72  | | | 
% 159.39/25.72  | | End of split
% 159.39/25.72  | | 
% 159.39/25.72  | Case 2:
% 159.39/25.72  | | 
% 159.39/25.72  | |   (194)  all_50_2 = e2
% 159.39/25.72  | |   (195)  ( ~ (all_50_0 = e3) & op(e2, e0) = all_50_0 & $i(all_50_0)) | ( ~
% 159.39/25.72  | |            (all_50_1 = e1) & op(e2, e2) = all_50_1 & $i(all_50_1))
% 159.39/25.72  | | 
% 159.39/25.72  | | COMBINE_EQS: (24), (194) imply:
% 159.39/25.72  | |   (196)  all_14_2 = e2
% 159.39/25.72  | | 
% 159.39/25.72  | | SIMP: (196) implies:
% 159.39/25.72  | |   (197)  all_14_2 = e2
% 159.39/25.72  | | 
% 159.39/25.72  | | REDUCE: (6), (197) imply:
% 159.39/25.72  | |   (198)   ~ (all_52_3 = e2)
% 159.39/25.72  | | 
% 159.39/25.72  | | REDUCE: (35), (197) imply:
% 159.39/25.72  | |   (199)   ~ (all_52_12 = e2)
% 159.39/25.72  | | 
% 159.39/25.72  | | REDUCE: (110), (197) imply:
% 159.39/25.72  | |   (200)   ~ (e3 = e2)
% 159.39/25.72  | | 
% 159.39/25.72  | | REDUCE: (66), (197) imply:
% 159.39/25.72  | |   (201)  op(e0, e0) = e2
% 159.39/25.72  | | 
% 159.39/25.72  | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (12), (14), (15), (16), (17),
% 159.39/25.72  | |            (19), (21), (22), (23), (25), (26), (27), (28), (29), (32), (33),
% 159.39/25.72  | |            (37), (39), (41), (43), (46), (47), (49), (50), (53), (54), (56),
% 159.39/25.72  | |            (57), (58), (59), (60), (61), (63), (64), (65), (67), (68), (70),
% 159.39/25.72  | |            (72), (73), (74), (75), (76), (77), (78), (80), (81), (82), (83),
% 159.39/25.72  | |            (84), (85), (86), (87), (88), (89), (90), (92), (93), (95), (96),
% 159.39/25.72  | |            (97), (100), (101), (102), (104), (105), (106), (111), (195),
% 159.39/25.72  | |            (198), (199), (201) are inconsistent by sub-proof #507.
% 159.39/25.72  | | 
% 159.39/25.72  | End of split
% 159.39/25.72  | 
% 159.39/25.72  End of proof
% 159.39/25.72  
% 159.39/25.72  Sub-proof #507 shows that the following formulas are inconsistent:
% 159.39/25.72  ----------------------------------------------------------------
% 159.39/25.72    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.39/25.72         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.39/25.72    (2)   ~ (all_52_1 = all_52_3)
% 159.39/25.72    (3)  all_54_5 = all_4_2
% 159.39/25.72    (4)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.39/25.72         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.39/25.72    (5)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.39/25.72         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.39/25.72    (6)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 159.39/25.72         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 159.39/25.72    (7)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.39/25.72         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.39/25.72    (8)   ~ (all_52_4 = e3)
% 159.39/25.72    (9)   ~ (all_52_12 = e2)
% 159.39/25.72    (10)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.39/25.72          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 159.39/25.72    (11)  all_54_12 = all_52_3
% 159.39/25.72    (12)   ~ (all_52_1 = e3)
% 159.39/25.72    (13)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.39/25.72    (14)  op(e1, e1) = e3
% 159.39/25.72    (15)  op(e0, e0) = e2
% 159.39/25.72    (16)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3)
% 159.39/25.72              | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.39/25.72            ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.39/25.72                = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3)
% 159.39/25.72              | ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.39/25.72          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2)
% 159.39/25.72              | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.39/25.72            ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.39/25.72                = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 159.39/25.72              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.39/25.72          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1)
% 159.39/25.72              | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.39/25.72            ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.39/25.72                = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1)
% 159.39/25.72              | ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.39/25.72          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0)
% 159.39/25.72              | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.39/25.72            ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2,
% 159.39/25.72                  e0) = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1,
% 159.39/25.72                  e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.39/25.72                $i(all_57_13))))
% 159.39/25.72    (17)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.39/25.72          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.39/25.72    (18)  op(e0, e1) = all_52_11
% 159.39/25.72    (19)   ~ (e3 = e2)
% 159.39/25.72    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.39/25.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.39/25.72    (21)  op(e0, e3) = all_52_3
% 159.39/25.72    (22)  op(e3, e1) = all_52_8
% 159.39/25.72    (23)   ~ (all_52_12 = e3)
% 159.39/25.72    (24)   ~ (all_52_9 = all_4_2)
% 159.39/25.72    (25)   ~ (all_4_2 = e3)
% 159.39/25.72    (26)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.39/25.72              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 159.39/25.72                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.39/25.72                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.39/25.72    (27)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.39/25.72          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.39/25.72    (28)  op(e1, e3) = all_52_2
% 159.39/25.72    (29)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.39/25.72          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.39/25.72    (30)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.39/25.72          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.39/25.72    (31)   ~ (all_52_13 = all_4_2)
% 159.39/25.72    (32)   ~ (all_32_2 = e0) | ( ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 &
% 159.39/25.72            $i(all_32_0)) | ( ~ (all_32_1 = e1) & op(e0, e0) = all_32_1 &
% 159.39/25.72            $i(all_32_1))
% 159.39/25.72    (33)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 159.39/25.72    (34)  ( ~ (all_50_0 = e3) & op(e2, e0) = all_50_0 & $i(all_50_0)) | ( ~
% 159.39/25.72            (all_50_1 = e1) & op(e2, e2) = all_50_1 & $i(all_50_1))
% 159.39/25.72    (35)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 159.39/25.72    (36)  all_56_10 = e3
% 159.39/25.72    (37)  op(e1, e0) = all_52_14
% 159.39/25.72    (38)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.39/25.72          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.39/25.72    (39)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 159.39/25.72          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.39/25.72    (40)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 159.39/25.72          (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 159.39/25.72    (41)  op(e2, e2) = all_4_2
% 159.39/25.72    (42)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.39/25.72    (43)   ~ (all_52_14 = e2)
% 159.39/25.72    (44)   ~ (all_52_3 = e2)
% 159.39/25.72    (45)   ~ (all_52_1 = all_52_2)
% 159.39/25.72    (46)  op(e3, e3) = e3
% 159.39/25.72    (47)  op(e2, e0) = e3
% 159.39/25.72    (48)  all_32_2 = all_4_2
% 159.39/25.72    (49)  op(e2, e3) = all_52_1
% 159.39/25.72    (50)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 159.39/25.72          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.39/25.72    (51)  op(e3, e2) = all_52_4
% 159.39/25.72    (52)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.39/25.72          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.39/25.72    (53)   ~ (all_52_1 = all_52_9)
% 159.39/25.72    (54)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.39/25.72          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.39/25.72    (55)   ~ (e1 = e0)
% 159.39/25.72    (56)  op(e2, e1) = all_52_9
% 159.39/25.72    (57)  all_54_4 = all_52_1
% 159.39/25.72    (58)   ~ (all_52_3 = e3)
% 159.39/25.72    (59)   ~ (all_52_8 = all_52_9)
% 159.39/25.72    (60)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.39/25.72          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.39/25.72    (61)  op(e2, e0) = all_52_13
% 159.39/25.72    (62)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 159.39/25.72          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 159.39/25.72    (63)  op(e0, e2) = e3
% 159.39/25.72    (64)   ~ (all_52_9 = e3)
% 159.39/25.72    (65)   ~ (e2 = e1)
% 159.39/25.72    (66)  op(e3, e0) = all_52_12
% 159.39/25.72    (67)  all_56_13 = e3
% 159.39/25.72    (68)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.39/25.72          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.39/25.72    (69)   ~ (all_52_3 = all_52_11)
% 159.39/25.72    (70)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.39/25.72          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.39/25.73    (71)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.39/25.73            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.39/25.73            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.39/25.73            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.39/25.73              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.39/25.73          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.39/25.73            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.39/25.73              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.39/25.73            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.39/25.73              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.39/25.73          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.39/25.73            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 159.39/25.73              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.39/25.73            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.39/25.73              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.39/25.73          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.39/25.73            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 159.39/25.73            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.39/25.73              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.39/25.73            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 159.39/25.73            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.39/25.73            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.39/25.73            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 159.39/25.73              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.39/25.73            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 159.39/25.73          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.39/25.73            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.39/25.73              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.39/25.73            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 159.39/25.73            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.39/25.73          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.39/25.73            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.39/25.73              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 159.39/25.73            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 159.39/25.73            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.39/25.73          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.39/25.73            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.39/25.73              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.39/25.73            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.39/25.73              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.39/25.73          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.39/25.73            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.39/25.73            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 159.39/25.73            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.39/25.73            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 159.39/25.73            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.73            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.39/25.73            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 159.39/25.73              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.39/25.73            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 159.39/25.73            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.39/25.73            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.39/25.73            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 159.39/25.73              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.39/25.73            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 159.39/25.73          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 159.39/25.73            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 159.39/25.73              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 159.39/25.73              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 159.39/25.73            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 159.39/25.73            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.39/25.73            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.39/25.73            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 159.39/25.73              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 159.39/25.73            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 159.39/25.73          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.39/25.73            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.39/25.73              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.39/25.73            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.39/25.73              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.39/25.73          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.39/25.73            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.39/25.73              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 159.39/25.73              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 159.39/25.73            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.39/25.73          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.39/25.73            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.39/25.73            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 159.39/25.73                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 159.39/25.73                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.39/25.73                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.73                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.39/25.73                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.73                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 159.39/25.73                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.73                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.39/25.73                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.73                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 159.39/25.73                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.39/25.73                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.39/25.73                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 159.39/25.73                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.39/25.73                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.39/25.73                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.39/25.73                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 159.39/25.73                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.39/25.73                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 159.39/25.73                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.39/25.73                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.39/25.73                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.39/25.73                op(e0, e1) = e0)))
% 159.39/25.73    (72)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.39/25.73          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.39/25.73            e1)
% 159.39/25.73    (73)   ~ (e3 = e1)
% 159.39/25.73    (74)   ~ (all_52_1 = all_4_2)
% 159.39/25.73    (75)  all_54_6 = all_52_9
% 159.39/25.73    (76)   ~ (e2 = e0)
% 159.39/25.73    (77)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 159.39/25.73          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 159.39/25.73    (78)   ~ (all_52_8 = e3)
% 159.39/25.73    (79)   ~ (e3 = e0)
% 159.39/25.73  
% 159.39/25.73  Begin of proof
% 159.39/25.73  | 
% 159.39/25.73  | BETA: splitting (34) gives:
% 159.39/25.73  | 
% 159.39/25.73  | Case 1:
% 159.39/25.73  | | 
% 159.39/25.73  | |   (80)   ~ (all_50_0 = e3) & op(e2, e0) = all_50_0 & $i(all_50_0)
% 159.39/25.73  | | 
% 159.39/25.73  | | ALPHA: (80) implies:
% 159.39/25.73  | |   (81)   ~ (all_50_0 = e3)
% 159.39/25.73  | |   (82)  op(e2, e0) = all_50_0
% 159.39/25.73  | | 
% 159.39/25.73  | | GROUND_INST: instantiating (20) with e3, all_50_0, e0, e2, simplifying with
% 159.39/25.73  | |              (47), (82) gives:
% 159.39/25.73  | |   (83)  all_50_0 = e3
% 159.39/25.73  | | 
% 159.39/25.73  | | REDUCE: (81), (83) imply:
% 159.39/25.73  | |   (84)  $false
% 159.39/25.73  | | 
% 159.39/25.73  | | CLOSE: (84) is inconsistent.
% 159.39/25.73  | | 
% 159.39/25.73  | Case 2:
% 159.39/25.73  | | 
% 159.39/25.73  | |   (85)   ~ (all_50_1 = e1) & op(e2, e2) = all_50_1 & $i(all_50_1)
% 159.39/25.73  | | 
% 159.39/25.73  | | ALPHA: (85) implies:
% 159.39/25.73  | |   (86)   ~ (all_50_1 = e1)
% 159.39/25.73  | |   (87)  op(e2, e2) = all_50_1
% 159.39/25.73  | | 
% 159.39/25.73  | | GROUND_INST: instantiating (20) with all_4_2, all_50_1, e2, e2, simplifying
% 159.39/25.73  | |              with (41), (87) gives:
% 159.39/25.73  | |   (88)  all_50_1 = all_4_2
% 159.39/25.73  | | 
% 159.39/25.73  | | REDUCE: (86), (88) imply:
% 159.39/25.73  | |   (89)   ~ (all_4_2 = e1)
% 159.39/25.73  | | 
% 159.39/25.73  | | BETA: splitting (32) gives:
% 159.39/25.73  | | 
% 159.39/25.73  | | Case 1:
% 159.39/25.73  | | | 
% 159.39/25.73  | | |   (90)   ~ (all_32_2 = e0)
% 159.39/25.73  | | | 
% 159.39/25.73  | | | REDUCE: (48), (90) imply:
% 159.39/25.73  | | |   (91)   ~ (all_4_2 = e0)
% 159.39/25.73  | | | 
% 159.39/25.73  | | | BETA: splitting (13) gives:
% 159.39/25.73  | | | 
% 159.39/25.73  | | | Case 1:
% 159.39/25.73  | | | | 
% 159.39/25.73  | | | |   (92)  all_54_5 = e3
% 159.39/25.73  | | | | 
% 159.39/25.73  | | | | REF_CLOSE: (3), (25), (92) are inconsistent by sub-proof #930.
% 159.39/25.73  | | | | 
% 159.39/25.73  | | | Case 2:
% 159.39/25.73  | | | | 
% 159.39/25.73  | | | |   (93)   ~ (all_54_5 = e3)
% 159.39/25.73  | | | |   (94)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.39/25.73  | | | | 
% 159.39/25.73  | | | | BETA: splitting (94) gives:
% 159.39/25.73  | | | | 
% 159.39/25.73  | | | | Case 1:
% 159.39/25.73  | | | | | 
% 159.39/25.73  | | | | |   (95)  all_54_5 = e2
% 159.39/25.73  | | | | | 
% 159.39/25.73  | | | | | COMBINE_EQS: (3), (95) imply:
% 159.39/25.73  | | | | |   (96)  all_4_2 = e2
% 159.39/25.73  | | | | | 
% 159.39/25.73  | | | | | SIMP: (96) implies:
% 159.39/25.73  | | | | |   (97)  all_4_2 = e2
% 159.39/25.73  | | | | | 
% 159.39/25.73  | | | | | REDUCE: (74), (97) imply:
% 159.39/25.73  | | | | |   (98)   ~ (all_52_1 = e2)
% 159.39/25.73  | | | | | 
% 159.39/25.73  | | | | | REDUCE: (24), (97) imply:
% 159.39/25.73  | | | | |   (99)   ~ (all_52_9 = e2)
% 159.39/25.73  | | | | | 
% 159.39/25.73  | | | | | REDUCE: (25), (97) imply:
% 159.39/25.73  | | | | |   (100)   ~ (e3 = e2)
% 159.39/25.73  | | | | | 
% 159.39/25.73  | | | | | REDUCE: (41), (97) imply:
% 159.39/25.73  | | | | |   (101)  op(e2, e2) = e2
% 159.39/25.73  | | | | | 
% 159.39/25.73  | | | | | BETA: splitting (7) gives:
% 159.39/25.73  | | | | | 
% 159.39/25.73  | | | | | Case 1:
% 159.39/25.73  | | | | | | 
% 159.39/25.73  | | | | | |   (102)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3,
% 159.39/25.73  | | | | | |              e2) = e2)
% 159.39/25.73  | | | | | | 
% 159.39/25.73  | | | | | | BETA: splitting (102) gives:
% 159.39/25.73  | | | | | | 
% 159.39/25.73  | | | | | | Case 1:
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | |   (103)  all_56_0 = e2 & op(e3, e3) = e2
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | | ALPHA: (103) implies:
% 159.39/25.73  | | | | | | |   (104)  op(e3, e3) = e2
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | | REF_CLOSE: (19), (20), (46), (104) are inconsistent by sub-proof
% 159.39/25.73  | | | | | | |            #958.
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | Case 2:
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | |   (105)  all_56_1 = e2 & op(e3, e2) = e2
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | | ALPHA: (105) implies:
% 159.39/25.73  | | | | | | |   (106)  all_56_1 = e2
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | | REF_CLOSE: (4), (10), (20), (55), (65), (67), (73), (76), (79),
% 159.39/25.73  | | | | | | |            (101), (106) are inconsistent by sub-proof #567.
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | End of split
% 159.39/25.73  | | | | | | 
% 159.39/25.73  | | | | | Case 2:
% 159.39/25.73  | | | | | | 
% 159.39/25.73  | | | | | |   (107)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3,
% 159.39/25.73  | | | | | |              e0) = e2)
% 159.39/25.73  | | | | | | 
% 159.39/25.73  | | | | | | BETA: splitting (107) gives:
% 159.39/25.73  | | | | | | 
% 159.39/25.73  | | | | | | Case 1:
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | |   (108)  all_56_4 = e2 & op(e3, e1) = e2
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | | ALPHA: (108) implies:
% 159.39/25.73  | | | | | | |   (109)  op(e3, e1) = e2
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | | BETA: splitting (71) gives:
% 159.39/25.73  | | | | | | | 
% 159.39/25.73  | | | | | | | Case 1:
% 159.39/25.73  | | | | | | | | 
% 159.39/25.73  | | | | | | | |   (110)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.39/25.73  | | | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3
% 159.39/25.73  | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.39/25.73  | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.39/25.73  | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.39/25.73  | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.39/25.73  | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.39/25.73  | | | | | | | |            all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 159.39/25.73  | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1,
% 159.39/25.73  | | | | | | | |              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.39/25.73  | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 159.39/25.73  | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.39/25.73  | | | | | | | |              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.39/25.73  | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 159.39/25.73  | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 159.39/25.73  | | | | | | | |            e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 159.39/25.73  | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.39/25.73  | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 159.39/25.73  | | | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 159.39/25.73  | | | | | | | |              e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.39/25.73  | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2,
% 159.39/25.73  | | | | | | | |              e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 &
% 159.39/25.73  | | | | | | | |            all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 159.39/25.73  | | | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.39/25.73  | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.39/25.73  | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 159.39/25.73  | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3
% 159.39/25.73  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.39/25.73  | | | | | | | |            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 &
% 159.39/25.73  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.39/25.73  | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 159.39/25.73  | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.39/25.73  | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 159.39/25.73  | | | | | | | |            op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 159.39/25.73  | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) =
% 159.39/25.73  | | | | | | | |            e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.39/25.73  | | | | | | | |            op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 159.39/25.73  | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 159.39/25.73  | | | | | | | |            & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1
% 159.39/25.73  | | | | | | | |            & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2
% 159.39/25.73  | | | | | | | |            = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10
% 159.39/25.73  | | | | | | | |              = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 159.39/25.73  | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.39/25.73  | | | | | | | |          (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.39/25.73  | | | | | | | |            (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2
% 159.39/25.73  | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.73  | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 159.39/25.73  | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 159.39/25.73  | | | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.39/25.73  | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.39/25.73  | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 159.39/25.73  | | | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1,
% 159.39/25.73  | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.39/25.73  | | | | | | | |          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1,
% 159.39/25.73  | | | | | | | |              e3) = e1 & op(e1, e1) = e1)
% 159.39/25.73  | | | | | | | | 
% 159.39/25.73  | | | | | | | | BETA: splitting (110) gives:
% 159.39/25.73  | | | | | | | | 
% 159.39/25.73  | | | | | | | | Case 1:
% 159.39/25.73  | | | | | | | | | 
% 159.39/25.74  | | | | | | | | |   (111)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.39/25.74  | | | | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) =
% 159.39/25.74  | | | | | | | | |            e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.39/25.74  | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.39/25.74  | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.39/25.74  | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.39/25.74  | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.39/25.74  | | | | | | | | |            all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.39/25.74  | | | | | | | | |              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.39/25.74  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 159.39/25.74  | | | | | | | | |          | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 159.39/25.74  | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.39/25.74  | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3
% 159.39/25.74  | | | | | | | | |            & $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 159.39/25.74  | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 159.39/25.74  | | | | | | | | |            e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 159.39/25.74  | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.39/25.74  | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.39/25.74  | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.39/25.74  | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.39/25.74  | | | | | | | | |          | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.39/25.74  | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3
% 159.39/25.74  | | | | | | | | |            & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.39/25.74  | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.39/25.74  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.39/25.74  | | | | | | | | |          | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 159.39/25.74  | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) =
% 159.39/25.74  | | | | | | | | |            e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.39/25.74  | | | | | | | | |            $i(all_57_12))
% 159.39/25.74  | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | BETA: splitting (111) gives:
% 159.39/25.74  | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | Case 1:
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | |   (112)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 159.39/25.74  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 159.39/25.74  | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.39/25.74  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.39/25.74  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 159.39/25.74  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.39/25.74  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 159.39/25.74  | | | | | | | | | |            & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12
% 159.39/25.74  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.39/25.74  | | | | | | | | | |            all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.39/25.74  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.39/25.74  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.39/25.74  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 &
% 159.39/25.74  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10))
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | REF_CLOSE: (20), (49), (98), (112) are inconsistent by
% 159.39/25.74  | | | | | | | | | |            sub-proof #1005.
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | Case 2:
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | |   (113)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.39/25.74  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2)
% 159.39/25.74  | | | | | | | | | |            = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.39/25.74  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.39/25.74  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 159.39/25.74  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 159.39/25.74  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 159.39/25.74  | | | | | | | | | |            & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 159.39/25.74  | | | | | | | | | |            & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 159.39/25.74  | | | | | | | | | |            e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.39/25.74  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.39/25.74  | | | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.39/25.74  | | | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 159.39/25.74  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 159.39/25.74  | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.39/25.74  | | | | | | | | | |            $i(all_57_12))
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | REF_CLOSE: (8), (20), (49), (51), (56), (98), (99), (113) are
% 159.39/25.74  | | | | | | | | | |            inconsistent by sub-proof #566.
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | End of split
% 159.39/25.74  | | | | | | | | | 
% 159.39/25.74  | | | | | | | | Case 2:
% 159.39/25.74  | | | | | | | | | 
% 159.39/25.74  | | | | | | | | |   (114)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.39/25.74  | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.39/25.74  | | | | | | | | |              e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.39/25.74  | | | | | | | | |            $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 & 
% 159.39/25.74  | | | | | | | | |            ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 159.39/25.74  | | | | | | | | |          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 159.39/25.74  | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 159.39/25.74  | | | | | | | | |            e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.39/25.74  | | | | | | | | |            $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.39/25.74  | | | | | | | | |            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) =
% 159.39/25.74  | | | | | | | | |            e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.39/25.74  | | | | | | | | |            = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.39/25.74  | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.39/25.74  | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 159.39/25.74  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.39/25.74  | | | | | | | | |          | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 159.39/25.74  | | | | | | | | |            ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 159.39/25.74  | | | | | | | | |            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.74  | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 159.39/25.74  | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 159.39/25.74  | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.39/25.74  | | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.39/25.74  | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.39/25.74  | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.39/25.74  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.39/25.74  | | | | | | | | |          | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 159.39/25.74  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.39/25.74  | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | BETA: splitting (114) gives:
% 159.39/25.74  | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | Case 1:
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | |   (115)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.39/25.74  | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.39/25.74  | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.39/25.74  | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.39/25.74  | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.39/25.74  | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 159.39/25.74  | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3)
% 159.39/25.74  | | | | | | | | | |            = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.39/25.74  | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1
% 159.39/25.74  | | | | | | | | | |            & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14
% 159.39/25.74  | | | | | | | | | |              = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.39/25.74  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.74  | | | | | | | | | |            $i(all_57_14))
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | BETA: splitting (115) gives:
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | Case 1:
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | |   (116)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.39/25.74  | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.39/25.74  | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.39/25.74  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.39/25.74  | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.39/25.74  | | | | | | | | | | |              e2) = e3)
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | | REF_CLOSE: (8), (9), (19), (20), (31), (37), (40), (41),
% 159.39/25.74  | | | | | | | | | | |            (43), (51), (61), (66), (101), (116) are
% 159.39/25.74  | | | | | | | | | | |            inconsistent by sub-proof #876.
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | Case 2:
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | |   (117)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 159.39/25.74  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 159.39/25.74  | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.39/25.74  | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 159.39/25.74  | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 159.39/25.74  | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.39/25.74  | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.74  | | | | | | | | | | |            $i(all_57_14))
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | | REF_CLOSE: (19), (20), (46), (47), (73), (117) are
% 159.39/25.74  | | | | | | | | | | |            inconsistent by sub-proof #579.
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | End of split
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | Case 2:
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | |   (118)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.39/25.74  | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.39/25.74  | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.39/25.74  | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 =
% 159.39/25.74  | | | | | | | | | |            e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 159.39/25.74  | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 159.39/25.74  | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.39/25.74  | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.39/25.74  | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1)
% 159.39/25.74  | | | | | | | | | |            = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.39/25.74  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.39/25.74  | | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 159.39/25.74  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 159.39/25.74  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 159.39/25.74  | | | | | | | | | |            & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1
% 159.39/25.74  | | | | | | | | | |            & op(e1, e1) = e1)
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | BETA: splitting (118) gives:
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | Case 1:
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | |   (119)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.39/25.74  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.39/25.74  | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.39/25.74  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 159.39/25.74  | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 159.39/25.74  | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 159.39/25.74  | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | | REF_CLOSE: (20), (22), (65), (78), (101), (119) are
% 159.39/25.74  | | | | | | | | | | |            inconsistent by sub-proof #565.
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | Case 2:
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | |   (120)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.39/25.74  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 159.39/25.74  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.39/25.74  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.39/25.74  | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.39/25.74  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.39/25.74  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.39/25.74  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.39/25.74  | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 159.39/25.74  | | | | | | | | | | |            e1)
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | | REF_CLOSE: (14), (15), (20), (23), (65), (66), (120) are
% 159.39/25.74  | | | | | | | | | | |            inconsistent by sub-proof #564.
% 159.39/25.74  | | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | | End of split
% 159.39/25.74  | | | | | | | | | | 
% 159.39/25.74  | | | | | | | | | End of split
% 159.39/25.74  | | | | | | | | | 
% 159.39/25.74  | | | | | | | | End of split
% 159.39/25.74  | | | | | | | | 
% 159.39/25.74  | | | | | | | Case 2:
% 159.39/25.74  | | | | | | | | 
% 159.39/25.74  | | | | | | | |   (121)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.39/25.74  | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3
% 159.39/25.74  | | | | | | | |            & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.74  | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.39/25.74  | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 159.39/25.74  | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.74  | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.39/25.74  | | | | | | | |            all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.39/25.74  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 159.39/25.74  | | | | | | | |              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.39/25.74  | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.39/25.74  | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.74  | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.39/25.74  | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 159.39/25.74  | | | | | | | |            all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 159.39/25.74  | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 159.39/25.74  | | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.39/25.74  | | | | | | | |            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 159.39/25.74  | | | | | | | |            op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.39/25.74  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.39/25.74  | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.39/25.74  | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 159.39/25.74  | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 159.39/25.74  | | | | | | | |            op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 159.39/25.74  | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 159.39/25.74  | | | | | | | |            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 159.39/25.74  | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 &
% 159.39/25.74  | | | | | | | |            all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 159.39/25.74  | | | | | | | |            & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 159.39/25.74  | | | | | | | |              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.39/25.74  | | | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2,
% 159.39/25.74  | | | | | | | |              e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 &
% 159.39/25.74  | | | | | | | |            all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 159.39/25.74  | | | | | | | |            & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 159.39/25.74  | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 159.39/25.74  | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~
% 159.39/25.74  | | | | | | | |            (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.39/25.74  | | | | | | | |              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.39/25.74  | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.39/25.74  | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 159.39/25.74  | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 &
% 159.39/25.74  | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 &
% 159.39/25.74  | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 159.39/25.74  | | | | | | | |            op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 159.39/25.74  | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.39/25.74  | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.39/25.74  | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.39/25.74  | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.39/25.74  | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.39/25.74  | | | | | | | |                  e3) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.39/25.74  | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 159.39/25.74  | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.39/25.74  | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 159.39/25.74  | | | | | | | |                e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 159.39/25.74  | | | | | | | |                = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.39/25.74  | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.39/25.74  | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.39/25.74  | | | | | | | |                e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10
% 159.39/25.74  | | | | | | | |                = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 159.39/25.74  | | | | | | | |                op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.39/25.74  | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.39/25.74  | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 159.39/25.74  | | | | | | | |                e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.39/25.74  | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.39/25.74  | | | | | | | |                  e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.39/25.74  | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.39/25.74  | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 159.39/25.74  | | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.39/25.74  | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) =
% 159.39/25.74  | | | | | | | |                e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.39/25.74  | | | | | | | |                all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.39/25.74  | | | | | | | |                  e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.39/25.74  | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.39/25.74  | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.39/25.74  | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.39/25.74  | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15
% 159.39/25.74  | | | | | | | |                = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.39/25.74  | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.39/25.74  | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 159.39/25.74  | | | | | | | |                &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.39/25.74  | | | | | | | | 
% 159.39/25.74  | | | | | | | | BETA: splitting (121) gives:
% 159.39/25.74  | | | | | | | | 
% 159.39/25.74  | | | | | | | | Case 1:
% 159.39/25.74  | | | | | | | | | 
% 159.39/25.74  | | | | | | | | |   (122)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.39/25.74  | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) =
% 159.39/25.74  | | | | | | | | |            e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.74  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.39/25.74  | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 159.39/25.74  | | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.39/25.74  | | | | | | | | |            = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.39/25.74  | | | | | | | | |            all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.39/25.74  | | | | | | | | |              e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.39/25.74  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 159.39/25.75  | | | | | | | | |          | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.39/25.75  | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.75  | | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.39/25.75  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 159.39/25.75  | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 159.39/25.75  | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 159.39/25.75  | | | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.39/25.75  | | | | | | | | |            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 159.39/25.75  | | | | | | | | |            op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.39/25.75  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.39/25.75  | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.39/25.75  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 159.39/25.75  | | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 159.39/25.75  | | | | | | | | |            op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 159.39/25.75  | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3)
% 159.39/25.75  | | | | | | | | |            = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 159.39/25.75  | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14))
% 159.39/25.75  | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | BETA: splitting (122) gives:
% 159.39/25.75  | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | Case 1:
% 159.39/25.75  | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | |   (123)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.39/25.75  | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 159.39/25.75  | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.75  | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.39/25.75  | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 159.39/25.75  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.39/25.75  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 159.39/25.75  | | | | | | | | | |            e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.39/25.75  | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.39/25.75  | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.75  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 =
% 159.39/25.75  | | | | | | | | | |            e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 159.39/25.75  | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 159.39/25.75  | | | | | | | | | |              e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.39/25.75  | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | BETA: splitting (123) gives:
% 159.39/25.75  | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | Case 1:
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | |   (124)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.39/25.75  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 159.39/25.75  | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.75  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.39/25.75  | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 159.39/25.75  | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.39/25.75  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.75  | | | | | | | | | | |            $i(all_57_14))
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | | REF_CLOSE: (20), (46), (65), (73), (101), (124) are
% 159.39/25.75  | | | | | | | | | | |            inconsistent by sub-proof #987.
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | Case 2:
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | |   (125)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 159.39/25.75  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.39/25.75  | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.75  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 159.39/25.75  | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 159.39/25.75  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.39/25.75  | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.39/25.75  | | | | | | | | | | |            $i(all_57_14))
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | | REF_CLOSE: (14), (15), (19), (20), (65), (125) are
% 159.39/25.75  | | | | | | | | | | |            inconsistent by sub-proof #563.
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | End of split
% 159.39/25.75  | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | Case 2:
% 159.39/25.75  | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | |   (126)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 159.39/25.75  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.39/25.75  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.75  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.39/25.75  | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.39/25.75  | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.39/25.75  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.39/25.75  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.39/25.75  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3
% 159.39/25.75  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3
% 159.39/25.75  | | | | | | | | | |            & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 =
% 159.39/25.75  | | | | | | | | | |            e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.39/25.75  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.39/25.75  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.39/25.75  | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | BETA: splitting (126) gives:
% 159.39/25.75  | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | Case 1:
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | |   (127)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 159.39/25.75  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.39/25.75  | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.39/25.75  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.39/25.75  | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.39/25.75  | | | | | | | | | | |              e1) = e1)
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | | REF_CLOSE: (14), (19), (20), (73), (127) are inconsistent by
% 159.39/25.75  | | | | | | | | | | |            sub-proof #644.
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | Case 2:
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | |   (128)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.39/25.75  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.39/25.75  | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.39/25.75  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 159.39/25.75  | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 159.39/25.75  | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 159.39/25.75  | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 159.39/25.75  | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.39/25.75  | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | | REF_CLOSE: (9), (19), (20), (22), (31), (37), (40), (41),
% 159.39/25.75  | | | | | | | | | | |            (43), (46), (61), (66), (73), (78), (101), (128)
% 159.39/25.75  | | | | | | | | | | |            are inconsistent by sub-proof #872.
% 159.39/25.75  | | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | | End of split
% 159.39/25.75  | | | | | | | | | | 
% 159.39/25.75  | | | | | | | | | End of split
% 159.39/25.75  | | | | | | | | | 
% 159.39/25.75  | | | | | | | | Case 2:
% 159.39/25.75  | | | | | | | | | 
% 159.45/25.75  | | | | | | | | |   (129)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.45/25.75  | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 159.45/25.75  | | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.45/25.75  | | | | | | | | |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 & 
% 159.45/25.75  | | | | | | | | |            ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 159.45/25.75  | | | | | | | | |          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 159.45/25.75  | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 159.45/25.75  | | | | | | | | |            e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.45/25.75  | | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.45/25.75  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.45/25.75  | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 159.45/25.75  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 &
% 159.45/25.75  | | | | | | | | |            all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.45/25.75  | | | | | | | | |              e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.45/25.75  | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 159.45/25.75  | | | | | | | | |          | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 159.45/25.75  | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 159.45/25.75  | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 159.45/25.75  | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14
% 159.45/25.75  | | | | | | | | |            = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0)
% 159.45/25.75  | | | | | | | | |            = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.45/25.75  | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.45/25.75  | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.75  | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.45/25.75  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.75  | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 159.45/25.75  | | | | | | | | |                = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.45/25.75  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.45/25.75  | | | | | | | | |                  = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.45/25.75  | | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 159.45/25.75  | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.45/25.75  | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.45/25.75  | | | | | | | | |                 ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.45/25.75  | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 159.45/25.75  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.75  | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 159.45/25.75  | | | | | | | | |                = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.45/25.75  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.45/25.75  | | | | | | | | |                  = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.45/25.75  | | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.45/25.75  | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.45/25.75  | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.45/25.75  | | | | | | | | |                 ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.45/25.75  | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.45/25.75  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.75  | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 159.45/25.75  | | | | | | | | |                = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.45/25.75  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.45/25.75  | | | | | | | | |                  = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.45/25.75  | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.45/25.75  | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.45/25.75  | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.45/25.75  | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 159.45/25.75  | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 159.45/25.75  | | | | | | | | |                = e0)))
% 159.45/25.75  | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | BETA: splitting (129) gives:
% 159.45/25.75  | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | Case 1:
% 159.45/25.75  | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | |   (130)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.45/25.75  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.45/25.75  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.45/25.75  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 159.45/25.75  | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 159.45/25.75  | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 159.45/25.75  | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2)
% 159.45/25.75  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 &
% 159.45/25.75  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0
% 159.45/25.75  | | | | | | | | | |            & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10
% 159.45/25.75  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 159.45/25.75  | | | | | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.45/25.75  | | | | | | | | | |            $i(all_57_10))
% 159.45/25.75  | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | REF_CLOSE: (9), (19), (20), (31), (37), (40), (41), (43),
% 159.45/25.75  | | | | | | | | | |            (56), (61), (65), (66), (99), (101), (130) are
% 159.45/25.75  | | | | | | | | | |            inconsistent by sub-proof #870.
% 159.45/25.75  | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | Case 2:
% 159.45/25.75  | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | |   (131)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 159.45/25.75  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.45/25.75  | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.45/25.75  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 159.45/25.75  | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 159.45/25.75  | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 & 
% 159.45/25.75  | | | | | | | | | |            ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2)
% 159.45/25.75  | | | | | | | | | |          | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.45/25.75  | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 159.45/25.75  | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.45/25.75  | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.45/25.75  | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.75  | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.75  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.75  | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.45/25.75  | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.75  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.75  | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.45/25.75  | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.75  | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.45/25.75  | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.45/25.75  | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.75  | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.45/25.75  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 = e2
% 159.45/25.75  | | | | | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.75  | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.45/25.75  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 = e1
% 159.45/25.75  | | | | | | | | | |                & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.75  | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.45/25.75  | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 = e0
% 159.45/25.75  | | | | | | | | | |                &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 159.45/25.75  | | | | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.45/25.75  | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.45/25.75  | | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.45/25.75  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.75  | | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.45/25.75  | | | | | | | | | |                  e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 159.45/25.75  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.75  | | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 159.45/25.75  | | | | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 159.45/25.75  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 159.45/25.75  | | | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.45/25.75  | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.45/25.75  | | | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 =
% 159.45/25.75  | | | | | | | | | |                e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.45/25.75  | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | BETA: splitting (131) gives:
% 159.45/25.75  | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | Case 1:
% 159.45/25.75  | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | |   (132)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 159.45/25.75  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.45/25.75  | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.45/25.75  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 159.45/25.75  | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 159.45/25.75  | | | | | | | | | | |              e0) = e3)
% 159.45/25.75  | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | REF_CLOSE: (19), (20), (23), (47), (66), (132) are
% 159.45/25.75  | | | | | | | | | | |            inconsistent by sub-proof #562.
% 159.45/25.75  | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | Case 2:
% 159.45/25.75  | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | |   (133)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.45/25.75  | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 159.45/25.75  | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 159.45/25.75  | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.45/25.75  | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.45/25.75  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.45/25.75  | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.75  | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.75  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.75  | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.45/25.75  | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.75  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.75  | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.45/25.75  | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.75  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.45/25.75  | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.45/25.75  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.75  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.45/25.75  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.45/25.75  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.75  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.45/25.75  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.45/25.75  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.75  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.45/25.75  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.45/25.75  | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.45/25.75  | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.45/25.75  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.45/25.75  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.45/25.75  | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.45/25.75  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.45/25.75  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.45/25.75  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.45/25.75  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.45/25.75  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.45/25.75  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.45/25.75  | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.45/25.75  | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.45/25.75  | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.45/25.75  | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.45/25.75  | | | | | | | | | | |                e0)))
% 159.45/25.75  | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | BETA: splitting (133) gives:
% 159.45/25.75  | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | Case 1:
% 159.45/25.75  | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | |   (134)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.45/25.75  | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 159.45/25.75  | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | | ALPHA: (134) implies:
% 159.45/25.75  | | | | | | | | | | | |   (135)  op(e2, e0) = e2
% 159.45/25.75  | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | | REF_CLOSE: (19), (20), (47), (135) are inconsistent by
% 159.45/25.75  | | | | | | | | | | | |            sub-proof #580.
% 159.45/25.75  | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | Case 2:
% 159.45/25.75  | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | |   (136)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.45/25.75  | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 159.45/25.75  | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.45/25.75  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.45/25.75  | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.75  | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.75  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.75  | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.45/25.75  | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.75  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.75  | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.45/25.75  | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.75  | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.45/25.75  | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.45/25.75  | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.75  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.45/25.75  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.45/25.75  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.75  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.45/25.75  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.45/25.75  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.75  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.45/25.75  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.45/25.75  | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.45/25.75  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.45/25.75  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.45/25.75  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.45/25.75  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.45/25.75  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.45/25.75  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.45/25.75  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.45/25.75  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.45/25.75  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.45/25.75  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.45/25.75  | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.45/25.75  | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.45/25.75  | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.45/25.75  | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.45/25.75  | | | | | | | | | | | |                e0)))
% 159.45/25.75  | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | | BETA: splitting (136) gives:
% 159.45/25.75  | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | | Case 1:
% 159.45/25.75  | | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | | |   (137)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.45/25.75  | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 159.45/25.75  | | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | | | ALPHA: (137) implies:
% 159.45/25.75  | | | | | | | | | | | | |   (138)  op(e1, e1) = e1
% 159.45/25.75  | | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | | | REF_CLOSE: (14), (20), (73), (138) are inconsistent by
% 159.45/25.75  | | | | | | | | | | | | |            sub-proof #1003.
% 159.45/25.75  | | | | | | | | | | | | | 
% 159.45/25.75  | | | | | | | | | | | | Case 2:
% 159.45/25.75  | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | |   (139)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.45/25.76  | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.45/25.76  | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.76  | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.45/25.76  | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.76  | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.45/25.76  | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.45/25.76  | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.76  | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.45/25.76  | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.45/25.76  | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.45/25.76  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 159.45/25.76  | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 159.45/25.76  | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.45/25.76  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.45/25.76  | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.45/25.76  | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.45/25.76  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.45/25.76  | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.45/25.76  | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.45/25.76  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 159.45/25.76  | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.45/25.76  | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.45/25.76  | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.45/25.76  | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 159.45/25.76  | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.76  | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 159.45/25.76  | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.45/25.76  | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 159.45/25.76  | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.45/25.76  | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.45/25.76  | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 159.45/25.76  | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.45/25.76  | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.45/25.76  | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.45/25.76  | | | | | | | | | | | | |              e0))
% 159.45/25.76  | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | ALPHA: (139) implies:
% 159.45/25.76  | | | | | | | | | | | | |   (140)  op(e0, e0) = all_57_15
% 159.45/25.76  | | | | | | | | | | | | |   (141)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.45/25.76  | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.76  | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.45/25.76  | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.45/25.76  | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.45/25.76  | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.45/25.76  | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.45/25.76  | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.45/25.76  | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.45/25.76  | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.45/25.76  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.45/25.76  | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.45/25.76  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.45/25.76  | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.76  | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.45/25.76  | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.45/25.76  | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.45/25.76  | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 159.45/25.76  | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 159.45/25.76  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 159.45/25.76  | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.76  | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.45/25.76  | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 159.45/25.76  | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 159.45/25.76  | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 159.45/25.76  | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 159.45/25.76  | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 159.45/25.76  | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.45/25.76  | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 159.45/25.76  | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 159.45/25.76  | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 159.45/25.76  | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.45/25.76  | | | | | | | | | | | | |            op(e0, e1) = e0)
% 159.45/25.76  | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | GROUND_INST: instantiating (20) with e2, all_57_15, e0, e0,
% 159.45/25.76  | | | | | | | | | | | | |              simplifying with (15), (140) gives:
% 159.45/25.76  | | | | | | | | | | | | |   (142)  all_57_15 = e2
% 159.45/25.76  | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_52_8, e2, e1, e3,
% 159.45/25.76  | | | | | | | | | | | | |              simplifying with (22), (109) gives:
% 159.45/25.76  | | | | | | | | | | | | |   (143)  all_52_8 = e2
% 159.45/25.76  | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | BETA: splitting (141) gives:
% 159.45/25.76  | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | |   (144)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.45/25.76  | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.76  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.45/25.76  | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.45/25.76  | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.45/25.76  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.45/25.76  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.45/25.76  | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.45/25.76  | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.45/25.76  | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.45/25.76  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.45/25.76  | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.76  | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.45/25.76  | | | | | | | | | | | | | |            e0)
% 159.45/25.76  | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 159.45/25.76  | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | |   (145)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.45/25.76  | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.76  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.45/25.76  | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.45/25.76  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.45/25.76  | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.45/25.76  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.45/25.76  | | | | | | | | | | | | | | |            e0)
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | |   (146)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.45/25.76  | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 159.45/25.76  | | | | | | | | | | | | | | | |          = e3 & op(e0, e3) = e0
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 159.45/25.76  | | | | | | | | | | | | | | | |   (147)  op(e3, e3) = e0
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | REF_CLOSE: (20), (46), (79), (147) are inconsistent by
% 159.45/25.76  | | | | | | | | | | | | | | | |            sub-proof #971.
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | Case 2:
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | |   (148)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.45/25.76  | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.45/25.76  | | | | | | | | | | | | | | | |              = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.45/25.76  | | | | | | | | | | | | | | | |            op(e0, e3) = e0)
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (20), (47), (79), (148) are
% 159.45/25.76  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #575.
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | Case 2:
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | |   (149)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.45/25.76  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 159.45/25.76  | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.76  | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.45/25.76  | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.45/25.76  | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.45/25.76  | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | |   (150)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.45/25.76  | | | | | | | | | | | | | | | |          op(e0, e3) = e0
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | REF_CLOSE: (76), (142), (150) are inconsistent by sub-proof
% 159.45/25.76  | | | | | | | | | | | | | | | |            #865.
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | Case 2:
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | |   (151)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.45/25.76  | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.45/25.76  | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.45/25.76  | | | | | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.45/25.76  | | | | | | | | | | | | | | | |            op(e0, e2) = e0)
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | REF_CLOSE: (19), (20), (46), (47), (79), (151) are
% 159.45/25.76  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #574.
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | Case 2:
% 159.45/25.76  | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | |   (152)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.45/25.76  | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.45/25.76  | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.45/25.76  | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.45/25.76  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.45/25.76  | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.45/25.76  | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.45/25.76  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.76  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.45/25.76  | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.45/25.76  | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 159.45/25.76  | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 159.45/25.76  | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.45/25.76  | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 159.45/25.76  | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | |   (153)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.45/25.76  | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.45/25.76  | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.45/25.76  | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.45/25.76  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (46), (63), (79), (153) are
% 159.45/25.76  | | | | | | | | | | | | | | |            inconsistent by sub-proof #573.
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | Case 2:
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | |   (154)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.45/25.76  | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.45/25.76  | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.45/25.76  | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.45/25.76  | | | | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.45/25.76  | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.45/25.76  | | | | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 159.45/25.76  | | | | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 159.45/25.76  | | | | | | | | | | | | | | |            = e0)
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | |   (155)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.45/25.76  | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.45/25.76  | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.45/25.76  | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (20), (47), (79), (155) are
% 159.45/25.76  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #572.
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | Case 2:
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | |   (156)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 159.45/25.76  | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.45/25.76  | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.45/25.76  | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 159.45/25.76  | | | | | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | |   (157)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 & 
% 159.45/25.76  | | | | | | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.45/25.76  | | | | | | | | | | | | | | | | |          op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)
% 159.45/25.76  | | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 159.45/25.76  | | | | | | | | | | | | | | | | |   (158)  all_57_15 = e1
% 159.45/25.76  | | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (158) imply:
% 159.45/25.76  | | | | | | | | | | | | | | | | |   (159)  e2 = e1
% 159.45/25.76  | | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | | REDUCE: (65), (159) imply:
% 159.45/25.76  | | | | | | | | | | | | | | | | |   (160)  $false
% 159.45/25.76  | | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 159.45/25.76  | | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.76  | | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | |   (161)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.45/25.76  | | | | | | | | | | | | | | | | |          op(e0, e1) = e0
% 159.45/25.76  | | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (142), (161) are inconsistent by sub-proof
% 159.45/25.76  | | | | | | | | | | | | | | | | |            #861.
% 159.45/25.76  | | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | | 
% 159.45/25.76  | | | | | | | | End of split
% 159.45/25.76  | | | | | | | | 
% 159.45/25.76  | | | | | | | End of split
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | Case 2:
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | |   (162)  all_56_9 = e2 & op(e3, e0) = e2
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | | REF_CLOSE: (9), (20), (66), (162) are inconsistent by sub-proof
% 159.45/25.76  | | | | | | |            #880.
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | End of split
% 159.45/25.76  | | | | | | 
% 159.45/25.76  | | | | | End of split
% 159.45/25.76  | | | | | 
% 159.45/25.76  | | | | Case 2:
% 159.45/25.76  | | | | | 
% 159.45/25.76  | | | | |   (163)  all_54_5 = e1 | all_54_5 = e0
% 159.45/25.76  | | | | | 
% 159.45/25.76  | | | | | REF_CLOSE: (3), (89), (91), (163) are inconsistent by sub-proof #962.
% 159.45/25.76  | | | | | 
% 159.45/25.76  | | | | End of split
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | End of split
% 159.45/25.76  | | | 
% 159.45/25.76  | | Case 2:
% 159.45/25.76  | | | 
% 159.45/25.76  | | |   (164)  all_32_2 = e0
% 159.45/25.76  | | |   (165)  ( ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 & $i(all_32_0)) | ( ~
% 159.45/25.76  | | |            (all_32_1 = e1) & op(e0, e0) = all_32_1 & $i(all_32_1))
% 159.45/25.76  | | | 
% 159.45/25.76  | | | COMBINE_EQS: (48), (164) imply:
% 159.45/25.76  | | |   (166)  all_4_2 = e0
% 159.45/25.76  | | | 
% 159.45/25.76  | | | REDUCE: (74), (166) imply:
% 159.45/25.76  | | |   (167)   ~ (all_52_1 = e0)
% 159.45/25.76  | | | 
% 159.45/25.76  | | | REDUCE: (24), (166) imply:
% 159.45/25.76  | | |   (168)   ~ (all_52_9 = e0)
% 159.45/25.76  | | | 
% 159.45/25.76  | | | REDUCE: (25), (166) imply:
% 159.45/25.76  | | |   (169)   ~ (e3 = e0)
% 159.45/25.76  | | | 
% 159.45/25.76  | | | REDUCE: (89), (166) imply:
% 159.45/25.76  | | |   (170)   ~ (e1 = e0)
% 159.45/25.76  | | | 
% 159.45/25.76  | | | REDUCE: (41), (166) imply:
% 159.45/25.76  | | |   (171)  op(e2, e2) = e0
% 159.45/25.76  | | | 
% 159.45/25.76  | | | BETA: splitting (165) gives:
% 159.45/25.76  | | | 
% 159.45/25.76  | | | Case 1:
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | |   (172)   ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 & $i(all_32_0)
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | | ALPHA: (172) implies:
% 159.45/25.76  | | | |   (173)   ~ (all_32_0 = e3)
% 159.45/25.76  | | | |   (174)  op(e0, e2) = all_32_0
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | | GROUND_INST: instantiating (20) with e3, all_32_0, e2, e0, simplifying
% 159.45/25.76  | | | |              with (63), (174) gives:
% 159.45/25.76  | | | |   (175)  all_32_0 = e3
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | | REDUCE: (173), (175) imply:
% 159.45/25.76  | | | |   (176)  $false
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | | CLOSE: (176) is inconsistent.
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | Case 2:
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | |   (177)   ~ (all_32_1 = e1) & op(e0, e0) = all_32_1 & $i(all_32_1)
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | | ALPHA: (177) implies:
% 159.45/25.76  | | | |   (178)   ~ (all_32_1 = e1)
% 159.45/25.76  | | | |   (179)  op(e0, e0) = all_32_1
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | | BETA: splitting (16) gives:
% 159.45/25.76  | | | | 
% 159.45/25.76  | | | | Case 1:
% 159.45/25.76  | | | | | 
% 159.45/25.76  | | | | |   (180)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2,
% 159.45/25.76  | | | | |                  e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 159.45/25.76  | | | | |                all_57_0 & $i(all_57_0))) & ((all_57_14 = e3 & op(e1,
% 159.45/25.76  | | | | |                  e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 159.45/25.76  | | | | |                all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 159.45/25.76  | | | | |                  e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 159.45/25.76  | | | | |                all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 159.45/25.76  | | | | |              e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 159.45/25.76  | | | | |                (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 159.45/25.76  | | | | |                $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) |
% 159.45/25.76  | | | | |              ( ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 159.45/25.76  | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.45/25.76  | | | | |              ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 159.45/25.76  | | | | |                $i(all_57_7))))
% 159.45/25.76  | | | | | 
% 159.45/25.76  | | | | | BETA: splitting (180) gives:
% 159.45/25.76  | | | | | 
% 159.45/25.76  | | | | | Case 1:
% 159.45/25.76  | | | | | | 
% 159.45/25.76  | | | | | |   (181)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 &
% 159.45/25.76  | | | | | |              op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 159.45/25.76  | | | | | |              all_57_0 & $i(all_57_0))) & ((all_57_14 = e3 & op(e1,
% 159.45/25.76  | | | | | |                e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 159.45/25.76  | | | | | |              all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 159.45/25.76  | | | | | |                e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 159.45/25.76  | | | | | |              all_57_6 & $i(all_57_6)))
% 159.45/25.76  | | | | | | 
% 159.45/25.76  | | | | | | ALPHA: (181) implies:
% 159.45/25.76  | | | | | |   (182)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) &
% 159.45/25.76  | | | | | |            op(e0, e3) = all_57_6 & $i(all_57_6))
% 159.45/25.76  | | | | | |   (183)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 159.45/25.76  | | | | | |            op(e2, e3) = all_57_0 & $i(all_57_0))
% 159.45/25.76  | | | | | | 
% 159.45/25.76  | | | | | | BETA: splitting (183) gives:
% 159.45/25.76  | | | | | | 
% 159.45/25.76  | | | | | | Case 1:
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | |   (184)  all_57_12 = e3 & op(e2, e2) = e3
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | | ALPHA: (184) implies:
% 159.45/25.76  | | | | | | |   (185)  op(e2, e2) = e3
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | | REF_CLOSE: (20), (79), (171), (185) are inconsistent by sub-proof
% 159.45/25.76  | | | | | | |            #945.
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | Case 2:
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | |   (186)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0)
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | | ALPHA: (186) implies:
% 159.45/25.76  | | | | | | |   (187)   ~ (all_57_0 = e2)
% 159.45/25.76  | | | | | | |   (188)  op(e2, e3) = all_57_0
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | | BETA: splitting (10) gives:
% 159.45/25.76  | | | | | | | 
% 159.45/25.76  | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | 
% 159.45/25.76  | | | | | | | |   (189)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 &
% 159.45/25.76  | | | | | | | |            op(e2, e2) = e0)
% 159.45/25.76  | | | | | | | | 
% 159.45/25.76  | | | | | | | | BETA: splitting (189) gives:
% 159.45/25.76  | | | | | | | | 
% 159.45/25.76  | | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | | 
% 159.45/25.76  | | | | | | | | |   (190)  all_56_1 = e0 & op(e3, e2) = e0
% 159.45/25.76  | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (14), (15), (17),
% 159.45/25.76  | | | | | | | | |            (19), (20), (26), (27), (29), (36), (39), (46),
% 159.45/25.76  | | | | | | | | |            (47), (52), (54), (55), (60), (62), (65), (66),
% 159.45/25.76  | | | | | | | | |            (67), (68), (70), (73), (76), (79), (171), (187),
% 159.45/25.76  | | | | | | | | |            (188), (190) are inconsistent by sub-proof #541.
% 159.45/25.76  | | | | | | | | | 
% 159.45/25.76  | | | | | | | | Case 2:
% 159.45/25.76  | | | | | | | | | 
% 159.45/25.76  | | | | | | | | |   (191)  all_56_3 = e0 & op(e2, e2) = e0
% 159.45/25.76  | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | ALPHA: (191) implies:
% 159.45/25.76  | | | | | | | | |   (192)  all_56_3 = e0
% 159.45/25.76  | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | BETA: splitting (71) gives:
% 159.45/25.76  | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | |   (193)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 159.45/25.76  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 159.45/25.76  | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.45/25.76  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.45/25.76  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 159.45/25.76  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.45/25.76  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 159.45/25.76  | | | | | | | | | |            & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12
% 159.45/25.76  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.45/25.76  | | | | | | | | | |            all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.45/25.76  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.45/25.76  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.45/25.76  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 &
% 159.45/25.76  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 159.45/25.76  | | | | | | | | | |            & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12
% 159.45/25.76  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.45/25.76  | | | | | | | | | |            all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.45/25.76  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.45/25.76  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 159.45/25.76  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 159.45/25.76  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 159.45/25.76  | | | | | | | | | |            & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 159.45/25.76  | | | | | | | | | |            & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 159.45/25.76  | | | | | | | | | |            e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.45/25.76  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.45/25.76  | | | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.45/25.76  | | | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 159.45/25.76  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 159.45/25.76  | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.45/25.76  | | | | | | | | | |            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 &
% 159.45/25.76  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 159.45/25.76  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 159.45/25.76  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 159.45/25.76  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3
% 159.45/25.76  | | | | | | | | | |            & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 =
% 159.45/25.76  | | | | | | | | | |            e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.45/25.76  | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.45/25.76  | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 159.45/25.76  | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.45/25.76  | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1)
% 159.45/25.76  | | | | | | | | | |            = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.45/25.76  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.45/25.76  | | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.45/25.76  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 159.45/25.76  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 159.45/25.76  | | | | | | | | | |            & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14
% 159.45/25.76  | | | | | | | | | |              = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.45/25.76  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.45/25.76  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 159.45/25.76  | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3)
% 159.45/25.76  | | | | | | | | | |            = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.45/25.76  | | | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1
% 159.45/25.76  | | | | | | | | | |            & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10
% 159.45/25.76  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 159.45/25.76  | | | | | | | | | |            e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.45/25.76  | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.45/25.76  | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.76  | | | | | | | | | |            e1)
% 159.45/25.76  | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | BETA: splitting (193) gives:
% 159.45/25.76  | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | Case 1:
% 159.45/25.76  | | | | | | | | | | | 
% 159.45/25.76  | | | | | | | | | | |   (194)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 159.45/25.76  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 159.45/25.76  | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.45/25.76  | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.45/25.76  | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.45/25.76  | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 159.45/25.76  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.45/25.76  | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 159.45/25.76  | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 159.45/25.76  | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 159.45/25.76  | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.45/25.76  | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 159.45/25.76  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.45/25.76  | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.45/25.76  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7
% 159.45/25.76  | | | | | | | | | | |            = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.45/25.76  | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.45/25.76  | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.45/25.76  | | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3
% 159.45/25.76  | | | | | | | | | | |            & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 159.45/25.76  | | | | | | | | | | |              e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3)
% 159.45/25.76  | | | | | | | | | | |            = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.45/25.76  | | | | | | | | | | |          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.45/25.76  | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 159.45/25.76  | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 159.45/25.77  | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.45/25.77  | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 159.45/25.77  | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.45/25.77  | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.45/25.77  | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.45/25.77  | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | BETA: splitting (194) gives:
% 159.45/25.77  | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | Case 1:
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | |   (195)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 159.45/25.77  | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 159.45/25.77  | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.45/25.77  | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.45/25.77  | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.45/25.77  | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 159.45/25.77  | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.45/25.77  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 159.45/25.77  | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 159.45/25.77  | | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 159.45/25.77  | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.45/25.77  | | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 159.45/25.77  | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.45/25.77  | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.45/25.77  | | | | | | | | | | | |            e3 & $i(all_57_10))
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | REF_CLOSE: (20), (187), (188), (195) are inconsistent by
% 159.45/25.77  | | | | | | | | | | | |            sub-proof #540.
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | Case 2:
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | |   (196)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.45/25.77  | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 159.45/25.77  | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.45/25.77  | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.45/25.77  | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.45/25.77  | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.45/25.77  | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.45/25.77  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 159.45/25.77  | | | | | | | | | | | |            &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 159.45/25.77  | | | | | | | | | | | |            e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 159.45/25.77  | | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.45/25.77  | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 159.45/25.77  | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 159.45/25.77  | | | | | | | | | | | |            e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 159.45/25.77  | | | | | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 159.45/25.77  | | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 159.45/25.77  | | | | | | | | | | | |            & $i(all_57_12))
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | BETA: splitting (196) gives:
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | Case 1:
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | |   (197)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.45/25.77  | | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 159.45/25.77  | | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.45/25.77  | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.45/25.77  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.45/25.77  | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.45/25.77  | | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.45/25.77  | | | | | | | | | | | | |            $i(all_57_10))
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | REF_CLOSE: (20), (187), (188), (197) are inconsistent by
% 159.45/25.77  | | | | | | | | | | | | |            sub-proof #539.
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | Case 2:
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | |   (198)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.45/25.77  | | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 159.45/25.77  | | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 159.45/25.77  | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.45/25.77  | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 159.45/25.77  | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.45/25.77  | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.45/25.77  | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | BETA: splitting (198) gives:
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | Case 1:
% 159.45/25.77  | | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | |   (199)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.45/25.77  | | | | | | | | | | | | | |          op(e2, e3) = e2 & op(e2, e2) = e2
% 159.45/25.77  | | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | | ALPHA: (199) implies:
% 159.45/25.77  | | | | | | | | | | | | | |   (200)  op(e2, e3) = e2
% 159.45/25.77  | | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | | REF_CLOSE: (20), (187), (188), (200) are inconsistent by
% 159.45/25.77  | | | | | | | | | | | | | |            sub-proof #783.
% 159.45/25.77  | | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | Case 2:
% 159.45/25.77  | | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | |   (201)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 159.45/25.77  | | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.45/25.77  | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 159.45/25.77  | | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.45/25.77  | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.45/25.77  | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.45/25.77  | | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | | REF_CLOSE: (8), (19), (20), (46), (51), (201) are
% 159.45/25.77  | | | | | | | | | | | | | |            inconsistent by sub-proof #538.
% 159.45/25.77  | | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | End of split
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | End of split
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | End of split
% 159.45/25.77  | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | Case 2:
% 159.45/25.77  | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | |   (202)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.45/25.77  | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.45/25.77  | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.45/25.77  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.45/25.77  | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.45/25.77  | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 159.45/25.77  | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 159.45/25.77  | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.45/25.77  | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 159.45/25.77  | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.45/25.77  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 159.45/25.77  | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.45/25.77  | | | | | | | | | | |            all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.45/25.77  | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 159.45/25.77  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.45/25.77  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2
% 159.45/25.77  | | | | | | | | | | |            & all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2,
% 159.45/25.77  | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 159.45/25.77  | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.45/25.77  | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.45/25.77  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 159.45/25.77  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.45/25.77  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.45/25.77  | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.45/25.77  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.45/25.77  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.45/25.77  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.45/25.77  | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | | |            e1)
% 159.45/25.77  | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | BETA: splitting (202) gives:
% 159.45/25.77  | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | Case 1:
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | |   (203)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.45/25.77  | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.45/25.77  | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.45/25.77  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.45/25.77  | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.45/25.77  | | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 159.45/25.77  | | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 159.45/25.77  | | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.45/25.77  | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 159.45/25.77  | | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.45/25.77  | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 159.45/25.77  | | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | BETA: splitting (203) gives:
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | Case 1:
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | |   (204)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.45/25.77  | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.45/25.77  | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.45/25.77  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.45/25.77  | | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.45/25.77  | | | | | | | | | | | | |              e2) = e3)
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | REF_CLOSE: (8), (15), (19), (20), (51), (204) are
% 159.45/25.77  | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | Case 2:
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | |   (205)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 159.45/25.77  | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 159.45/25.77  | | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.45/25.77  | | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 159.45/25.77  | | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 159.45/25.77  | | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.45/25.77  | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.45/25.77  | | | | | | | | | | | | |            $i(all_57_14))
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | REF_CLOSE: (19), (20), (46), (47), (73), (205) are
% 159.45/25.77  | | | | | | | | | | | | |            inconsistent by sub-proof #579.
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | End of split
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | Case 2:
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | |   (206)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.45/25.77  | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.45/25.77  | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 159.45/25.77  | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 159.45/25.77  | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 159.45/25.77  | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.45/25.77  | | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.45/25.77  | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 159.45/25.77  | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.45/25.77  | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.45/25.77  | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.45/25.77  | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.45/25.77  | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.45/25.77  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.45/25.77  | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | | | |            e1)
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | BETA: splitting (206) gives:
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | Case 1:
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | |   (207)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.45/25.77  | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.45/25.77  | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 159.45/25.77  | | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 159.45/25.77  | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 159.45/25.77  | | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | REF_CLOSE: (20), (22), (55), (78), (171), (207) are
% 159.45/25.77  | | | | | | | | | | | | |            inconsistent by sub-proof #537.
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | Case 2:
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | |   (208)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.45/25.77  | | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 159.45/25.77  | | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.45/25.77  | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.45/25.77  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.45/25.77  | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.45/25.77  | | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.45/25.77  | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.45/25.77  | | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | | | | |            e1)
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | | REF_CLOSE: (14), (15), (20), (23), (65), (66), (208) are
% 159.45/25.77  | | | | | | | | | | | | |            inconsistent by sub-proof #564.
% 159.45/25.77  | | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | | End of split
% 159.45/25.77  | | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | | End of split
% 159.45/25.77  | | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | End of split
% 159.45/25.77  | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | Case 2:
% 159.45/25.77  | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | |   (209)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.45/25.77  | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 159.45/25.77  | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.45/25.77  | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.45/25.77  | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 159.45/25.77  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.45/25.77  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 159.45/25.77  | | | | | | | | | |            e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.45/25.77  | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.45/25.77  | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 =
% 159.45/25.77  | | | | | | | | | |            e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 159.45/25.77  | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 159.45/25.77  | | | | | | | | | |              e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 159.45/25.77  | | | | | | | | | |          (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 159.45/25.77  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.45/25.77  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.45/25.77  | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.45/25.77  | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.45/25.77  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.45/25.77  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.45/25.77  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3
% 159.45/25.77  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3
% 159.45/25.77  | | | | | | | | | |            & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 =
% 159.45/25.77  | | | | | | | | | |            e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.45/25.77  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.45/25.77  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 159.45/25.77  | | | | | | | | | |          (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.45/25.77  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.45/25.77  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.45/25.77  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 159.45/25.77  | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 159.45/25.77  | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 159.45/25.77  | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2)
% 159.45/25.77  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 &
% 159.45/25.77  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0
% 159.45/25.77  | | | | | | | | | |            & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10
% 159.45/25.77  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 159.45/25.77  | | | | | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.45/25.77  | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 159.45/25.77  | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 159.45/25.77  | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 159.45/25.77  | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.45/25.77  | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 159.45/25.77  | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 159.45/25.77  | | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 159.45/25.77  | | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 159.45/25.77  | | | | | | | | | |            all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.45/25.77  | | | | | | | | | |            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 159.45/25.77  | | | | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 159.45/25.77  | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3,
% 159.45/25.77  | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 159.45/25.77  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_11 = e2 &
% 159.45/25.77  | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2,
% 159.45/25.77  | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 159.45/25.77  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 159.45/25.77  | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 159.45/25.77  | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.45/25.77  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.45/25.77  | | | | | | | | | |                (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0
% 159.45/25.77  | | | | | | | | | |                & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.45/25.77  | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.45/25.77  | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.45/25.77  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.77  | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 159.45/25.77  | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 159.45/25.77  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.77  | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.45/25.77  | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.45/25.77  | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 159.45/25.77  | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 159.45/25.77  | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.77  | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.45/25.77  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 = e2
% 159.45/25.77  | | | | | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.77  | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.45/25.77  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 159.45/25.77  | | | | | | | | | |                & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.77  | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.45/25.77  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 159.45/25.77  | | | | | | | | | |                & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.45/25.77  | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.45/25.77  | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 159.45/25.77  | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0,
% 159.45/25.77  | | | | | | | | | |                  e1) = e0)))
% 159.45/25.77  | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | BETA: splitting (209) gives:
% 159.45/25.77  | | | | | | | | | | 
% 159.45/25.77  | | | | | | | | | | Case 1:
% 159.45/25.77  | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | |   (210)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.45/25.78  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 159.45/25.78  | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.45/25.78  | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 159.45/25.78  | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.45/25.78  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.45/25.78  | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 159.45/25.78  | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 159.45/25.78  | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 159.45/25.78  | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.45/25.78  | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.45/25.78  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 159.45/25.78  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.45/25.78  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.45/25.78  | | | | | | | | | | |            all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12
% 159.45/25.78  | | | | | | | | | | |              = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 159.45/25.78  | | | | | | | | | | |            e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.45/25.78  | | | | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1
% 159.45/25.78  | | | | | | | | | | |            &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | |            e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 159.45/25.78  | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.45/25.78  | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.45/25.78  | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 159.45/25.78  | | | | | | | | | | |            e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 159.45/25.78  | | | | | | | | | | |            = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 159.45/25.78  | | | | | | | | | | |            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14
% 159.45/25.78  | | | | | | | | | | |              = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.45/25.78  | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.45/25.78  | | | | | | | | | | |            $i(all_57_14))
% 159.45/25.78  | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | BETA: splitting (210) gives:
% 159.45/25.78  | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | Case 1:
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | |   (211)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.45/25.78  | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 159.45/25.78  | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.45/25.78  | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 159.45/25.78  | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.45/25.78  | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.45/25.78  | | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 159.45/25.78  | | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 159.45/25.78  | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 159.45/25.78  | | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.45/25.78  | | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.45/25.78  | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 159.45/25.78  | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.45/25.78  | | | | | | | | | | | |            = e1 & $i(all_57_14))
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | BETA: splitting (211) gives:
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | Case 1:
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | |   (212)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.45/25.78  | | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 159.45/25.78  | | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.45/25.78  | | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 159.45/25.78  | | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.45/25.78  | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.45/25.78  | | | | | | | | | | | | |            $i(all_57_14))
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | REF_CLOSE: (20), (46), (55), (73), (171), (212) are
% 159.45/25.78  | | | | | | | | | | | | |            inconsistent by sub-proof #920.
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | Case 2:
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | |   (213)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 159.45/25.78  | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.45/25.78  | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 159.45/25.78  | | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 159.45/25.78  | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.45/25.78  | | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.45/25.78  | | | | | | | | | | | | |            $i(all_57_14))
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | REF_CLOSE: (14), (15), (19), (20), (65), (213) are
% 159.45/25.78  | | | | | | | | | | | | |            inconsistent by sub-proof #563.
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | End of split
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | Case 2:
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | |   (214)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 159.45/25.78  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.45/25.78  | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.45/25.78  | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.45/25.78  | | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.45/25.78  | | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 159.45/25.78  | | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 159.45/25.78  | | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.45/25.78  | | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 159.45/25.78  | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 159.45/25.78  | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 159.45/25.78  | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 159.45/25.78  | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 159.45/25.78  | | | | | | | | | | | |            & $i(all_57_14))
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | BETA: splitting (214) gives:
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | Case 1:
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | |   (215)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 159.45/25.78  | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.45/25.78  | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.45/25.78  | | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.45/25.78  | | | | | | | | | | | | |              e1) = e1)
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | REF_CLOSE: (14), (19), (20), (73), (215) are inconsistent by
% 159.45/25.78  | | | | | | | | | | | | |            sub-proof #644.
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | Case 2:
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | |   (216)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.45/25.78  | | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.45/25.78  | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.45/25.78  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 159.45/25.78  | | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 159.45/25.78  | | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 159.45/25.78  | | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 159.45/25.78  | | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | REF_CLOSE: (15), (19), (20), (22), (46), (73), (78), (216)
% 159.45/25.78  | | | | | | | | | | | | |            are inconsistent by sub-proof #855.
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | End of split
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | End of split
% 159.45/25.78  | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | Case 2:
% 159.45/25.78  | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | |   (217)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.45/25.78  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.45/25.78  | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.45/25.78  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 159.45/25.78  | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 159.45/25.78  | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 159.45/25.78  | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 159.45/25.78  | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 159.45/25.78  | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 159.45/25.78  | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 159.45/25.78  | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.45/25.78  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 159.45/25.78  | | | | | | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.45/25.78  | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.45/25.78  | | | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.45/25.78  | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3
% 159.45/25.78  | | | | | | | | | | |            &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 159.45/25.78  | | | | | | | | | | |            e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2
% 159.45/25.78  | | | | | | | | | | |              = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.45/25.78  | | | | | | | | | | |          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.45/25.78  | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 159.45/25.78  | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.45/25.78  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.45/25.78  | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.78  | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.78  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.78  | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.45/25.78  | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.78  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.78  | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.45/25.78  | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.78  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.45/25.78  | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.45/25.78  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.78  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.45/25.78  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.45/25.78  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.78  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.45/25.78  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.45/25.78  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.78  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.45/25.78  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.45/25.78  | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.45/25.78  | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.45/25.78  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.45/25.78  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.45/25.78  | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.45/25.78  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.45/25.78  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.45/25.78  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.45/25.78  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.45/25.78  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.45/25.78  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.45/25.78  | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.45/25.78  | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.45/25.78  | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.45/25.78  | | | | | | | | | | |                e0)))
% 159.45/25.78  | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | BETA: splitting (217) gives:
% 159.45/25.78  | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | Case 1:
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | |   (218)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.45/25.78  | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.45/25.78  | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.45/25.78  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 159.45/25.78  | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 159.45/25.78  | | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 159.45/25.78  | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 159.45/25.78  | | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 159.45/25.78  | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 159.45/25.78  | | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 159.45/25.78  | | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 159.45/25.78  | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.45/25.78  | | | | | | | | | | | |            e3 & $i(all_57_10))
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | BETA: splitting (218) gives:
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | Case 1:
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | |   (219)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.45/25.78  | | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.45/25.78  | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.45/25.78  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 159.45/25.78  | | | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 159.45/25.78  | | | | | | | | | | | | |              e1) = e2)
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | BETA: splitting (219) gives:
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | Case 1:
% 159.45/25.78  | | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | |   (220)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.45/25.78  | | | | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.45/25.78  | | | | | | | | | | | | | |          op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.45/25.78  | | | | | | | | | | | | | |          e2 & $i(all_57_12)
% 159.45/25.78  | | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | | ALPHA: (220) implies:
% 159.45/25.78  | | | | | | | | | | | | | |   (221)  op(e0, e2) = e0
% 159.45/25.78  | | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | | REF_CLOSE: (20), (63), (79), (221) are inconsistent by
% 159.45/25.78  | | | | | | | | | | | | | |            sub-proof #726.
% 159.45/25.78  | | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | Case 2:
% 159.45/25.78  | | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | |   (222)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 159.45/25.78  | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e1) = e2
% 159.45/25.78  | | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | | ALPHA: (222) implies:
% 159.45/25.78  | | | | | | | | | | | | | |   (223)  op(e2, e2) = e2
% 159.45/25.78  | | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | | REF_CLOSE: (20), (76), (171), (223) are inconsistent by
% 159.45/25.78  | | | | | | | | | | | | | |            sub-proof #942.
% 159.45/25.78  | | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | End of split
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | Case 2:
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | |   (224)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 159.45/25.78  | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 159.45/25.78  | | | | | | | | | | | | |              e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 159.45/25.78  | | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 159.45/25.78  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 159.45/25.78  | | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.45/25.78  | | | | | | | | | | | | |            & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.45/25.78  | | | | | | | | | | | | |            $i(all_57_10))
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | REF_CLOSE: (15), (19), (20), (55), (171), (224) are
% 159.45/25.78  | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | End of split
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | Case 2:
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | |   (225)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 159.45/25.78  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.45/25.78  | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.45/25.78  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 159.45/25.78  | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 159.45/25.78  | | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 159.45/25.78  | | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 159.45/25.78  | | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 159.45/25.78  | | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 159.45/25.78  | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.45/25.78  | | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.45/25.78  | | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 159.45/25.78  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.45/25.78  | | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 159.45/25.78  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 159.45/25.78  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.45/25.78  | | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 159.45/25.78  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.45/25.78  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 159.45/25.78  | | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 159.45/25.78  | | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.45/25.78  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.45/25.78  | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.45/25.78  | | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.45/25.78  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.78  | | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 159.45/25.78  | | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 159.45/25.78  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.78  | | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.45/25.78  | | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.45/25.78  | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 159.45/25.78  | | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 159.45/25.78  | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.78  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.45/25.78  | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 159.45/25.78  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.78  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.45/25.78  | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.45/25.78  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.78  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.45/25.78  | | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.45/25.78  | | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.45/25.78  | | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.45/25.78  | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 159.45/25.78  | | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.45/25.78  | | | | | | | | | | | |                op(e0, e1) = e0)))
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | BETA: splitting (225) gives:
% 159.45/25.78  | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | Case 1:
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | |   (226)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 159.45/25.78  | | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.45/25.78  | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.45/25.78  | | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 159.45/25.78  | | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 159.45/25.78  | | | | | | | | | | | | |              e0) = e3)
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | | REF_CLOSE: (19), (20), (23), (47), (66), (226) are
% 159.45/25.78  | | | | | | | | | | | | |            inconsistent by sub-proof #562.
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.78  | | | | | | | | | | | | Case 2:
% 159.45/25.78  | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | |   (227)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.45/25.79  | | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 159.45/25.79  | | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 159.45/25.79  | | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.45/25.79  | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.45/25.79  | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.45/25.79  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.79  | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.79  | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.79  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.45/25.79  | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.79  | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.79  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.45/25.79  | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.79  | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.45/25.79  | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.45/25.79  | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.79  | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.45/25.79  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.45/25.79  | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.79  | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.45/25.79  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.45/25.79  | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.79  | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.45/25.79  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.45/25.79  | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.45/25.79  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.45/25.79  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.45/25.79  | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.45/25.79  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.45/25.79  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.45/25.79  | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.45/25.79  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.45/25.79  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.45/25.79  | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.45/25.79  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.45/25.79  | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.45/25.79  | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.45/25.79  | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.45/25.79  | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.45/25.79  | | | | | | | | | | | | |                e0)))
% 159.45/25.79  | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | BETA: splitting (227) gives:
% 159.45/25.79  | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | |   (228)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.45/25.79  | | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 159.45/25.79  | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | ALPHA: (228) implies:
% 159.45/25.79  | | | | | | | | | | | | | |   (229)  op(e2, e2) = e2
% 159.45/25.79  | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | REF_CLOSE: (20), (76), (171), (229) are inconsistent by
% 159.45/25.79  | | | | | | | | | | | | | |            sub-proof #942.
% 159.45/25.79  | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | |   (230)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.45/25.79  | | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 159.45/25.79  | | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.45/25.79  | | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.45/25.79  | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.79  | | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.79  | | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.79  | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.45/25.79  | | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.79  | | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.79  | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.45/25.79  | | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.45/25.79  | | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.45/25.79  | | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.45/25.79  | | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.79  | | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.45/25.79  | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.45/25.79  | | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.79  | | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.45/25.79  | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.45/25.79  | | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.79  | | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.45/25.79  | | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.45/25.79  | | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.45/25.79  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.45/25.79  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.45/25.79  | | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.45/25.79  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.45/25.79  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.45/25.79  | | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.45/25.79  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.45/25.79  | | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.45/25.79  | | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.45/25.79  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.45/25.79  | | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.45/25.79  | | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.45/25.79  | | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.45/25.79  | | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.45/25.79  | | | | | | | | | | | | | |                e0)))
% 159.45/25.79  | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 159.45/25.79  | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | |   (231)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.45/25.79  | | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 159.45/25.79  | | | | | | | | | | | | | | |   (232)  op(e1, e1) = e1
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (73), (232) are inconsistent by
% 159.45/25.79  | | | | | | | | | | | | | | |            sub-proof #1003.
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | |   (233)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.45/25.79  | | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.45/25.79  | | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.79  | | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.45/25.79  | | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.45/25.79  | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.45/25.79  | | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.45/25.79  | | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.45/25.79  | | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.45/25.79  | | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.45/25.79  | | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.45/25.79  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 159.45/25.79  | | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 159.45/25.79  | | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.45/25.79  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.45/25.79  | | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.45/25.79  | | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.45/25.79  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.45/25.79  | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.45/25.79  | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.45/25.79  | | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 159.45/25.79  | | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.45/25.79  | | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.45/25.79  | | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.45/25.79  | | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 159.45/25.79  | | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.79  | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 159.45/25.79  | | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.45/25.79  | | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 159.45/25.79  | | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.45/25.79  | | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.45/25.79  | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 159.45/25.79  | | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.45/25.79  | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.45/25.79  | | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.45/25.79  | | | | | | | | | | | | | | |              e0))
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 159.45/25.79  | | | | | | | | | | | | | | |   (234)  op(e0, e0) = all_57_15
% 159.45/25.79  | | | | | | | | | | | | | | |   (235)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.45/25.79  | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.79  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.45/25.79  | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.45/25.79  | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.45/25.79  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.45/25.79  | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.45/25.79  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.45/25.79  | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.45/25.79  | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.45/25.79  | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.45/25.79  | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.45/25.79  | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.45/25.79  | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.79  | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.45/25.79  | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.45/25.79  | | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.45/25.79  | | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 159.45/25.79  | | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 159.45/25.79  | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 159.45/25.79  | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.79  | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.45/25.79  | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 159.45/25.79  | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 159.45/25.79  | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 159.45/25.79  | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 159.45/25.79  | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 159.45/25.79  | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.45/25.79  | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 159.45/25.79  | | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 159.45/25.79  | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 159.45/25.79  | | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.45/25.79  | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with e2, all_57_15, e0, e0,
% 159.45/25.79  | | | | | | | | | | | | | | |              simplifying with (15), (234) gives:
% 159.45/25.79  | | | | | | | | | | | | | | |   (236)  all_57_15 = e2
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_32_1, all_57_15, e0,
% 159.45/25.79  | | | | | | | | | | | | | | |              e0, simplifying with (179), (234) gives:
% 159.45/25.79  | | | | | | | | | | | | | | |   (237)  all_57_15 = all_32_1
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_52_1, all_57_0, e3,
% 159.45/25.79  | | | | | | | | | | | | | | |              e2, simplifying with (49), (188) gives:
% 159.45/25.79  | | | | | | | | | | | | | | |   (238)  all_57_0 = all_52_1
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | COMBINE_EQS: (236), (237) imply:
% 159.45/25.79  | | | | | | | | | | | | | | |   (239)  all_32_1 = e2
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | REDUCE: (187), (238) imply:
% 159.45/25.79  | | | | | | | | | | | | | | |   (240)   ~ (all_52_1 = e2)
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | |   (241)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 159.45/25.79  | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 159.45/25.79  | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | REF_CLOSE: (20), (76), (171), (187), (188), (241) are
% 159.45/25.79  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #536.
% 159.45/25.79  | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | |   (242)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 159.45/25.79  | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 159.45/25.79  | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | |   (243)  all_56_5 = e2 & op(e2, e1) = e2
% 159.45/25.79  | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | |   (244)  all_56_5 = e2
% 159.45/25.79  | | | | | | | | | | | | | | | | |   (245)  op(e2, e1) = e2
% 159.45/25.79  | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | |   (246)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 159.45/25.79  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (20), (46), (187), (188), (246) are
% 159.45/25.79  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #550.
% 159.45/25.79  | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | |   (247)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 159.45/25.79  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | |   (248)  all_56_6 = e2 & op(e1, e3) = e2
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | |   (249)  all_56_6 = e2
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | |   (250)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (251)  all_56_6 = e0 & op(e1, e3) = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (252)  all_56_6 = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (252) imply:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (253)  e2 = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | SIMP: (253) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (254)  e2 = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (254) imply:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (255)  all_56_5 = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (20), (36), (47), (54), (55), (65), (68),
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |            (73), (76), (171), (255) are inconsistent by
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |            sub-proof #552.
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (256)  all_56_7 = e0 & op(e1, e2) = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (257)  all_56_7 = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (9), (14), (15), (17), (19),
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |            (20), (26), (27), (29), (30), (36), (38), (39),
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |            (46), (47), (52), (54), (55), (60), (65), (66),
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |            (67), (68), (70), (72), (73), (76), (79), (171),
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |            (187), (188), (249), (257) are inconsistent by
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |            sub-proof #520.
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | |   (258)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (259)  all_56_8 = e0 & op(e1, e1) = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (260)  op(e1, e1) = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (79), (260) are inconsistent by
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |            sub-proof #912.
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (261)  all_56_11 = e0 & op(e1, e0) = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | |   (262)  op(e1, e0) = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | |   (263)  all_54_4 = e3
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (57), (263) are inconsistent by sub-proof
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | |            #931.
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | |   (264)   ~ (all_54_4 = e3)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | |   (265)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_54_4 = e2
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (240), (266) are inconsistent by sub-proof
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | |            #519.
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_54_4 = e1 | all_54_4 = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_54_4 = e1
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (268) imply:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_52_1 = e1
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (269) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_52_1 = e1
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (270) imply:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | |   (271)   ~ (all_52_2 = e1)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (271) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | |   (272)   ~ (all_52_2 = e1)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (270) imply:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | |   (273)   ~ (all_52_3 = e1)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (273) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | |   (274)   ~ (all_52_3 = e1)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (270) imply:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | |   (275)   ~ (all_52_9 = e1)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (275) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | |   (276)   ~ (all_52_9 = e1)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (270) imply:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | |   (277)   ~ (e3 = e1)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_54_6 = e3
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (75), (278) are inconsistent by sub-proof
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | |            #518.
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (279)   ~ (all_54_6 = e3)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_56_6 = e1 & op(e1, e3) = e1
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  op(e1, e3) = e1
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (28), (272), (283) are inconsistent by
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #990.
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  all_56_7 = e1 & op(e1, e2) = e1
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  all_56_7 = e1
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_54_6 = e2
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (286) imply:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_52_9 = e2
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (287) implies:
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_52_9 = e2
% 159.45/25.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (288) imply:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)   ~ (all_52_8 = e2)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (288) imply:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)   ~ (e3 = e2)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)  all_54_12 = e3
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (58), (291) are inconsistent by sub-proof
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #697.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)   ~ (all_54_12 = e3)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  all_56_1 = e2 & op(e3, e2) = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (295) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_56_1 = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  all_56_12 = e1 & op(e0, e3) = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (274), (298) are inconsistent by
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #852.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_56_13 = e1 & op(e0, e2) = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  all_56_13 = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (73), (300) are inconsistent by sub-proof
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_56_14 = e1 & op(e0, e1) = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_56_14 = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_56_0 = e0 & op(e3, e3) = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  op(e3, e3) = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (46), (79), (306) are inconsistent by
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #971.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  all_56_1 = e0 & op(e3, e2) = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (14), (15), (17),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (20), (26), (27), (29), (36), (39), (46),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (47), (52), (54), (55), (60), (62), (65), (66),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (68), (70), (73), (76), (79), (171), (187),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (188), (307) are inconsistent by sub-proof #541.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_56_4 = e0 & op(e3, e1) = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_56_4 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_54_12 = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (44), (311) are inconsistent by sub-proof
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #696.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)   ~ (all_54_12 = e2)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_54_12 = e1 | all_54_12 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  all_54_12 = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (274), (314) are inconsistent by sub-proof
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #695.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  all_54_12 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (315) imply:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  all_52_3 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (316) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  all_52_3 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (317) imply:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)   ~ (all_52_11 = e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (318) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)   ~ (all_52_11 = e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (317) imply:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)   ~ (e2 = e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (20), (47), (79), (182), (322) are
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #517.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e0, e3) = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  all_57_15 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (236), (325) imply:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  e2 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (326) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  e2 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (296), (327) imply:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  all_56_1 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19), (20), (22), (46), (52), (55), (65),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (73), (76), (289), (310), (328) are inconsistent
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #514.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (20), (46), (47), (79), (329) are
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #574.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (18), (19), (20), (46), (47), (63), (79),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (319), (330) are inconsistent by sub-proof #571.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  all_56_9 = e0 & op(e3, e0) = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14), (19), (20), (36), (46), (47), (52),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (55), (65), (68), (73), (76), (79), (171),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (296), (303), (331) are inconsistent by sub-proof
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #524.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)  all_56_15 = e1 & op(e0, e0) = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (333)  op(e0, e0) = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (178), (179), (234), (333) are inconsistent
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #513.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (334)  all_56_3 = e2 & op(e2, e2) = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  op(e2, e2) = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (76), (171), (335) are inconsistent by
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #942.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)  all_56_7 = e2 & op(e1, e2) = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  all_56_7 = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (285), (338) imply:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  e2 = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (339) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  e2 = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (340) imply:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_56_5 = e1
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (14), (19), (20), (27), (46), (47), (55),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (60), (65), (68), (70), (73), (76), (79), (171),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (187), (188), (262), (338), (341) are inconsistent
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #543.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)  all_56_13 = e2 & op(e0, e2) = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)  all_56_13 = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (344)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (10), (17), (19), (20), (38), (46),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (55), (65), (73), (76), (79), (192), (343),
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (344) are inconsistent by sub-proof #512.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (345)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (22), (66), (289), (345) are
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #511.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (346)   ~ (all_54_6 = e2)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (346) imply:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (347)   ~ (all_52_9 = e2)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (56), (245), (347) are inconsistent by
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1002.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (55), (73), (262), (348) are
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #544.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | |   (349)  all_54_4 = e0
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (167), (349) are inconsistent by sub-proof
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | |            #510.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | |   (350)  all_56_12 = e2 & op(e0, e3) = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (44), (350) are inconsistent by
% 159.45/25.80  | | | | | | | | | | | | | | | | | | |            sub-proof #858.
% 159.45/25.80  | | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | |   (351)  all_56_10 = e2 & op(e2, e0) = e2
% 159.45/25.80  | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (15), (17), (19), (20), (26), (39),
% 159.45/25.80  | | | | | | | | | | | | | | | | |            (46), (52), (55), (65), (66), (73), (76), (79),
% 159.45/25.80  | | | | | | | | | | | | | | | | |            (351) are inconsistent by sub-proof #528.
% 159.45/25.80  | | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | | 
% 159.45/25.80  | | | | | | | | End of split
% 159.45/25.80  | | | | | | | | 
% 159.45/25.80  | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | 
% 159.45/25.80  | | | | | | | |   (352)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 &
% 159.45/25.80  | | | | | | | |            op(e0, e2) = e0)
% 159.45/25.80  | | | | | | | | 
% 159.45/25.80  | | | | | | | | BETA: splitting (352) gives:
% 159.45/25.80  | | | | | | | | 
% 159.45/25.80  | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | 
% 159.45/25.80  | | | | | | | | |   (353)  all_56_7 = e0 & op(e1, e2) = e0
% 159.45/25.80  | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | ALPHA: (353) implies:
% 159.45/25.80  | | | | | | | | |   (354)  all_56_7 = e0
% 159.45/25.80  | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | BETA: splitting (77) gives:
% 159.45/25.80  | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | |   (355)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 159.45/25.80  | | | | | | | | | |            & op(e1, e2) = e2)
% 159.45/25.80  | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | BETA: splitting (355) gives:
% 159.45/25.80  | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | Case 1:
% 159.45/25.80  | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | |   (356)  all_56_6 = e2 & op(e1, e3) = e2
% 159.45/25.80  | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | ALPHA: (356) implies:
% 159.45/25.80  | | | | | | | | | | |   (357)  all_56_6 = e2
% 159.45/25.80  | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (9), (14), (15), (17), (19),
% 159.45/25.80  | | | | | | | | | | |            (20), (26), (27), (29), (30), (36), (38), (39),
% 159.45/25.80  | | | | | | | | | | |            (46), (47), (52), (54), (55), (60), (65), (66),
% 159.45/25.80  | | | | | | | | | | |            (67), (68), (70), (72), (73), (76), (79), (171),
% 159.45/25.80  | | | | | | | | | | |            (187), (188), (354), (357) are inconsistent by
% 159.45/25.80  | | | | | | | | | | |            sub-proof #520.
% 159.45/25.80  | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | Case 2:
% 159.45/25.80  | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | |   (358)  all_56_7 = e2 & op(e1, e2) = e2
% 159.45/25.80  | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | ALPHA: (358) implies:
% 159.45/25.80  | | | | | | | | | | |   (359)  all_56_7 = e2
% 159.45/25.80  | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | COMBINE_EQS: (354), (359) imply:
% 159.45/25.80  | | | | | | | | | | |   (360)  e2 = e0
% 159.45/25.80  | | | | | | | | | | | 
% 159.45/25.80  | | | | | | | | | | | REDUCE: (76), (360) imply:
% 159.45/25.80  | | | | | | | | | | |   (361)  $false
% 159.45/25.81  | | | | | | | | | | | 
% 159.45/25.81  | | | | | | | | | | | CLOSE: (361) is inconsistent.
% 159.45/25.81  | | | | | | | | | | | 
% 159.45/25.81  | | | | | | | | | | End of split
% 159.45/25.81  | | | | | | | | | | 
% 159.45/25.81  | | | | | | | | | Case 2:
% 159.45/25.81  | | | | | | | | | | 
% 159.45/25.81  | | | | | | | | | |   (362)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2
% 159.45/25.81  | | | | | | | | | |            & op(e1, e0) = e2)
% 159.45/25.81  | | | | | | | | | | 
% 159.45/25.81  | | | | | | | | | | REF_CLOSE: (14), (19), (20), (37), (43), (362) are
% 159.45/25.81  | | | | | | | | | |            inconsistent by sub-proof #509.
% 159.45/25.81  | | | | | | | | | | 
% 159.45/25.81  | | | | | | | | | End of split
% 159.45/25.81  | | | | | | | | | 
% 159.45/25.81  | | | | | | | | Case 2:
% 159.45/25.81  | | | | | | | | | 
% 159.45/25.81  | | | | | | | | |   (363)  all_56_13 = e0 & op(e0, e2) = e0
% 159.45/25.81  | | | | | | | | | 
% 159.45/25.81  | | | | | | | | | ALPHA: (363) implies:
% 159.45/25.81  | | | | | | | | |   (364)  op(e0, e2) = e0
% 159.45/25.81  | | | | | | | | | 
% 159.45/25.81  | | | | | | | | | REF_CLOSE: (20), (63), (79), (364) are inconsistent by
% 159.45/25.81  | | | | | | | | |            sub-proof #726.
% 159.45/25.81  | | | | | | | | | 
% 159.45/25.81  | | | | | | | | End of split
% 159.45/25.81  | | | | | | | | 
% 159.45/25.81  | | | | | | | End of split
% 159.45/25.81  | | | | | | | 
% 159.45/25.81  | | | | | | End of split
% 159.45/25.81  | | | | | | 
% 159.45/25.81  | | | | | Case 2:
% 159.45/25.81  | | | | | | 
% 159.45/25.81  | | | | | |   (365)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 &
% 159.45/25.81  | | | | | |              op(e3, e3) = e2) | ( ~ (all_57_1 = e3) & op(e3, e2) =
% 159.45/25.81  | | | | | |              all_57_1 & $i(all_57_1))) & ((all_57_14 = e2 & op(e1,
% 159.45/25.81  | | | | | |                e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 159.45/25.81  | | | | | |              all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0,
% 159.45/25.81  | | | | | |                e0) = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 159.45/25.81  | | | | | |              all_57_7 & $i(all_57_7)))
% 159.45/25.81  | | | | | | 
% 159.45/25.81  | | | | | | ALPHA: (365) implies:
% 159.45/25.81  | | | | | |   (366)  op(e2, e2) = e2
% 159.45/25.81  | | | | | | 
% 159.45/25.81  | | | | | | REF_CLOSE: (20), (76), (171), (366) are inconsistent by sub-proof
% 159.45/25.81  | | | | | |            #942.
% 159.45/25.81  | | | | | | 
% 159.45/25.81  | | | | | End of split
% 159.45/25.81  | | | | | 
% 159.45/25.81  | | | | Case 2:
% 159.45/25.81  | | | | | 
% 159.45/25.81  | | | | |   (367)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3,
% 159.45/25.81  | | | | |                  e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) =
% 159.45/25.81  | | | | |                all_57_4 & $i(all_57_4))) & ((all_57_12 = e1 & op(e2,
% 159.45/25.81  | | | | |                  e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 159.45/25.81  | | | | |                all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 159.45/25.81  | | | | |                  e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 159.45/25.81  | | | | |                all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 159.45/25.81  | | | | |              e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 159.45/25.81  | | | | |                (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.45/25.81  | | | | |                $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) |
% 159.45/25.81  | | | | |              ( ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 159.45/25.81  | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0) |
% 159.45/25.81  | | | | |              ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.45/25.81  | | | | |                $i(all_57_13))))
% 159.45/25.81  | | | | | 
% 159.45/25.81  | | | | | REF_CLOSE: (14), (15), (20), (73), (76), (367) are inconsistent by
% 159.45/25.81  | | | | |            sub-proof #508.
% 159.45/25.81  | | | | | 
% 159.45/25.81  | | | | End of split
% 159.45/25.81  | | | | 
% 159.45/25.81  | | | End of split
% 159.45/25.81  | | | 
% 159.45/25.81  | | End of split
% 159.45/25.81  | | 
% 159.45/25.81  | End of split
% 159.45/25.81  | 
% 159.45/25.81  End of proof
% 159.45/25.81  
% 159.45/25.81  Sub-proof #508 shows that the following formulas are inconsistent:
% 159.45/25.81  ----------------------------------------------------------------
% 159.45/25.81    (1)  op(e1, e1) = e3
% 159.45/25.81    (2)  op(e0, e0) = e2
% 159.45/25.81    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.81    (4)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.45/25.81             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.45/25.81           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.45/25.81               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.45/25.81             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.45/25.81         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.45/25.81             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.45/25.81           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.45/25.81               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.45/25.81             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.45/25.81    (5)   ~ (e3 = e1)
% 159.45/25.81    (6)   ~ (e2 = e0)
% 159.45/25.81  
% 159.45/25.81  Begin of proof
% 159.45/25.81  | 
% 159.45/25.81  | BETA: splitting (4) gives:
% 159.45/25.81  | 
% 159.45/25.81  | Case 1:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.45/25.81  | |            e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.45/25.81  | |            $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.45/25.81  | |            (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.45/25.81  | |        ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.45/25.81  | |              e1) = all_57_8 & $i(all_57_8)))
% 159.45/25.81  | | 
% 159.45/25.81  | | ALPHA: (7) implies:
% 159.45/25.81  | |   (8)  op(e1, e1) = e1
% 159.45/25.81  | | 
% 159.45/25.81  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1003.
% 159.45/25.81  | | 
% 159.45/25.81  | Case 2:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 159.45/25.81  | |            e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.45/25.81  | |            $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 159.45/25.81  | |            (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 159.45/25.81  | |        ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 159.45/25.81  | |              e0) = all_57_13 & $i(all_57_13)))
% 159.45/25.81  | | 
% 159.45/25.81  | | ALPHA: (9) implies:
% 159.45/25.81  | |   (10)  op(e0, e0) = e0
% 159.45/25.81  | | 
% 159.45/25.81  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #979.
% 159.45/25.81  | | 
% 159.45/25.81  | End of split
% 159.45/25.81  | 
% 159.45/25.81  End of proof
% 159.45/25.81  
% 159.45/25.81  Sub-proof #509 shows that the following formulas are inconsistent:
% 159.45/25.81  ----------------------------------------------------------------
% 159.45/25.81    (1)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 159.45/25.81    (2)  op(e1, e1) = e3
% 159.45/25.81    (3)   ~ (e3 = e2)
% 159.45/25.81    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.81    (5)  op(e1, e0) = all_52_14
% 159.45/25.81    (6)   ~ (all_52_14 = e2)
% 159.45/25.81  
% 159.45/25.81  Begin of proof
% 159.45/25.81  | 
% 159.45/25.81  | BETA: splitting (1) gives:
% 159.45/25.81  | 
% 159.45/25.81  | Case 1:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (7)  all_56_8 = e2 & op(e1, e1) = e2
% 159.45/25.81  | | 
% 159.45/25.81  | | ALPHA: (7) implies:
% 159.45/25.81  | |   (8)  op(e1, e1) = e2
% 159.45/25.81  | | 
% 159.45/25.81  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #646.
% 159.45/25.81  | | 
% 159.45/25.81  | Case 2:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (9)  all_56_11 = e2 & op(e1, e0) = e2
% 159.45/25.81  | | 
% 159.45/25.81  | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #879.
% 159.45/25.81  | | 
% 159.45/25.81  | End of split
% 159.45/25.81  | 
% 159.45/25.81  End of proof
% 159.45/25.81  
% 159.45/25.81  Sub-proof #510 shows that the following formulas are inconsistent:
% 159.45/25.81  ----------------------------------------------------------------
% 159.45/25.81    (1)  all_54_4 = all_52_1
% 159.45/25.81    (2)  all_54_4 = e0
% 159.45/25.81    (3)   ~ (all_52_1 = e0)
% 159.45/25.81  
% 159.45/25.81  Begin of proof
% 159.45/25.81  | 
% 159.45/25.81  | COMBINE_EQS: (1), (2) imply:
% 159.45/25.81  |   (4)  all_52_1 = e0
% 159.45/25.81  | 
% 159.45/25.81  | SIMP: (4) implies:
% 159.45/25.81  |   (5)  all_52_1 = e0
% 159.45/25.81  | 
% 159.45/25.81  | REDUCE: (3), (5) imply:
% 159.45/25.81  |   (6)  $false
% 159.45/25.81  | 
% 159.45/25.81  | CLOSE: (6) is inconsistent.
% 159.45/25.81  | 
% 159.45/25.81  End of proof
% 159.45/25.81  
% 159.45/25.81  Sub-proof #511 shows that the following formulas are inconsistent:
% 159.45/25.81  ----------------------------------------------------------------
% 159.45/25.81    (1)   ~ (all_52_12 = e2)
% 159.45/25.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.81    (3)  op(e3, e1) = all_52_8
% 159.45/25.81    (4)  op(e3, e0) = all_52_12
% 159.45/25.81    (5)   ~ (all_52_8 = e2)
% 159.45/25.81    (6)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.45/25.81  
% 159.45/25.81  Begin of proof
% 159.45/25.81  | 
% 159.45/25.81  | BETA: splitting (6) gives:
% 159.45/25.81  | 
% 159.45/25.81  | Case 1:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (7)  all_56_4 = e2 & op(e3, e1) = e2
% 159.45/25.81  | | 
% 159.45/25.81  | | ALPHA: (7) implies:
% 159.45/25.81  | |   (8)  op(e3, e1) = e2
% 159.45/25.81  | | 
% 159.45/25.81  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #670.
% 159.45/25.81  | | 
% 159.45/25.81  | Case 2:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (9)  all_56_9 = e2 & op(e3, e0) = e2
% 159.45/25.81  | | 
% 159.45/25.81  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #880.
% 159.45/25.81  | | 
% 159.45/25.81  | End of split
% 159.45/25.81  | 
% 159.45/25.81  End of proof
% 159.45/25.81  
% 159.45/25.81  Sub-proof #512 shows that the following formulas are inconsistent:
% 159.45/25.81  ----------------------------------------------------------------
% 159.45/25.81    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.45/25.81         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.45/25.81    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.45/25.81         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.45/25.81    (3)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.45/25.81         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 159.45/25.81    (4)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.45/25.81         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.45/25.81    (5)   ~ (e3 = e2)
% 159.45/25.81    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.81    (7)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2)
% 159.45/25.81    (8)  all_56_13 = e2
% 159.45/25.81    (9)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.45/25.81         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.45/25.81    (10)  op(e3, e3) = e3
% 159.45/25.81    (11)  all_56_3 = e0
% 159.45/25.81    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.45/25.81          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.45/25.81    (13)   ~ (e1 = e0)
% 159.45/25.81    (14)   ~ (e2 = e1)
% 159.45/25.81    (15)   ~ (e3 = e1)
% 159.45/25.81    (16)   ~ (e2 = e0)
% 159.45/25.81    (17)   ~ (e3 = e0)
% 159.45/25.81  
% 159.45/25.81  Begin of proof
% 159.45/25.81  | 
% 159.45/25.81  | BETA: splitting (7) gives:
% 159.45/25.81  | 
% 159.45/25.81  | Case 1:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (18)  all_56_0 = e2 & op(e3, e3) = e2
% 159.45/25.81  | | 
% 159.45/25.81  | | ALPHA: (18) implies:
% 159.45/25.81  | |   (19)  op(e3, e3) = e2
% 159.45/25.81  | | 
% 159.45/25.81  | | REF_CLOSE: (5), (6), (10), (19) are inconsistent by sub-proof #958.
% 159.45/25.81  | | 
% 159.45/25.81  | Case 2:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (20)  all_56_1 = e2 & op(e3, e2) = e2
% 159.45/25.81  | | 
% 159.45/25.81  | | ALPHA: (20) implies:
% 159.45/25.81  | |   (21)  all_56_1 = e2
% 159.45/25.81  | | 
% 159.45/25.81  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 159.45/25.81  | |            (14), (15), (16), (17), (21) are inconsistent by sub-proof #905.
% 159.45/25.81  | | 
% 159.45/25.81  | End of split
% 159.45/25.81  | 
% 159.45/25.81  End of proof
% 159.45/25.81  
% 159.45/25.81  Sub-proof #513 shows that the following formulas are inconsistent:
% 159.45/25.81  ----------------------------------------------------------------
% 159.45/25.81    (1)  op(e0, e0) = e1
% 159.45/25.81    (2)  op(e0, e0) = all_32_1
% 159.45/25.81    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.81    (4)  op(e0, e0) = all_57_15
% 159.45/25.81    (5)   ~ (all_32_1 = e1)
% 159.45/25.81  
% 159.45/25.81  Begin of proof
% 159.45/25.81  | 
% 159.45/25.81  | GROUND_INST: instantiating (3) with e1, all_57_15, e0, e0, simplifying with
% 159.45/25.81  |              (1), (4) gives:
% 159.45/25.81  |   (6)  all_57_15 = e1
% 159.45/25.81  | 
% 159.45/25.81  | GROUND_INST: instantiating (3) with all_32_1, all_57_15, e0, e0, simplifying
% 159.45/25.81  |              with (2), (4) gives:
% 159.45/25.81  |   (7)  all_57_15 = all_32_1
% 159.45/25.81  | 
% 159.45/25.81  | COMBINE_EQS: (6), (7) imply:
% 159.45/25.81  |   (8)  all_32_1 = e1
% 159.45/25.81  | 
% 159.45/25.81  | REDUCE: (5), (8) imply:
% 159.45/25.81  |   (9)  $false
% 159.45/25.81  | 
% 159.45/25.81  | CLOSE: (9) is inconsistent.
% 159.45/25.81  | 
% 159.45/25.81  End of proof
% 159.45/25.81  
% 159.45/25.81  Sub-proof #514 shows that the following formulas are inconsistent:
% 159.45/25.81  ----------------------------------------------------------------
% 159.45/25.81    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.45/25.81         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.45/25.81    (2)   ~ (e3 = e2)
% 159.45/25.81    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.81    (4)  op(e3, e1) = all_52_8
% 159.45/25.81    (5)  op(e3, e3) = e3
% 159.45/25.81    (6)  all_56_1 = e0
% 159.45/25.81    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.45/25.81         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.45/25.81    (8)   ~ (e1 = e0)
% 159.45/25.81    (9)   ~ (e2 = e1)
% 159.45/25.81    (10)   ~ (all_52_8 = e2)
% 159.45/25.81    (11)   ~ (e3 = e1)
% 159.45/25.81    (12)   ~ (e2 = e0)
% 159.45/25.81    (13)  all_56_4 = e0
% 159.45/25.81  
% 159.45/25.81  Begin of proof
% 159.45/25.81  | 
% 159.45/25.81  | BETA: splitting (1) gives:
% 159.45/25.81  | 
% 159.45/25.81  | Case 1:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (14)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) =
% 159.45/25.81  | |           e2)
% 159.45/25.81  | | 
% 159.45/25.81  | | BETA: splitting (14) gives:
% 159.45/25.81  | | 
% 159.45/25.81  | | Case 1:
% 159.45/25.81  | | | 
% 159.45/25.81  | | |   (15)  all_56_0 = e2 & op(e3, e3) = e2
% 159.45/25.81  | | | 
% 159.45/25.81  | | | ALPHA: (15) implies:
% 159.45/25.81  | | |   (16)  op(e3, e3) = e2
% 159.45/25.81  | | | 
% 159.45/25.81  | | | REF_CLOSE: (2), (3), (5), (16) are inconsistent by sub-proof #958.
% 159.45/25.81  | | | 
% 159.45/25.81  | | Case 2:
% 159.45/25.81  | | | 
% 159.45/25.81  | | |   (17)  all_56_1 = e2 & op(e3, e2) = e2
% 159.45/25.81  | | | 
% 159.45/25.81  | | | ALPHA: (17) implies:
% 159.45/25.81  | | |   (18)  all_56_1 = e2
% 159.45/25.81  | | | 
% 159.45/25.81  | | | REF_CLOSE: (6), (12), (18) are inconsistent by sub-proof #943.
% 159.45/25.81  | | | 
% 159.45/25.81  | | End of split
% 159.45/25.81  | | 
% 159.45/25.81  | Case 2:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (19)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 159.45/25.81  | |           e2)
% 159.45/25.81  | | 
% 159.45/25.81  | | BETA: splitting (19) gives:
% 159.45/25.81  | | 
% 159.45/25.81  | | Case 1:
% 159.45/25.81  | | | 
% 159.45/25.81  | | |   (20)  all_56_4 = e2 & op(e3, e1) = e2
% 159.45/25.81  | | | 
% 159.45/25.81  | | | ALPHA: (20) implies:
% 159.45/25.81  | | |   (21)  op(e3, e1) = e2
% 159.45/25.81  | | | 
% 159.45/25.81  | | | REF_CLOSE: (3), (4), (10), (21) are inconsistent by sub-proof #670.
% 159.45/25.81  | | | 
% 159.45/25.81  | | Case 2:
% 159.45/25.81  | | | 
% 159.45/25.81  | | |   (22)  all_56_9 = e2 & op(e3, e0) = e2
% 159.45/25.81  | | | 
% 159.45/25.81  | | | ALPHA: (22) implies:
% 159.45/25.81  | | |   (23)  all_56_9 = e2
% 159.45/25.81  | | | 
% 159.45/25.81  | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (11), (13), (23) are inconsistent
% 159.45/25.81  | | |            by sub-proof #515.
% 159.45/25.81  | | | 
% 159.45/25.81  | | End of split
% 159.45/25.81  | | 
% 159.45/25.81  | End of split
% 159.45/25.81  | 
% 159.45/25.81  End of proof
% 159.45/25.81  
% 159.45/25.81  Sub-proof #515 shows that the following formulas are inconsistent:
% 159.45/25.81  ----------------------------------------------------------------
% 159.45/25.81    (1)  all_56_9 = e2
% 159.45/25.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.81    (3)  op(e3, e3) = e3
% 159.45/25.81    (4)  all_56_1 = e0
% 159.45/25.81    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.45/25.81         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.45/25.81    (6)   ~ (e1 = e0)
% 159.45/25.81    (7)   ~ (e2 = e1)
% 159.45/25.81    (8)   ~ (e3 = e1)
% 159.45/25.81    (9)  all_56_4 = e0
% 159.45/25.81  
% 159.45/25.81  Begin of proof
% 159.45/25.81  | 
% 159.45/25.81  | BETA: splitting (5) gives:
% 159.45/25.81  | 
% 159.45/25.81  | Case 1:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 159.45/25.81  | |           e1)
% 159.45/25.81  | | 
% 159.45/25.81  | | REF_CLOSE: (2), (3), (4), (6), (8), (10) are inconsistent by sub-proof #561.
% 159.45/25.81  | | 
% 159.45/25.81  | Case 2:
% 159.45/25.81  | | 
% 159.45/25.81  | |   (11)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 159.45/25.81  | |           e1)
% 159.45/25.81  | | 
% 159.45/25.81  | | REF_CLOSE: (1), (6), (7), (9), (11) are inconsistent by sub-proof #516.
% 159.45/25.81  | | 
% 159.45/25.81  | End of split
% 159.45/25.81  | 
% 159.45/25.81  End of proof
% 159.45/25.81  
% 159.45/25.81  Sub-proof #516 shows that the following formulas are inconsistent:
% 159.45/25.81  ----------------------------------------------------------------
% 159.45/25.81    (1)  all_56_9 = e2
% 159.45/25.82    (2)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.45/25.82    (3)   ~ (e1 = e0)
% 159.45/25.82    (4)   ~ (e2 = e1)
% 159.45/25.82    (5)  all_56_4 = e0
% 159.45/25.82  
% 159.45/25.82  Begin of proof
% 159.45/25.82  | 
% 159.45/25.82  | BETA: splitting (2) gives:
% 159.45/25.82  | 
% 159.45/25.82  | Case 1:
% 159.45/25.82  | | 
% 159.45/25.82  | |   (6)  all_56_4 = e1 & op(e3, e1) = e1
% 159.45/25.82  | | 
% 159.45/25.82  | | ALPHA: (6) implies:
% 159.45/25.82  | |   (7)  all_56_4 = e1
% 159.45/25.82  | | 
% 159.45/25.82  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #526.
% 159.45/25.82  | | 
% 159.45/25.82  | Case 2:
% 159.45/25.82  | | 
% 159.45/25.82  | |   (8)  all_56_9 = e1 & op(e3, e0) = e1
% 159.45/25.82  | | 
% 159.45/25.82  | | ALPHA: (8) implies:
% 159.45/25.82  | |   (9)  all_56_9 = e1
% 159.45/25.82  | | 
% 159.45/25.82  | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #896.
% 159.45/25.82  | | 
% 159.45/25.82  | End of split
% 159.45/25.82  | 
% 159.45/25.82  End of proof
% 159.45/25.82  
% 159.45/25.82  Sub-proof #517 shows that the following formulas are inconsistent:
% 159.45/25.82  ----------------------------------------------------------------
% 159.45/25.82    (1)  op(e1, e1) = e3
% 159.45/25.82    (2)   ~ (e3 = e2)
% 159.45/25.82    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.82    (4)  op(e2, e0) = e3
% 159.45/25.82    (5)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.45/25.82           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.45/25.82           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 159.45/25.82           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 159.45/25.82           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 159.45/25.82           e1 & op(e0, e3) = e0)
% 159.45/25.82    (6)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 159.45/25.82           all_57_6 & $i(all_57_6))
% 159.45/25.82    (7)   ~ (e3 = e0)
% 159.45/25.82  
% 159.45/25.82  Begin of proof
% 159.45/25.82  | 
% 159.45/25.82  | BETA: splitting (5) gives:
% 159.45/25.82  | 
% 159.45/25.82  | Case 1:
% 159.45/25.82  | | 
% 159.45/25.82  | |   (8)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 159.45/25.82  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 159.45/25.82  | | 
% 159.45/25.82  | | ALPHA: (8) implies:
% 159.45/25.82  | |   (9)  all_57_6 = e0
% 159.45/25.82  | |   (10)   ~ (all_57_15 = e3)
% 159.45/25.82  | | 
% 159.45/25.82  | | REF_CLOSE: (6), (9), (10) are inconsistent by sub-proof #684.
% 159.45/25.82  | | 
% 159.45/25.82  | Case 2:
% 159.45/25.82  | | 
% 159.45/25.82  | |   (11)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.45/25.82  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.45/25.82  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.45/25.82  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.45/25.82  | | 
% 159.45/25.82  | | REF_CLOSE: (1), (2), (3), (4), (7), (11) are inconsistent by sub-proof #575.
% 159.45/25.82  | | 
% 159.45/25.82  | End of split
% 159.45/25.82  | 
% 159.45/25.82  End of proof
% 159.45/25.82  
% 159.45/25.82  Sub-proof #518 shows that the following formulas are inconsistent:
% 159.45/25.82  ----------------------------------------------------------------
% 159.45/25.82    (1)  all_54_6 = all_52_9
% 159.45/25.82    (2)  all_54_6 = e3
% 159.45/25.82    (3)   ~ (all_52_9 = e3)
% 159.45/25.82  
% 159.45/25.82  Begin of proof
% 159.45/25.82  | 
% 159.45/25.82  | COMBINE_EQS: (1), (2) imply:
% 159.45/25.82  |   (4)  all_52_9 = e3
% 159.45/25.82  | 
% 159.45/25.82  | SIMP: (4) implies:
% 159.45/25.82  |   (5)  all_52_9 = e3
% 159.45/25.82  | 
% 159.45/25.82  | REDUCE: (3), (5) imply:
% 159.45/25.82  |   (6)  $false
% 159.45/25.82  | 
% 159.45/25.82  | CLOSE: (6) is inconsistent.
% 159.45/25.82  | 
% 159.45/25.82  End of proof
% 159.45/25.82  
% 159.45/25.82  Sub-proof #519 shows that the following formulas are inconsistent:
% 159.45/25.82  ----------------------------------------------------------------
% 159.45/25.82    (1)  all_54_4 = all_52_1
% 159.45/25.82    (2)  all_54_4 = e2
% 159.45/25.82    (3)   ~ (all_52_1 = e2)
% 159.45/25.82  
% 159.45/25.82  Begin of proof
% 159.45/25.82  | 
% 159.45/25.82  | COMBINE_EQS: (1), (2) imply:
% 159.45/25.82  |   (4)  all_52_1 = e2
% 159.45/25.82  | 
% 159.45/25.82  | SIMP: (4) implies:
% 159.45/25.82  |   (5)  all_52_1 = e2
% 159.45/25.82  | 
% 159.45/25.82  | REDUCE: (3), (5) imply:
% 159.45/25.82  |   (6)  $false
% 159.45/25.82  | 
% 159.45/25.82  | CLOSE: (6) is inconsistent.
% 159.45/25.82  | 
% 159.45/25.82  End of proof
% 159.45/25.82  
% 159.45/25.82  Sub-proof #520 shows that the following formulas are inconsistent:
% 159.45/25.82  ----------------------------------------------------------------
% 159.45/25.82    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.45/25.82         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.45/25.82    (2)  op(e2, e3) = all_57_0
% 159.45/25.82    (3)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.45/25.82         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.45/25.82    (4)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 159.45/25.82         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 159.45/25.82    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.45/25.82         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.45/25.82    (6)   ~ (all_52_12 = e2)
% 159.45/25.82    (7)  op(e1, e1) = e3
% 159.45/25.82    (8)  op(e0, e0) = e2
% 159.45/25.82    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.45/25.82         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.45/25.82    (10)   ~ (e3 = e2)
% 159.45/25.82    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.82    (12)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.45/25.82              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 159.45/25.82                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.45/25.82                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.45/25.82    (13)  all_56_6 = e2
% 159.45/25.82    (14)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.45/25.82          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.45/25.82    (15)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.45/25.82          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.45/25.82    (16)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.45/25.82          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.45/25.82    (17)  all_56_10 = e3
% 159.45/25.82    (18)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.45/25.82          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.45/25.82    (19)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 159.45/25.82          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.45/25.82    (20)  op(e3, e3) = e3
% 159.45/25.82    (21)  op(e2, e0) = e3
% 159.45/25.82    (22)  op(e2, e2) = e0
% 159.45/25.82    (23)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.45/25.82          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.45/25.82    (24)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.45/25.82          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.45/25.82    (25)   ~ (e1 = e0)
% 159.45/25.82    (26)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.45/25.82          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.45/25.82    (27)   ~ (e2 = e1)
% 159.45/25.82    (28)  op(e3, e0) = all_52_12
% 159.45/25.82    (29)  all_56_13 = e3
% 159.45/25.82    (30)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.45/25.82          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.45/25.82    (31)   ~ (all_57_0 = e2)
% 159.45/25.82    (32)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.45/25.82          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.45/25.82    (33)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.45/25.82          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.45/25.82            e1)
% 159.45/25.82    (34)  all_56_7 = e0
% 159.45/25.82    (35)   ~ (e3 = e1)
% 159.45/25.82    (36)   ~ (e2 = e0)
% 159.45/25.82    (37)   ~ (e3 = e0)
% 159.45/25.82  
% 159.45/25.82  Begin of proof
% 159.45/25.82  | 
% 159.45/25.82  | BETA: splitting (26) gives:
% 159.45/25.82  | 
% 159.45/25.82  | Case 1:
% 159.45/25.82  | | 
% 159.45/25.82  | |   (38)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 159.45/25.82  | |           e0)
% 159.45/25.82  | | 
% 159.45/25.82  | | BETA: splitting (38) gives:
% 159.45/25.82  | | 
% 159.45/25.82  | | Case 1:
% 159.45/25.82  | | | 
% 159.45/25.82  | | |   (39)  all_56_0 = e0 & op(e3, e3) = e0
% 159.45/25.82  | | | 
% 159.45/25.82  | | | ALPHA: (39) implies:
% 159.45/25.82  | | |   (40)  op(e3, e3) = e0
% 159.45/25.82  | | | 
% 159.45/25.82  | | | REF_CLOSE: (11), (20), (37), (40) are inconsistent by sub-proof #971.
% 159.45/25.82  | | | 
% 159.45/25.82  | | Case 2:
% 159.45/25.82  | | | 
% 159.45/25.82  | | |   (41)  all_56_2 = e0 & op(e2, e3) = e0
% 159.45/25.82  | | | 
% 159.45/25.82  | | | ALPHA: (41) implies:
% 159.45/25.82  | | |   (42)  all_56_2 = e0
% 159.45/25.82  | | | 
% 159.45/25.82  | | | BETA: splitting (30) gives:
% 159.45/25.82  | | | 
% 159.45/25.82  | | | Case 1:
% 159.45/25.82  | | | | 
% 159.45/25.82  | | | |   (43)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2)
% 159.45/25.82  | | | |           = e2)
% 159.45/25.82  | | | | 
% 159.45/25.82  | | | | REF_CLOSE: (2), (11), (22), (31), (36), (43) are inconsistent by
% 159.45/25.82  | | | |            sub-proof #536.
% 159.45/25.82  | | | | 
% 159.45/25.82  | | | Case 2:
% 159.45/25.82  | | | | 
% 159.45/25.82  | | | |   (44)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0)
% 159.45/25.82  | | | |           = e2)
% 159.45/25.82  | | | | 
% 159.45/25.82  | | | | BETA: splitting (44) gives:
% 159.45/25.82  | | | | 
% 159.45/25.82  | | | | Case 1:
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | |   (45)  all_56_5 = e2 & op(e2, e1) = e2
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | | ALPHA: (45) implies:
% 159.45/25.82  | | | | |   (46)  all_56_5 = e2
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | | BETA: splitting (24) gives:
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | | Case 1:
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | |   (47)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2,
% 159.45/25.82  | | | | | |             e2) = e1)
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | | REF_CLOSE: (11), (22), (25), (42), (47) are inconsistent by
% 159.45/25.82  | | | | | |            sub-proof #535.
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | Case 2:
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | |   (48)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2,
% 159.45/25.82  | | | | | |             e0) = e1)
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | | BETA: splitting (48) gives:
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | | Case 1:
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | |   (49)  all_56_5 = e1 & op(e2, e1) = e1
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | | ALPHA: (49) implies:
% 159.45/25.82  | | | | | | |   (50)  all_56_5 = e1
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | | COMBINE_EQS: (46), (50) imply:
% 159.45/25.82  | | | | | | |   (51)  e2 = e1
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | | COMBINE_EQS: (13), (51) imply:
% 159.45/25.82  | | | | | | |   (52)  all_56_6 = e1
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | | REF_CLOSE: (1), (10), (11), (16), (20), (22), (25), (26), (27),
% 159.45/25.82  | | | | | | |            (30), (32), (35), (36), (37), (42), (50), (52) are
% 159.45/25.82  | | | | | | |            inconsistent by sub-proof #529.
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | Case 2:
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | |   (53)  all_56_10 = e1 & op(e2, e0) = e1
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | | REF_CLOSE: (17), (35), (53) are inconsistent by sub-proof #556.
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | End of split
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | End of split
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | Case 2:
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | |   (54)  all_56_10 = e2 & op(e2, e0) = e2
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | | REF_CLOSE: (3), (5), (6), (8), (9), (10), (11), (12), (19), (20),
% 159.45/25.82  | | | | |            (23), (25), (27), (28), (35), (36), (37), (54) are
% 159.45/25.82  | | | | |            inconsistent by sub-proof #528.
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | End of split
% 159.45/25.82  | | | | 
% 159.45/25.82  | | | End of split
% 159.45/25.82  | | | 
% 159.45/25.82  | | End of split
% 159.45/25.82  | | 
% 159.45/25.82  | Case 2:
% 159.45/25.82  | | 
% 159.45/25.82  | |   (55)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 159.45/25.82  | |           e0)
% 159.45/25.82  | | 
% 159.45/25.82  | | BETA: splitting (55) gives:
% 159.45/25.82  | | 
% 159.45/25.82  | | Case 1:
% 159.45/25.82  | | | 
% 159.45/25.82  | | |   (56)  all_56_6 = e0 & op(e1, e3) = e0
% 159.45/25.82  | | | 
% 159.45/25.82  | | | ALPHA: (56) implies:
% 159.45/25.82  | | |   (57)  all_56_6 = e0
% 159.45/25.82  | | | 
% 159.45/25.82  | | | REF_CLOSE: (13), (36), (57) are inconsistent by sub-proof #916.
% 159.45/25.82  | | | 
% 159.45/25.82  | | Case 2:
% 159.45/25.82  | | | 
% 159.45/25.82  | | |   (58)  all_56_12 = e0 & op(e0, e3) = e0
% 159.45/25.82  | | | 
% 159.45/25.82  | | | ALPHA: (58) implies:
% 159.45/25.82  | | |   (59)  all_56_12 = e0
% 159.45/25.82  | | | 
% 159.45/25.82  | | | BETA: splitting (15) gives:
% 159.45/25.82  | | | 
% 159.45/25.82  | | | Case 1:
% 159.45/25.82  | | | | 
% 159.45/25.82  | | | |   (60)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2)
% 159.45/25.82  | | | |           = e2)
% 159.45/25.82  | | | | 
% 159.45/25.82  | | | | BETA: splitting (60) gives:
% 159.45/25.82  | | | | 
% 159.45/25.82  | | | | Case 1:
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | |   (61)  all_56_1 = e2 & op(e3, e2) = e2
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | | ALPHA: (61) implies:
% 159.45/25.82  | | | | |   (62)  all_56_1 = e2
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | | BETA: splitting (14) gives:
% 159.45/25.82  | | | | | 
% 159.45/25.82  | | | | | Case 1:
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | |   (63)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1,
% 159.45/25.82  | | | | | |             e2) = e1)
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | | REF_CLOSE: (13), (25), (27), (34), (63) are inconsistent by
% 159.45/25.82  | | | | | |            sub-proof #527.
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | Case 2:
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | |   (64)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1,
% 159.45/25.82  | | | | | |             e0) = e1)
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | | BETA: splitting (64) gives:
% 159.45/25.82  | | | | | | 
% 159.45/25.82  | | | | | | Case 1:
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | |   (65)  all_56_8 = e1 & op(e1, e1) = e1
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | | ALPHA: (65) implies:
% 159.45/25.82  | | | | | | |   (66)  op(e1, e1) = e1
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | | REF_CLOSE: (7), (11), (35), (66) are inconsistent by sub-proof
% 159.45/25.82  | | | | | | |            #1003.
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | Case 2:
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | |   (67)  all_56_11 = e1 & op(e1, e0) = e1
% 159.45/25.82  | | | | | | | 
% 159.45/25.82  | | | | | | | ALPHA: (67) implies:
% 159.45/25.83  | | | | | | |   (68)  op(e1, e0) = e1
% 159.45/25.83  | | | | | | | 
% 159.45/25.83  | | | | | | | BETA: splitting (33) gives:
% 159.45/25.83  | | | | | | | 
% 159.45/25.83  | | | | | | | Case 1:
% 159.45/25.83  | | | | | | | | 
% 159.45/25.83  | | | | | | | |   (69)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 &
% 159.45/25.83  | | | | | | | |           op(e0, e2) = e1)
% 159.45/25.83  | | | | | | | | 
% 159.45/25.83  | | | | | | | | BETA: splitting (69) gives:
% 159.45/25.83  | | | | | | | | 
% 159.45/25.83  | | | | | | | | Case 1:
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | |   (70)  all_56_12 = e1 & op(e0, e3) = e1
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | REF_CLOSE: (25), (59), (70) are inconsistent by sub-proof
% 159.45/25.83  | | | | | | | | |            #771.
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | Case 2:
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | |   (71)  all_56_13 = e1 & op(e0, e2) = e1
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | REF_CLOSE: (29), (35), (71) are inconsistent by sub-proof
% 159.45/25.83  | | | | | | | | |            #728.
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | End of split
% 159.45/25.83  | | | | | | | | 
% 159.45/25.83  | | | | | | | Case 2:
% 159.45/25.83  | | | | | | | | 
% 159.45/25.83  | | | | | | | |   (72)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 &
% 159.45/25.83  | | | | | | | |           op(e0, e0) = e1)
% 159.45/25.83  | | | | | | | | 
% 159.45/25.83  | | | | | | | | BETA: splitting (72) gives:
% 159.45/25.83  | | | | | | | | 
% 159.45/25.83  | | | | | | | | Case 1:
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | |   (73)  all_56_14 = e1 & op(e0, e1) = e1
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | ALPHA: (73) implies:
% 159.45/25.83  | | | | | | | | |   (74)  all_56_14 = e1
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | BETA: splitting (12) gives:
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | Case 1:
% 159.45/25.83  | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | |   (75)  all_56_15 = e0 & op(e0, e0) = e0
% 159.45/25.83  | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | ALPHA: (75) implies:
% 159.45/25.83  | | | | | | | | | |   (76)  op(e0, e0) = e0
% 159.45/25.83  | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | REF_CLOSE: (8), (11), (36), (76) are inconsistent by
% 159.45/25.83  | | | | | | | | | |            sub-proof #979.
% 159.45/25.83  | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | Case 2:
% 159.45/25.83  | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | |   (77)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0
% 159.45/25.83  | | | | | | | | | |             & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 159.45/25.83  | | | | | | | | | |               e0) = e0)) & ((all_56_12 = e0 & op(e0, e3) =
% 159.45/25.83  | | | | | | | | | |             e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 159.45/25.83  | | | | | | | | | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 159.45/25.83  | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | ALPHA: (77) implies:
% 159.45/25.83  | | | | | | | | | |   (78)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0
% 159.45/25.83  | | | | | | | | | |           & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 159.45/25.83  | | | | | | | | | |           = e0)
% 159.45/25.83  | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | BETA: splitting (78) gives:
% 159.45/25.83  | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | Case 1:
% 159.45/25.83  | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | |   (79)  all_56_9 = e0 & op(e3, e0) = e0
% 159.45/25.83  | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | REF_CLOSE: (4), (7), (10), (11), (17), (20), (21), (22),
% 159.45/25.83  | | | | | | | | | | |            (23), (24), (25), (27), (30), (35), (36), (37),
% 159.45/25.83  | | | | | | | | | | |            (62), (74), (79) are inconsistent by sub-proof
% 159.45/25.83  | | | | | | | | | | |            #524.
% 159.45/25.83  | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | Case 2:
% 159.45/25.83  | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | |   (80)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 159.45/25.83  | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 159.45/25.83  | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | BETA: splitting (80) gives:
% 159.45/25.83  | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | Case 1:
% 159.45/25.83  | | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | |   (81)  all_56_10 = e0 & op(e2, e0) = e0
% 159.45/25.83  | | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | | ALPHA: (81) implies:
% 159.45/25.83  | | | | | | | | | | | |   (82)  all_56_10 = e0
% 159.45/25.83  | | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | | REF_CLOSE: (17), (37), (82) are inconsistent by sub-proof
% 159.45/25.83  | | | | | | | | | | | |            #740.
% 159.45/25.83  | | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | Case 2:
% 159.45/25.83  | | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | |   (83)  all_56_11 = e0 & op(e1, e0) = e0
% 159.45/25.83  | | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | | ALPHA: (83) implies:
% 159.45/25.83  | | | | | | | | | | | |   (84)  op(e1, e0) = e0
% 159.45/25.83  | | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | | REF_CLOSE: (11), (25), (68), (84) are inconsistent by
% 159.45/25.83  | | | | | | | | | | | |            sub-proof #545.
% 159.45/25.83  | | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | | End of split
% 159.45/25.83  | | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | | End of split
% 159.45/25.83  | | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | End of split
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | Case 2:
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | |   (85)  all_56_15 = e1 & op(e0, e0) = e1
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | ALPHA: (85) implies:
% 159.45/25.83  | | | | | | | | |   (86)  op(e0, e0) = e1
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | | REF_CLOSE: (8), (11), (27), (86) are inconsistent by sub-proof
% 159.45/25.83  | | | | | | | | |            #875.
% 159.45/25.83  | | | | | | | | | 
% 159.45/25.83  | | | | | | | | End of split
% 159.45/25.83  | | | | | | | | 
% 159.45/25.83  | | | | | | | End of split
% 159.45/25.83  | | | | | | | 
% 159.45/25.83  | | | | | | End of split
% 159.45/25.83  | | | | | | 
% 159.45/25.83  | | | | | End of split
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | Case 2:
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | |   (87)  all_56_3 = e2 & op(e2, e2) = e2
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | | ALPHA: (87) implies:
% 159.45/25.83  | | | | |   (88)  op(e2, e2) = e2
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | | REF_CLOSE: (11), (22), (36), (88) are inconsistent by sub-proof #942.
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | End of split
% 159.45/25.83  | | | | 
% 159.45/25.83  | | | Case 2:
% 159.45/25.83  | | | | 
% 159.45/25.83  | | | |   (89)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2)
% 159.45/25.83  | | | |           = e2)
% 159.45/25.83  | | | | 
% 159.45/25.83  | | | | BETA: splitting (89) gives:
% 159.45/25.83  | | | | 
% 159.45/25.83  | | | | Case 1:
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | |   (90)  all_56_7 = e2 & op(e1, e2) = e2
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | | ALPHA: (90) implies:
% 159.45/25.83  | | | | |   (91)  all_56_7 = e2
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | | REF_CLOSE: (34), (36), (91) are inconsistent by sub-proof #523.
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | Case 2:
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | |   (92)  all_56_13 = e2 & op(e0, e2) = e2
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | | ALPHA: (92) implies:
% 159.45/25.83  | | | | |   (93)  all_56_13 = e2
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | | REF_CLOSE: (5), (9), (10), (11), (18), (20), (22), (23), (25), (27),
% 159.45/25.83  | | | | |            (34), (35), (36), (37), (93) are inconsistent by sub-proof
% 159.45/25.83  | | | | |            #521.
% 159.45/25.83  | | | | | 
% 159.45/25.83  | | | | End of split
% 159.45/25.83  | | | | 
% 159.45/25.83  | | | End of split
% 159.45/25.83  | | | 
% 159.45/25.83  | | End of split
% 159.45/25.83  | | 
% 159.45/25.83  | End of split
% 159.45/25.83  | 
% 159.45/25.83  End of proof
% 159.45/25.83  
% 159.45/25.83  Sub-proof #521 shows that the following formulas are inconsistent:
% 159.45/25.83  ----------------------------------------------------------------
% 159.45/25.83    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.45/25.83         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.45/25.83    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.45/25.83         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.45/25.83    (3)   ~ (e3 = e2)
% 159.45/25.83    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.83    (5)  all_56_13 = e2
% 159.45/25.83    (6)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.45/25.83         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.45/25.83    (7)  op(e3, e3) = e3
% 159.45/25.83    (8)  op(e2, e2) = e0
% 159.45/25.83    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.45/25.83         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.45/25.83    (10)   ~ (e1 = e0)
% 159.45/25.83    (11)   ~ (e2 = e1)
% 159.45/25.83    (12)  all_56_7 = e0
% 159.45/25.83    (13)   ~ (e3 = e1)
% 159.45/25.83    (14)   ~ (e2 = e0)
% 159.45/25.83    (15)   ~ (e3 = e0)
% 159.45/25.83  
% 159.45/25.83  Begin of proof
% 159.45/25.83  | 
% 159.45/25.83  | BETA: splitting (6) gives:
% 159.45/25.83  | 
% 159.45/25.83  | Case 1:
% 159.45/25.83  | | 
% 159.45/25.83  | |   (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 159.45/25.83  | |           e3)
% 159.45/25.83  | | 
% 159.45/25.83  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (13), (14), (15),
% 159.45/25.83  | |            (16) are inconsistent by sub-proof #944.
% 159.45/25.83  | | 
% 159.45/25.83  | Case 2:
% 159.45/25.83  | | 
% 159.45/25.83  | |   (17)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 159.45/25.83  | |           e3)
% 159.45/25.83  | | 
% 159.45/25.83  | | BETA: splitting (17) gives:
% 159.45/25.83  | | 
% 159.45/25.83  | | Case 1:
% 159.45/25.83  | | | 
% 159.45/25.83  | | |   (18)  all_56_7 = e3 & op(e1, e2) = e3
% 159.45/25.83  | | | 
% 159.45/25.83  | | | REF_CLOSE: (12), (15), (18) are inconsistent by sub-proof #522.
% 159.45/25.83  | | | 
% 159.45/25.83  | | Case 2:
% 159.45/25.83  | | | 
% 159.45/25.83  | | |   (19)  all_56_13 = e3 & op(e0, e2) = e3
% 159.45/25.83  | | | 
% 159.45/25.83  | | | REF_CLOSE: (3), (5), (19) are inconsistent by sub-proof #906.
% 159.45/25.83  | | | 
% 159.45/25.83  | | End of split
% 159.45/25.83  | | 
% 159.45/25.83  | End of split
% 159.45/25.83  | 
% 159.45/25.83  End of proof
% 159.45/25.83  
% 159.45/25.83  Sub-proof #522 shows that the following formulas are inconsistent:
% 159.45/25.83  ----------------------------------------------------------------
% 159.45/25.83    (1)  all_56_7 = e3 & op(e1, e2) = e3
% 159.45/25.83    (2)  all_56_7 = e0
% 159.45/25.83    (3)   ~ (e3 = e0)
% 159.45/25.83  
% 159.45/25.83  Begin of proof
% 159.45/25.83  | 
% 159.45/25.83  | ALPHA: (1) implies:
% 159.45/25.83  |   (4)  all_56_7 = e3
% 159.45/25.83  | 
% 159.45/25.83  | COMBINE_EQS: (2), (4) imply:
% 159.45/25.83  |   (5)  e3 = e0
% 159.45/25.83  | 
% 159.45/25.83  | SIMP: (5) implies:
% 159.45/25.83  |   (6)  e3 = e0
% 159.45/25.83  | 
% 159.45/25.83  | REDUCE: (3), (6) imply:
% 159.45/25.83  |   (7)  $false
% 159.45/25.83  | 
% 159.45/25.83  | CLOSE: (7) is inconsistent.
% 159.45/25.83  | 
% 159.45/25.83  End of proof
% 159.45/25.83  
% 159.45/25.83  Sub-proof #523 shows that the following formulas are inconsistent:
% 159.45/25.83  ----------------------------------------------------------------
% 159.45/25.83    (1)  all_56_7 = e2
% 159.45/25.83    (2)  all_56_7 = e0
% 159.45/25.83    (3)   ~ (e2 = e0)
% 159.45/25.83  
% 159.45/25.83  Begin of proof
% 159.45/25.83  | 
% 159.45/25.83  | COMBINE_EQS: (1), (2) imply:
% 159.45/25.83  |   (4)  e2 = e0
% 159.45/25.83  | 
% 159.45/25.83  | SIMP: (4) implies:
% 159.45/25.83  |   (5)  e2 = e0
% 159.45/25.83  | 
% 159.45/25.83  | REDUCE: (3), (5) imply:
% 159.45/25.83  |   (6)  $false
% 159.45/25.83  | 
% 159.45/25.83  | CLOSE: (6) is inconsistent.
% 159.45/25.83  | 
% 159.45/25.83  End of proof
% 159.45/25.83  
% 159.45/25.83  Sub-proof #524 shows that the following formulas are inconsistent:
% 159.45/25.83  ----------------------------------------------------------------
% 159.45/25.83    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 159.45/25.83         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 159.45/25.83    (2)  op(e1, e1) = e3
% 159.45/25.83    (3)   ~ (e3 = e2)
% 159.45/25.83    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.83    (5)  all_56_10 = e3
% 159.45/25.83    (6)  all_56_14 = e1
% 159.45/25.83    (7)  all_56_1 = e2
% 159.45/25.83    (8)  op(e3, e3) = e3
% 159.45/25.83    (9)  op(e2, e0) = e3
% 159.45/25.83    (10)  all_56_9 = e0 & op(e3, e0) = e0
% 159.45/25.83    (11)  op(e2, e2) = e0
% 159.45/25.83    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.45/25.83          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.45/25.83    (13)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.45/25.83          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.45/25.83    (14)   ~ (e1 = e0)
% 159.45/25.83    (15)   ~ (e2 = e1)
% 159.45/25.83    (16)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.45/25.83          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.45/25.83    (17)   ~ (e3 = e1)
% 159.45/25.83    (18)   ~ (e2 = e0)
% 159.45/25.83    (19)   ~ (e3 = e0)
% 159.45/25.83  
% 159.45/25.83  Begin of proof
% 159.45/25.83  | 
% 159.45/25.83  | ALPHA: (10) implies:
% 159.45/25.83  |   (20)  all_56_9 = e0
% 159.45/25.83  | 
% 159.45/25.83  | BETA: splitting (1) gives:
% 159.45/25.83  | 
% 159.45/25.83  | Case 1:
% 159.45/25.83  | | 
% 159.45/25.83  | |   (21)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 159.45/25.83  | |           e0)
% 159.45/25.83  | | 
% 159.45/25.83  | | BETA: splitting (21) gives:
% 159.45/25.83  | | 
% 159.45/25.83  | | Case 1:
% 159.45/25.83  | | | 
% 159.45/25.83  | | |   (22)  all_56_4 = e0 & op(e3, e1) = e0
% 159.45/25.83  | | | 
% 159.45/25.83  | | | ALPHA: (22) implies:
% 159.45/25.83  | | |   (23)  all_56_4 = e0
% 159.45/25.83  | | | 
% 159.45/25.83  | | | REF_CLOSE: (4), (7), (8), (12), (14), (15), (17), (20), (23) are
% 159.45/25.83  | | |            inconsistent by sub-proof #525.
% 159.45/25.83  | | | 
% 159.45/25.83  | | Case 2:
% 159.45/25.83  | | | 
% 159.45/25.83  | | |   (24)  all_56_5 = e0 & op(e2, e1) = e0
% 159.45/25.83  | | | 
% 159.45/25.83  | | | ALPHA: (24) implies:
% 159.45/25.83  | | |   (25)  all_56_5 = e0
% 159.45/25.83  | | | 
% 159.45/25.83  | | | REF_CLOSE: (3), (4), (5), (9), (11), (13), (14), (15), (16), (17), (18),
% 159.45/25.83  | | |            (25) are inconsistent by sub-proof #552.
% 159.45/25.83  | | | 
% 159.45/25.83  | | End of split
% 159.45/25.83  | | 
% 159.45/25.83  | Case 2:
% 159.45/25.83  | | 
% 159.45/25.83  | |   (26)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 159.45/25.83  | |           e0)
% 159.45/25.83  | | 
% 159.45/25.83  | | BETA: splitting (26) gives:
% 159.45/25.83  | | 
% 159.45/25.83  | | Case 1:
% 159.45/25.83  | | | 
% 159.45/25.83  | | |   (27)  all_56_8 = e0 & op(e1, e1) = e0
% 159.45/25.83  | | | 
% 159.45/25.83  | | | ALPHA: (27) implies:
% 159.45/25.83  | | |   (28)  op(e1, e1) = e0
% 159.45/25.83  | | | 
% 159.45/25.83  | | | REF_CLOSE: (2), (4), (19), (28) are inconsistent by sub-proof #912.
% 159.45/25.83  | | | 
% 159.45/25.83  | | Case 2:
% 159.45/25.83  | | | 
% 159.45/25.83  | | |   (29)  all_56_14 = e0 & op(e0, e1) = e0
% 159.45/25.83  | | | 
% 159.45/25.83  | | | ALPHA: (29) implies:
% 159.45/25.83  | | |   (30)  all_56_14 = e0
% 159.45/25.83  | | | 
% 159.45/25.83  | | | REF_CLOSE: (6), (14), (30) are inconsistent by sub-proof #542.
% 159.45/25.83  | | | 
% 159.45/25.83  | | End of split
% 159.45/25.83  | | 
% 159.45/25.83  | End of split
% 159.45/25.83  | 
% 159.45/25.83  End of proof
% 159.45/25.83  
% 159.45/25.83  Sub-proof #525 shows that the following formulas are inconsistent:
% 159.45/25.83  ----------------------------------------------------------------
% 159.45/25.83    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.83    (2)  all_56_1 = e2
% 159.45/25.83    (3)  op(e3, e3) = e3
% 159.45/25.83    (4)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.45/25.83         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.45/25.83    (5)  all_56_9 = e0
% 159.45/25.83    (6)   ~ (e1 = e0)
% 159.45/25.83    (7)   ~ (e2 = e1)
% 159.45/25.83    (8)   ~ (e3 = e1)
% 159.45/25.83    (9)  all_56_4 = e0
% 159.45/25.83  
% 159.45/25.83  Begin of proof
% 159.45/25.83  | 
% 159.45/25.83  | BETA: splitting (4) gives:
% 159.45/25.83  | 
% 159.45/25.83  | Case 1:
% 159.45/25.83  | | 
% 159.45/25.83  | |   (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 159.45/25.83  | |           e1)
% 159.45/25.83  | | 
% 159.45/25.83  | | REF_CLOSE: (1), (2), (3), (7), (8), (10) are inconsistent by sub-proof #635.
% 159.45/25.83  | | 
% 159.45/25.83  | Case 2:
% 159.45/25.83  | | 
% 159.45/25.83  | |   (11)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 159.45/25.83  | |           e1)
% 159.45/25.83  | | 
% 159.45/25.83  | | BETA: splitting (11) gives:
% 159.45/25.83  | | 
% 159.45/25.83  | | Case 1:
% 159.45/25.83  | | | 
% 159.45/25.83  | | |   (12)  all_56_4 = e1 & op(e3, e1) = e1
% 159.45/25.83  | | | 
% 159.45/25.83  | | | ALPHA: (12) implies:
% 159.45/25.83  | | |   (13)  all_56_4 = e1
% 159.45/25.83  | | | 
% 159.45/25.83  | | | REF_CLOSE: (6), (9), (13) are inconsistent by sub-proof #526.
% 159.45/25.83  | | | 
% 159.45/25.83  | | Case 2:
% 159.45/25.83  | | | 
% 159.45/25.83  | | |   (14)  all_56_9 = e1 & op(e3, e0) = e1
% 159.45/25.83  | | | 
% 159.45/25.83  | | | ALPHA: (14) implies:
% 159.45/25.83  | | |   (15)  all_56_9 = e1
% 159.45/25.83  | | | 
% 159.45/25.84  | | | REF_CLOSE: (5), (6), (15) are inconsistent by sub-proof #756.
% 159.45/25.84  | | | 
% 159.45/25.84  | | End of split
% 159.45/25.84  | | 
% 159.45/25.84  | End of split
% 159.45/25.84  | 
% 159.45/25.84  End of proof
% 159.45/25.84  
% 159.45/25.84  Sub-proof #526 shows that the following formulas are inconsistent:
% 159.45/25.84  ----------------------------------------------------------------
% 159.45/25.84    (1)  all_56_4 = e1
% 159.45/25.84    (2)  all_56_4 = e0
% 159.45/25.84    (3)   ~ (e1 = e0)
% 159.45/25.84  
% 159.45/25.84  Begin of proof
% 159.45/25.84  | 
% 159.45/25.84  | COMBINE_EQS: (1), (2) imply:
% 159.45/25.84  |   (4)  e1 = e0
% 159.45/25.84  | 
% 159.45/25.84  | SIMP: (4) implies:
% 159.45/25.84  |   (5)  e1 = e0
% 159.45/25.84  | 
% 159.45/25.84  | REDUCE: (3), (5) imply:
% 159.45/25.84  |   (6)  $false
% 159.45/25.84  | 
% 159.45/25.84  | CLOSE: (6) is inconsistent.
% 159.45/25.84  | 
% 159.45/25.84  End of proof
% 159.45/25.84  
% 159.45/25.84  Sub-proof #527 shows that the following formulas are inconsistent:
% 159.45/25.84  ----------------------------------------------------------------
% 159.45/25.84    (1)  all_56_6 = e2
% 159.45/25.84    (2)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1)
% 159.45/25.84    (3)   ~ (e1 = e0)
% 159.45/25.84    (4)   ~ (e2 = e1)
% 159.45/25.84    (5)  all_56_7 = e0
% 159.45/25.84  
% 159.45/25.84  Begin of proof
% 159.45/25.84  | 
% 159.45/25.84  | BETA: splitting (2) gives:
% 159.45/25.84  | 
% 159.45/25.84  | Case 1:
% 159.45/25.84  | | 
% 159.45/25.84  | |   (6)  all_56_6 = e1 & op(e1, e3) = e1
% 159.45/25.84  | | 
% 159.45/25.84  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #772.
% 159.45/25.84  | | 
% 159.45/25.84  | Case 2:
% 159.45/25.84  | | 
% 159.45/25.84  | |   (7)  all_56_7 = e1 & op(e1, e2) = e1
% 159.45/25.84  | | 
% 159.45/25.84  | | ALPHA: (7) implies:
% 159.45/25.84  | |   (8)  all_56_7 = e1
% 159.45/25.84  | | 
% 159.45/25.84  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #560.
% 159.45/25.84  | | 
% 159.45/25.84  | End of split
% 159.45/25.84  | 
% 159.45/25.84  End of proof
% 159.45/25.84  
% 159.45/25.84  Sub-proof #528 shows that the following formulas are inconsistent:
% 159.45/25.84  ----------------------------------------------------------------
% 159.45/25.84    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.45/25.84         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.45/25.84    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.45/25.84         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.45/25.84    (3)   ~ (all_52_12 = e2)
% 159.45/25.84    (4)  op(e0, e0) = e2
% 159.45/25.84    (5)  all_56_10 = e2 & op(e2, e0) = e2
% 159.45/25.84    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.45/25.84         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.45/25.84    (7)   ~ (e3 = e2)
% 159.45/25.84    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.84    (9)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.45/25.84             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.45/25.84               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.45/25.84               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.45/25.84    (10)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 159.45/25.84          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.45/25.84    (11)  op(e3, e3) = e3
% 159.45/25.84    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.45/25.84          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.45/25.84    (13)   ~ (e1 = e0)
% 159.45/25.84    (14)   ~ (e2 = e1)
% 159.45/25.84    (15)  op(e3, e0) = all_52_12
% 159.45/25.84    (16)   ~ (e3 = e1)
% 159.45/25.84    (17)   ~ (e2 = e0)
% 159.45/25.84    (18)   ~ (e3 = e0)
% 159.45/25.84  
% 159.45/25.84  Begin of proof
% 159.45/25.84  | 
% 159.45/25.84  | ALPHA: (5) implies:
% 159.45/25.84  |   (19)  all_56_10 = e2
% 159.45/25.84  | 
% 159.45/25.84  | BETA: splitting (2) gives:
% 159.45/25.84  | 
% 159.45/25.84  | Case 1:
% 159.45/25.84  | | 
% 159.45/25.84  | |   (20)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) =
% 159.45/25.84  | |           e2)
% 159.45/25.84  | | 
% 159.45/25.84  | | BETA: splitting (20) gives:
% 159.45/25.84  | | 
% 159.45/25.84  | | Case 1:
% 159.45/25.84  | | | 
% 159.45/25.84  | | |   (21)  all_56_0 = e2 & op(e3, e3) = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | ALPHA: (21) implies:
% 159.45/25.84  | | |   (22)  op(e3, e3) = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | REF_CLOSE: (7), (8), (11), (22) are inconsistent by sub-proof #958.
% 159.45/25.84  | | | 
% 159.45/25.84  | | Case 2:
% 159.45/25.84  | | | 
% 159.45/25.84  | | |   (23)  all_56_1 = e2 & op(e3, e2) = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | ALPHA: (23) implies:
% 159.45/25.84  | | |   (24)  all_56_1 = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | BETA: splitting (10) gives:
% 159.45/25.84  | | | 
% 159.45/25.84  | | | Case 1:
% 159.45/25.84  | | | | 
% 159.45/25.84  | | | |   (25)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0)
% 159.45/25.84  | | | |           = e3)
% 159.45/25.84  | | | | 
% 159.45/25.84  | | | | BETA: splitting (25) gives:
% 159.45/25.84  | | | | 
% 159.45/25.84  | | | | Case 1:
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | |   (26)  all_56_9 = e3 & op(e3, e0) = e3
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | | ALPHA: (26) implies:
% 159.45/25.84  | | | | |   (27)  all_56_9 = e3
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | | REF_CLOSE: (6), (8), (11), (12), (13), (14), (16), (17), (18), (24),
% 159.45/25.84  | | | | |            (27) are inconsistent by sub-proof #633.
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | Case 2:
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | |   (28)  all_56_10 = e3 & op(e2, e0) = e3
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | | REF_CLOSE: (7), (19), (28) are inconsistent by sub-proof #894.
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | End of split
% 159.45/25.84  | | | | 
% 159.45/25.84  | | | Case 2:
% 159.45/25.84  | | | | 
% 159.45/25.84  | | | |   (29)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0,
% 159.45/25.84  | | | |             e0) = e3)
% 159.45/25.84  | | | | 
% 159.45/25.84  | | | | BETA: splitting (29) gives:
% 159.45/25.84  | | | | 
% 159.45/25.84  | | | | Case 1:
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | |   (30)  all_56_11 = e3 & op(e1, e0) = e3
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | | ALPHA: (30) implies:
% 159.45/25.84  | | | | |   (31)  all_56_11 = e3
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | | REF_CLOSE: (1), (4), (8), (9), (13), (14), (16), (17), (18), (19),
% 159.45/25.84  | | | | |            (31) are inconsistent by sub-proof #753.
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | Case 2:
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | |   (32)  all_56_15 = e3 & op(e0, e0) = e3
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | | ALPHA: (32) implies:
% 159.45/25.84  | | | | |   (33)  op(e0, e0) = e3
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | | REF_CLOSE: (4), (7), (8), (33) are inconsistent by sub-proof #878.
% 159.45/25.84  | | | | | 
% 159.45/25.84  | | | | End of split
% 159.45/25.84  | | | | 
% 159.45/25.84  | | | End of split
% 159.45/25.84  | | | 
% 159.45/25.84  | | End of split
% 159.45/25.84  | | 
% 159.45/25.84  | Case 2:
% 159.45/25.84  | | 
% 159.45/25.84  | |   (34)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 159.45/25.84  | |           e2)
% 159.45/25.84  | | 
% 159.45/25.84  | | BETA: splitting (34) gives:
% 159.45/25.84  | | 
% 159.45/25.84  | | Case 1:
% 159.45/25.84  | | | 
% 159.45/25.84  | | |   (35)  all_56_4 = e2 & op(e3, e1) = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | ALPHA: (35) implies:
% 159.45/25.84  | | |   (36)  all_56_4 = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 159.45/25.84  | | |            (16), (17), (18), (19), (36) are inconsistent by sub-proof
% 159.45/25.84  | | |            #752.
% 159.45/25.84  | | | 
% 159.45/25.84  | | Case 2:
% 159.45/25.84  | | | 
% 159.45/25.84  | | |   (37)  all_56_9 = e2 & op(e3, e0) = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | REF_CLOSE: (3), (8), (15), (37) are inconsistent by sub-proof #880.
% 159.45/25.84  | | | 
% 159.45/25.84  | | End of split
% 159.45/25.84  | | 
% 159.45/25.84  | End of split
% 159.45/25.84  | 
% 159.45/25.84  End of proof
% 159.45/25.84  
% 159.45/25.84  Sub-proof #529 shows that the following formulas are inconsistent:
% 159.45/25.84  ----------------------------------------------------------------
% 159.45/25.84    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.45/25.84         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.45/25.84    (2)  all_56_2 = e0
% 159.45/25.84    (3)   ~ (e3 = e2)
% 159.45/25.84    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.84    (5)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.45/25.84         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.45/25.84    (6)  all_56_5 = e1
% 159.45/25.84    (7)  op(e3, e3) = e3
% 159.45/25.84    (8)  op(e2, e2) = e0
% 159.45/25.84    (9)   ~ (e1 = e0)
% 159.45/25.84    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.45/25.84          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.45/25.84    (11)   ~ (e2 = e1)
% 159.45/25.84    (12)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.45/25.84          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.45/25.84    (13)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.45/25.84          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.45/25.84    (14)  all_56_6 = e1
% 159.45/25.84    (15)   ~ (e3 = e1)
% 159.45/25.84    (16)   ~ (e2 = e0)
% 159.45/25.84    (17)   ~ (e3 = e0)
% 159.45/25.84  
% 159.45/25.84  Begin of proof
% 159.45/25.84  | 
% 159.45/25.84  | BETA: splitting (1) gives:
% 159.45/25.84  | 
% 159.45/25.84  | Case 1:
% 159.45/25.84  | | 
% 159.45/25.84  | |   (18)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 159.45/25.84  | |           e2)
% 159.45/25.84  | | 
% 159.45/25.84  | | REF_CLOSE: (2), (3), (4), (7), (16), (18) are inconsistent by sub-proof
% 159.45/25.84  | |            #534.
% 159.45/25.84  | | 
% 159.45/25.84  | Case 2:
% 159.45/25.84  | | 
% 159.45/25.84  | |   (19)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 159.45/25.84  | |           e2)
% 159.45/25.84  | | 
% 159.45/25.84  | | BETA: splitting (19) gives:
% 159.45/25.84  | | 
% 159.45/25.84  | | Case 1:
% 159.45/25.84  | | | 
% 159.45/25.84  | | |   (20)  all_56_6 = e2 & op(e1, e3) = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | ALPHA: (20) implies:
% 159.45/25.84  | | |   (21)  all_56_6 = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | REF_CLOSE: (11), (14), (21) are inconsistent by sub-proof #533.
% 159.45/25.84  | | | 
% 159.45/25.84  | | Case 2:
% 159.45/25.84  | | | 
% 159.45/25.84  | | |   (22)  all_56_12 = e2 & op(e0, e3) = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | ALPHA: (22) implies:
% 159.45/25.84  | | |   (23)  all_56_12 = e2
% 159.45/25.84  | | | 
% 159.45/25.84  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.45/25.84  | | |            (15), (16), (17), (23) are inconsistent by sub-proof #530.
% 159.45/25.84  | | | 
% 159.45/25.84  | | End of split
% 159.45/25.84  | | 
% 159.45/25.84  | End of split
% 159.45/25.84  | 
% 159.45/25.84  End of proof
% 159.45/25.84  
% 159.45/25.84  Sub-proof #530 shows that the following formulas are inconsistent:
% 159.45/25.84  ----------------------------------------------------------------
% 159.45/25.84    (1)   ~ (e3 = e2)
% 159.45/25.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.84    (3)  all_56_12 = e2
% 159.45/25.84    (4)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 159.45/25.84         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 159.45/25.84    (5)  all_56_5 = e1
% 159.45/25.84    (6)  op(e3, e3) = e3
% 159.45/25.84    (7)  op(e2, e2) = e0
% 159.45/25.84    (8)   ~ (e1 = e0)
% 159.45/25.84    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.45/25.84         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.45/25.84    (10)   ~ (e2 = e1)
% 159.45/25.84    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.45/25.84          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.45/25.84    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.45/25.84          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.45/25.84    (13)   ~ (e3 = e1)
% 159.45/25.84    (14)   ~ (e2 = e0)
% 159.45/25.84    (15)   ~ (e3 = e0)
% 159.45/25.84  
% 159.45/25.84  Begin of proof
% 159.45/25.84  | 
% 159.45/25.84  | BETA: splitting (4) gives:
% 159.45/25.84  | 
% 159.45/25.84  | Case 1:
% 159.45/25.84  | | 
% 159.45/25.84  | |   (16)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 159.45/25.84  | |           e3)
% 159.45/25.84  | | 
% 159.45/25.84  | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (12), (13), (14), (15), (16)
% 159.45/25.84  | |            are inconsistent by sub-proof #532.
% 159.45/25.84  | | 
% 159.45/25.84  | Case 2:
% 159.45/25.84  | | 
% 159.45/25.84  | |   (17)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 159.45/25.84  | |           e3)
% 159.45/25.84  | | 
% 159.45/25.84  | | BETA: splitting (17) gives:
% 159.45/25.84  | | 
% 159.45/25.84  | | Case 1:
% 159.45/25.84  | | | 
% 159.45/25.84  | | |   (18)  all_56_5 = e3 & op(e2, e1) = e3
% 159.45/25.84  | | | 
% 159.45/25.84  | | | ALPHA: (18) implies:
% 159.45/25.84  | | |   (19)  all_56_5 = e3
% 159.45/25.84  | | | 
% 159.45/25.84  | | | REF_CLOSE: (5), (13), (19) are inconsistent by sub-proof #531.
% 159.45/25.84  | | | 
% 159.45/25.84  | | Case 2:
% 159.45/25.84  | | | 
% 159.45/25.84  | | |   (20)  all_56_10 = e3 & op(e2, e0) = e3
% 159.45/25.84  | | | 
% 159.45/25.84  | | | ALPHA: (20) implies:
% 159.45/25.84  | | |   (21)  op(e2, e0) = e3
% 159.45/25.84  | | | 
% 159.45/25.84  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.45/25.84  | | |            (14), (15), (21) are inconsistent by sub-proof #547.
% 159.45/25.84  | | | 
% 159.45/25.84  | | End of split
% 159.45/25.84  | | 
% 159.45/25.84  | End of split
% 159.45/25.84  | 
% 159.45/25.84  End of proof
% 159.45/25.84  
% 159.45/25.84  Sub-proof #531 shows that the following formulas are inconsistent:
% 159.45/25.84  ----------------------------------------------------------------
% 159.45/25.84    (1)  all_56_5 = e3
% 159.45/25.84    (2)  all_56_5 = e1
% 159.45/25.84    (3)   ~ (e3 = e1)
% 159.45/25.84  
% 159.45/25.84  Begin of proof
% 159.45/25.84  | 
% 159.45/25.84  | COMBINE_EQS: (1), (2) imply:
% 159.45/25.84  |   (4)  e3 = e1
% 159.45/25.84  | 
% 159.45/25.84  | SIMP: (4) implies:
% 159.45/25.84  |   (5)  e3 = e1
% 159.45/25.84  | 
% 159.45/25.84  | REDUCE: (3), (5) imply:
% 159.45/25.84  |   (6)  $false
% 159.45/25.84  | 
% 159.45/25.84  | CLOSE: (6) is inconsistent.
% 159.45/25.84  | 
% 159.45/25.84  End of proof
% 159.45/25.84  
% 159.45/25.84  Sub-proof #532 shows that the following formulas are inconsistent:
% 159.45/25.84  ----------------------------------------------------------------
% 159.45/25.84    (1)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 159.45/25.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.84    (3)  all_56_12 = e2
% 159.45/25.84    (4)  op(e3, e3) = e3
% 159.45/25.84    (5)  op(e2, e2) = e0
% 159.45/25.84    (6)   ~ (e1 = e0)
% 159.45/25.84    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.45/25.84         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.45/25.84    (8)   ~ (e2 = e1)
% 159.45/25.84    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.45/25.84         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.45/25.84    (10)   ~ (e3 = e1)
% 159.45/25.84    (11)   ~ (e2 = e0)
% 159.45/25.84    (12)   ~ (e3 = e0)
% 159.45/25.84  
% 159.45/25.84  Begin of proof
% 159.45/25.84  | 
% 159.45/25.84  | BETA: splitting (1) gives:
% 159.45/25.84  | 
% 159.45/25.84  | Case 1:
% 159.45/25.84  | | 
% 159.45/25.84  | |   (13)  all_56_2 = e3 & op(e2, e3) = e3
% 159.45/25.84  | | 
% 159.45/25.84  | | ALPHA: (13) implies:
% 159.45/25.84  | |   (14)  all_56_2 = e3
% 159.45/25.84  | | 
% 159.45/25.84  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14) are
% 159.45/25.84  | |            inconsistent by sub-proof #766.
% 159.45/25.84  | | 
% 159.45/25.84  | Case 2:
% 159.45/25.84  | | 
% 159.45/25.84  | |   (15)  all_56_3 = e3 & op(e2, e2) = e3
% 159.45/25.84  | | 
% 159.45/25.84  | | ALPHA: (15) implies:
% 159.45/25.84  | |   (16)  op(e2, e2) = e3
% 159.45/25.84  | | 
% 159.45/25.84  | | REF_CLOSE: (2), (5), (12), (16) are inconsistent by sub-proof #945.
% 159.45/25.84  | | 
% 159.45/25.84  | End of split
% 159.45/25.84  | 
% 159.45/25.84  End of proof
% 159.45/25.84  
% 159.45/25.84  Sub-proof #533 shows that the following formulas are inconsistent:
% 159.45/25.84  ----------------------------------------------------------------
% 159.45/25.84    (1)  all_56_6 = e2
% 159.45/25.84    (2)  all_56_6 = e1
% 159.45/25.84    (3)   ~ (e2 = e1)
% 159.45/25.84  
% 159.45/25.84  Begin of proof
% 159.45/25.84  | 
% 159.45/25.84  | COMBINE_EQS: (1), (2) imply:
% 159.45/25.84  |   (4)  e2 = e1
% 159.45/25.84  | 
% 159.45/25.84  | SIMP: (4) implies:
% 159.45/25.84  |   (5)  e2 = e1
% 159.45/25.84  | 
% 159.45/25.84  | REDUCE: (3), (5) imply:
% 159.45/25.84  |   (6)  $false
% 159.45/25.84  | 
% 159.45/25.84  | CLOSE: (6) is inconsistent.
% 159.45/25.84  | 
% 159.45/25.84  End of proof
% 159.45/25.84  
% 159.45/25.84  Sub-proof #534 shows that the following formulas are inconsistent:
% 159.45/25.84  ----------------------------------------------------------------
% 159.45/25.84    (1)  all_56_2 = e0
% 159.45/25.84    (2)   ~ (e3 = e2)
% 159.45/25.84    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.84    (4)  op(e3, e3) = e3
% 159.45/25.84    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 159.45/25.84    (6)   ~ (e2 = e0)
% 159.45/25.84  
% 159.45/25.84  Begin of proof
% 159.45/25.84  | 
% 159.45/25.84  | BETA: splitting (5) gives:
% 159.45/25.84  | 
% 159.45/25.85  | Case 1:
% 159.45/25.85  | | 
% 159.45/25.85  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 159.45/25.85  | | 
% 159.45/25.85  | | ALPHA: (7) implies:
% 159.45/25.85  | |   (8)  op(e3, e3) = e2
% 159.45/25.85  | | 
% 159.45/25.85  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #958.
% 159.45/25.85  | | 
% 159.45/25.85  | Case 2:
% 159.45/25.85  | | 
% 159.45/25.85  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 159.45/25.85  | | 
% 159.45/25.85  | | ALPHA: (9) implies:
% 159.45/25.85  | |   (10)  all_56_2 = e2
% 159.45/25.85  | | 
% 159.45/25.85  | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #602.
% 159.45/25.85  | | 
% 159.45/25.85  | End of split
% 159.45/25.85  | 
% 159.45/25.85  End of proof
% 159.45/25.85  
% 159.45/25.85  Sub-proof #535 shows that the following formulas are inconsistent:
% 159.45/25.85  ----------------------------------------------------------------
% 159.45/25.85    (1)  all_56_2 = e0
% 159.45/25.85    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.45/25.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.45/25.85    (3)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 159.45/25.85    (4)  op(e2, e2) = e0
% 159.45/25.85    (5)   ~ (e1 = e0)
% 159.45/25.85  
% 159.45/25.85  Begin of proof
% 159.45/25.85  | 
% 159.45/25.85  | BETA: splitting (3) gives:
% 159.45/25.85  | 
% 159.45/25.85  | Case 1:
% 159.45/25.85  | | 
% 159.45/25.85  | |   (6)  all_56_2 = e1 & op(e2, e3) = e1
% 159.45/25.85  | | 
% 159.45/25.85  | | ALPHA: (6) implies:
% 159.45/25.85  | |   (7)  all_56_2 = e1
% 159.45/25.85  | | 
% 159.45/25.85  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #733.
% 159.45/25.85  | | 
% 159.45/25.85  | Case 2:
% 159.45/25.85  | | 
% 159.45/25.85  | |   (8)  all_56_3 = e1 & op(e2, e2) = e1
% 159.45/25.85  | | 
% 159.45/25.85  | | ALPHA: (8) implies:
% 159.45/25.85  | |   (9)  op(e2, e2) = e1
% 159.45/25.85  | | 
% 159.55/25.85  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #960.
% 159.55/25.85  | | 
% 159.55/25.85  | End of split
% 159.55/25.85  | 
% 159.55/25.85  End of proof
% 159.55/25.85  
% 159.55/25.85  Sub-proof #536 shows that the following formulas are inconsistent:
% 159.55/25.85  ----------------------------------------------------------------
% 159.55/25.85    (1)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 159.55/25.85    (2)  op(e2, e3) = all_57_0
% 159.55/25.85    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.85    (4)  op(e2, e2) = e0
% 159.55/25.85    (5)   ~ (all_57_0 = e2)
% 159.55/25.85    (6)   ~ (e2 = e0)
% 159.55/25.85  
% 159.55/25.85  Begin of proof
% 159.55/25.85  | 
% 159.55/25.85  | BETA: splitting (1) gives:
% 159.55/25.85  | 
% 159.55/25.85  | Case 1:
% 159.55/25.85  | | 
% 159.55/25.85  | |   (7)  all_56_2 = e2 & op(e2, e3) = e2
% 159.55/25.85  | | 
% 159.55/25.85  | | ALPHA: (7) implies:
% 159.55/25.85  | |   (8)  op(e2, e3) = e2
% 159.55/25.85  | | 
% 159.55/25.85  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #783.
% 159.55/25.85  | | 
% 159.55/25.85  | Case 2:
% 159.55/25.85  | | 
% 159.55/25.85  | |   (9)  all_56_3 = e2 & op(e2, e2) = e2
% 159.55/25.85  | | 
% 159.55/25.85  | | ALPHA: (9) implies:
% 159.55/25.85  | |   (10)  op(e2, e2) = e2
% 159.55/25.85  | | 
% 159.55/25.85  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #942.
% 159.55/25.85  | | 
% 159.55/25.85  | End of split
% 159.55/25.85  | 
% 159.55/25.85  End of proof
% 159.55/25.85  
% 159.55/25.85  Sub-proof #537 shows that the following formulas are inconsistent:
% 159.55/25.85  ----------------------------------------------------------------
% 159.55/25.85    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.55/25.85           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.55/25.85           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 159.55/25.85           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 159.55/25.85           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.55/25.85    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.85    (3)  op(e3, e1) = all_52_8
% 159.55/25.85    (4)  op(e2, e2) = e0
% 159.55/25.85    (5)   ~ (e1 = e0)
% 159.55/25.85    (6)   ~ (all_52_8 = e3)
% 159.55/25.85  
% 159.55/25.85  Begin of proof
% 159.55/25.85  | 
% 159.55/25.85  | BETA: splitting (1) gives:
% 159.55/25.85  | 
% 159.55/25.85  | Case 1:
% 159.55/25.85  | | 
% 159.55/25.85  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 159.55/25.85  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.55/25.85  | |          e1) = e3 & $i(all_57_10)
% 159.55/25.85  | | 
% 159.55/25.85  | | ALPHA: (7) implies:
% 159.55/25.85  | |   (8)  op(e3, e1) = e3
% 159.55/25.85  | | 
% 159.55/25.85  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #982.
% 159.55/25.85  | | 
% 159.55/25.85  | Case 2:
% 159.55/25.85  | | 
% 159.55/25.85  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 159.55/25.85  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 159.55/25.85  | |        all_57_14 & $i(all_57_14)
% 159.55/25.85  | | 
% 159.55/25.85  | | ALPHA: (9) implies:
% 159.55/25.85  | |   (10)  op(e2, e2) = e1
% 159.55/25.85  | | 
% 159.55/25.85  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #960.
% 159.55/25.85  | | 
% 159.55/25.85  | End of split
% 159.55/25.85  | 
% 159.55/25.85  End of proof
% 159.55/25.85  
% 159.55/25.85  Sub-proof #538 shows that the following formulas are inconsistent:
% 159.55/25.85  ----------------------------------------------------------------
% 159.55/25.85    (1)   ~ (all_52_4 = e3)
% 159.55/25.85    (2)   ~ (e3 = e2)
% 159.55/25.85    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.85    (4)  op(e3, e3) = e3
% 159.55/25.85    (5)  op(e3, e2) = all_52_4
% 159.55/25.85    (6)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.55/25.85           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.55/25.85           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 159.55/25.85           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 159.55/25.85           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.55/25.85  
% 159.55/25.85  Begin of proof
% 159.55/25.85  | 
% 159.55/25.85  | BETA: splitting (6) gives:
% 159.55/25.85  | 
% 159.55/25.85  | Case 1:
% 159.55/25.85  | | 
% 159.55/25.85  | |   (7)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 159.55/25.85  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 159.55/25.85  | |          e1) = e3 & $i(all_57_10)
% 159.55/25.85  | | 
% 159.55/25.85  | | ALPHA: (7) implies:
% 159.55/25.85  | |   (8)  op(e3, e2) = e3
% 159.55/25.85  | | 
% 159.55/25.85  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #998.
% 159.55/25.85  | | 
% 159.55/25.85  | Case 2:
% 159.55/25.85  | | 
% 159.55/25.85  | |   (9)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 159.55/25.85  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.55/25.85  | |          e1) = e2 & $i(all_57_12)
% 159.55/25.85  | | 
% 159.55/25.85  | | ALPHA: (9) implies:
% 159.55/25.85  | |   (10)  op(e3, e3) = e2
% 159.55/25.85  | | 
% 159.55/25.85  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #958.
% 159.55/25.85  | | 
% 159.55/25.85  | End of split
% 159.55/25.85  | 
% 159.55/25.85  End of proof
% 159.55/25.85  
% 159.55/25.85  Sub-proof #539 shows that the following formulas are inconsistent:
% 159.55/25.85  ----------------------------------------------------------------
% 159.55/25.85    (1)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.55/25.85           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.55/25.85           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 159.55/25.85           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.55/25.85           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.55/25.85    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.85    (3)  op(e2, e3) = all_57_0
% 159.55/25.85    (4)   ~ (all_57_0 = e2)
% 159.55/25.85  
% 159.55/25.85  Begin of proof
% 159.55/25.85  | 
% 159.55/25.85  | BETA: splitting (1) gives:
% 159.55/25.85  | 
% 159.55/25.85  | Case 1:
% 159.55/25.85  | | 
% 159.55/25.85  | |   (5)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 159.55/25.85  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 159.55/25.85  | |          e0) = e2 & $i(all_57_12)
% 159.55/25.85  | | 
% 159.55/25.85  | | ALPHA: (5) implies:
% 159.55/25.85  | |   (6)  op(e2, e3) = e2
% 159.55/25.85  | | 
% 159.55/25.85  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #783.
% 159.55/25.85  | | 
% 159.55/25.85  | Case 2:
% 159.55/25.85  | | 
% 159.55/25.85  | |   (7)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 159.55/25.85  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 159.55/25.85  | |          e2) = e3 & $i(all_57_10)
% 159.55/25.85  | | 
% 159.55/25.85  | | ALPHA: (7) implies:
% 159.55/25.85  | |   (8)  op(e2, e3) = e2
% 159.55/25.85  | | 
% 159.55/25.85  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #783.
% 159.55/25.85  | | 
% 159.55/25.85  | End of split
% 159.55/25.85  | 
% 159.55/25.85  End of proof
% 159.55/25.85  
% 159.55/25.85  Sub-proof #540 shows that the following formulas are inconsistent:
% 159.55/25.85  ----------------------------------------------------------------
% 159.55/25.85    (1)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.55/25.85           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.55/25.85           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 159.55/25.85           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.55/25.85           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.55/25.85           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 159.55/25.85           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.55/25.85           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 159.55/25.85           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 159.55/25.85             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.55/25.85    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.85    (3)  op(e2, e3) = all_57_0
% 159.55/25.85    (4)   ~ (all_57_0 = e2)
% 159.55/25.85  
% 159.55/25.85  Begin of proof
% 159.55/25.85  | 
% 159.55/25.85  | BETA: splitting (1) gives:
% 159.55/25.85  | 
% 159.55/25.85  | Case 1:
% 159.55/25.85  | | 
% 159.55/25.85  | |   (5)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 159.55/25.85  | |          & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 159.55/25.85  | |          = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.55/25.85  | |          all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.55/25.85  | |          op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.55/25.85  | |          $i(all_57_10))
% 159.55/25.85  | | 
% 159.55/25.85  | | BETA: splitting (5) gives:
% 159.55/25.85  | | 
% 159.55/25.85  | | Case 1:
% 159.55/25.85  | | | 
% 159.55/25.85  | | |   (6)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 =
% 159.55/25.85  | | |          e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.55/25.85  | | |        op(e2, e2) = all_57_12 & $i(all_57_12)
% 159.55/25.85  | | | 
% 159.55/25.85  | | | ALPHA: (6) implies:
% 159.55/25.85  | | |   (7)  op(e2, e3) = e2
% 159.55/25.85  | | | 
% 159.55/25.85  | | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #783.
% 159.55/25.85  | | | 
% 159.55/25.85  | | Case 2:
% 159.55/25.85  | | | 
% 159.55/25.85  | | |   (8)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.55/25.85  | | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2
% 159.55/25.85  | | |        & op(e2, e2) = e3 & $i(all_57_10)
% 159.55/25.85  | | | 
% 159.55/25.85  | | | ALPHA: (8) implies:
% 159.55/25.85  | | |   (9)  op(e2, e3) = e2
% 159.55/25.85  | | | 
% 159.55/25.85  | | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #783.
% 159.55/25.85  | | | 
% 159.55/25.85  | | End of split
% 159.55/25.85  | | 
% 159.55/25.85  | Case 2:
% 159.55/25.85  | | 
% 159.55/25.85  | |   (10)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.55/25.85  | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 159.55/25.85  | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 =
% 159.55/25.85  | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 159.55/25.85  | |           & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.55/25.85  | |           $i(all_57_10))
% 159.55/25.85  | | 
% 159.55/25.85  | | BETA: splitting (10) gives:
% 159.55/25.85  | | 
% 159.55/25.85  | | Case 1:
% 159.55/25.85  | | | 
% 159.55/25.85  | | |   (11)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.55/25.85  | | |           e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 159.55/25.85  | | |         & op(e1, e1) = e2 & $i(all_57_12)
% 159.55/25.85  | | | 
% 159.55/25.85  | | | ALPHA: (11) implies:
% 159.55/25.85  | | |   (12)  op(e2, e3) = e2
% 159.55/25.85  | | | 
% 159.55/25.85  | | | REF_CLOSE: (2), (3), (4), (12) are inconsistent by sub-proof #783.
% 159.55/25.85  | | | 
% 159.55/25.85  | | Case 2:
% 159.55/25.85  | | | 
% 159.55/25.85  | | |   (13)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.55/25.85  | | |           e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2
% 159.55/25.85  | | |         & op(e2, e2) = e3 & $i(all_57_10)
% 159.55/25.85  | | | 
% 159.55/25.85  | | | ALPHA: (13) implies:
% 159.55/25.85  | | |   (14)  op(e2, e3) = e2
% 159.55/25.85  | | | 
% 159.55/25.85  | | | REF_CLOSE: (2), (3), (4), (14) are inconsistent by sub-proof #783.
% 159.55/25.85  | | | 
% 159.55/25.85  | | End of split
% 159.55/25.85  | | 
% 159.55/25.85  | End of split
% 159.55/25.85  | 
% 159.55/25.85  End of proof
% 159.55/25.85  
% 159.55/25.85  Sub-proof #541 shows that the following formulas are inconsistent:
% 159.55/25.85  ----------------------------------------------------------------
% 159.55/25.85    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.55/25.85         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.55/25.85    (2)  op(e2, e3) = all_57_0
% 159.55/25.85    (3)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.55/25.85         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.55/25.85    (4)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.55/25.85         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.55/25.85    (5)  all_56_1 = e0 & op(e3, e2) = e0
% 159.55/25.85    (6)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 159.55/25.85         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 159.55/25.85    (7)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.55/25.85         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.55/25.85    (8)   ~ (all_52_12 = e2)
% 159.55/25.85    (9)  op(e1, e1) = e3
% 159.55/25.85    (10)  op(e0, e0) = e2
% 159.55/25.85    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.55/25.85          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.55/25.85    (12)   ~ (e3 = e2)
% 159.55/25.85    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.85    (14)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.55/25.85              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 159.55/25.85                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.55/25.85                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.55/25.85    (15)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.55/25.85          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.55/25.85    (16)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.55/25.85          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.55/25.85    (17)  all_56_10 = e3
% 159.55/25.86    (18)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 159.55/25.86          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.55/25.86    (19)  op(e3, e3) = e3
% 159.55/25.86    (20)  op(e2, e0) = e3
% 159.55/25.86    (21)  op(e2, e2) = e0
% 159.55/25.86    (22)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.55/25.86          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.55/25.86    (23)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.55/25.86          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.55/25.86    (24)   ~ (e1 = e0)
% 159.55/25.86    (25)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.55/25.86          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.55/25.86    (26)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 159.55/25.86          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 159.55/25.86    (27)   ~ (e2 = e1)
% 159.55/25.86    (28)  op(e3, e0) = all_52_12
% 159.55/25.86    (29)  all_56_13 = e3
% 159.55/25.86    (30)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.55/25.86          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.55/25.86    (31)   ~ (all_57_0 = e2)
% 159.55/25.86    (32)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.55/25.86          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.55/25.86    (33)   ~ (e3 = e1)
% 159.55/25.86    (34)   ~ (e2 = e0)
% 159.55/25.86    (35)   ~ (e3 = e0)
% 159.55/25.86  
% 159.55/25.86  Begin of proof
% 159.55/25.86  | 
% 159.55/25.86  | ALPHA: (5) implies:
% 159.55/25.86  |   (36)  all_56_1 = e0
% 159.55/25.86  | 
% 159.55/25.86  | BETA: splitting (7) gives:
% 159.55/25.86  | 
% 159.55/25.86  | Case 1:
% 159.55/25.86  | | 
% 159.55/25.86  | |   (37)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) =
% 159.55/25.86  | |           e2)
% 159.55/25.86  | | 
% 159.55/25.86  | | BETA: splitting (37) gives:
% 159.55/25.86  | | 
% 159.55/25.86  | | Case 1:
% 159.55/25.86  | | | 
% 159.55/25.86  | | |   (38)  all_56_0 = e2 & op(e3, e3) = e2
% 159.55/25.86  | | | 
% 159.55/25.86  | | | ALPHA: (38) implies:
% 159.55/25.86  | | |   (39)  op(e3, e3) = e2
% 159.55/25.86  | | | 
% 159.55/25.86  | | | REF_CLOSE: (12), (13), (19), (39) are inconsistent by sub-proof #958.
% 159.55/25.86  | | | 
% 159.55/25.86  | | Case 2:
% 159.55/25.86  | | | 
% 159.55/25.86  | | |   (40)  all_56_1 = e2 & op(e3, e2) = e2
% 159.55/25.86  | | | 
% 159.55/25.86  | | | ALPHA: (40) implies:
% 159.55/25.86  | | |   (41)  all_56_1 = e2
% 159.55/25.86  | | | 
% 159.55/25.86  | | | COMBINE_EQS: (36), (41) imply:
% 159.55/25.86  | | |   (42)  e2 = e0
% 159.55/25.86  | | | 
% 159.55/25.86  | | | REDUCE: (34), (42) imply:
% 159.55/25.86  | | |   (43)  $false
% 159.55/25.86  | | | 
% 159.55/25.86  | | | CLOSE: (43) is inconsistent.
% 159.55/25.86  | | | 
% 159.55/25.86  | | End of split
% 159.55/25.86  | | 
% 159.55/25.86  | Case 2:
% 159.55/25.86  | | 
% 159.55/25.86  | |   (44)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 159.55/25.86  | |           e2)
% 159.55/25.86  | | 
% 159.55/25.86  | | BETA: splitting (44) gives:
% 159.55/25.86  | | 
% 159.55/25.86  | | Case 1:
% 159.55/25.86  | | | 
% 159.55/25.86  | | |   (45)  all_56_4 = e2 & op(e3, e1) = e2
% 159.55/25.86  | | | 
% 159.55/25.86  | | | ALPHA: (45) implies:
% 159.55/25.86  | | |   (46)  all_56_4 = e2
% 159.55/25.86  | | | 
% 159.55/25.86  | | | BETA: splitting (16) gives:
% 159.55/25.86  | | | 
% 159.55/25.86  | | | Case 1:
% 159.55/25.86  | | | | 
% 159.55/25.86  | | | |   (47)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2)
% 159.55/25.86  | | | |           = e2)
% 159.55/25.86  | | | | 
% 159.55/25.86  | | | | REF_CLOSE: (13), (21), (34), (36), (47) are inconsistent by sub-proof
% 159.55/25.86  | | | |            #941.
% 159.55/25.86  | | | | 
% 159.55/25.86  | | | Case 2:
% 159.55/25.86  | | | | 
% 159.55/25.86  | | | |   (48)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2)
% 159.55/25.86  | | | |           = e2)
% 159.55/25.86  | | | | 
% 159.55/25.86  | | | | BETA: splitting (48) gives:
% 159.55/25.86  | | | | 
% 159.55/25.86  | | | | Case 1:
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | |   (49)  all_56_7 = e2 & op(e1, e2) = e2
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | | ALPHA: (49) implies:
% 159.55/25.86  | | | | |   (50)  all_56_7 = e2
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | | BETA: splitting (22) gives:
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | | Case 1:
% 159.55/25.86  | | | | | | 
% 159.55/25.86  | | | | | |   (51)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3,
% 159.55/25.86  | | | | | |             e2) = e1)
% 159.55/25.86  | | | | | | 
% 159.55/25.86  | | | | | | REF_CLOSE: (13), (19), (24), (33), (36), (51) are inconsistent by
% 159.55/25.86  | | | | | |            sub-proof #561.
% 159.55/25.86  | | | | | | 
% 159.55/25.86  | | | | | Case 2:
% 159.55/25.86  | | | | | | 
% 159.55/25.86  | | | | | |   (52)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3,
% 159.55/25.86  | | | | | |             e0) = e1)
% 159.55/25.86  | | | | | | 
% 159.55/25.86  | | | | | | BETA: splitting (52) gives:
% 159.55/25.86  | | | | | | 
% 159.55/25.86  | | | | | | Case 1:
% 159.55/25.86  | | | | | | | 
% 159.55/25.86  | | | | | | |   (53)  all_56_4 = e1 & op(e3, e1) = e1
% 159.55/25.86  | | | | | | | 
% 159.55/25.86  | | | | | | | REF_CLOSE: (27), (46), (53) are inconsistent by sub-proof #956.
% 159.55/25.86  | | | | | | | 
% 159.55/25.86  | | | | | | Case 2:
% 159.55/25.86  | | | | | | | 
% 159.55/25.86  | | | | | | |   (54)  all_56_9 = e1 & op(e3, e0) = e1
% 159.55/25.86  | | | | | | | 
% 159.55/25.86  | | | | | | | ALPHA: (54) implies:
% 159.55/25.86  | | | | | | |   (55)  all_56_9 = e1
% 159.55/25.86  | | | | | | | 
% 159.55/25.86  | | | | | | | BETA: splitting (6) gives:
% 159.55/25.86  | | | | | | | 
% 159.55/25.86  | | | | | | | Case 1:
% 159.55/25.86  | | | | | | | | 
% 159.55/25.86  | | | | | | | |   (56)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 &
% 159.55/25.86  | | | | | | | |           op(e2, e1) = e0)
% 159.55/25.86  | | | | | | | | 
% 159.55/25.86  | | | | | | | | BETA: splitting (56) gives:
% 159.55/25.86  | | | | | | | | 
% 159.55/25.86  | | | | | | | | Case 1:
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | |   (57)  all_56_4 = e0 & op(e3, e1) = e0
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | ALPHA: (57) implies:
% 159.55/25.86  | | | | | | | | |   (58)  all_56_4 = e0
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | COMBINE_EQS: (46), (58) imply:
% 159.55/25.86  | | | | | | | | |   (59)  e2 = e0
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | COMBINE_EQS: (50), (59) imply:
% 159.55/25.86  | | | | | | | | |   (60)  all_56_7 = e0
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | REF_CLOSE: (3), (13), (21), (24), (29), (33), (36), (60) are
% 159.55/25.86  | | | | | | | | |            inconsistent by sub-proof #558.
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | Case 2:
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | |   (61)  all_56_5 = e0 & op(e2, e1) = e0
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | ALPHA: (61) implies:
% 159.55/25.86  | | | | | | | | |   (62)  all_56_5 = e0
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | REF_CLOSE: (12), (13), (17), (20), (21), (23), (24), (27),
% 159.55/25.86  | | | | | | | | |            (30), (33), (34), (62) are inconsistent by
% 159.55/25.86  | | | | | | | | |            sub-proof #552.
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | End of split
% 159.55/25.86  | | | | | | | | 
% 159.55/25.86  | | | | | | | Case 2:
% 159.55/25.86  | | | | | | | | 
% 159.55/25.86  | | | | | | | |   (63)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 &
% 159.55/25.86  | | | | | | | |           op(e0, e1) = e0)
% 159.55/25.86  | | | | | | | | 
% 159.55/25.86  | | | | | | | | BETA: splitting (63) gives:
% 159.55/25.86  | | | | | | | | 
% 159.55/25.86  | | | | | | | | Case 1:
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | |   (64)  all_56_8 = e0 & op(e1, e1) = e0
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | ALPHA: (64) implies:
% 159.55/25.86  | | | | | | | | |   (65)  op(e1, e1) = e0
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | REF_CLOSE: (9), (13), (35), (65) are inconsistent by sub-proof
% 159.55/25.86  | | | | | | | | |            #912.
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | Case 2:
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | |   (66)  all_56_14 = e0 & op(e0, e1) = e0
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | ALPHA: (66) implies:
% 159.55/25.86  | | | | | | | | |   (67)  all_56_14 = e0
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | BETA: splitting (14) gives:
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | Case 1:
% 159.55/25.86  | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | |   (68)  all_56_15 = e0 & op(e0, e0) = e0
% 159.55/25.86  | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | ALPHA: (68) implies:
% 159.55/25.86  | | | | | | | | | |   (69)  op(e0, e0) = e0
% 159.55/25.86  | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | REF_CLOSE: (10), (13), (34), (69) are inconsistent by
% 159.55/25.86  | | | | | | | | | |            sub-proof #979.
% 159.55/25.86  | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | Case 2:
% 159.55/25.86  | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | |   (70)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0
% 159.55/25.86  | | | | | | | | | |             & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 159.55/25.86  | | | | | | | | | |               e0) = e0)) & ((all_56_12 = e0 & op(e0, e3) =
% 159.55/25.86  | | | | | | | | | |             e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 159.55/25.86  | | | | | | | | | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 159.55/25.86  | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | ALPHA: (70) implies:
% 159.55/25.86  | | | | | | | | | |   (71)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0
% 159.55/25.86  | | | | | | | | | |           & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 159.55/25.86  | | | | | | | | | |           = e0)
% 159.55/25.86  | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | BETA: splitting (71) gives:
% 159.55/25.86  | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | Case 1:
% 159.55/25.86  | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | |   (72)  all_56_9 = e0 & op(e3, e0) = e0
% 159.55/25.86  | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | REF_CLOSE: (24), (55), (72) are inconsistent by sub-proof
% 159.55/25.86  | | | | | | | | | | |            #952.
% 159.55/25.86  | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | Case 2:
% 159.55/25.86  | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | |   (73)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 159.55/25.86  | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 159.55/25.86  | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | BETA: splitting (73) gives:
% 159.55/25.86  | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | Case 1:
% 159.55/25.86  | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | |   (74)  all_56_10 = e0 & op(e2, e0) = e0
% 159.55/25.86  | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | REF_CLOSE: (17), (35), (74) are inconsistent by sub-proof
% 159.55/25.86  | | | | | | | | | | | |            #551.
% 159.55/25.86  | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | Case 2:
% 159.55/25.86  | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | |   (75)  all_56_11 = e0 & op(e1, e0) = e0
% 159.55/25.86  | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | ALPHA: (75) implies:
% 159.55/25.86  | | | | | | | | | | | |   (76)  op(e1, e0) = e0
% 159.55/25.86  | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | BETA: splitting (26) gives:
% 159.55/25.86  | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | Case 1:
% 159.55/25.86  | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | |   (77)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 159.55/25.86  | | | | | | | | | | | | |           & op(e2, e1) = e1)
% 159.55/25.86  | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | BETA: splitting (77) gives:
% 159.55/25.86  | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | Case 1:
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | |   (78)  all_56_4 = e1 & op(e3, e1) = e1
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | | REF_CLOSE: (27), (46), (78) are inconsistent by sub-proof
% 159.55/25.86  | | | | | | | | | | | | | |            #956.
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | Case 2:
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | |   (79)  all_56_5 = e1 & op(e2, e1) = e1
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | | ALPHA: (79) implies:
% 159.55/25.86  | | | | | | | | | | | | | |   (80)  all_56_5 = e1
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (9), (12), (13), (15), (19), (20), (21),
% 159.55/25.86  | | | | | | | | | | | | | |            (24), (25), (27), (30), (31), (32), (33), (34),
% 159.55/25.86  | | | | | | | | | | | | | |            (35), (50), (76), (80) are inconsistent by
% 159.55/25.86  | | | | | | | | | | | | | |            sub-proof #543.
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | End of split
% 159.55/25.86  | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | Case 2:
% 159.55/25.86  | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | |   (81)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 159.55/25.86  | | | | | | | | | | | | |           e1 & op(e0, e1) = e1)
% 159.55/25.86  | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | BETA: splitting (81) gives:
% 159.55/25.86  | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | Case 1:
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | |   (82)  all_56_8 = e1 & op(e1, e1) = e1
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | | ALPHA: (82) implies:
% 159.55/25.86  | | | | | | | | | | | | | |   (83)  op(e1, e1) = e1
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | | REF_CLOSE: (9), (13), (33), (83) are inconsistent by
% 159.55/25.86  | | | | | | | | | | | | | |            sub-proof #1003.
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | Case 2:
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | |   (84)  all_56_14 = e1 & op(e0, e1) = e1
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | | ALPHA: (84) implies:
% 159.55/25.86  | | | | | | | | | | | | | |   (85)  all_56_14 = e1
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | | REF_CLOSE: (24), (67), (85) are inconsistent by sub-proof
% 159.55/25.86  | | | | | | | | | | | | | |            #542.
% 159.55/25.86  | | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | | End of split
% 159.55/25.86  | | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | | End of split
% 159.55/25.86  | | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | | End of split
% 159.55/25.86  | | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | | End of split
% 159.55/25.86  | | | | | | | | | | 
% 159.55/25.86  | | | | | | | | | End of split
% 159.55/25.86  | | | | | | | | | 
% 159.55/25.86  | | | | | | | | End of split
% 159.55/25.86  | | | | | | | | 
% 159.55/25.86  | | | | | | | End of split
% 159.55/25.86  | | | | | | | 
% 159.55/25.86  | | | | | | End of split
% 159.55/25.86  | | | | | | 
% 159.55/25.86  | | | | | End of split
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | Case 2:
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | |   (86)  all_56_13 = e2 & op(e0, e2) = e2
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | | ALPHA: (86) implies:
% 159.55/25.86  | | | | |   (87)  all_56_13 = e2
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | | COMBINE_EQS: (29), (87) imply:
% 159.55/25.86  | | | | |   (88)  e3 = e2
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | | COMBINE_EQS: (17), (88) imply:
% 159.55/25.86  | | | | |   (89)  all_56_10 = e2
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | | REF_CLOSE: (4), (10), (11), (12), (13), (14), (18), (19), (22), (24),
% 159.55/25.86  | | | | |            (27), (33), (34), (35), (46), (89) are inconsistent by
% 159.55/25.86  | | | | |            sub-proof #752.
% 159.55/25.86  | | | | | 
% 159.55/25.86  | | | | End of split
% 159.55/25.86  | | | | 
% 159.55/25.86  | | | End of split
% 159.55/25.86  | | | 
% 159.55/25.86  | | Case 2:
% 159.55/25.86  | | | 
% 159.55/25.86  | | |   (90)  all_56_9 = e2 & op(e3, e0) = e2
% 159.55/25.86  | | | 
% 159.55/25.86  | | | REF_CLOSE: (8), (13), (28), (90) are inconsistent by sub-proof #880.
% 159.55/25.86  | | | 
% 159.55/25.86  | | End of split
% 159.55/25.86  | | 
% 159.55/25.86  | End of split
% 159.55/25.86  | 
% 159.55/25.86  End of proof
% 159.55/25.86  
% 159.55/25.86  Sub-proof #542 shows that the following formulas are inconsistent:
% 159.55/25.86  ----------------------------------------------------------------
% 159.55/25.86    (1)  all_56_14 = e1
% 159.55/25.86    (2)  all_56_14 = e0
% 159.55/25.86    (3)   ~ (e1 = e0)
% 159.55/25.86  
% 159.55/25.86  Begin of proof
% 159.55/25.86  | 
% 159.55/25.86  | COMBINE_EQS: (1), (2) imply:
% 159.55/25.86  |   (4)  e1 = e0
% 159.55/25.86  | 
% 159.55/25.86  | SIMP: (4) implies:
% 159.55/25.86  |   (5)  e1 = e0
% 159.55/25.86  | 
% 159.55/25.86  | REDUCE: (3), (5) imply:
% 159.55/25.86  |   (6)  $false
% 159.55/25.86  | 
% 159.55/25.86  | CLOSE: (6) is inconsistent.
% 159.55/25.86  | 
% 159.55/25.86  End of proof
% 159.55/25.86  
% 159.55/25.86  Sub-proof #543 shows that the following formulas are inconsistent:
% 159.55/25.86  ----------------------------------------------------------------
% 159.55/25.86    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.55/25.86         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.55/25.86    (2)  op(e2, e3) = all_57_0
% 159.55/25.86    (3)  op(e1, e1) = e3
% 159.55/25.86    (4)   ~ (e3 = e2)
% 159.55/25.86    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.86    (6)  all_56_7 = e2
% 159.55/25.86    (7)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.55/25.86         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.55/25.86    (8)  op(e1, e0) = e0
% 159.55/25.86    (9)  all_56_5 = e1
% 159.55/25.86    (10)  op(e3, e3) = e3
% 159.55/25.86    (11)  op(e2, e0) = e3
% 159.55/25.86    (12)  op(e2, e2) = e0
% 159.55/25.86    (13)   ~ (e1 = e0)
% 159.55/25.86    (14)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.55/25.86          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.55/25.86    (15)   ~ (e2 = e1)
% 159.55/25.86    (16)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.55/25.86          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.55/25.86    (17)   ~ (all_57_0 = e2)
% 159.55/25.86    (18)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.55/25.86          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.55/25.86    (19)   ~ (e3 = e1)
% 159.55/25.86    (20)   ~ (e2 = e0)
% 159.55/25.86    (21)   ~ (e3 = e0)
% 159.55/25.86  
% 159.55/25.86  Begin of proof
% 159.55/25.86  | 
% 159.55/25.86  | BETA: splitting (7) gives:
% 159.55/25.86  | 
% 159.55/25.86  | Case 1:
% 159.55/25.86  | | 
% 159.55/25.86  | |   (22)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 159.55/25.86  | |           e1)
% 159.55/25.86  | | 
% 159.55/25.86  | | BETA: splitting (22) gives:
% 159.55/25.86  | | 
% 159.55/25.86  | | Case 1:
% 159.55/25.86  | | | 
% 159.55/25.86  | | |   (23)  all_56_6 = e1 & op(e1, e3) = e1
% 159.55/25.86  | | | 
% 159.55/25.86  | | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (11), (12), (13), (14), (15),
% 159.55/25.86  | | |            (16), (17), (18), (19), (20), (21), (23) are inconsistent by
% 159.55/25.86  | | |            sub-proof #546.
% 159.55/25.86  | | | 
% 159.55/25.86  | | Case 2:
% 159.55/25.86  | | | 
% 159.55/25.86  | | |   (24)  all_56_7 = e1 & op(e1, e2) = e1
% 159.55/25.86  | | | 
% 159.55/25.86  | | | REF_CLOSE: (6), (15), (24) are inconsistent by sub-proof #604.
% 159.55/25.86  | | | 
% 159.55/25.86  | | End of split
% 159.55/25.86  | | 
% 159.55/25.86  | Case 2:
% 159.55/25.86  | | 
% 159.55/25.86  | |   (25)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 159.55/25.86  | |           e1)
% 159.55/25.86  | | 
% 159.55/25.86  | | REF_CLOSE: (3), (5), (8), (13), (19), (25) are inconsistent by sub-proof
% 159.55/25.86  | |            #544.
% 159.55/25.86  | | 
% 159.55/25.86  | End of split
% 159.55/25.86  | 
% 159.55/25.86  End of proof
% 159.55/25.86  
% 159.55/25.86  Sub-proof #544 shows that the following formulas are inconsistent:
% 159.55/25.86  ----------------------------------------------------------------
% 159.55/25.86    (1)  op(e1, e1) = e3
% 159.55/25.86    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.86    (3)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.55/25.86    (4)  op(e1, e0) = e0
% 159.55/25.86    (5)   ~ (e1 = e0)
% 159.55/25.86    (6)   ~ (e3 = e1)
% 159.55/25.86  
% 159.55/25.86  Begin of proof
% 159.55/25.86  | 
% 159.55/25.86  | BETA: splitting (3) gives:
% 159.55/25.86  | 
% 159.55/25.86  | Case 1:
% 159.55/25.86  | | 
% 159.55/25.86  | |   (7)  all_56_8 = e1 & op(e1, e1) = e1
% 159.55/25.86  | | 
% 159.55/25.86  | | ALPHA: (7) implies:
% 159.55/25.86  | |   (8)  op(e1, e1) = e1
% 159.55/25.86  | | 
% 159.55/25.86  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #1003.
% 159.55/25.86  | | 
% 159.55/25.86  | Case 2:
% 159.55/25.86  | | 
% 159.55/25.86  | |   (9)  all_56_11 = e1 & op(e1, e0) = e1
% 159.55/25.86  | | 
% 159.55/25.86  | | ALPHA: (9) implies:
% 159.55/25.86  | |   (10)  op(e1, e0) = e1
% 159.55/25.86  | | 
% 159.55/25.86  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #545.
% 159.55/25.86  | | 
% 159.55/25.86  | End of split
% 159.55/25.86  | 
% 159.55/25.86  End of proof
% 159.55/25.86  
% 159.55/25.86  Sub-proof #545 shows that the following formulas are inconsistent:
% 159.55/25.86  ----------------------------------------------------------------
% 159.55/25.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.87    (2)  op(e1, e0) = e1
% 159.55/25.87    (3)  op(e1, e0) = e0
% 159.55/25.87    (4)   ~ (e1 = e0)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | GROUND_INST: instantiating (1) with e0, e1, e0, e1, simplifying with (2), (3)
% 159.55/25.87  |              gives:
% 159.55/25.87  |   (5)  e1 = e0
% 159.55/25.87  | 
% 159.55/25.87  | REDUCE: (4), (5) imply:
% 159.55/25.87  |   (6)  $false
% 159.55/25.87  | 
% 159.55/25.87  | CLOSE: (6) is inconsistent.
% 159.55/25.87  | 
% 159.55/25.87  End of proof
% 159.55/25.87  
% 159.55/25.87  Sub-proof #546 shows that the following formulas are inconsistent:
% 159.55/25.87  ----------------------------------------------------------------
% 159.55/25.87    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.55/25.87         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.55/25.87    (2)  op(e2, e3) = all_57_0
% 159.55/25.87    (3)   ~ (e3 = e2)
% 159.55/25.87    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.87    (5)  all_56_5 = e1
% 159.55/25.87    (6)  all_56_6 = e1 & op(e1, e3) = e1
% 159.55/25.87    (7)  op(e3, e3) = e3
% 159.55/25.87    (8)  op(e2, e0) = e3
% 159.55/25.87    (9)  op(e2, e2) = e0
% 159.55/25.87    (10)   ~ (e1 = e0)
% 159.55/25.87    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.55/25.87          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.55/25.87    (12)   ~ (e2 = e1)
% 159.55/25.87    (13)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.55/25.87          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.55/25.87    (14)   ~ (all_57_0 = e2)
% 159.55/25.87    (15)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.55/25.87          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.55/25.87    (16)   ~ (e3 = e1)
% 159.55/25.87    (17)   ~ (e2 = e0)
% 159.55/25.87    (18)   ~ (e3 = e0)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | ALPHA: (6) implies:
% 159.55/25.87  |   (19)  all_56_6 = e1
% 159.55/25.87  | 
% 159.55/25.87  | BETA: splitting (1) gives:
% 159.55/25.87  | 
% 159.55/25.87  | Case 1:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (20)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 159.55/25.87  | |           e2)
% 159.55/25.87  | | 
% 159.55/25.87  | | REF_CLOSE: (2), (3), (4), (7), (14), (20) are inconsistent by sub-proof
% 159.55/25.87  | |            #550.
% 159.55/25.87  | | 
% 159.55/25.87  | Case 2:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (21)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 159.55/25.87  | |           e2)
% 159.55/25.87  | | 
% 159.55/25.87  | | BETA: splitting (21) gives:
% 159.55/25.87  | | 
% 159.55/25.87  | | Case 1:
% 159.55/25.87  | | | 
% 159.55/25.87  | | |   (22)  all_56_6 = e2 & op(e1, e3) = e2
% 159.55/25.87  | | | 
% 159.55/25.87  | | | ALPHA: (22) implies:
% 159.55/25.87  | | |   (23)  all_56_6 = e2
% 159.55/25.87  | | | 
% 159.55/25.87  | | | COMBINE_EQS: (19), (23) imply:
% 159.55/25.87  | | |   (24)  e2 = e1
% 159.55/25.87  | | | 
% 159.55/25.87  | | | REDUCE: (12), (24) imply:
% 159.55/25.87  | | |   (25)  $false
% 159.55/25.87  | | | 
% 159.55/25.87  | | | CLOSE: (25) is inconsistent.
% 159.55/25.87  | | | 
% 159.55/25.87  | | Case 2:
% 159.55/25.87  | | | 
% 159.55/25.87  | | |   (26)  all_56_12 = e2 & op(e0, e3) = e2
% 159.55/25.87  | | | 
% 159.55/25.87  | | | ALPHA: (26) implies:
% 159.55/25.87  | | |   (27)  all_56_12 = e2
% 159.55/25.87  | | | 
% 159.55/25.87  | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (15),
% 159.55/25.87  | | |            (16), (17), (18), (27) are inconsistent by sub-proof #547.
% 159.55/25.87  | | | 
% 159.55/25.87  | | End of split
% 159.55/25.87  | | 
% 159.55/25.87  | End of split
% 159.55/25.87  | 
% 159.55/25.87  End of proof
% 159.55/25.87  
% 159.55/25.87  Sub-proof #547 shows that the following formulas are inconsistent:
% 159.55/25.87  ----------------------------------------------------------------
% 159.55/25.87    (1)   ~ (e3 = e2)
% 159.55/25.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.87    (3)  all_56_12 = e2
% 159.55/25.87    (4)  all_56_5 = e1
% 159.55/25.87    (5)  op(e3, e3) = e3
% 159.55/25.87    (6)  op(e2, e0) = e3
% 159.55/25.87    (7)  op(e2, e2) = e0
% 159.55/25.87    (8)   ~ (e1 = e0)
% 159.55/25.87    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.55/25.87         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.55/25.87    (10)   ~ (e2 = e1)
% 159.55/25.87    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.55/25.87          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.55/25.87    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.55/25.87          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.55/25.87    (13)   ~ (e3 = e1)
% 159.55/25.87    (14)   ~ (e2 = e0)
% 159.55/25.87    (15)   ~ (e3 = e0)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | BETA: splitting (11) gives:
% 159.55/25.87  | 
% 159.55/25.87  | Case 1:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (16)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 159.55/25.87  | |           e2)
% 159.55/25.87  | | 
% 159.55/25.87  | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (12), (13), (14), (15), (16)
% 159.55/25.87  | |            are inconsistent by sub-proof #549.
% 159.55/25.87  | | 
% 159.55/25.87  | Case 2:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (17)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 159.55/25.87  | |           e2)
% 159.55/25.87  | | 
% 159.55/25.87  | | BETA: splitting (17) gives:
% 159.55/25.87  | | 
% 159.55/25.87  | | Case 1:
% 159.55/25.87  | | | 
% 159.55/25.87  | | |   (18)  all_56_5 = e2 & op(e2, e1) = e2
% 159.55/25.87  | | | 
% 159.55/25.87  | | | REF_CLOSE: (4), (10), (18) are inconsistent by sub-proof #548.
% 159.55/25.87  | | | 
% 159.55/25.87  | | Case 2:
% 159.55/25.87  | | | 
% 159.55/25.87  | | |   (19)  all_56_10 = e2 & op(e2, e0) = e2
% 159.55/25.87  | | | 
% 159.55/25.87  | | | ALPHA: (19) implies:
% 159.55/25.87  | | |   (20)  op(e2, e0) = e2
% 159.55/25.87  | | | 
% 159.55/25.87  | | | REF_CLOSE: (1), (2), (6), (20) are inconsistent by sub-proof #580.
% 159.55/25.87  | | | 
% 159.55/25.87  | | End of split
% 159.55/25.87  | | 
% 159.55/25.87  | End of split
% 159.55/25.87  | 
% 159.55/25.87  End of proof
% 159.55/25.87  
% 159.55/25.87  Sub-proof #548 shows that the following formulas are inconsistent:
% 159.55/25.87  ----------------------------------------------------------------
% 159.55/25.87    (1)  all_56_5 = e2 & op(e2, e1) = e2
% 159.55/25.87    (2)  all_56_5 = e1
% 159.55/25.87    (3)   ~ (e2 = e1)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | ALPHA: (1) implies:
% 159.55/25.87  |   (4)  all_56_5 = e2
% 159.55/25.87  | 
% 159.55/25.87  | COMBINE_EQS: (2), (4) imply:
% 159.55/25.87  |   (5)  e2 = e1
% 159.55/25.87  | 
% 159.55/25.87  | SIMP: (5) implies:
% 159.55/25.87  |   (6)  e2 = e1
% 159.55/25.87  | 
% 159.55/25.87  | REDUCE: (3), (6) imply:
% 159.55/25.87  |   (7)  $false
% 159.55/25.87  | 
% 159.55/25.87  | CLOSE: (7) is inconsistent.
% 159.55/25.87  | 
% 159.55/25.87  End of proof
% 159.55/25.87  
% 159.55/25.87  Sub-proof #549 shows that the following formulas are inconsistent:
% 159.55/25.87  ----------------------------------------------------------------
% 159.55/25.87    (1)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 159.55/25.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.87    (3)  all_56_12 = e2
% 159.55/25.87    (4)  op(e3, e3) = e3
% 159.55/25.87    (5)  op(e2, e2) = e0
% 159.55/25.87    (6)   ~ (e1 = e0)
% 159.55/25.87    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.55/25.87         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.55/25.87    (8)   ~ (e2 = e1)
% 159.55/25.87    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.55/25.87         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.55/25.87    (10)   ~ (e3 = e1)
% 159.55/25.87    (11)   ~ (e2 = e0)
% 159.55/25.87    (12)   ~ (e3 = e0)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | BETA: splitting (1) gives:
% 159.55/25.87  | 
% 159.55/25.87  | Case 1:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (13)  all_56_2 = e2 & op(e2, e3) = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | ALPHA: (13) implies:
% 159.55/25.87  | |   (14)  all_56_2 = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14) are
% 159.55/25.87  | |            inconsistent by sub-proof #597.
% 159.55/25.87  | | 
% 159.55/25.87  | Case 2:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (15)  all_56_3 = e2 & op(e2, e2) = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | ALPHA: (15) implies:
% 159.55/25.87  | |   (16)  op(e2, e2) = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | REF_CLOSE: (2), (5), (11), (16) are inconsistent by sub-proof #942.
% 159.55/25.87  | | 
% 159.55/25.87  | End of split
% 159.55/25.87  | 
% 159.55/25.87  End of proof
% 159.55/25.87  
% 159.55/25.87  Sub-proof #550 shows that the following formulas are inconsistent:
% 159.55/25.87  ----------------------------------------------------------------
% 159.55/25.87    (1)  op(e2, e3) = all_57_0
% 159.55/25.87    (2)   ~ (e3 = e2)
% 159.55/25.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.87    (4)  op(e3, e3) = e3
% 159.55/25.87    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 159.55/25.87    (6)   ~ (all_57_0 = e2)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | BETA: splitting (5) gives:
% 159.55/25.87  | 
% 159.55/25.87  | Case 1:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | ALPHA: (7) implies:
% 159.55/25.87  | |   (8)  op(e3, e3) = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #958.
% 159.55/25.87  | | 
% 159.55/25.87  | Case 2:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | ALPHA: (9) implies:
% 159.55/25.87  | |   (10)  op(e2, e3) = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #783.
% 159.55/25.87  | | 
% 159.55/25.87  | End of split
% 159.55/25.87  | 
% 159.55/25.87  End of proof
% 159.55/25.87  
% 159.55/25.87  Sub-proof #551 shows that the following formulas are inconsistent:
% 159.55/25.87  ----------------------------------------------------------------
% 159.55/25.87    (1)  all_56_10 = e0 & op(e2, e0) = e0
% 159.55/25.87    (2)  all_56_10 = e3
% 159.55/25.87    (3)   ~ (e3 = e0)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | ALPHA: (1) implies:
% 159.55/25.87  |   (4)  all_56_10 = e0
% 159.55/25.87  | 
% 159.55/25.87  | COMBINE_EQS: (2), (4) imply:
% 159.55/25.87  |   (5)  e3 = e0
% 159.55/25.87  | 
% 159.55/25.87  | REDUCE: (3), (5) imply:
% 159.55/25.87  |   (6)  $false
% 159.55/25.87  | 
% 159.55/25.87  | CLOSE: (6) is inconsistent.
% 159.55/25.87  | 
% 159.55/25.87  End of proof
% 159.55/25.87  
% 159.55/25.87  Sub-proof #552 shows that the following formulas are inconsistent:
% 159.55/25.87  ----------------------------------------------------------------
% 159.55/25.87    (1)   ~ (e3 = e2)
% 159.55/25.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.87    (3)  all_56_10 = e3
% 159.55/25.87    (4)  op(e2, e0) = e3
% 159.55/25.87    (5)  op(e2, e2) = e0
% 159.55/25.87    (6)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.55/25.87         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.55/25.87    (7)   ~ (e1 = e0)
% 159.55/25.87    (8)   ~ (e2 = e1)
% 159.55/25.87    (9)  all_56_5 = e0
% 159.55/25.87    (10)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.55/25.87          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.55/25.87    (11)   ~ (e3 = e1)
% 159.55/25.87    (12)   ~ (e2 = e0)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | BETA: splitting (10) gives:
% 159.55/25.87  | 
% 159.55/25.87  | Case 1:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (13)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 159.55/25.87  | |           e2)
% 159.55/25.87  | | 
% 159.55/25.87  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (12), (13) are
% 159.55/25.87  | |            inconsistent by sub-proof #554.
% 159.55/25.87  | | 
% 159.55/25.87  | Case 2:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (14)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 159.55/25.87  | |           e2)
% 159.55/25.87  | | 
% 159.55/25.87  | | BETA: splitting (14) gives:
% 159.55/25.87  | | 
% 159.55/25.87  | | Case 1:
% 159.55/25.87  | | | 
% 159.55/25.87  | | |   (15)  all_56_5 = e2 & op(e2, e1) = e2
% 159.55/25.87  | | | 
% 159.55/25.87  | | | REF_CLOSE: (9), (12), (15) are inconsistent by sub-proof #553.
% 159.55/25.87  | | | 
% 159.55/25.87  | | Case 2:
% 159.55/25.87  | | | 
% 159.55/25.87  | | |   (16)  all_56_10 = e2 & op(e2, e0) = e2
% 159.55/25.87  | | | 
% 159.55/25.87  | | | ALPHA: (16) implies:
% 159.55/25.87  | | |   (17)  op(e2, e0) = e2
% 159.55/25.87  | | | 
% 159.55/25.87  | | | REF_CLOSE: (1), (2), (4), (17) are inconsistent by sub-proof #580.
% 159.55/25.87  | | | 
% 159.55/25.87  | | End of split
% 159.55/25.87  | | 
% 159.55/25.87  | End of split
% 159.55/25.87  | 
% 159.55/25.87  End of proof
% 159.55/25.87  
% 159.55/25.87  Sub-proof #553 shows that the following formulas are inconsistent:
% 159.55/25.87  ----------------------------------------------------------------
% 159.55/25.87    (1)  all_56_5 = e2 & op(e2, e1) = e2
% 159.55/25.87    (2)  all_56_5 = e0
% 159.55/25.87    (3)   ~ (e2 = e0)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | ALPHA: (1) implies:
% 159.55/25.87  |   (4)  all_56_5 = e2
% 159.55/25.87  | 
% 159.55/25.87  | COMBINE_EQS: (2), (4) imply:
% 159.55/25.87  |   (5)  e2 = e0
% 159.55/25.87  | 
% 159.55/25.87  | SIMP: (5) implies:
% 159.55/25.87  |   (6)  e2 = e0
% 159.55/25.87  | 
% 159.55/25.87  | REDUCE: (3), (6) imply:
% 159.55/25.87  |   (7)  $false
% 159.55/25.87  | 
% 159.55/25.87  | CLOSE: (7) is inconsistent.
% 159.55/25.87  | 
% 159.55/25.87  End of proof
% 159.55/25.87  
% 159.55/25.87  Sub-proof #554 shows that the following formulas are inconsistent:
% 159.55/25.87  ----------------------------------------------------------------
% 159.55/25.87    (1)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 159.55/25.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.87    (3)  all_56_10 = e3
% 159.55/25.87    (4)  op(e2, e2) = e0
% 159.55/25.87    (5)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.55/25.87         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.55/25.87    (6)   ~ (e1 = e0)
% 159.55/25.87    (7)   ~ (e2 = e1)
% 159.55/25.87    (8)  all_56_5 = e0
% 159.55/25.87    (9)   ~ (e3 = e1)
% 159.55/25.87    (10)   ~ (e2 = e0)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | BETA: splitting (1) gives:
% 159.55/25.87  | 
% 159.55/25.87  | Case 1:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (11)  all_56_2 = e2 & op(e2, e3) = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | ALPHA: (11) implies:
% 159.55/25.87  | |   (12)  all_56_2 = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12) are inconsistent by
% 159.55/25.87  | |            sub-proof #555.
% 159.55/25.87  | | 
% 159.55/25.87  | Case 2:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (13)  all_56_3 = e2 & op(e2, e2) = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | ALPHA: (13) implies:
% 159.55/25.87  | |   (14)  op(e2, e2) = e2
% 159.55/25.87  | | 
% 159.55/25.87  | | REF_CLOSE: (2), (4), (10), (14) are inconsistent by sub-proof #942.
% 159.55/25.87  | | 
% 159.55/25.87  | End of split
% 159.55/25.87  | 
% 159.55/25.87  End of proof
% 159.55/25.87  
% 159.55/25.87  Sub-proof #555 shows that the following formulas are inconsistent:
% 159.55/25.87  ----------------------------------------------------------------
% 159.55/25.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.87    (2)  all_56_10 = e3
% 159.55/25.87    (3)  all_56_2 = e2
% 159.55/25.87    (4)  op(e2, e2) = e0
% 159.55/25.87    (5)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.55/25.87         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 159.55/25.87    (6)   ~ (e1 = e0)
% 159.55/25.87    (7)   ~ (e2 = e1)
% 159.55/25.87    (8)  all_56_5 = e0
% 159.55/25.87    (9)   ~ (e3 = e1)
% 159.55/25.87  
% 159.55/25.87  Begin of proof
% 159.55/25.87  | 
% 159.55/25.87  | BETA: splitting (5) gives:
% 159.55/25.87  | 
% 159.55/25.87  | Case 1:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (10)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 159.55/25.87  | |           e1)
% 159.55/25.87  | | 
% 159.55/25.87  | | REF_CLOSE: (1), (3), (4), (6), (7), (10) are inconsistent by sub-proof #557.
% 159.55/25.87  | | 
% 159.55/25.87  | Case 2:
% 159.55/25.87  | | 
% 159.55/25.87  | |   (11)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 159.55/25.87  | |           e1)
% 159.55/25.87  | | 
% 159.55/25.87  | | BETA: splitting (11) gives:
% 159.55/25.87  | | 
% 159.55/25.87  | | Case 1:
% 159.55/25.87  | | | 
% 159.55/25.87  | | |   (12)  all_56_5 = e1 & op(e2, e1) = e1
% 159.55/25.87  | | | 
% 159.55/25.87  | | | ALPHA: (12) implies:
% 159.55/25.87  | | |   (13)  all_56_5 = e1
% 159.55/25.87  | | | 
% 159.55/25.87  | | | COMBINE_EQS: (8), (13) imply:
% 159.55/25.87  | | |   (14)  e1 = e0
% 159.55/25.87  | | | 
% 159.55/25.87  | | | REDUCE: (6), (14) imply:
% 159.55/25.87  | | |   (15)  $false
% 159.55/25.87  | | | 
% 159.55/25.87  | | | CLOSE: (15) is inconsistent.
% 159.55/25.88  | | | 
% 159.55/25.88  | | Case 2:
% 159.55/25.88  | | | 
% 159.55/25.88  | | |   (16)  all_56_10 = e1 & op(e2, e0) = e1
% 159.55/25.88  | | | 
% 159.55/25.88  | | | REF_CLOSE: (2), (9), (16) are inconsistent by sub-proof #556.
% 159.55/25.88  | | | 
% 159.55/25.88  | | End of split
% 159.55/25.88  | | 
% 159.55/25.88  | End of split
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #556 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)  all_56_10 = e1 & op(e2, e0) = e1
% 159.55/25.88    (2)  all_56_10 = e3
% 159.55/25.88    (3)   ~ (e3 = e1)
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.88  | 
% 159.55/25.88  | ALPHA: (1) implies:
% 159.55/25.88  |   (4)  all_56_10 = e1
% 159.55/25.88  | 
% 159.55/25.88  | COMBINE_EQS: (2), (4) imply:
% 159.55/25.88  |   (5)  e3 = e1
% 159.55/25.88  | 
% 159.55/25.88  | REDUCE: (3), (5) imply:
% 159.55/25.88  |   (6)  $false
% 159.55/25.88  | 
% 159.55/25.88  | CLOSE: (6) is inconsistent.
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #557 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.88    (2)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 159.55/25.88    (3)  all_56_2 = e2
% 159.55/25.88    (4)  op(e2, e2) = e0
% 159.55/25.88    (5)   ~ (e1 = e0)
% 159.55/25.88    (6)   ~ (e2 = e1)
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.88  | 
% 159.55/25.88  | BETA: splitting (2) gives:
% 159.55/25.88  | 
% 159.55/25.88  | Case 1:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (7)  all_56_2 = e1 & op(e2, e3) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (7) implies:
% 159.55/25.88  | |   (8)  all_56_2 = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #600.
% 159.55/25.88  | | 
% 159.55/25.88  | Case 2:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (9)  all_56_3 = e1 & op(e2, e2) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (9) implies:
% 159.55/25.88  | |   (10)  op(e2, e2) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #960.
% 159.55/25.88  | | 
% 159.55/25.88  | End of split
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #558 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.55/25.88         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.55/25.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.88    (3)  op(e2, e2) = e0
% 159.55/25.88    (4)  all_56_1 = e0
% 159.55/25.88    (5)   ~ (e1 = e0)
% 159.55/25.88    (6)  all_56_13 = e3
% 159.55/25.88    (7)  all_56_7 = e0
% 159.55/25.88    (8)   ~ (e3 = e1)
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.88  | 
% 159.55/25.88  | BETA: splitting (1) gives:
% 159.55/25.88  | 
% 159.55/25.88  | Case 1:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (9)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (2), (3), (4), (5), (9) are inconsistent by sub-proof #959.
% 159.55/25.88  | | 
% 159.55/25.88  | Case 2:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (10)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 159.55/25.88  | |           e1)
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (5), (6), (7), (8), (10) are inconsistent by sub-proof #559.
% 159.55/25.88  | | 
% 159.55/25.88  | End of split
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #559 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.55/25.88    (2)   ~ (e1 = e0)
% 159.55/25.88    (3)  all_56_13 = e3
% 159.55/25.88    (4)  all_56_7 = e0
% 159.55/25.88    (5)   ~ (e3 = e1)
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.88  | 
% 159.55/25.88  | BETA: splitting (1) gives:
% 159.55/25.88  | 
% 159.55/25.88  | Case 1:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (6)  all_56_7 = e1 & op(e1, e2) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (6) implies:
% 159.55/25.88  | |   (7)  all_56_7 = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #560.
% 159.55/25.88  | | 
% 159.55/25.88  | Case 2:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (8)  all_56_13 = e1 & op(e0, e2) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #728.
% 159.55/25.88  | | 
% 159.55/25.88  | End of split
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #560 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)  all_56_7 = e1
% 159.55/25.88    (2)  all_56_7 = e0
% 159.55/25.88    (3)   ~ (e1 = e0)
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.88  | 
% 159.55/25.88  | COMBINE_EQS: (1), (2) imply:
% 159.55/25.88  |   (4)  e1 = e0
% 159.55/25.88  | 
% 159.55/25.88  | SIMP: (4) implies:
% 159.55/25.88  |   (5)  e1 = e0
% 159.55/25.88  | 
% 159.55/25.88  | REDUCE: (3), (5) imply:
% 159.55/25.88  |   (6)  $false
% 159.55/25.88  | 
% 159.55/25.88  | CLOSE: (6) is inconsistent.
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #561 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.88    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1)
% 159.55/25.88    (3)  op(e3, e3) = e3
% 159.55/25.88    (4)  all_56_1 = e0
% 159.55/25.88    (5)   ~ (e1 = e0)
% 159.55/25.88    (6)   ~ (e3 = e1)
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.88  | 
% 159.55/25.88  | BETA: splitting (2) gives:
% 159.55/25.88  | 
% 159.55/25.88  | Case 1:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (7) implies:
% 159.55/25.88  | |   (8)  op(e3, e3) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #995.
% 159.55/25.88  | | 
% 159.55/25.88  | Case 2:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (9)  all_56_1 = e1 & op(e3, e2) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (9) implies:
% 159.55/25.88  | |   (10)  all_56_1 = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #961.
% 159.55/25.88  | | 
% 159.55/25.88  | End of split
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #562 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)   ~ (e3 = e2)
% 159.55/25.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.88    (3)   ~ (all_52_12 = e3)
% 159.55/25.88    (4)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.55/25.88           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.55/25.88           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 159.55/25.88           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 159.55/25.88    (5)  op(e2, e0) = e3
% 159.55/25.88    (6)  op(e3, e0) = all_52_12
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.88  | 
% 159.55/25.88  | BETA: splitting (4) gives:
% 159.55/25.88  | 
% 159.55/25.88  | Case 1:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (7)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 159.55/25.88  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.55/25.88  | |          e0) = e2 & $i(all_57_12)
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (7) implies:
% 159.55/25.88  | |   (8)  op(e2, e0) = e2
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #580.
% 159.55/25.88  | | 
% 159.55/25.88  | Case 2:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (9)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 159.55/25.88  | |        op(e3, e0) = e3
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (9) implies:
% 159.55/25.88  | |   (10)  op(e3, e0) = e3
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #976.
% 159.55/25.88  | | 
% 159.55/25.88  | End of split
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #563 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)  op(e1, e1) = e3
% 159.55/25.88    (2)  op(e0, e0) = e2
% 159.55/25.88    (3)   ~ (e3 = e2)
% 159.55/25.88    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.88    (5)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 159.55/25.88           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.55/25.88           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 159.55/25.88           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.55/25.88           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.55/25.88    (6)   ~ (e2 = e1)
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.88  | 
% 159.55/25.88  | BETA: splitting (5) gives:
% 159.55/25.88  | 
% 159.55/25.88  | Case 1:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (7)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.55/25.88  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.55/25.88  | |          e1) = e2 & $i(all_57_12)
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (7) implies:
% 159.55/25.88  | |   (8)  op(e1, e1) = e2
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #646.
% 159.55/25.88  | | 
% 159.55/25.88  | Case 2:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (9)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 159.55/25.88  | |        & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.55/25.88  | |          e0) = e1 & $i(all_57_14)
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (9) implies:
% 159.55/25.88  | |   (10)  op(e0, e0) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #875.
% 159.55/25.88  | | 
% 159.55/25.88  | End of split
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #564 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)  op(e1, e1) = e3
% 159.55/25.88    (2)  op(e0, e0) = e2
% 159.55/25.88    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.88    (4)   ~ (all_52_12 = e3)
% 159.55/25.88    (5)   ~ (e2 = e1)
% 159.55/25.88    (6)  op(e3, e0) = all_52_12
% 159.55/25.88    (7)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.55/25.88           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.55/25.88           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 159.55/25.88           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.55/25.88           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 159.55/25.88           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.88  | 
% 159.55/25.88  | BETA: splitting (7) gives:
% 159.55/25.88  | 
% 159.55/25.88  | Case 1:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (8)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 159.55/25.88  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.55/25.88  | |          e0) = e1 & $i(all_57_14)
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (8) implies:
% 159.55/25.88  | |   (9)  op(e0, e0) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #875.
% 159.55/25.88  | | 
% 159.55/25.88  | Case 2:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (10)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.55/25.88  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 159.55/25.88  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 159.55/25.88  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (1), (3), (4), (6), (10) are inconsistent by sub-proof #578.
% 159.55/25.88  | | 
% 159.55/25.88  | End of split
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #565 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.55/25.88           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.55/25.88           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 159.55/25.88           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 159.55/25.88           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.55/25.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.88    (3)  op(e3, e1) = all_52_8
% 159.55/25.88    (4)  op(e2, e2) = e2
% 159.55/25.88    (5)   ~ (e2 = e1)
% 159.55/25.88    (6)   ~ (all_52_8 = e3)
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.88  | 
% 159.55/25.88  | BETA: splitting (1) gives:
% 159.55/25.88  | 
% 159.55/25.88  | Case 1:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 159.55/25.88  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.55/25.88  | |          e1) = e3 & $i(all_57_10)
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (7) implies:
% 159.55/25.88  | |   (8)  op(e3, e1) = e3
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #982.
% 159.55/25.88  | | 
% 159.55/25.88  | Case 2:
% 159.55/25.88  | | 
% 159.55/25.88  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 159.55/25.88  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 159.55/25.88  | |        all_57_14 & $i(all_57_14)
% 159.55/25.88  | | 
% 159.55/25.88  | | ALPHA: (9) implies:
% 159.55/25.88  | |   (10)  op(e2, e2) = e1
% 159.55/25.88  | | 
% 159.55/25.88  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #993.
% 159.55/25.88  | | 
% 159.55/25.88  | End of split
% 159.55/25.88  | 
% 159.55/25.88  End of proof
% 159.55/25.88  
% 159.55/25.88  Sub-proof #566 shows that the following formulas are inconsistent:
% 159.55/25.88  ----------------------------------------------------------------
% 159.55/25.88    (1)   ~ (all_52_1 = e2)
% 159.55/25.88    (2)   ~ (all_52_4 = e3)
% 159.55/25.88    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.88    (4)  op(e2, e3) = all_52_1
% 159.55/25.88    (5)  op(e3, e2) = all_52_4
% 159.55/25.88    (6)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.55/25.88           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.55/25.88           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 159.55/25.88           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.55/25.88           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.55/25.88           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 159.55/25.88         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.55/25.88           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.55/25.88           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 159.55/25.88           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 159.55/25.88           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.55/25.88    (7)  op(e2, e1) = all_52_9
% 159.55/25.88    (8)   ~ (all_52_9 = e2)
% 159.55/25.88  
% 159.55/25.88  Begin of proof
% 159.55/25.89  | 
% 159.55/25.89  | BETA: splitting (6) gives:
% 159.55/25.89  | 
% 159.55/25.89  | Case 1:
% 159.55/25.89  | | 
% 159.55/25.89  | |   (9)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 159.55/25.89  | |          & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 159.55/25.89  | |          op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.55/25.89  | |          all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 159.55/25.89  | |          op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.55/25.89  | |          $i(all_57_10))
% 159.55/25.89  | | 
% 159.55/25.89  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #1004.
% 159.55/25.89  | | 
% 159.55/25.89  | Case 2:
% 159.55/25.89  | | 
% 159.55/25.89  | |   (10)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.55/25.89  | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3
% 159.55/25.89  | |           &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.55/25.89  | |           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 159.55/25.89  | |           e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3,
% 159.55/25.89  | |             e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1)
% 159.55/25.89  | |           = e2 & $i(all_57_12))
% 159.55/25.89  | | 
% 159.55/25.89  | | BETA: splitting (10) gives:
% 159.55/25.89  | | 
% 159.55/25.89  | | Case 1:
% 159.55/25.89  | | | 
% 159.55/25.89  | | |   (11)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.55/25.89  | | |         op(e2, e2) = e2
% 159.55/25.89  | | | 
% 159.55/25.89  | | | ALPHA: (11) implies:
% 159.55/25.89  | | |   (12)  op(e2, e3) = e2
% 159.55/25.89  | | | 
% 159.55/25.89  | | | REF_CLOSE: (1), (3), (4), (12) are inconsistent by sub-proof #1007.
% 159.55/25.89  | | | 
% 159.55/25.89  | | Case 2:
% 159.55/25.89  | | | 
% 159.55/25.89  | | |   (13)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.55/25.89  | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) =
% 159.55/25.89  | | |           e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.55/25.89  | | |           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3,
% 159.55/25.89  | | |             e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.55/25.89  | | |             e1) = e2 & $i(all_57_12))
% 159.55/25.89  | | | 
% 159.55/25.89  | | | REF_CLOSE: (2), (3), (5), (7), (8), (13) are inconsistent by sub-proof
% 159.55/25.89  | | |            #750.
% 159.55/25.89  | | | 
% 159.55/25.89  | | End of split
% 159.55/25.89  | | 
% 159.55/25.89  | End of split
% 159.55/25.89  | 
% 159.55/25.89  End of proof
% 159.55/25.89  
% 159.55/25.89  Sub-proof #567 shows that the following formulas are inconsistent:
% 159.55/25.89  ----------------------------------------------------------------
% 159.55/25.89    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.55/25.89         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.55/25.89    (2)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.55/25.89         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 159.55/25.89    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.89    (4)  op(e2, e2) = e2
% 159.55/25.89    (5)  all_56_1 = e2
% 159.55/25.89    (6)   ~ (e1 = e0)
% 159.55/25.89    (7)   ~ (e2 = e1)
% 159.55/25.89    (8)  all_56_13 = e3
% 159.55/25.89    (9)   ~ (e3 = e1)
% 159.55/25.89    (10)   ~ (e2 = e0)
% 159.55/25.89    (11)   ~ (e3 = e0)
% 159.55/25.89  
% 159.55/25.89  Begin of proof
% 159.55/25.89  | 
% 159.55/25.89  | BETA: splitting (1) gives:
% 159.55/25.89  | 
% 159.55/25.89  | Case 1:
% 159.55/25.89  | | 
% 159.55/25.89  | |   (12)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 159.55/25.89  | |           e1)
% 159.55/25.89  | | 
% 159.55/25.89  | | BETA: splitting (12) gives:
% 159.55/25.89  | | 
% 159.55/25.89  | | Case 1:
% 159.55/25.89  | | | 
% 159.55/25.89  | | |   (13)  all_56_1 = e1 & op(e3, e2) = e1
% 159.55/25.89  | | | 
% 159.55/25.89  | | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #911.
% 159.55/25.89  | | | 
% 159.55/25.89  | | Case 2:
% 159.55/25.89  | | | 
% 159.55/25.89  | | |   (14)  all_56_3 = e1 & op(e2, e2) = e1
% 159.55/25.89  | | | 
% 159.55/25.89  | | | ALPHA: (14) implies:
% 159.55/25.89  | | |   (15)  op(e2, e2) = e1
% 159.55/25.89  | | | 
% 159.55/25.89  | | | REF_CLOSE: (3), (4), (7), (15) are inconsistent by sub-proof #993.
% 159.55/25.89  | | | 
% 159.55/25.89  | | End of split
% 159.55/25.89  | | 
% 159.55/25.89  | Case 2:
% 159.55/25.89  | | 
% 159.55/25.89  | |   (16)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 159.55/25.89  | |           e1)
% 159.55/25.89  | | 
% 159.55/25.89  | | BETA: splitting (16) gives:
% 159.55/25.89  | | 
% 159.55/25.89  | | Case 1:
% 159.55/25.89  | | | 
% 159.55/25.89  | | |   (17)  all_56_7 = e1 & op(e1, e2) = e1
% 159.55/25.89  | | | 
% 159.55/25.89  | | | ALPHA: (17) implies:
% 159.55/25.89  | | |   (18)  all_56_7 = e1
% 159.55/25.89  | | | 
% 159.55/25.89  | | | BETA: splitting (2) gives:
% 159.55/25.89  | | | 
% 159.55/25.89  | | | Case 1:
% 159.55/25.89  | | | | 
% 159.55/25.89  | | | |   (19)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2)
% 159.55/25.89  | | | |           = e0)
% 159.55/25.89  | | | | 
% 159.55/25.89  | | | | REF_CLOSE: (3), (4), (5), (10), (19) are inconsistent by sub-proof #568.
% 159.55/25.89  | | | | 
% 159.55/25.89  | | | Case 2:
% 159.55/25.89  | | | | 
% 159.55/25.89  | | | |   (20)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2)
% 159.55/25.89  | | | |           = e0)
% 159.55/25.89  | | | | 
% 159.55/25.89  | | | | BETA: splitting (20) gives:
% 159.55/25.89  | | | | 
% 159.55/25.89  | | | | Case 1:
% 159.55/25.89  | | | | | 
% 159.55/25.89  | | | | |   (21)  all_56_7 = e0 & op(e1, e2) = e0
% 159.55/25.89  | | | | | 
% 159.55/25.89  | | | | | ALPHA: (21) implies:
% 159.55/25.89  | | | | |   (22)  all_56_7 = e0
% 159.55/25.89  | | | | | 
% 159.55/25.89  | | | | | COMBINE_EQS: (18), (22) imply:
% 159.55/25.89  | | | | |   (23)  e1 = e0
% 159.55/25.89  | | | | | 
% 159.55/25.89  | | | | | REDUCE: (6), (23) imply:
% 159.55/25.89  | | | | |   (24)  $false
% 159.55/25.89  | | | | | 
% 159.55/25.89  | | | | | CLOSE: (24) is inconsistent.
% 159.55/25.89  | | | | | 
% 159.55/25.89  | | | | Case 2:
% 159.55/25.89  | | | | | 
% 159.55/25.89  | | | | |   (25)  all_56_13 = e0 & op(e0, e2) = e0
% 159.55/25.89  | | | | | 
% 159.55/25.89  | | | | | REF_CLOSE: (8), (11), (25) are inconsistent by sub-proof #679.
% 159.55/25.89  | | | | | 
% 159.55/25.89  | | | | End of split
% 159.55/25.89  | | | | 
% 159.55/25.89  | | | End of split
% 159.55/25.89  | | | 
% 159.55/25.89  | | Case 2:
% 159.55/25.89  | | | 
% 159.55/25.89  | | |   (26)  all_56_13 = e1 & op(e0, e2) = e1
% 159.55/25.89  | | | 
% 159.55/25.89  | | | ALPHA: (26) implies:
% 159.55/25.89  | | |   (27)  all_56_13 = e1
% 159.55/25.89  | | | 
% 159.55/25.89  | | | REF_CLOSE: (8), (9), (27) are inconsistent by sub-proof #936.
% 159.55/25.89  | | | 
% 159.55/25.89  | | End of split
% 159.55/25.89  | | 
% 159.55/25.89  | End of split
% 159.55/25.89  | 
% 159.55/25.89  End of proof
% 159.55/25.89  
% 159.55/25.89  Sub-proof #568 shows that the following formulas are inconsistent:
% 159.55/25.89  ----------------------------------------------------------------
% 159.55/25.89    (1)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 159.55/25.89    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.89    (3)  op(e2, e2) = e2
% 159.55/25.89    (4)  all_56_1 = e2
% 159.55/25.89    (5)   ~ (e2 = e0)
% 159.55/25.89  
% 159.55/25.89  Begin of proof
% 159.55/25.89  | 
% 159.55/25.89  | BETA: splitting (1) gives:
% 159.55/25.89  | 
% 159.55/25.89  | Case 1:
% 159.55/25.89  | | 
% 159.55/25.89  | |   (6)  all_56_1 = e0 & op(e3, e2) = e0
% 159.55/25.89  | | 
% 159.55/25.89  | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #910.
% 159.55/25.89  | | 
% 159.55/25.89  | Case 2:
% 159.55/25.89  | | 
% 159.55/25.89  | |   (7)  all_56_3 = e0 & op(e2, e2) = e0
% 159.55/25.89  | | 
% 159.55/25.89  | | ALPHA: (7) implies:
% 159.55/25.89  | |   (8)  op(e2, e2) = e0
% 159.55/25.89  | | 
% 159.55/25.89  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #942.
% 159.55/25.89  | | 
% 159.55/25.89  | End of split
% 159.55/25.89  | 
% 159.55/25.89  End of proof
% 159.55/25.89  
% 159.55/25.89  Sub-proof #569 shows that the following formulas are inconsistent:
% 159.55/25.89  ----------------------------------------------------------------
% 159.55/25.89    (1)  op(e1, e1) = e3
% 159.55/25.89    (2)  op(e0, e1) = all_52_11
% 159.55/25.89    (3)   ~ (e3 = e2)
% 159.55/25.89    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.89    (5)  op(e0, e3) = all_52_3
% 159.55/25.89    (6)   ~ (all_52_3 = e0)
% 159.55/25.89    (7)  op(e3, e3) = e3
% 159.55/25.89    (8)  op(e2, e0) = e3
% 159.55/25.89    (9)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.55/25.89           op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6
% 159.55/25.89               = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.55/25.89               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.55/25.89               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2,
% 159.55/25.89                 e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.55/25.89               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1)
% 159.55/25.89               = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.55/25.89               all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.55/25.89               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) =
% 159.55/25.89               e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.55/25.89               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2)
% 159.55/25.89               = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.55/25.89               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1, e1)
% 159.55/25.89               = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.55/25.89               all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.55/25.89               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) =
% 159.55/25.89               e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.55/25.89               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2)
% 159.55/25.89               = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.55/25.89               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1)
% 159.55/25.89               = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.55/25.89               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1)
% 159.55/25.89               = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 159.55/25.89             (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.55/25.89    (10)  op(e0, e2) = e3
% 159.55/25.89    (11)   ~ (all_52_11 = e0)
% 159.55/25.89    (12)   ~ (e3 = e1)
% 159.55/25.89    (13)   ~ (e3 = e0)
% 159.55/25.89  
% 159.55/25.89  Begin of proof
% 159.55/25.89  | 
% 159.55/25.89  | BETA: splitting (9) gives:
% 159.55/25.89  | 
% 159.55/25.89  | Case 1:
% 159.55/25.89  | | 
% 159.55/25.89  | |   (14)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.55/25.89  | |         op(e1, e0) = e1
% 159.55/25.89  | | 
% 159.55/25.89  | | ALPHA: (14) implies:
% 159.55/25.89  | |   (15)  op(e1, e1) = e1
% 159.55/25.89  | | 
% 159.55/25.89  | | REF_CLOSE: (1), (4), (12), (15) are inconsistent by sub-proof #1003.
% 159.55/25.89  | | 
% 159.55/25.89  | Case 2:
% 159.55/25.89  | | 
% 159.55/25.89  | |   (16)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9
% 159.55/25.89  | |             = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 159.55/25.89  | |             op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 159.55/25.89  | |             = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 159.55/25.89  | |             op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13
% 159.55/25.89  | |             = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.55/25.89  | |             op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15
% 159.55/25.89  | |             = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.55/25.89  | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 159.55/25.89  | |               e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 159.55/25.89  | |             & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.55/25.89  | |               e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0
% 159.55/25.89  | |             & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.55/25.89  | |               e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0
% 159.55/25.89  | |             & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 =
% 159.55/25.89  | |             e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.55/25.89  | |             op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8
% 159.55/25.89  | |             = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.55/25.89  | |             op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8
% 159.55/25.89  | |             = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.55/25.89  | |             op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8
% 159.55/25.89  | |             = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.55/25.89  | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.55/25.89  | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 159.55/25.89  | |             & op(e0, e1) = e0))
% 159.55/25.89  | | 
% 159.55/25.89  | | ALPHA: (16) implies:
% 159.55/25.89  | |   (17)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.55/25.89  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.55/25.89  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.55/25.89  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.55/25.89  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.55/25.89  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 159.55/25.89  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.55/25.89  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.55/25.89  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.55/25.89  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.55/25.89  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) |
% 159.55/25.89  | |         (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.55/25.89  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 159.55/25.89  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.55/25.89  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.55/25.89  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.55/25.89  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.55/25.89  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.55/25.89  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.55/25.89  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.55/25.89  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.55/25.89  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.55/25.89  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 159.55/25.89  | |           & op(e0, e1) = e0)
% 159.55/25.89  | | 
% 159.55/25.89  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (17)
% 159.55/25.89  | |            are inconsistent by sub-proof #570.
% 159.55/25.89  | | 
% 159.55/25.89  | End of split
% 159.55/25.89  | 
% 159.55/25.89  End of proof
% 159.55/25.89  
% 159.55/25.89  Sub-proof #570 shows that the following formulas are inconsistent:
% 159.55/25.89  ----------------------------------------------------------------
% 159.55/25.89    (1)  op(e1, e1) = e3
% 159.55/25.89    (2)  op(e0, e1) = all_52_11
% 159.55/25.89    (3)   ~ (e3 = e2)
% 159.55/25.89    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.55/25.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.55/25.89    (5)  op(e0, e3) = all_52_3
% 159.55/25.89    (6)   ~ (all_52_3 = e0)
% 159.55/25.89    (7)  op(e3, e3) = e3
% 159.55/25.89    (8)  op(e2, e0) = e3
% 159.55/25.89    (9)  op(e0, e2) = e3
% 159.55/25.89    (10)   ~ (all_52_11 = e0)
% 159.61/25.89    (11)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.61/25.89            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.61/25.89            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 159.61/25.89            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.61/25.89            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.61/25.89              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.61/25.89            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 159.61/25.89            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 159.61/25.89            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.61/25.89            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/25.89              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/25.89            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.61/25.89            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.61/25.89            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/25.89              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.61/25.89          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.61/25.89            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.61/25.89            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 159.61/25.89            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.61/25.89            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.61/25.89            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.61/25.89            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.61/25.89    (12)   ~ (e3 = e0)
% 159.61/25.89  
% 159.61/25.89  Begin of proof
% 159.61/25.89  | 
% 159.61/25.89  | BETA: splitting (11) gives:
% 159.61/25.89  | 
% 159.61/25.89  | Case 1:
% 159.61/25.89  | | 
% 159.61/25.89  | |   (13)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.89  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.61/25.89  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.89  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.61/25.89  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.89  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 159.61/25.89  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.61/25.89  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.89  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.61/25.89  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.89  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.61/25.89  | | 
% 159.61/25.89  | | BETA: splitting (13) gives:
% 159.61/25.89  | | 
% 159.61/25.89  | | Case 1:
% 159.61/25.89  | | | 
% 159.61/25.90  | | |   (14)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.61/25.90  | | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.61/25.90  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.61/25.90  | | | 
% 159.61/25.90  | | | BETA: splitting (14) gives:
% 159.61/25.90  | | | 
% 159.61/25.90  | | | Case 1:
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | |   (15)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | | | |           e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | | ALPHA: (15) implies:
% 159.61/25.90  | | | |   (16)  op(e0, e3) = e0
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | | REF_CLOSE: (4), (5), (6), (16) are inconsistent by sub-proof #973.
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | Case 2:
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | |   (17)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.61/25.90  | | | |             = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0)
% 159.61/25.90  | | | |         | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/25.90  | | | |           (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/25.90  | | | |             e3) = e0)
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | | REF_CLOSE: (1), (3), (4), (8), (12), (17) are inconsistent by sub-proof
% 159.61/25.90  | | | |            #575.
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | End of split
% 159.61/25.90  | | | 
% 159.61/25.90  | | Case 2:
% 159.61/25.90  | | | 
% 159.61/25.90  | | |   (18)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0)
% 159.61/25.90  | | |         | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/25.90  | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.61/25.90  | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.61/25.90  | | | 
% 159.61/25.90  | | | BETA: splitting (18) gives:
% 159.61/25.90  | | | 
% 159.61/25.90  | | | Case 1:
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | |   (19)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | | ALPHA: (19) implies:
% 159.61/25.90  | | | |   (20)  op(e0, e3) = e0
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | | REF_CLOSE: (4), (5), (6), (20) are inconsistent by sub-proof #973.
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | Case 2:
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | |   (21)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/25.90  | | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0)
% 159.61/25.90  | | | |         | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/25.90  | | | |           (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/25.90  | | | |             e2) = e0)
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | | REF_CLOSE: (3), (4), (7), (8), (12), (21) are inconsistent by sub-proof
% 159.61/25.90  | | | |            #574.
% 159.61/25.90  | | | | 
% 159.61/25.90  | | | End of split
% 159.61/25.90  | | | 
% 159.61/25.90  | | End of split
% 159.61/25.90  | | 
% 159.61/25.90  | Case 2:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (22)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 159.61/25.90  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.61/25.90  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.61/25.90  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.61/25.90  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.61/25.90  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.61/25.90  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.61/25.90  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 159.61/25.90  | |           & op(e0, e1) = e0)
% 159.61/25.90  | | 
% 159.61/25.90  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (12), (22) are
% 159.61/25.90  | |            inconsistent by sub-proof #571.
% 159.61/25.90  | | 
% 159.61/25.90  | End of split
% 159.61/25.90  | 
% 159.61/25.90  End of proof
% 159.61/25.90  
% 159.61/25.90  Sub-proof #571 shows that the following formulas are inconsistent:
% 159.61/25.90  ----------------------------------------------------------------
% 159.61/25.90    (1)  op(e1, e1) = e3
% 159.61/25.90    (2)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.61/25.90           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.61/25.90           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.61/25.90           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 159.61/25.90           & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 = e2
% 159.61/25.90           & all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 159.61/25.90           e2 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.61/25.90           e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/25.90             e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 159.61/25.90           (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.61/25.90             e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1
% 159.61/25.90             = e0) & op(e0, e1) = e0)
% 159.61/25.90    (3)  op(e0, e1) = all_52_11
% 159.61/25.90    (4)   ~ (e3 = e2)
% 159.61/25.90    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.90    (6)  op(e3, e3) = e3
% 159.61/25.90    (7)  op(e2, e0) = e3
% 159.61/25.90    (8)  op(e0, e2) = e3
% 159.61/25.90    (9)   ~ (all_52_11 = e0)
% 159.61/25.90    (10)   ~ (e3 = e0)
% 159.61/25.90  
% 159.61/25.90  Begin of proof
% 159.61/25.90  | 
% 159.61/25.90  | BETA: splitting (2) gives:
% 159.61/25.90  | 
% 159.61/25.90  | Case 1:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (11)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 159.61/25.90  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.61/25.90  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.61/25.90  | | 
% 159.61/25.90  | | REF_CLOSE: (1), (5), (6), (8), (10), (11) are inconsistent by sub-proof
% 159.61/25.90  | |            #573.
% 159.61/25.90  | | 
% 159.61/25.90  | Case 2:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (12)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.61/25.90  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.61/25.90  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.61/25.90  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.61/25.90  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 159.61/25.90  | |           & op(e0, e1) = e0)
% 159.61/25.90  | | 
% 159.61/25.90  | | BETA: splitting (12) gives:
% 159.61/25.90  | | 
% 159.61/25.90  | | Case 1:
% 159.61/25.90  | | | 
% 159.61/25.90  | | |   (13)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.61/25.90  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0)
% 159.61/25.90  | | | 
% 159.61/25.90  | | | REF_CLOSE: (1), (4), (5), (7), (10), (13) are inconsistent by sub-proof
% 159.61/25.90  | | |            #572.
% 159.61/25.90  | | | 
% 159.61/25.90  | | Case 2:
% 159.61/25.90  | | | 
% 159.61/25.90  | | |   (14)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.61/25.90  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.61/25.90  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 159.61/25.90  | | |             e0) & op(e0, e1) = e0)
% 159.61/25.90  | | | 
% 159.61/25.90  | | | REF_CLOSE: (3), (5), (9), (14) are inconsistent by sub-proof #965.
% 159.61/25.90  | | | 
% 159.61/25.90  | | End of split
% 159.61/25.90  | | 
% 159.61/25.90  | End of split
% 159.61/25.90  | 
% 159.61/25.90  End of proof
% 159.61/25.90  
% 159.61/25.90  Sub-proof #572 shows that the following formulas are inconsistent:
% 159.61/25.90  ----------------------------------------------------------------
% 159.61/25.90    (1)  op(e1, e1) = e3
% 159.61/25.90    (2)   ~ (e3 = e2)
% 159.61/25.90    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.90    (4)  op(e2, e0) = e3
% 159.61/25.90    (5)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.61/25.90           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.61/25.90           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 159.61/25.90           & op(e1, e0) = e1 & op(e0, e1) = e0)
% 159.61/25.90    (6)   ~ (e3 = e0)
% 159.61/25.90  
% 159.61/25.90  Begin of proof
% 159.61/25.90  | 
% 159.61/25.90  | BETA: splitting (5) gives:
% 159.61/25.90  | 
% 159.61/25.90  | Case 1:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (7)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1)
% 159.61/25.90  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | ALPHA: (7) implies:
% 159.61/25.90  | |   (8)  op(e2, e0) = e2
% 159.61/25.90  | | 
% 159.61/25.90  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #580.
% 159.61/25.90  | | 
% 159.61/25.90  | Case 2:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (9)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1)
% 159.61/25.90  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | ALPHA: (9) implies:
% 159.61/25.90  | |   (10)  op(e1, e1) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #912.
% 159.61/25.90  | | 
% 159.61/25.90  | End of split
% 159.61/25.90  | 
% 159.61/25.90  End of proof
% 159.61/25.90  
% 159.61/25.90  Sub-proof #573 shows that the following formulas are inconsistent:
% 159.61/25.90  ----------------------------------------------------------------
% 159.61/25.90    (1)  op(e1, e1) = e3
% 159.61/25.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.90    (3)  op(e3, e3) = e3
% 159.61/25.90    (4)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.61/25.90           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.61/25.90           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.61/25.90           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 159.61/25.90           & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.61/25.90    (5)  op(e0, e2) = e3
% 159.61/25.90    (6)   ~ (e3 = e0)
% 159.61/25.90  
% 159.61/25.90  Begin of proof
% 159.61/25.90  | 
% 159.61/25.90  | BETA: splitting (4) gives:
% 159.61/25.90  | 
% 159.61/25.90  | Case 1:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (7)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 159.61/25.90  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | ALPHA: (7) implies:
% 159.61/25.90  | |   (8)  op(e1, e1) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #912.
% 159.61/25.90  | | 
% 159.61/25.90  | Case 2:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (9)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.61/25.90  | |        (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 159.61/25.90  | |          & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.61/25.90  | | 
% 159.61/25.90  | | BETA: splitting (9) gives:
% 159.61/25.90  | | 
% 159.61/25.90  | | Case 1:
% 159.61/25.90  | | | 
% 159.61/25.90  | | |   (10)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 159.61/25.90  | | | 
% 159.61/25.90  | | | ALPHA: (10) implies:
% 159.61/25.90  | | |   (11)  op(e0, e2) = e0
% 159.61/25.90  | | | 
% 159.61/25.90  | | | REF_CLOSE: (2), (5), (6), (11) are inconsistent by sub-proof #726.
% 159.61/25.90  | | | 
% 159.61/25.90  | | Case 2:
% 159.61/25.90  | | | 
% 159.61/25.90  | | |   (12)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.90  | | |           e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 159.61/25.90  | | | 
% 159.61/25.90  | | | ALPHA: (12) implies:
% 159.61/25.90  | | |   (13)  op(e3, e3) = e0
% 159.61/25.90  | | | 
% 159.61/25.90  | | | REF_CLOSE: (2), (3), (6), (13) are inconsistent by sub-proof #971.
% 159.61/25.90  | | | 
% 159.61/25.90  | | End of split
% 159.61/25.90  | | 
% 159.61/25.90  | End of split
% 159.61/25.90  | 
% 159.61/25.90  End of proof
% 159.61/25.90  
% 159.61/25.90  Sub-proof #574 shows that the following formulas are inconsistent:
% 159.61/25.90  ----------------------------------------------------------------
% 159.61/25.90    (1)   ~ (e3 = e2)
% 159.61/25.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.90    (3)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.61/25.90           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.61/25.90           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 159.61/25.90           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.61/25.90    (4)  op(e3, e3) = e3
% 159.61/25.90    (5)  op(e2, e0) = e3
% 159.61/25.90    (6)   ~ (e3 = e0)
% 159.61/25.90  
% 159.61/25.90  Begin of proof
% 159.61/25.90  | 
% 159.61/25.90  | BETA: splitting (3) gives:
% 159.61/25.90  | 
% 159.61/25.90  | Case 1:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (7)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 159.61/25.90  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | ALPHA: (7) implies:
% 159.61/25.90  | |   (8)  op(e3, e3) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #971.
% 159.61/25.90  | | 
% 159.61/25.90  | Case 2:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (9)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2)
% 159.61/25.90  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | ALPHA: (9) implies:
% 159.61/25.90  | |   (10)  op(e2, e0) = e2
% 159.61/25.90  | | 
% 159.61/25.90  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #580.
% 159.61/25.90  | | 
% 159.61/25.90  | End of split
% 159.61/25.90  | 
% 159.61/25.90  End of proof
% 159.61/25.90  
% 159.61/25.90  Sub-proof #575 shows that the following formulas are inconsistent:
% 159.61/25.90  ----------------------------------------------------------------
% 159.61/25.90    (1)  op(e1, e1) = e3
% 159.61/25.90    (2)   ~ (e3 = e2)
% 159.61/25.90    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.90    (4)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.61/25.90           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.61/25.90           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 159.61/25.90           & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.61/25.90    (5)  op(e2, e0) = e3
% 159.61/25.90    (6)   ~ (e3 = e0)
% 159.61/25.90  
% 159.61/25.90  Begin of proof
% 159.61/25.90  | 
% 159.61/25.90  | BETA: splitting (4) gives:
% 159.61/25.90  | 
% 159.61/25.90  | Case 1:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (7)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3)
% 159.61/25.90  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | ALPHA: (7) implies:
% 159.61/25.90  | |   (8)  op(e2, e0) = e2
% 159.61/25.90  | | 
% 159.61/25.90  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #580.
% 159.61/25.90  | | 
% 159.61/25.90  | Case 2:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (9)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3)
% 159.61/25.90  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | ALPHA: (9) implies:
% 159.61/25.90  | |   (10)  op(e1, e1) = e0
% 159.61/25.90  | | 
% 159.61/25.90  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #912.
% 159.61/25.90  | | 
% 159.61/25.90  | End of split
% 159.61/25.90  | 
% 159.61/25.90  End of proof
% 159.61/25.90  
% 159.61/25.90  Sub-proof #576 shows that the following formulas are inconsistent:
% 159.61/25.90  ----------------------------------------------------------------
% 159.61/25.90    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.90    (2)  op(e0, e0) = e0
% 159.61/25.90    (3)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.61/25.90           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.61/25.90           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 159.61/25.90           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.61/25.90    (4)  op(e2, e2) = e1
% 159.61/25.90    (5)   ~ (e2 = e0)
% 159.61/25.90  
% 159.61/25.90  Begin of proof
% 159.61/25.90  | 
% 159.61/25.90  | BETA: splitting (3) gives:
% 159.61/25.90  | 
% 159.61/25.90  | Case 1:
% 159.61/25.90  | | 
% 159.61/25.90  | |   (6)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 159.61/25.90  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 159.61/25.90  | |          e0) = e2 & $i(all_57_12)
% 159.61/25.90  | | 
% 159.61/25.90  | | ALPHA: (6) implies:
% 159.61/25.90  | |   (7)  op(e0, e0) = e2
% 159.61/25.90  | | 
% 159.61/25.91  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #979.
% 159.61/25.91  | | 
% 159.61/25.91  | Case 2:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (8)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 159.61/25.91  | |        op(e2, e1) = e2
% 159.61/25.91  | | 
% 159.61/25.91  | | ALPHA: (8) implies:
% 159.61/25.91  | |   (9)   ~ (e2 = e1)
% 159.61/25.91  | |   (10)  op(e2, e2) = e2
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (1), (4), (9), (10) are inconsistent by sub-proof #993.
% 159.61/25.91  | | 
% 159.61/25.91  | End of split
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #577 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)  op(e1, e1) = e3
% 159.61/25.91    (2)   ~ (e3 = e2)
% 159.61/25.91    (3)  all_54_15 = e1 | all_54_15 = e0
% 159.61/25.91    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.91    (5)  all_54_15 = all_14_2
% 159.61/25.91    (6)  op(e0, e0) = all_14_2
% 159.61/25.91    (7)   ~ (all_14_2 = e1)
% 159.61/25.91    (8)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 159.61/25.91           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.61/25.91           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 159.61/25.91           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/25.91           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | BETA: splitting (8) gives:
% 159.61/25.91  | 
% 159.61/25.91  | Case 1:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.61/25.91  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.61/25.91  | |          e1) = e2 & $i(all_57_12)
% 159.61/25.91  | | 
% 159.61/25.91  | | ALPHA: (9) implies:
% 159.61/25.91  | |   (10)  op(e1, e1) = e2
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #646.
% 159.61/25.91  | | 
% 159.61/25.91  | Case 2:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (11)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 159.61/25.91  | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.61/25.91  | |         op(e0, e0) = e1 & $i(all_57_14)
% 159.61/25.91  | | 
% 159.61/25.91  | | ALPHA: (11) implies:
% 159.61/25.91  | |   (12)  op(e0, e0) = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (3), (4), (5), (6), (7), (12) are inconsistent by sub-proof #790.
% 159.61/25.91  | | 
% 159.61/25.91  | End of split
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #578 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)  op(e1, e1) = e3
% 159.61/25.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.91    (3)   ~ (all_52_12 = e3)
% 159.61/25.91    (4)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) &
% 159.61/25.91           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.61/25.91           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1)
% 159.61/25.91           & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.61/25.91    (5)  op(e3, e0) = all_52_12
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | BETA: splitting (4) gives:
% 159.61/25.91  | 
% 159.61/25.91  | Case 1:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (6)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 159.61/25.91  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 159.61/25.91  | |          e1) = e3 & $i(all_57_10)
% 159.61/25.91  | | 
% 159.61/25.91  | | ALPHA: (6) implies:
% 159.61/25.91  | |   (7)  op(e3, e0) = e3
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #976.
% 159.61/25.91  | | 
% 159.61/25.91  | Case 2:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (8)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.61/25.91  | |        op(e1, e1) = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | ALPHA: (8) implies:
% 159.61/25.91  | |   (9)   ~ (e3 = e1)
% 159.61/25.91  | |   (10)  op(e1, e1) = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #1003.
% 159.61/25.91  | | 
% 159.61/25.91  | End of split
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #579 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)   ~ (e3 = e2)
% 159.61/25.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.91    (3)  op(e3, e3) = e3
% 159.61/25.91    (4)  op(e2, e0) = e3
% 159.61/25.91    (5)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.61/25.91           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.61/25.91           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 159.61/25.91           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 159.61/25.91           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.61/25.91    (6)   ~ (e3 = e1)
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | BETA: splitting (5) gives:
% 159.61/25.91  | 
% 159.61/25.91  | Case 1:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (7)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 159.61/25.91  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.61/25.91  | |          e0) = e2 & $i(all_57_12)
% 159.61/25.91  | | 
% 159.61/25.91  | | ALPHA: (7) implies:
% 159.61/25.91  | |   (8)  op(e2, e0) = e2
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #580.
% 159.61/25.91  | | 
% 159.61/25.91  | Case 2:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (9)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 159.61/25.91  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/25.91  | |        all_57_14 & $i(all_57_14)
% 159.61/25.91  | | 
% 159.61/25.91  | | ALPHA: (9) implies:
% 159.61/25.91  | |   (10)  op(e3, e3) = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #995.
% 159.61/25.91  | | 
% 159.61/25.91  | End of split
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #580 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.91    (2)  op(e2, e0) = e3
% 159.61/25.91    (3)  op(e2, e0) = e2
% 159.61/25.91    (4)   ~ (e3 = e2)
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | GROUND_INST: instantiating (1) with e3, e2, e0, e2, simplifying with (2), (3)
% 159.61/25.91  |              gives:
% 159.61/25.91  |   (5)  e3 = e2
% 159.61/25.91  | 
% 159.61/25.91  | REDUCE: (4), (5) imply:
% 159.61/25.91  |   (6)  $false
% 159.61/25.91  | 
% 159.61/25.91  | CLOSE: (6) is inconsistent.
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #581 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)  all_54_2 = all_52_8
% 159.61/25.91    (2)   ~ (all_52_9 = all_52_11)
% 159.61/25.91    (3)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.61/25.91    (4)   ~ (all_52_14 = e0)
% 159.61/25.91    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.91    (6)   ~ (all_52_12 = e3)
% 159.61/25.91    (7)  all_54_11 = e1 | all_54_11 = e0
% 159.61/25.91    (8)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.61/25.91    (9)   ~ (all_52_12 = all_52_14)
% 159.61/25.91    (10)   ~ (all_52_8 = e0)
% 159.61/25.91    (11)   ~ (all_52_8 = all_52_12)
% 159.61/25.91    (12)  all_54_3 = all_52_12
% 159.61/25.91    (13)   ~ (all_52_8 = all_52_11)
% 159.61/25.91    (14)  op(e2, e1) = all_52_9
% 159.61/25.91    (15)  all_54_14 = all_52_11
% 159.61/25.91    (16)   ~ (all_52_12 = e0)
% 159.61/25.91    (17)  op(e2, e1) = e2
% 159.61/25.91    (18)   ~ (all_52_11 = e0)
% 159.61/25.91    (19)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.61/25.91    (20)  all_54_11 = all_52_14
% 159.61/25.91    (21)   ~ (all_52_11 = e3)
% 159.61/25.91    (22)   ~ (all_52_8 = e3)
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | BETA: splitting (7) gives:
% 159.61/25.91  | 
% 159.61/25.91  | Case 1:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (23)  all_54_11 = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | COMBINE_EQS: (20), (23) imply:
% 159.61/25.91  | |   (24)  all_52_14 = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | SIMP: (24) implies:
% 159.61/25.91  | |   (25)  all_52_14 = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | REDUCE: (9), (25) imply:
% 159.61/25.91  | |   (26)   ~ (all_52_12 = e1)
% 159.61/25.91  | | 
% 159.61/25.91  | | BETA: splitting (19) gives:
% 159.61/25.91  | | 
% 159.61/25.91  | | Case 1:
% 159.61/25.91  | | | 
% 159.61/25.91  | | |   (27)  all_54_3 = e3
% 159.61/25.91  | | | 
% 159.61/25.91  | | | COMBINE_EQS: (12), (27) imply:
% 159.61/25.91  | | |   (28)  all_52_12 = e3
% 159.61/25.91  | | | 
% 159.61/25.91  | | | REDUCE: (6), (28) imply:
% 159.61/25.91  | | |   (29)  $false
% 159.61/25.91  | | | 
% 159.61/25.91  | | | CLOSE: (29) is inconsistent.
% 159.61/25.91  | | | 
% 159.61/25.91  | | Case 2:
% 159.61/25.91  | | | 
% 159.61/25.91  | | |   (30)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.61/25.91  | | | 
% 159.61/25.91  | | | BETA: splitting (30) gives:
% 159.61/25.91  | | | 
% 159.61/25.91  | | | Case 1:
% 159.61/25.91  | | | | 
% 159.61/25.91  | | | |   (31)  all_54_3 = e2
% 159.61/25.91  | | | | 
% 159.61/25.91  | | | | COMBINE_EQS: (12), (31) imply:
% 159.61/25.91  | | | |   (32)  all_52_12 = e2
% 159.61/25.91  | | | | 
% 159.61/25.91  | | | | REDUCE: (11), (32) imply:
% 159.61/25.91  | | | |   (33)   ~ (all_52_8 = e2)
% 159.61/25.91  | | | | 
% 159.61/25.91  | | | | BETA: splitting (8) gives:
% 159.61/25.91  | | | | 
% 159.61/25.91  | | | | Case 1:
% 159.61/25.91  | | | | | 
% 159.61/25.91  | | | | |   (34)  all_54_2 = e3
% 159.61/25.91  | | | | | 
% 159.61/25.91  | | | | | COMBINE_EQS: (1), (34) imply:
% 159.61/25.91  | | | | |   (35)  all_52_8 = e3
% 159.61/25.91  | | | | | 
% 159.61/25.91  | | | | | REDUCE: (22), (35) imply:
% 159.61/25.91  | | | | |   (36)  $false
% 159.61/25.91  | | | | | 
% 159.61/25.91  | | | | | CLOSE: (36) is inconsistent.
% 159.61/25.91  | | | | | 
% 159.61/25.91  | | | | Case 2:
% 159.61/25.91  | | | | | 
% 159.61/25.91  | | | | |   (37)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.61/25.91  | | | | | 
% 159.61/25.91  | | | | | BETA: splitting (37) gives:
% 159.61/25.91  | | | | | 
% 159.61/25.91  | | | | | Case 1:
% 159.61/25.91  | | | | | | 
% 159.61/25.91  | | | | | |   (38)  all_54_2 = e2
% 159.61/25.91  | | | | | | 
% 159.61/25.91  | | | | | | COMBINE_EQS: (1), (38) imply:
% 159.61/25.91  | | | | | |   (39)  all_52_8 = e2
% 159.61/25.91  | | | | | | 
% 159.61/25.91  | | | | | | REDUCE: (33), (39) imply:
% 159.61/25.91  | | | | | |   (40)  $false
% 159.61/25.91  | | | | | | 
% 159.61/25.91  | | | | | | CLOSE: (40) is inconsistent.
% 159.61/25.91  | | | | | | 
% 159.61/25.91  | | | | | Case 2:
% 159.61/25.91  | | | | | | 
% 159.61/25.91  | | | | | |   (41)  all_54_2 = e1 | all_54_2 = e0
% 159.61/25.91  | | | | | | 
% 159.61/25.91  | | | | | | REF_CLOSE: (1), (2), (3), (5), (10), (13), (14), (15), (17), (18),
% 159.61/25.91  | | | | | |            (21), (41) are inconsistent by sub-proof #583.
% 159.61/25.91  | | | | | | 
% 159.61/25.91  | | | | | End of split
% 159.61/25.91  | | | | | 
% 159.61/25.91  | | | | End of split
% 159.61/25.91  | | | | 
% 159.61/25.91  | | | Case 2:
% 159.61/25.91  | | | | 
% 159.61/25.91  | | | |   (42)  all_54_3 = e1 | all_54_3 = e0
% 159.61/25.91  | | | | 
% 159.61/25.91  | | | | REF_CLOSE: (12), (16), (26), (42) are inconsistent by sub-proof #582.
% 159.61/25.91  | | | | 
% 159.61/25.91  | | | End of split
% 159.61/25.91  | | | 
% 159.61/25.91  | | End of split
% 159.61/25.91  | | 
% 159.61/25.91  | Case 2:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (43)  all_54_11 = e0
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (4), (20), (43) are inconsistent by sub-proof #624.
% 159.61/25.91  | | 
% 159.61/25.91  | End of split
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #582 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)  all_54_3 = e1 | all_54_3 = e0
% 159.61/25.91    (2)  all_54_3 = all_52_12
% 159.61/25.91    (3)   ~ (all_52_12 = e1)
% 159.61/25.91    (4)   ~ (all_52_12 = e0)
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | BETA: splitting (1) gives:
% 159.61/25.91  | 
% 159.61/25.91  | Case 1:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (5)  all_54_3 = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | COMBINE_EQS: (2), (5) imply:
% 159.61/25.91  | |   (6)  all_52_12 = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | REDUCE: (3), (6) imply:
% 159.61/25.91  | |   (7)  $false
% 159.61/25.91  | | 
% 159.61/25.91  | | CLOSE: (7) is inconsistent.
% 159.61/25.91  | | 
% 159.61/25.91  | Case 2:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (8)  all_54_3 = e0
% 159.61/25.91  | | 
% 159.61/25.91  | | COMBINE_EQS: (2), (8) imply:
% 159.61/25.91  | |   (9)  all_52_12 = e0
% 159.61/25.91  | | 
% 159.61/25.91  | | REDUCE: (4), (9) imply:
% 159.61/25.91  | |   (10)  $false
% 159.61/25.91  | | 
% 159.61/25.91  | | CLOSE: (10) is inconsistent.
% 159.61/25.91  | | 
% 159.61/25.91  | End of split
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #583 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)  all_54_2 = all_52_8
% 159.61/25.91    (2)   ~ (all_52_9 = all_52_11)
% 159.61/25.91    (3)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.61/25.91    (4)  all_54_2 = e1 | all_54_2 = e0
% 159.61/25.91    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.91    (6)   ~ (all_52_8 = e0)
% 159.61/25.91    (7)   ~ (all_52_8 = all_52_11)
% 159.61/25.91    (8)  op(e2, e1) = all_52_9
% 159.61/25.91    (9)  all_54_14 = all_52_11
% 159.61/25.91    (10)  op(e2, e1) = e2
% 159.61/25.91    (11)   ~ (all_52_11 = e0)
% 159.61/25.91    (12)   ~ (all_52_11 = e3)
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | BETA: splitting (4) gives:
% 159.61/25.91  | 
% 159.61/25.91  | Case 1:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (13)  all_54_2 = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | COMBINE_EQS: (1), (13) imply:
% 159.61/25.91  | |   (14)  all_52_8 = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | REDUCE: (7), (14) imply:
% 159.61/25.91  | |   (15)   ~ (all_52_11 = e1)
% 159.61/25.91  | | 
% 159.61/25.91  | | SIMP: (15) implies:
% 159.61/25.91  | |   (16)   ~ (all_52_11 = e1)
% 159.61/25.91  | | 
% 159.61/25.91  | | BETA: splitting (3) gives:
% 159.61/25.91  | | 
% 159.61/25.91  | | Case 1:
% 159.61/25.91  | | | 
% 159.61/25.91  | | |   (17)  all_54_14 = e3
% 159.61/25.91  | | | 
% 159.61/25.91  | | | REF_CLOSE: (9), (12), (17) are inconsistent by sub-proof #587.
% 159.61/25.91  | | | 
% 159.61/25.91  | | Case 2:
% 159.61/25.91  | | | 
% 159.61/25.91  | | |   (18)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.61/25.91  | | | 
% 159.61/25.91  | | | REF_CLOSE: (2), (5), (8), (9), (10), (11), (16), (18) are inconsistent by
% 159.61/25.91  | | |            sub-proof #584.
% 159.61/25.91  | | | 
% 159.61/25.91  | | End of split
% 159.61/25.91  | | 
% 159.61/25.91  | Case 2:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (19)  all_54_2 = e0
% 159.61/25.91  | | 
% 159.61/25.91  | | COMBINE_EQS: (1), (19) imply:
% 159.61/25.91  | |   (20)  all_52_8 = e0
% 159.61/25.91  | | 
% 159.61/25.91  | | REDUCE: (6), (20) imply:
% 159.61/25.91  | |   (21)  $false
% 159.61/25.91  | | 
% 159.61/25.91  | | CLOSE: (21) is inconsistent.
% 159.61/25.91  | | 
% 159.61/25.91  | End of split
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #584 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)   ~ (all_52_9 = all_52_11)
% 159.61/25.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.91    (3)   ~ (all_52_11 = e1)
% 159.61/25.91    (4)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.61/25.91    (5)  op(e2, e1) = all_52_9
% 159.61/25.91    (6)  all_54_14 = all_52_11
% 159.61/25.91    (7)  op(e2, e1) = e2
% 159.61/25.91    (8)   ~ (all_52_11 = e0)
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | BETA: splitting (4) gives:
% 159.61/25.91  | 
% 159.61/25.91  | Case 1:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (9)  all_54_14 = e2
% 159.61/25.91  | | 
% 159.61/25.91  | | COMBINE_EQS: (6), (9) imply:
% 159.61/25.91  | |   (10)  all_52_11 = e2
% 159.61/25.91  | | 
% 159.61/25.91  | | SIMP: (10) implies:
% 159.61/25.91  | |   (11)  all_52_11 = e2
% 159.61/25.91  | | 
% 159.61/25.91  | | REDUCE: (1), (11) imply:
% 159.61/25.91  | |   (12)   ~ (all_52_9 = e2)
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (2), (5), (7), (12) are inconsistent by sub-proof #1002.
% 159.61/25.91  | | 
% 159.61/25.91  | Case 2:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (13)  all_54_14 = e1 | all_54_14 = e0
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (3), (6), (8), (13) are inconsistent by sub-proof #585.
% 159.61/25.91  | | 
% 159.61/25.91  | End of split
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #585 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)  all_54_14 = e1 | all_54_14 = e0
% 159.61/25.91    (2)  all_54_14 = all_52_11
% 159.61/25.91    (3)   ~ (all_52_11 = e1)
% 159.61/25.91    (4)   ~ (all_52_11 = e0)
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | BETA: splitting (1) gives:
% 159.61/25.91  | 
% 159.61/25.91  | Case 1:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (5)  all_54_14 = e1
% 159.61/25.91  | | 
% 159.61/25.91  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #586.
% 159.61/25.91  | | 
% 159.61/25.91  | Case 2:
% 159.61/25.91  | | 
% 159.61/25.91  | |   (6)  all_54_14 = e0
% 159.61/25.91  | | 
% 159.61/25.91  | | COMBINE_EQS: (2), (6) imply:
% 159.61/25.91  | |   (7)  all_52_11 = e0
% 159.61/25.91  | | 
% 159.61/25.91  | | SIMP: (7) implies:
% 159.61/25.91  | |   (8)  all_52_11 = e0
% 159.61/25.91  | | 
% 159.61/25.91  | | REDUCE: (4), (8) imply:
% 159.61/25.91  | |   (9)  $false
% 159.61/25.91  | | 
% 159.61/25.91  | | CLOSE: (9) is inconsistent.
% 159.61/25.91  | | 
% 159.61/25.91  | End of split
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #586 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)  all_54_14 = all_52_11
% 159.61/25.91    (2)  all_54_14 = e1
% 159.61/25.91    (3)   ~ (all_52_11 = e1)
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.91  |   (4)  all_52_11 = e1
% 159.61/25.91  | 
% 159.61/25.91  | SIMP: (4) implies:
% 159.61/25.91  |   (5)  all_52_11 = e1
% 159.61/25.91  | 
% 159.61/25.91  | REDUCE: (3), (5) imply:
% 159.61/25.91  |   (6)  $false
% 159.61/25.91  | 
% 159.61/25.91  | CLOSE: (6) is inconsistent.
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #587 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)  all_54_14 = all_52_11
% 159.61/25.91    (2)  all_54_14 = e3
% 159.61/25.91    (3)   ~ (all_52_11 = e3)
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.91  |   (4)  all_52_11 = e3
% 159.61/25.91  | 
% 159.61/25.91  | SIMP: (4) implies:
% 159.61/25.91  |   (5)  all_52_11 = e3
% 159.61/25.91  | 
% 159.61/25.91  | REDUCE: (3), (5) imply:
% 159.61/25.91  |   (6)  $false
% 159.61/25.91  | 
% 159.61/25.91  | CLOSE: (6) is inconsistent.
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #588 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.91    (1)  all_54_11 = all_52_14
% 159.61/25.91    (2)  all_54_11 = e2
% 159.61/25.91    (3)   ~ (all_52_14 = e2)
% 159.61/25.91  
% 159.61/25.91  Begin of proof
% 159.61/25.91  | 
% 159.61/25.91  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.91  |   (4)  all_52_14 = e2
% 159.61/25.91  | 
% 159.61/25.91  | SIMP: (4) implies:
% 159.61/25.91  |   (5)  all_52_14 = e2
% 159.61/25.91  | 
% 159.61/25.91  | REDUCE: (3), (5) imply:
% 159.61/25.91  |   (6)  $false
% 159.61/25.91  | 
% 159.61/25.91  | CLOSE: (6) is inconsistent.
% 159.61/25.91  | 
% 159.61/25.91  End of proof
% 159.61/25.91  
% 159.61/25.91  Sub-proof #589 shows that the following formulas are inconsistent:
% 159.61/25.91  ----------------------------------------------------------------
% 159.61/25.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.92    (2)  op(e0, e3) = all_52_3
% 159.61/25.92    (3)  op(e1, e3) = all_52_2
% 159.61/25.92    (4)   ~ (all_52_2 = e2)
% 159.61/25.92    (5)  op(e0, e3) = e0
% 159.61/25.92    (6)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.61/25.92    (7)   ~ (e2 = e0)
% 159.61/25.92  
% 159.61/25.92  Begin of proof
% 159.61/25.92  | 
% 159.61/25.92  | BETA: splitting (6) gives:
% 159.61/25.92  | 
% 159.61/25.92  | Case 1:
% 159.61/25.92  | | 
% 159.61/25.92  | |   (8)  all_56_6 = e2 & op(e1, e3) = e2
% 159.61/25.92  | | 
% 159.61/25.92  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #761.
% 159.61/25.92  | | 
% 159.61/25.92  | Case 2:
% 159.61/25.92  | | 
% 159.61/25.92  | |   (9)  all_56_12 = e2 & op(e0, e3) = e2
% 159.61/25.92  | | 
% 159.61/25.92  | | ALPHA: (9) implies:
% 159.61/25.92  | |   (10)  op(e0, e3) = e2
% 159.61/25.92  | | 
% 159.61/25.92  | | REF_CLOSE: (1), (2), (5), (7), (10) are inconsistent by sub-proof #689.
% 159.61/25.92  | | 
% 159.61/25.92  | End of split
% 159.61/25.92  | 
% 159.61/25.92  End of proof
% 159.61/25.92  
% 159.61/25.92  Sub-proof #590 shows that the following formulas are inconsistent:
% 159.61/25.92  ----------------------------------------------------------------
% 159.61/25.92    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.61/25.92         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.61/25.92    (2)   ~ (e3 = e2)
% 159.61/25.92    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.92    (4)  all_56_7 = e2
% 159.61/25.92    (5)  op(e0, e2) = all_52_7
% 159.61/25.92    (6)  all_56_10 = e3
% 159.61/25.92    (7)  op(e3, e3) = e3
% 159.61/25.92    (8)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 159.61/25.92    (9)  all_56_1 = e0
% 159.61/25.92    (10)   ~ (e1 = e0)
% 159.61/25.92    (11)   ~ (e2 = e1)
% 159.61/25.92    (12)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.61/25.92          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 159.61/25.92    (13)   ~ (all_52_7 = e1)
% 159.61/25.92    (14)  all_56_5 = e3
% 159.61/25.92    (15)   ~ (e2 = e0)
% 159.61/25.92    (16)   ~ (e3 = e0)
% 159.61/25.92  
% 159.61/25.92  Begin of proof
% 159.61/25.92  | 
% 159.61/25.92  | BETA: splitting (8) gives:
% 159.61/25.92  | 
% 159.61/25.92  | Case 1:
% 159.61/25.92  | | 
% 159.61/25.92  | |   (17)  all_56_0 = e2 & op(e3, e3) = e2
% 159.61/25.92  | | 
% 159.61/25.92  | | ALPHA: (17) implies:
% 159.61/25.92  | |   (18)  op(e3, e3) = e2
% 159.61/25.92  | | 
% 159.61/25.92  | | REF_CLOSE: (2), (3), (7), (18) are inconsistent by sub-proof #958.
% 159.61/25.92  | | 
% 159.61/25.92  | Case 2:
% 159.61/25.92  | | 
% 159.61/25.92  | |   (19)  all_56_2 = e2 & op(e2, e3) = e2
% 159.61/25.92  | | 
% 159.61/25.92  | | ALPHA: (19) implies:
% 159.61/25.92  | |   (20)  all_56_2 = e2
% 159.61/25.92  | | 
% 159.61/25.92  | | BETA: splitting (12) gives:
% 159.61/25.92  | | 
% 159.61/25.92  | | Case 1:
% 159.61/25.92  | | | 
% 159.61/25.92  | | |   (21)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 159.61/25.92  | | |           e0)
% 159.61/25.92  | | | 
% 159.61/25.92  | | | BETA: splitting (21) gives:
% 159.61/25.92  | | | 
% 159.61/25.92  | | | Case 1:
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | |   (22)  all_56_2 = e0 & op(e2, e3) = e0
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | | REF_CLOSE: (15), (20), (22) are inconsistent by sub-proof #846.
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | Case 2:
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | |   (23)  all_56_3 = e0 & op(e2, e2) = e0
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | | ALPHA: (23) implies:
% 159.61/25.92  | | | |   (24)  op(e2, e2) = e0
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | | REF_CLOSE: (1), (3), (4), (5), (9), (10), (11), (13), (24) are
% 159.61/25.92  | | | |            inconsistent by sub-proof #603.
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | End of split
% 159.61/25.92  | | | 
% 159.61/25.92  | | Case 2:
% 159.61/25.92  | | | 
% 159.61/25.92  | | |   (25)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 159.61/25.92  | | |           e0)
% 159.61/25.92  | | | 
% 159.61/25.92  | | | BETA: splitting (25) gives:
% 159.61/25.92  | | | 
% 159.61/25.92  | | | Case 1:
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | |   (26)  all_56_5 = e0 & op(e2, e1) = e0
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | | ALPHA: (26) implies:
% 159.61/25.92  | | | |   (27)  all_56_5 = e0
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | | REF_CLOSE: (14), (16), (27) are inconsistent by sub-proof #591.
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | Case 2:
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | |   (28)  all_56_10 = e0 & op(e2, e0) = e0
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | | ALPHA: (28) implies:
% 159.61/25.92  | | | |   (29)  all_56_10 = e0
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | | REF_CLOSE: (6), (16), (29) are inconsistent by sub-proof #740.
% 159.61/25.92  | | | | 
% 159.61/25.92  | | | End of split
% 159.61/25.92  | | | 
% 159.61/25.92  | | End of split
% 159.61/25.92  | | 
% 159.61/25.92  | End of split
% 159.61/25.92  | 
% 159.61/25.92  End of proof
% 159.61/25.92  
% 159.61/25.92  Sub-proof #591 shows that the following formulas are inconsistent:
% 159.61/25.92  ----------------------------------------------------------------
% 159.61/25.92    (1)  all_56_5 = e3
% 159.61/25.92    (2)  all_56_5 = e0
% 159.61/25.92    (3)   ~ (e3 = e0)
% 159.61/25.92  
% 159.61/25.92  Begin of proof
% 159.61/25.92  | 
% 159.61/25.92  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.92  |   (4)  e3 = e0
% 159.61/25.92  | 
% 159.61/25.92  | SIMP: (4) implies:
% 159.61/25.92  |   (5)  e3 = e0
% 159.61/25.92  | 
% 159.61/25.92  | REDUCE: (3), (5) imply:
% 159.61/25.92  |   (6)  $false
% 159.61/25.92  | 
% 159.61/25.92  | CLOSE: (6) is inconsistent.
% 159.61/25.92  | 
% 159.61/25.92  End of proof
% 159.61/25.92  
% 159.61/25.92  Sub-proof #592 shows that the following formulas are inconsistent:
% 159.61/25.92  ----------------------------------------------------------------
% 159.61/25.92    (1)  op(e0, e0) = e1
% 159.61/25.92    (2)   ~ (all_52_6 = e1)
% 159.61/25.92    (3)  op(e1, e1) = e0
% 159.61/25.92    (4)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.61/25.92             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.61/25.92           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.61/25.92               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.61/25.92             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.61/25.92         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.61/25.92             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.61/25.92           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.61/25.92               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.61/25.92             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.61/25.92         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.61/25.92             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.61/25.92           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.61/25.92               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.61/25.92             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.61/25.92         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.61/25.92             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.61/25.92           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.61/25.92               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.61/25.92             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.61/25.92    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.92    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.61/25.92         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.61/25.92    (7)  op(e1, e3) = all_52_2
% 159.61/25.92    (8)  op(e1, e2) = all_52_6
% 159.61/25.92    (9)  op(e1, e0) = all_52_14
% 159.61/25.92    (10)  op(e0, e0) = all_14_2
% 159.61/25.92    (11)  op(e2, e2) = e1
% 159.61/25.92    (12)   ~ (e1 = e0)
% 159.61/25.92    (13)   ~ (e2 = e1)
% 159.61/25.92    (14)   ~ (all_52_14 = e1)
% 159.61/25.92    (15)   ~ (e3 = e0)
% 159.61/25.92  
% 159.61/25.92  Begin of proof
% 159.61/25.92  | 
% 159.61/25.92  | BETA: splitting (4) gives:
% 159.61/25.92  | 
% 159.61/25.92  | Case 1:
% 159.61/25.92  | | 
% 159.61/25.92  | |   (16)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.61/25.92  | |               e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.61/25.92  | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.61/25.92  | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.61/25.92  | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.61/25.92  | |                 e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 159.61/25.92  | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 159.61/25.92  | |                 e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 159.61/25.92  | |               e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 159.61/25.92  | |               all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 159.61/25.92  | |               e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 159.61/25.92  | |               $i(all_57_7))))
% 159.61/25.92  | | 
% 159.61/25.92  | | BETA: splitting (16) gives:
% 159.61/25.92  | | 
% 159.61/25.92  | | Case 1:
% 159.61/25.92  | | | 
% 159.61/25.92  | | |   (17)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.61/25.92  | | |             e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.61/25.92  | | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.61/25.92  | | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.61/25.92  | | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.61/25.92  | | |               e3) = all_57_6 & $i(all_57_6)))
% 159.61/25.92  | | | 
% 159.61/25.92  | | | ALPHA: (17) implies:
% 159.61/25.92  | | |   (18)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1,
% 159.61/25.92  | | |             e3) = all_57_2 & $i(all_57_2))
% 159.61/25.92  | | | 
% 159.61/25.92  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (12), (14), (15), (18) are
% 159.61/25.92  | | |            inconsistent by sub-proof #605.
% 159.61/25.92  | | | 
% 159.61/25.92  | | Case 2:
% 159.61/25.92  | | | 
% 159.61/25.92  | | |   (19)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 159.61/25.92  | | |             e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 159.61/25.92  | | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 159.61/25.92  | | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 159.61/25.92  | | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 159.61/25.92  | | |               e2) = all_57_7 & $i(all_57_7)))
% 159.61/25.92  | | | 
% 159.61/25.92  | | | ALPHA: (19) implies:
% 159.61/25.92  | | |   (20)  op(e2, e2) = e2
% 159.61/25.92  | | | 
% 159.61/25.92  | | | REF_CLOSE: (5), (11), (13), (20) are inconsistent by sub-proof #993.
% 159.61/25.92  | | | 
% 159.61/25.92  | | End of split
% 159.61/25.92  | | 
% 159.61/25.92  | Case 2:
% 159.61/25.92  | | 
% 159.61/25.92  | |   (21)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.61/25.92  | |               e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.61/25.92  | |               $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.61/25.92  | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.61/25.92  | |           ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.61/25.92  | |                 e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 159.61/25.92  | |             e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 159.61/25.92  | |                 e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 =
% 159.61/25.92  | |               e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 159.61/25.92  | |               all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 159.61/25.92  | |               e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.61/25.92  | |               $i(all_57_13))))
% 159.61/25.92  | | 
% 159.61/25.92  | | REF_CLOSE: (1), (3), (5), (10), (12), (21) are inconsistent by sub-proof
% 159.61/25.92  | |            #629.
% 159.61/25.92  | | 
% 159.61/25.92  | End of split
% 159.61/25.92  | 
% 159.61/25.92  End of proof
% 159.61/25.92  
% 159.61/25.92  Sub-proof #593 shows that the following formulas are inconsistent:
% 159.61/25.92  ----------------------------------------------------------------
% 159.61/25.92    (1)  all_56_5 = e3
% 159.61/25.92    (2)  all_56_5 = e2
% 159.61/25.92    (3)   ~ (e3 = e2)
% 159.61/25.92  
% 159.61/25.92  Begin of proof
% 159.61/25.92  | 
% 159.61/25.92  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.92  |   (4)  e3 = e2
% 159.61/25.92  | 
% 159.61/25.92  | SIMP: (4) implies:
% 159.61/25.92  |   (5)  e3 = e2
% 159.61/25.92  | 
% 159.61/25.92  | REDUCE: (3), (5) imply:
% 159.61/25.92  |   (6)  $false
% 159.61/25.92  | 
% 159.61/25.92  | CLOSE: (6) is inconsistent.
% 159.61/25.92  | 
% 159.61/25.92  End of proof
% 159.61/25.92  
% 159.61/25.92  Sub-proof #594 shows that the following formulas are inconsistent:
% 159.61/25.92  ----------------------------------------------------------------
% 159.61/25.92    (1)  all_56_13 = e2 & op(e0, e2) = e2
% 159.61/25.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.92    (3)  op(e0, e2) = all_52_7
% 159.61/25.92    (4)   ~ (all_52_7 = e2)
% 159.61/25.92  
% 159.61/25.92  Begin of proof
% 159.61/25.92  | 
% 159.61/25.92  | ALPHA: (1) implies:
% 159.61/25.92  |   (5)  op(e0, e2) = e2
% 159.61/25.92  | 
% 159.61/25.92  | GROUND_INST: instantiating (2) with all_52_7, e2, e2, e0, simplifying with
% 159.61/25.92  |              (3), (5) gives:
% 159.61/25.92  |   (6)  all_52_7 = e2
% 159.61/25.92  | 
% 159.61/25.92  | REDUCE: (4), (6) imply:
% 159.61/25.92  |   (7)  $false
% 159.61/25.92  | 
% 159.61/25.92  | CLOSE: (7) is inconsistent.
% 159.61/25.92  | 
% 159.61/25.92  End of proof
% 159.61/25.92  
% 159.61/25.92  Sub-proof #595 shows that the following formulas are inconsistent:
% 159.61/25.92  ----------------------------------------------------------------
% 159.61/25.92    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.61/25.92         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.61/25.92    (2)   ~ (e3 = e2)
% 159.61/25.92    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.92    (4)  all_56_12 = e2
% 159.61/25.92    (5)   ~ (all_57_11 = e2)
% 159.61/25.92    (6)  op(e3, e3) = e3
% 159.61/25.92    (7)  op(e2, e2) = e1
% 159.61/25.92    (8)   ~ (e1 = e0)
% 159.61/25.92    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.61/25.92         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.61/25.92    (10)  op(e2, e0) = all_52_13
% 159.61/25.92    (11)   ~ (e2 = e1)
% 159.61/25.92    (12)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.61/25.92          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 159.61/25.92            e3)
% 159.61/25.92    (13)  all_56_13 = e3
% 159.61/25.92    (14)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.61/25.92          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 159.61/25.92    (15)  all_56_15 = e0
% 159.61/25.92    (16)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.61/25.92          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.61/25.92    (17)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.61/25.92          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.61/25.92            e1)
% 159.61/25.92    (18)  all_56_5 = e3
% 159.61/25.92    (19)   ~ (e3 = e1)
% 159.61/25.92    (20)   ~ (e2 = e0)
% 159.61/25.92    (21)  op(e2, e0) = all_57_11
% 159.61/25.92    (22)   ~ (e3 = e0)
% 159.61/25.92  
% 159.61/25.92  Begin of proof
% 159.61/25.92  | 
% 159.61/25.92  | BETA: splitting (14) gives:
% 159.61/25.92  | 
% 159.61/25.92  | Case 1:
% 159.61/25.92  | | 
% 159.61/25.92  | |   (23)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 159.61/25.92  | |           e2)
% 159.61/25.92  | | 
% 159.61/25.92  | | BETA: splitting (23) gives:
% 159.61/25.92  | | 
% 159.61/25.92  | | Case 1:
% 159.61/25.92  | | | 
% 159.61/25.92  | | |   (24)  all_56_2 = e2 & op(e2, e3) = e2
% 159.61/25.92  | | | 
% 159.61/25.92  | | | ALPHA: (24) implies:
% 159.61/25.92  | | |   (25)  all_56_2 = e2
% 159.61/25.92  | | | 
% 159.61/25.92  | | | REF_CLOSE: (3), (4), (6), (8), (9), (11), (16), (19), (20), (22), (25) are
% 159.61/25.92  | | |            inconsistent by sub-proof #597.
% 159.61/25.92  | | | 
% 159.61/25.92  | | Case 2:
% 159.61/25.92  | | | 
% 159.61/25.92  | | |   (26)  all_56_3 = e2 & op(e2, e2) = e2
% 159.61/25.92  | | | 
% 159.61/25.92  | | | ALPHA: (26) implies:
% 159.61/25.92  | | |   (27)  op(e2, e2) = e2
% 159.61/25.92  | | | 
% 159.61/25.92  | | | REF_CLOSE: (3), (7), (11), (27) are inconsistent by sub-proof #993.
% 159.61/25.92  | | | 
% 159.61/25.92  | | End of split
% 159.61/25.92  | | 
% 159.61/25.92  | Case 2:
% 159.61/25.92  | | 
% 159.61/25.92  | |   (28)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 159.61/25.92  | |           e2)
% 159.61/25.92  | | 
% 159.61/25.92  | | BETA: splitting (28) gives:
% 159.61/25.92  | | 
% 159.61/25.92  | | Case 1:
% 159.61/25.92  | | | 
% 159.61/25.92  | | |   (29)  all_56_5 = e2 & op(e2, e1) = e2
% 159.61/25.92  | | | 
% 159.61/25.92  | | | ALPHA: (29) implies:
% 159.61/25.92  | | |   (30)  all_56_5 = e2
% 159.61/25.92  | | | 
% 159.61/25.92  | | | COMBINE_EQS: (18), (30) imply:
% 159.61/25.93  | | |   (31)  e3 = e2
% 159.61/25.93  | | | 
% 159.61/25.93  | | | SIMP: (31) implies:
% 159.61/25.93  | | |   (32)  e3 = e2
% 159.61/25.93  | | | 
% 159.61/25.93  | | | COMBINE_EQS: (13), (32) imply:
% 159.61/25.93  | | |   (33)  all_56_13 = e2
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (11), (12), (15), (16),
% 159.61/25.93  | | |            (17), (19), (20), (22), (33) are inconsistent by sub-proof
% 159.61/25.93  | | |            #596.
% 159.61/25.93  | | | 
% 159.61/25.93  | | Case 2:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (34)  all_56_10 = e2 & op(e2, e0) = e2
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (34) implies:
% 159.61/25.93  | | |   (35)  op(e2, e0) = e2
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (3), (5), (10), (21), (35) are inconsistent by sub-proof #627.
% 159.61/25.93  | | | 
% 159.61/25.93  | | End of split
% 159.61/25.93  | | 
% 159.61/25.93  | End of split
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #596 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.93    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.61/25.93         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.61/25.93    (2)   ~ (e3 = e2)
% 159.61/25.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.93    (4)  all_56_12 = e2
% 159.61/25.93    (5)  all_56_13 = e2
% 159.61/25.93    (6)  op(e3, e3) = e3
% 159.61/25.93    (7)   ~ (e1 = e0)
% 159.61/25.93    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.61/25.93         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.61/25.93    (9)   ~ (e2 = e1)
% 159.61/25.93    (10)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.61/25.93          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 159.61/25.93            e3)
% 159.61/25.93    (11)  all_56_15 = e0
% 159.61/25.93    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.61/25.93          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.61/25.93    (13)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.61/25.93          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.61/25.93            e1)
% 159.61/25.93    (14)   ~ (e3 = e1)
% 159.61/25.93    (15)   ~ (e2 = e0)
% 159.61/25.93    (16)   ~ (e3 = e0)
% 159.61/25.93  
% 159.61/25.93  Begin of proof
% 159.61/25.93  | 
% 159.61/25.93  | BETA: splitting (10) gives:
% 159.61/25.93  | 
% 159.61/25.93  | Case 1:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (17)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 159.61/25.93  | |           e3)
% 159.61/25.93  | | 
% 159.61/25.93  | | BETA: splitting (17) gives:
% 159.61/25.93  | | 
% 159.61/25.93  | | Case 1:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (18)  all_56_12 = e3 & op(e0, e3) = e3
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (18) implies:
% 159.61/25.93  | | |   (19)  all_56_12 = e3
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (12), (14), (15), (16), (19)
% 159.61/25.93  | | |            are inconsistent by sub-proof #729.
% 159.61/25.93  | | | 
% 159.61/25.93  | | Case 2:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (20)  all_56_13 = e3 & op(e0, e2) = e3
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (20) implies:
% 159.61/25.93  | | |   (21)  all_56_13 = e3
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (2), (5), (21) are inconsistent by sub-proof #688.
% 159.61/25.93  | | | 
% 159.61/25.93  | | End of split
% 159.61/25.93  | | 
% 159.61/25.93  | Case 2:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (22)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 159.61/25.93  | |           e3)
% 159.61/25.93  | | 
% 159.61/25.93  | | BETA: splitting (22) gives:
% 159.61/25.93  | | 
% 159.61/25.93  | | Case 1:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (23)  all_56_14 = e3 & op(e0, e1) = e3
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (23) implies:
% 159.61/25.93  | | |   (24)  all_56_14 = e3
% 159.61/25.93  | | | 
% 159.61/25.93  | | | BETA: splitting (13) gives:
% 159.61/25.93  | | | 
% 159.61/25.93  | | | Case 1:
% 159.61/25.93  | | | | 
% 159.61/25.93  | | | |   (25)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0,
% 159.61/25.93  | | | |             e2) = e1)
% 159.61/25.93  | | | | 
% 159.61/25.93  | | | | BETA: splitting (25) gives:
% 159.61/25.93  | | | | 
% 159.61/25.93  | | | | Case 1:
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | |   (26)  all_56_12 = e1 & op(e0, e3) = e1
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | | REF_CLOSE: (4), (9), (26) are inconsistent by sub-proof #769.
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | Case 2:
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | |   (27)  all_56_13 = e1 & op(e0, e2) = e1
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | | REF_CLOSE: (5), (9), (27) are inconsistent by sub-proof #938.
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | End of split
% 159.61/25.93  | | | | 
% 159.61/25.93  | | | Case 2:
% 159.61/25.93  | | | | 
% 159.61/25.93  | | | |   (28)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0,
% 159.61/25.93  | | | |             e0) = e1)
% 159.61/25.93  | | | | 
% 159.61/25.93  | | | | BETA: splitting (28) gives:
% 159.61/25.93  | | | | 
% 159.61/25.93  | | | | Case 1:
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | |   (29)  all_56_14 = e1 & op(e0, e1) = e1
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | | REF_CLOSE: (14), (24), (29) are inconsistent by sub-proof #667.
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | Case 2:
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | |   (30)  all_56_15 = e1 & op(e0, e0) = e1
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | | REF_CLOSE: (7), (11), (30) are inconsistent by sub-proof #884.
% 159.61/25.93  | | | | | 
% 159.61/25.93  | | | | End of split
% 159.61/25.93  | | | | 
% 159.61/25.93  | | | End of split
% 159.61/25.93  | | | 
% 159.61/25.93  | | Case 2:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (31)  all_56_15 = e3 & op(e0, e0) = e3
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (11), (16), (31) are inconsistent by sub-proof #892.
% 159.61/25.93  | | | 
% 159.61/25.93  | | End of split
% 159.61/25.93  | | 
% 159.61/25.93  | End of split
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #597 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.93    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.93    (2)  all_56_12 = e2
% 159.61/25.93    (3)  all_56_2 = e2
% 159.61/25.93    (4)  op(e3, e3) = e3
% 159.61/25.93    (5)   ~ (e1 = e0)
% 159.61/25.93    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.61/25.93         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.61/25.93    (7)   ~ (e2 = e1)
% 159.61/25.93    (8)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.61/25.93         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.61/25.93    (9)   ~ (e3 = e1)
% 159.61/25.93    (10)   ~ (e2 = e0)
% 159.61/25.93    (11)   ~ (e3 = e0)
% 159.61/25.93  
% 159.61/25.93  Begin of proof
% 159.61/25.93  | 
% 159.61/25.93  | BETA: splitting (6) gives:
% 159.61/25.93  | 
% 159.61/25.93  | Case 1:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 159.61/25.93  | |           e0)
% 159.61/25.93  | | 
% 159.61/25.93  | | REF_CLOSE: (1), (3), (4), (10), (11), (12) are inconsistent by sub-proof
% 159.61/25.93  | |            #601.
% 159.61/25.93  | | 
% 159.61/25.93  | Case 2:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (13)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 159.61/25.93  | |           e0)
% 159.61/25.93  | | 
% 159.61/25.93  | | BETA: splitting (13) gives:
% 159.61/25.93  | | 
% 159.61/25.93  | | Case 1:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (14)  all_56_6 = e0 & op(e1, e3) = e0
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (14) implies:
% 159.61/25.93  | | |   (15)  all_56_6 = e0
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (15) are inconsistent
% 159.61/25.93  | | |            by sub-proof #598.
% 159.61/25.93  | | | 
% 159.61/25.93  | | Case 2:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (16)  all_56_12 = e0 & op(e0, e3) = e0
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (16) implies:
% 159.61/25.93  | | |   (17)  all_56_12 = e0
% 159.61/25.93  | | | 
% 159.61/25.93  | | | COMBINE_EQS: (2), (17) imply:
% 159.61/25.93  | | |   (18)  e2 = e0
% 159.61/25.93  | | | 
% 159.61/25.93  | | | SIMP: (18) implies:
% 159.61/25.93  | | |   (19)  e2 = e0
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REDUCE: (10), (19) imply:
% 159.61/25.93  | | |   (20)  $false
% 159.61/25.93  | | | 
% 159.61/25.93  | | | CLOSE: (20) is inconsistent.
% 159.61/25.93  | | | 
% 159.61/25.93  | | End of split
% 159.61/25.93  | | 
% 159.61/25.93  | End of split
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #598 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.93    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.93    (2)  all_56_12 = e2
% 159.61/25.93    (3)  all_56_2 = e2
% 159.61/25.93    (4)  op(e3, e3) = e3
% 159.61/25.93    (5)  all_56_6 = e0
% 159.61/25.93    (6)   ~ (e1 = e0)
% 159.61/25.93    (7)   ~ (e2 = e1)
% 159.61/25.93    (8)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.61/25.93         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.61/25.93    (9)   ~ (e3 = e1)
% 159.61/25.93  
% 159.61/25.93  Begin of proof
% 159.61/25.93  | 
% 159.61/25.93  | BETA: splitting (8) gives:
% 159.61/25.93  | 
% 159.61/25.93  | Case 1:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 159.61/25.93  | |           e1)
% 159.61/25.93  | | 
% 159.61/25.93  | | BETA: splitting (10) gives:
% 159.61/25.93  | | 
% 159.61/25.93  | | Case 1:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (11)  all_56_0 = e1 & op(e3, e3) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (11) implies:
% 159.61/25.93  | | |   (12)  op(e3, e3) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (1), (4), (9), (12) are inconsistent by sub-proof #995.
% 159.61/25.93  | | | 
% 159.61/25.93  | | Case 2:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (13)  all_56_2 = e1 & op(e2, e3) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (13) implies:
% 159.61/25.93  | | |   (14)  all_56_2 = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (3), (7), (14) are inconsistent by sub-proof #600.
% 159.61/25.93  | | | 
% 159.61/25.93  | | End of split
% 159.61/25.93  | | 
% 159.61/25.93  | Case 2:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (15)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 159.61/25.93  | |           e1)
% 159.61/25.93  | | 
% 159.61/25.93  | | BETA: splitting (15) gives:
% 159.61/25.93  | | 
% 159.61/25.93  | | Case 1:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (16)  all_56_6 = e1 & op(e1, e3) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (5), (6), (16) are inconsistent by sub-proof #599.
% 159.61/25.93  | | | 
% 159.61/25.93  | | Case 2:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (17)  all_56_12 = e1 & op(e0, e3) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (17) implies:
% 159.61/25.93  | | |   (18)  all_56_12 = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (2), (7), (18) are inconsistent by sub-proof #718.
% 159.61/25.93  | | | 
% 159.61/25.93  | | End of split
% 159.61/25.93  | | 
% 159.61/25.93  | End of split
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #599 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.93    (1)  all_56_6 = e1 & op(e1, e3) = e1
% 159.61/25.93    (2)  all_56_6 = e0
% 159.61/25.93    (3)   ~ (e1 = e0)
% 159.61/25.93  
% 159.61/25.93  Begin of proof
% 159.61/25.93  | 
% 159.61/25.93  | ALPHA: (1) implies:
% 159.61/25.93  |   (4)  all_56_6 = e1
% 159.61/25.93  | 
% 159.61/25.93  | COMBINE_EQS: (2), (4) imply:
% 159.61/25.93  |   (5)  e1 = e0
% 159.61/25.93  | 
% 159.61/25.93  | REDUCE: (3), (5) imply:
% 159.61/25.93  |   (6)  $false
% 159.61/25.93  | 
% 159.61/25.93  | CLOSE: (6) is inconsistent.
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #600 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.93    (1)  all_56_2 = e2
% 159.61/25.93    (2)  all_56_2 = e1
% 159.61/25.93    (3)   ~ (e2 = e1)
% 159.61/25.93  
% 159.61/25.93  Begin of proof
% 159.61/25.93  | 
% 159.61/25.93  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.93  |   (4)  e2 = e1
% 159.61/25.93  | 
% 159.61/25.93  | SIMP: (4) implies:
% 159.61/25.93  |   (5)  e2 = e1
% 159.61/25.93  | 
% 159.61/25.93  | REDUCE: (3), (5) imply:
% 159.61/25.93  |   (6)  $false
% 159.61/25.93  | 
% 159.61/25.93  | CLOSE: (6) is inconsistent.
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #601 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.93    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.93    (2)  all_56_2 = e2
% 159.61/25.93    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 159.61/25.93    (4)  op(e3, e3) = e3
% 159.61/25.93    (5)   ~ (e2 = e0)
% 159.61/25.93    (6)   ~ (e3 = e0)
% 159.61/25.93  
% 159.61/25.93  Begin of proof
% 159.61/25.93  | 
% 159.61/25.93  | BETA: splitting (3) gives:
% 159.61/25.93  | 
% 159.61/25.93  | Case 1:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 159.61/25.93  | | 
% 159.61/25.93  | | ALPHA: (7) implies:
% 159.61/25.93  | |   (8)  op(e3, e3) = e0
% 159.61/25.93  | | 
% 159.61/25.93  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #971.
% 159.61/25.93  | | 
% 159.61/25.93  | Case 2:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (9)  all_56_2 = e0 & op(e2, e3) = e0
% 159.61/25.93  | | 
% 159.61/25.93  | | ALPHA: (9) implies:
% 159.61/25.93  | |   (10)  all_56_2 = e0
% 159.61/25.93  | | 
% 159.61/25.93  | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #602.
% 159.61/25.93  | | 
% 159.61/25.93  | End of split
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #602 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.93    (1)  all_56_2 = e2
% 159.61/25.93    (2)  all_56_2 = e0
% 159.61/25.93    (3)   ~ (e2 = e0)
% 159.61/25.93  
% 159.61/25.93  Begin of proof
% 159.61/25.93  | 
% 159.61/25.93  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.93  |   (4)  e2 = e0
% 159.61/25.93  | 
% 159.61/25.93  | SIMP: (4) implies:
% 159.61/25.93  |   (5)  e2 = e0
% 159.61/25.93  | 
% 159.61/25.93  | REDUCE: (3), (5) imply:
% 159.61/25.93  |   (6)  $false
% 159.61/25.93  | 
% 159.61/25.93  | CLOSE: (6) is inconsistent.
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #603 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.93    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.61/25.93         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.61/25.93    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.93    (3)  all_56_7 = e2
% 159.61/25.93    (4)  op(e0, e2) = all_52_7
% 159.61/25.93    (5)  op(e2, e2) = e0
% 159.61/25.93    (6)  all_56_1 = e0
% 159.61/25.93    (7)   ~ (e1 = e0)
% 159.61/25.93    (8)   ~ (e2 = e1)
% 159.61/25.93    (9)   ~ (all_52_7 = e1)
% 159.61/25.93  
% 159.61/25.93  Begin of proof
% 159.61/25.93  | 
% 159.61/25.93  | BETA: splitting (1) gives:
% 159.61/25.93  | 
% 159.61/25.93  | Case 1:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (10)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 159.61/25.93  | |           e1)
% 159.61/25.93  | | 
% 159.61/25.93  | | REF_CLOSE: (2), (5), (6), (7), (10) are inconsistent by sub-proof #959.
% 159.61/25.93  | | 
% 159.61/25.93  | Case 2:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (11)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 159.61/25.93  | |           e1)
% 159.61/25.93  | | 
% 159.61/25.93  | | BETA: splitting (11) gives:
% 159.61/25.93  | | 
% 159.61/25.93  | | Case 1:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (12)  all_56_7 = e1 & op(e1, e2) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (3), (8), (12) are inconsistent by sub-proof #604.
% 159.61/25.93  | | | 
% 159.61/25.93  | | Case 2:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (13)  all_56_13 = e1 & op(e0, e2) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (2), (4), (9), (13) are inconsistent by sub-proof #712.
% 159.61/25.93  | | | 
% 159.61/25.93  | | End of split
% 159.61/25.93  | | 
% 159.61/25.93  | End of split
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #604 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.93    (1)  all_56_7 = e1 & op(e1, e2) = e1
% 159.61/25.93    (2)  all_56_7 = e2
% 159.61/25.93    (3)   ~ (e2 = e1)
% 159.61/25.93  
% 159.61/25.93  Begin of proof
% 159.61/25.93  | 
% 159.61/25.93  | ALPHA: (1) implies:
% 159.61/25.93  |   (4)  all_56_7 = e1
% 159.61/25.93  | 
% 159.61/25.93  | COMBINE_EQS: (2), (4) imply:
% 159.61/25.93  |   (5)  e2 = e1
% 159.61/25.93  | 
% 159.61/25.93  | REDUCE: (3), (5) imply:
% 159.61/25.93  |   (6)  $false
% 159.61/25.93  | 
% 159.61/25.93  | CLOSE: (6) is inconsistent.
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #605 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.93    (1)   ~ (all_52_6 = e1)
% 159.61/25.93    (2)  op(e1, e1) = e0
% 159.61/25.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.93    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.61/25.93         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.61/25.93    (5)  op(e1, e3) = all_52_2
% 159.61/25.93    (6)  op(e1, e2) = all_52_6
% 159.61/25.93    (7)  op(e1, e0) = all_52_14
% 159.61/25.93    (8)   ~ (e1 = e0)
% 159.61/25.93    (9)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 159.61/25.93           all_57_2 & $i(all_57_2))
% 159.61/25.93    (10)   ~ (all_52_14 = e1)
% 159.61/25.93    (11)   ~ (e3 = e0)
% 159.61/25.93  
% 159.61/25.93  Begin of proof
% 159.61/25.93  | 
% 159.61/25.93  | BETA: splitting (4) gives:
% 159.61/25.93  | 
% 159.61/25.93  | Case 1:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (12)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 159.61/25.93  | |           e1)
% 159.61/25.93  | | 
% 159.61/25.93  | | BETA: splitting (12) gives:
% 159.61/25.93  | | 
% 159.61/25.93  | | Case 1:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (13)  all_56_6 = e1 & op(e1, e3) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (13) implies:
% 159.61/25.93  | | |   (14)  op(e1, e3) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (2), (3), (5), (9), (11), (14) are inconsistent by sub-proof
% 159.61/25.93  | | |            #606.
% 159.61/25.93  | | | 
% 159.61/25.93  | | Case 2:
% 159.61/25.93  | | | 
% 159.61/25.93  | | |   (15)  all_56_7 = e1 & op(e1, e2) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | ALPHA: (15) implies:
% 159.61/25.93  | | |   (16)  op(e1, e2) = e1
% 159.61/25.93  | | | 
% 159.61/25.93  | | | REF_CLOSE: (1), (3), (6), (16) are inconsistent by sub-proof #984.
% 159.61/25.93  | | | 
% 159.61/25.93  | | End of split
% 159.61/25.93  | | 
% 159.61/25.93  | Case 2:
% 159.61/25.93  | | 
% 159.61/25.93  | |   (17)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 159.61/25.93  | |           e1)
% 159.61/25.93  | | 
% 159.61/25.93  | | REF_CLOSE: (2), (3), (7), (8), (10), (17) are inconsistent by sub-proof
% 159.61/25.93  | |            #902.
% 159.61/25.93  | | 
% 159.61/25.93  | End of split
% 159.61/25.93  | 
% 159.61/25.93  End of proof
% 159.61/25.93  
% 159.61/25.93  Sub-proof #606 shows that the following formulas are inconsistent:
% 159.61/25.93  ----------------------------------------------------------------
% 159.61/25.94    (1)  op(e1, e1) = e0
% 159.61/25.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (3)  op(e1, e3) = all_52_2
% 159.61/25.94    (4)  op(e1, e3) = e1
% 159.61/25.94    (5)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 159.61/25.94           all_57_2 & $i(all_57_2))
% 159.61/25.94    (6)   ~ (e3 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | BETA: splitting (5) gives:
% 159.61/25.94  | 
% 159.61/25.94  | Case 1:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (7)  all_57_14 = e3 & op(e1, e1) = e3
% 159.61/25.94  | | 
% 159.61/25.94  | | ALPHA: (7) implies:
% 159.61/25.94  | |   (8)  op(e1, e1) = e3
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #912.
% 159.61/25.94  | | 
% 159.61/25.94  | Case 2:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (9)   ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #607.
% 159.61/25.94  | | 
% 159.61/25.94  | End of split
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #607 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)   ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)
% 159.61/25.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (3)  op(e1, e3) = all_52_2
% 159.61/25.94    (4)  op(e1, e3) = e1
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | ALPHA: (1) implies:
% 159.61/25.94  |   (5)   ~ (all_57_2 = e1)
% 159.61/25.94  |   (6)  op(e1, e3) = all_57_2
% 159.61/25.94  | 
% 159.61/25.94  | GROUND_INST: instantiating (2) with all_52_2, all_57_2, e3, e1, simplifying
% 159.61/25.94  |              with (3), (6) gives:
% 159.61/25.94  |   (7)  all_57_2 = all_52_2
% 159.61/25.94  | 
% 159.61/25.94  | GROUND_INST: instantiating (2) with e1, all_57_2, e3, e1, simplifying with
% 159.61/25.94  |              (4), (6) gives:
% 159.61/25.94  |   (8)  all_57_2 = e1
% 159.61/25.94  | 
% 159.61/25.94  | COMBINE_EQS: (7), (8) imply:
% 159.61/25.94  |   (9)  all_52_2 = e1
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (5), (8) imply:
% 159.61/25.94  |   (10)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (10) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #608 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_54_8 = all_52_2
% 159.61/25.94    (2)  all_54_8 = e2
% 159.61/25.94    (3)   ~ (all_52_2 = e2)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.94  |   (4)  all_52_2 = e2
% 159.61/25.94  | 
% 159.61/25.94  | SIMP: (4) implies:
% 159.61/25.94  |   (5)  all_52_2 = e2
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (3), (5) imply:
% 159.61/25.94  |   (6)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (6) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #609 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_54_1 = all_52_4
% 159.61/25.94    (2)  all_54_1 = e2
% 159.61/25.94    (3)   ~ (all_52_4 = e2)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.94  |   (4)  all_52_4 = e2
% 159.61/25.94  | 
% 159.61/25.94  | SIMP: (4) implies:
% 159.61/25.94  |   (5)  all_52_4 = e2
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (3), (5) imply:
% 159.61/25.94  |   (6)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (6) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #610 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (2)  op(e1, e2) = all_24_0
% 159.61/25.94    (3)  op(e1, e2) = e3
% 159.61/25.94    (4)   ~ (all_24_0 = e3)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | GROUND_INST: instantiating (1) with e3, all_24_0, e2, e1, simplifying with
% 159.61/25.94  |              (2), (3) gives:
% 159.61/25.94  |   (5)  all_24_0 = e3
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (4), (5) imply:
% 159.61/25.94  |   (6)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (6) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #611 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)   ~ (all_42_1 = e0) & op(e1, e1) = all_42_1 & $i(all_42_1)
% 159.61/25.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (3)  op(e1, e1) = e0
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | ALPHA: (1) implies:
% 159.61/25.94  |   (4)   ~ (all_42_1 = e0)
% 159.61/25.94  |   (5)  op(e1, e1) = all_42_1
% 159.61/25.94  | 
% 159.61/25.94  | GROUND_INST: instantiating (2) with e0, all_42_1, e1, e1, simplifying with
% 159.61/25.94  |              (3), (5) gives:
% 159.61/25.94  |   (6)  all_42_1 = e0
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (4), (6) imply:
% 159.61/25.94  |   (7)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (7) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #612 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_54_8 = e1 | all_54_8 = e0
% 159.61/25.94    (2)  all_54_8 = all_52_2
% 159.61/25.94    (3)   ~ (all_52_2 = e1)
% 159.61/25.94    (4)   ~ (all_52_2 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | BETA: splitting (1) gives:
% 159.61/25.94  | 
% 159.61/25.94  | Case 1:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (5)  all_54_8 = e1
% 159.61/25.94  | | 
% 159.61/25.94  | | COMBINE_EQS: (2), (5) imply:
% 159.61/25.94  | |   (6)  all_52_2 = e1
% 159.61/25.94  | | 
% 159.61/25.94  | | SIMP: (6) implies:
% 159.61/25.94  | |   (7)  all_52_2 = e1
% 159.61/25.94  | | 
% 159.61/25.94  | | REDUCE: (3), (7) imply:
% 159.61/25.94  | |   (8)  $false
% 159.61/25.94  | | 
% 159.61/25.94  | | CLOSE: (8) is inconsistent.
% 159.61/25.94  | | 
% 159.61/25.94  | Case 2:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (9)  all_54_8 = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #613.
% 159.61/25.94  | | 
% 159.61/25.94  | End of split
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #613 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_54_8 = all_52_2
% 159.61/25.94    (2)  all_54_8 = e0
% 159.61/25.94    (3)   ~ (all_52_2 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.94  |   (4)  all_52_2 = e0
% 159.61/25.94  | 
% 159.61/25.94  | SIMP: (4) implies:
% 159.61/25.94  |   (5)  all_52_2 = e0
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (3), (5) imply:
% 159.61/25.94  |   (6)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (6) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #614 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)   ~ (all_52_14 = e3)
% 159.61/25.94    (2)  op(e1, e1) = e0
% 159.61/25.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (4)  op(e1, e0) = all_52_14
% 159.61/25.94    (5)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 159.61/25.94    (6)   ~ (e3 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | BETA: splitting (5) gives:
% 159.61/25.94  | 
% 159.61/25.94  | Case 1:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (7)  all_56_8 = e3 & op(e1, e1) = e3
% 159.61/25.94  | | 
% 159.61/25.94  | | ALPHA: (7) implies:
% 159.61/25.94  | |   (8)  op(e1, e1) = e3
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #912.
% 159.61/25.94  | | 
% 159.61/25.94  | Case 2:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (9)  all_56_11 = e3 & op(e1, e0) = e3
% 159.61/25.94  | | 
% 159.61/25.94  | | ALPHA: (9) implies:
% 159.61/25.94  | |   (10)  op(e1, e0) = e3
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #677.
% 159.61/25.94  | | 
% 159.61/25.94  | End of split
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #615 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (2)  all_56_12 = e3
% 159.61/25.94    (3)  op(e1, e3) = e3
% 159.61/25.94    (4)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.61/25.94    (5)   ~ (e3 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | BETA: splitting (4) gives:
% 159.61/25.94  | 
% 159.61/25.94  | Case 1:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (6)  all_56_6 = e0 & op(e1, e3) = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | ALPHA: (6) implies:
% 159.61/25.94  | |   (7)  op(e1, e3) = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #913.
% 159.61/25.94  | | 
% 159.61/25.94  | Case 2:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (8)  all_56_12 = e0 & op(e0, e3) = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | ALPHA: (8) implies:
% 159.61/25.94  | |   (9)  all_56_12 = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | COMBINE_EQS: (2), (9) imply:
% 159.61/25.94  | |   (10)  e3 = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | SIMP: (10) implies:
% 159.61/25.94  | |   (11)  e3 = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | REDUCE: (5), (11) imply:
% 159.61/25.94  | |   (12)  $false
% 159.61/25.94  | | 
% 159.61/25.94  | | CLOSE: (12) is inconsistent.
% 159.61/25.94  | | 
% 159.61/25.94  | End of split
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #616 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_56_12 = e3
% 159.61/25.94    (2)  all_56_12 = e2
% 159.61/25.94    (3)   ~ (e3 = e2)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.94  |   (4)  e3 = e2
% 159.61/25.94  | 
% 159.61/25.94  | SIMP: (4) implies:
% 159.61/25.94  |   (5)  e3 = e2
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (3), (5) imply:
% 159.61/25.94  |   (6)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (6) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #617 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (2)  op(e1, e3) = e3
% 159.61/25.94    (3)  op(e1, e3) = e2
% 159.61/25.94    (4)   ~ (e3 = e2)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | GROUND_INST: instantiating (1) with e2, e3, e3, e1, simplifying with (2), (3)
% 159.61/25.94  |              gives:
% 159.61/25.94  |   (5)  e3 = e2
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (4), (5) imply:
% 159.61/25.94  |   (6)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (6) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #618 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_56_2 = e3
% 159.61/25.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 159.61/25.94    (4)  op(e3, e3) = e1
% 159.61/25.94    (5)   ~ (e1 = e0)
% 159.61/25.94    (6)   ~ (e3 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | BETA: splitting (3) gives:
% 159.61/25.94  | 
% 159.61/25.94  | Case 1:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | ALPHA: (7) implies:
% 159.61/25.94  | |   (8)  op(e3, e3) = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #834.
% 159.61/25.94  | | 
% 159.61/25.94  | Case 2:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (9)  all_56_2 = e0 & op(e2, e3) = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #777.
% 159.61/25.94  | | 
% 159.61/25.94  | End of split
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #619 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_54_12 = e1 | all_54_12 = e0
% 159.61/25.94    (2)  all_54_12 = all_52_3
% 159.61/25.94    (3)   ~ (all_52_3 = e1)
% 159.61/25.94    (4)   ~ (all_52_3 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | BETA: splitting (1) gives:
% 159.61/25.94  | 
% 159.61/25.94  | Case 1:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (5)  all_54_12 = e1
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #695.
% 159.61/25.94  | | 
% 159.61/25.94  | Case 2:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (6)  all_54_12 = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | COMBINE_EQS: (2), (6) imply:
% 159.61/25.94  | |   (7)  all_52_3 = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | SIMP: (7) implies:
% 159.61/25.94  | |   (8)  all_52_3 = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | REDUCE: (4), (8) imply:
% 159.61/25.94  | |   (9)  $false
% 159.61/25.94  | | 
% 159.61/25.94  | | CLOSE: (9) is inconsistent.
% 159.61/25.94  | | 
% 159.61/25.94  | End of split
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #620 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_56_9 = e0 & op(e3, e0) = e0
% 159.61/25.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (3)  op(e3, e0) = all_52_12
% 159.61/25.94    (4)   ~ (all_52_12 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | ALPHA: (1) implies:
% 159.61/25.94  |   (5)  op(e3, e0) = e0
% 159.61/25.94  | 
% 159.61/25.94  | GROUND_INST: instantiating (2) with all_52_12, e0, e0, e3, simplifying with
% 159.61/25.94  |              (3), (5) gives:
% 159.61/25.94  |   (6)  all_52_12 = e0
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (4), (6) imply:
% 159.61/25.94  |   (7)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (7) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #621 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_56_11 = e2
% 159.61/25.94    (2)  all_56_11 = e1
% 159.61/25.94    (3)   ~ (e2 = e1)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.94  |   (4)  e2 = e1
% 159.61/25.94  | 
% 159.61/25.94  | SIMP: (4) implies:
% 159.61/25.94  |   (5)  e2 = e1
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (3), (5) imply:
% 159.61/25.94  |   (6)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (6) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #622 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)   ~ (all_52_14 = e3)
% 159.61/25.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (3)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.61/25.94    (4)  op(e0, e0) = e0
% 159.61/25.94    (5)  op(e1, e0) = all_52_14
% 159.61/25.94    (6)   ~ (e3 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | BETA: splitting (3) gives:
% 159.61/25.94  | 
% 159.61/25.94  | Case 1:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (7)  all_56_11 = e3 & op(e1, e0) = e3
% 159.61/25.94  | | 
% 159.61/25.94  | | ALPHA: (7) implies:
% 159.61/25.94  | |   (8)  op(e1, e0) = e3
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #677.
% 159.61/25.94  | | 
% 159.61/25.94  | Case 2:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (9)  all_56_15 = e3 & op(e0, e0) = e3
% 159.61/25.94  | | 
% 159.61/25.94  | | ALPHA: (9) implies:
% 159.61/25.94  | |   (10)  op(e0, e0) = e3
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #999.
% 159.61/25.94  | | 
% 159.61/25.94  | End of split
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #623 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_54_11 = e1 | all_54_11 = e0
% 159.61/25.94    (2)  all_54_11 = all_52_14
% 159.61/25.94    (3)   ~ (all_52_14 = e1)
% 159.61/25.94    (4)   ~ (all_52_14 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | BETA: splitting (1) gives:
% 159.61/25.94  | 
% 159.61/25.94  | Case 1:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (5)  all_54_11 = e1
% 159.61/25.94  | | 
% 159.61/25.94  | | COMBINE_EQS: (2), (5) imply:
% 159.61/25.94  | |   (6)  all_52_14 = e1
% 159.61/25.94  | | 
% 159.61/25.94  | | SIMP: (6) implies:
% 159.61/25.94  | |   (7)  all_52_14 = e1
% 159.61/25.94  | | 
% 159.61/25.94  | | REDUCE: (3), (7) imply:
% 159.61/25.94  | |   (8)  $false
% 159.61/25.94  | | 
% 159.61/25.94  | | CLOSE: (8) is inconsistent.
% 159.61/25.94  | | 
% 159.61/25.94  | Case 2:
% 159.61/25.94  | | 
% 159.61/25.94  | |   (9)  all_54_11 = e0
% 159.61/25.94  | | 
% 159.61/25.94  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #624.
% 159.61/25.94  | | 
% 159.61/25.94  | End of split
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #624 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  all_54_11 = all_52_14
% 159.61/25.94    (2)  all_54_11 = e0
% 159.61/25.94    (3)   ~ (all_52_14 = e0)
% 159.61/25.94  
% 159.61/25.94  Begin of proof
% 159.61/25.94  | 
% 159.61/25.94  | COMBINE_EQS: (1), (2) imply:
% 159.61/25.94  |   (4)  all_52_14 = e0
% 159.61/25.94  | 
% 159.61/25.94  | SIMP: (4) implies:
% 159.61/25.94  |   (5)  all_52_14 = e0
% 159.61/25.94  | 
% 159.61/25.94  | REDUCE: (3), (5) imply:
% 159.61/25.94  |   (6)  $false
% 159.61/25.94  | 
% 159.61/25.94  | CLOSE: (6) is inconsistent.
% 159.61/25.94  | 
% 159.61/25.94  End of proof
% 159.61/25.94  
% 159.61/25.94  Sub-proof #625 shows that the following formulas are inconsistent:
% 159.61/25.94  ----------------------------------------------------------------
% 159.61/25.94    (1)  op(e0, e3) = e2
% 159.61/25.94    (2)  op(e0, e1) = all_52_11
% 159.61/25.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.94    (4)  op(e0, e3) = all_52_3
% 159.61/25.94    (5)   ~ (all_57_11 = e2)
% 159.61/25.94    (6)  op(e1, e0) = all_52_14
% 159.61/25.94    (7)  op(e3, e3) = e1
% 159.61/25.94    (8)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) =
% 159.61/25.94           all_57_13 & $i(all_57_13))
% 159.61/25.94    (9)   ~ (e1 = e0)
% 159.61/25.94    (10)  op(e2, e0) = all_52_13
% 159.61/25.94    (11)  op(e0, e2) = e3
% 159.61/25.94    (12)   ~ (all_52_11 = e0)
% 159.61/25.95    (13)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.61/25.95            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.61/25.95            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 159.61/25.95            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.61/25.95            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.61/25.95              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.61/25.95            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 159.61/25.95            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 159.61/25.95            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.61/25.95            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/25.95              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/25.95            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.61/25.95            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.61/25.95            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/25.95              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.61/25.95          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.61/25.95            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.61/25.95            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 159.61/25.95            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.61/25.95            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.61/25.95            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.61/25.95            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.61/25.95    (14)   ~ (e2 = e0)
% 159.61/25.95    (15)  op(e2, e0) = all_57_11
% 159.61/25.95    (16)   ~ (e3 = e0)
% 159.61/25.95  
% 159.61/25.95  Begin of proof
% 159.61/25.95  | 
% 159.61/25.95  | BETA: splitting (13) gives:
% 159.61/25.95  | 
% 159.61/25.95  | Case 1:
% 159.61/25.95  | | 
% 159.61/25.95  | |   (17)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.61/25.95  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.61/25.95  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 159.61/25.95  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.61/25.95  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.61/25.95  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.61/25.95  | | 
% 159.61/25.95  | | BETA: splitting (17) gives:
% 159.61/25.95  | | 
% 159.61/25.95  | | Case 1:
% 159.61/25.95  | | | 
% 159.61/25.95  | | |   (18)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.61/25.95  | | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.61/25.95  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.61/25.95  | | | 
% 159.61/25.95  | | | BETA: splitting (18) gives:
% 159.61/25.95  | | | 
% 159.61/25.95  | | | Case 1:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | |   (19)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | | | |           e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | ALPHA: (19) implies:
% 159.61/25.95  | | | |   (20)  op(e0, e3) = e0
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | REF_CLOSE: (1), (3), (4), (14), (20) are inconsistent by sub-proof #689.
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | Case 2:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | |   (21)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.61/25.95  | | | |             = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0)
% 159.61/25.95  | | | |         | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/25.95  | | | |           (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/25.95  | | | |             e3) = e0)
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | BETA: splitting (21) gives:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | Case 1:
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | |   (22)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/25.95  | | | | |         (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/25.95  | | | | |           e3) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | ALPHA: (22) implies:
% 159.61/25.95  | | | | |   (23)  op(e2, e0) = e2
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | REF_CLOSE: (3), (5), (10), (15), (23) are inconsistent by sub-proof
% 159.61/25.95  | | | | |            #627.
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | Case 2:
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | |   (24)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/25.95  | | | | |         (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/25.95  | | | | |           e3) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | ALPHA: (24) implies:
% 159.61/25.95  | | | | |   (25)  op(e0, e3) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | REF_CLOSE: (1), (3), (4), (14), (25) are inconsistent by sub-proof
% 159.61/25.95  | | | | |            #689.
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | End of split
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | End of split
% 159.61/25.95  | | | 
% 159.61/25.95  | | Case 2:
% 159.61/25.95  | | | 
% 159.61/25.95  | | |   (26)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0)
% 159.61/25.95  | | |         | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/25.95  | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.61/25.95  | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.61/25.95  | | | 
% 159.61/25.95  | | | BETA: splitting (26) gives:
% 159.61/25.95  | | | 
% 159.61/25.95  | | | Case 1:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | |   (27)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | ALPHA: (27) implies:
% 159.61/25.95  | | | |   (28)  op(e0, e3) = e0
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | REF_CLOSE: (1), (3), (4), (14), (28) are inconsistent by sub-proof #689.
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | Case 2:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | |   (29)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/25.95  | | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0)
% 159.61/25.95  | | | |         | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/25.95  | | | |           (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/25.95  | | | |             e2) = e0)
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | BETA: splitting (29) gives:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | Case 1:
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | |   (30)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/25.95  | | | | |           = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | ALPHA: (30) implies:
% 159.61/25.95  | | | | |   (31)  op(e3, e3) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | REF_CLOSE: (3), (7), (9), (31) are inconsistent by sub-proof #834.
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | Case 2:
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | |   (32)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/25.95  | | | | |         (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/25.95  | | | | |           e2) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | ALPHA: (32) implies:
% 159.61/25.95  | | | | |   (33)  op(e2, e0) = e2
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | REF_CLOSE: (3), (5), (10), (15), (33) are inconsistent by sub-proof
% 159.61/25.95  | | | | |            #627.
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | End of split
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | End of split
% 159.61/25.95  | | | 
% 159.61/25.95  | | End of split
% 159.61/25.95  | | 
% 159.61/25.95  | Case 2:
% 159.61/25.95  | | 
% 159.61/25.95  | |   (34)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 159.61/25.95  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.61/25.95  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.61/25.95  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.61/25.95  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.61/25.95  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.61/25.95  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.61/25.95  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 159.61/25.95  | |           & op(e0, e1) = e0)
% 159.61/25.95  | | 
% 159.61/25.95  | | BETA: splitting (34) gives:
% 159.61/25.95  | | 
% 159.61/25.95  | | Case 1:
% 159.61/25.95  | | | 
% 159.61/25.95  | | |   (35)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 159.61/25.95  | | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.61/25.95  | | |         | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/25.95  | | |             = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.61/25.95  | | | 
% 159.61/25.95  | | | BETA: splitting (35) gives:
% 159.61/25.95  | | | 
% 159.61/25.95  | | | Case 1:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | |   (36)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.61/25.95  | | | |           = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | ALPHA: (36) implies:
% 159.61/25.95  | | | |   (37)  op(e0, e2) = e0
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | REF_CLOSE: (3), (11), (16), (37) are inconsistent by sub-proof #726.
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | Case 2:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | |   (38)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.61/25.95  | | | |           e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.61/25.95  | | | |           (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.61/25.95  | | | |             e1) = e0)
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | BETA: splitting (38) gives:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | Case 1:
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | |   (39)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.61/25.95  | | | | |         e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | ALPHA: (39) implies:
% 159.61/25.95  | | | | |   (40)  op(e0, e2) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | REF_CLOSE: (3), (11), (16), (40) are inconsistent by sub-proof #726.
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | Case 2:
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | |   (41)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/25.95  | | | | |           = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | ALPHA: (41) implies:
% 159.61/25.95  | | | | |   (42)  op(e3, e3) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | REF_CLOSE: (3), (7), (9), (42) are inconsistent by sub-proof #834.
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | End of split
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | End of split
% 159.61/25.95  | | | 
% 159.61/25.95  | | Case 2:
% 159.61/25.95  | | | 
% 159.61/25.95  | | |   (43)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.61/25.95  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.61/25.95  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.61/25.95  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.61/25.95  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.61/25.95  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 159.61/25.95  | | |             e0) & op(e0, e1) = e0)
% 159.61/25.95  | | | 
% 159.61/25.95  | | | BETA: splitting (43) gives:
% 159.61/25.95  | | | 
% 159.61/25.95  | | | Case 1:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | |   (44)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.61/25.95  | | | |             = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 159.61/25.95  | | | |         | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/25.95  | | | |           (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/25.95  | | | |             e1) = e0)
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | BETA: splitting (44) gives:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | Case 1:
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | |   (45)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/25.95  | | | | |         (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/25.95  | | | | |           e1) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | ALPHA: (45) implies:
% 159.61/25.95  | | | | |   (46)  op(e2, e0) = e2
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | REF_CLOSE: (3), (5), (10), (15), (46) are inconsistent by sub-proof
% 159.61/25.95  | | | | |            #627.
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | Case 2:
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | |   (47)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/25.95  | | | | |         (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/25.95  | | | | |           e1) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | ALPHA: (47) implies:
% 159.61/25.95  | | | | |   (48)  op(e0, e1) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | REF_CLOSE: (2), (3), (12), (48) are inconsistent by sub-proof #966.
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | End of split
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | Case 2:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | |   (49)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 159.61/25.95  | | | |             = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.61/25.95  | | | |             e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 159.61/25.95  | | | |           &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | BETA: splitting (49) gives:
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | | Case 1:
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | |   (50)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 159.61/25.95  | | | | |         (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/25.95  | | | | |         op(e0, e1) = e0 & $i(all_57_14)
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | ALPHA: (50) implies:
% 159.61/25.95  | | | | |   (51)   ~ (all_57_14 = e0)
% 159.61/25.95  | | | | |   (52)  op(e1, e0) = e1
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | REF_CLOSE: (3), (6), (8), (51), (52) are inconsistent by sub-proof
% 159.61/25.95  | | | | |            #626.
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | Case 2:
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | |   (53)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.61/25.95  | | | | |         e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | ALPHA: (53) implies:
% 159.61/25.95  | | | | |   (54)  op(e0, e1) = e0
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | | REF_CLOSE: (2), (3), (12), (54) are inconsistent by sub-proof #966.
% 159.61/25.95  | | | | | 
% 159.61/25.95  | | | | End of split
% 159.61/25.95  | | | | 
% 159.61/25.95  | | | End of split
% 159.61/25.95  | | | 
% 159.61/25.95  | | End of split
% 159.61/25.95  | | 
% 159.61/25.95  | End of split
% 159.61/25.95  | 
% 159.61/25.95  End of proof
% 159.61/25.95  
% 159.61/25.95  Sub-proof #626 shows that the following formulas are inconsistent:
% 159.61/25.95  ----------------------------------------------------------------
% 159.61/25.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.95    (2)   ~ (all_57_14 = e0)
% 159.61/25.95    (3)  op(e1, e0) = all_52_14
% 159.61/25.95    (4)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0) =
% 159.61/25.95           all_57_13 & $i(all_57_13))
% 159.61/25.95    (5)  op(e1, e0) = e1
% 159.61/25.95  
% 159.61/25.95  Begin of proof
% 159.61/25.95  | 
% 159.61/25.95  | BETA: splitting (4) gives:
% 159.61/25.95  | 
% 159.61/25.95  | Case 1:
% 159.61/25.95  | | 
% 159.61/25.95  | |   (6)  all_57_14 = e0 & op(e1, e1) = e0
% 159.61/25.95  | | 
% 159.61/25.95  | | ALPHA: (6) implies:
% 159.61/25.95  | |   (7)  all_57_14 = e0
% 159.61/25.95  | | 
% 159.61/25.95  | | REDUCE: (2), (7) imply:
% 159.61/25.95  | |   (8)  $false
% 159.61/25.95  | | 
% 159.61/25.95  | | CLOSE: (8) is inconsistent.
% 159.61/25.95  | | 
% 159.61/25.95  | Case 2:
% 159.61/25.95  | | 
% 159.61/25.95  | |   (9)   ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13)
% 159.61/25.95  | | 
% 159.61/25.95  | | ALPHA: (9) implies:
% 159.61/25.95  | |   (10)   ~ (all_57_13 = e1)
% 159.61/25.95  | |   (11)  op(e1, e0) = all_57_13
% 159.61/25.95  | | 
% 159.61/25.95  | | REF_CLOSE: (1), (3), (5), (10), (11) are inconsistent by sub-proof #637.
% 159.61/25.95  | | 
% 159.61/25.95  | End of split
% 159.61/25.95  | 
% 159.61/25.95  End of proof
% 159.61/25.95  
% 159.61/25.95  Sub-proof #627 shows that the following formulas are inconsistent:
% 159.61/25.95  ----------------------------------------------------------------
% 159.61/25.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.95    (2)   ~ (all_57_11 = e2)
% 159.61/25.95    (3)  op(e2, e0) = e2
% 159.61/25.95    (4)  op(e2, e0) = all_52_13
% 159.61/25.95    (5)  op(e2, e0) = all_57_11
% 159.61/25.95  
% 159.61/25.95  Begin of proof
% 159.61/25.95  | 
% 159.61/25.95  | GROUND_INST: instantiating (1) with all_52_13, all_57_11, e0, e2, simplifying
% 159.61/25.95  |              with (4), (5) gives:
% 159.61/25.95  |   (6)  all_57_11 = all_52_13
% 159.61/25.95  | 
% 159.61/25.95  | GROUND_INST: instantiating (1) with e2, all_57_11, e0, e2, simplifying with
% 159.61/25.95  |              (3), (5) gives:
% 159.61/25.95  |   (7)  all_57_11 = e2
% 159.61/25.95  | 
% 159.61/25.95  | COMBINE_EQS: (6), (7) imply:
% 159.61/25.95  |   (8)  all_52_13 = e2
% 159.61/25.95  | 
% 159.61/25.95  | REDUCE: (2), (7) imply:
% 159.61/25.95  |   (9)  $false
% 159.61/25.95  | 
% 159.61/25.95  | CLOSE: (9) is inconsistent.
% 159.61/25.95  | 
% 159.61/25.95  End of proof
% 159.61/25.95  
% 159.61/25.95  Sub-proof #628 shows that the following formulas are inconsistent:
% 159.61/25.95  ----------------------------------------------------------------
% 159.61/25.95    (1)  op(e0, e0) = e1
% 159.61/25.95    (2)  op(e1, e1) = e0
% 159.61/25.96    (3)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.61/25.96             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.61/25.96           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.61/25.96               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.61/25.96             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.61/25.96         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.61/25.96             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.61/25.96           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.61/25.96               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.61/25.96             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.61/25.96         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.61/25.96             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.61/25.96           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.61/25.96               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.61/25.96             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.61/25.96         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.61/25.96             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.61/25.96           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.61/25.96               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.61/25.96             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.61/25.96    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.96    (5)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.61/25.96         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.61/25.96    (6)  op(e1, e3) = all_52_2
% 159.61/25.96    (7)   ~ (all_52_2 = e1)
% 159.61/25.96    (8)  op(e1, e0) = all_52_14
% 159.61/25.96    (9)  op(e0, e0) = all_14_2
% 159.61/25.96    (10)  op(e3, e3) = e1
% 159.61/25.96    (11)   ~ (e1 = e0)
% 159.61/25.96    (12)   ~ (all_52_14 = e1)
% 159.61/25.96    (13)   ~ (e3 = e1)
% 159.61/25.96    (14)   ~ (e2 = e0)
% 159.61/25.96  
% 159.61/25.96  Begin of proof
% 159.61/25.96  | 
% 159.61/25.96  | BETA: splitting (3) gives:
% 159.61/25.96  | 
% 159.61/25.96  | Case 1:
% 159.61/25.96  | | 
% 159.61/25.96  | |   (15)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.61/25.96  | |               e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.61/25.96  | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.61/25.96  | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.61/25.96  | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.61/25.96  | |                 e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 159.61/25.96  | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 159.61/25.96  | |                 e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 159.61/25.96  | |               e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 159.61/25.96  | |               all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 159.61/25.96  | |               e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 159.61/25.96  | |               $i(all_57_7))))
% 159.61/25.96  | | 
% 159.61/25.96  | | BETA: splitting (15) gives:
% 159.61/25.96  | | 
% 159.61/25.96  | | Case 1:
% 159.61/25.96  | | | 
% 159.61/25.96  | | |   (16)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.61/25.96  | | |             e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.61/25.96  | | |             $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.61/25.96  | | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.61/25.96  | | |         ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.61/25.96  | | |               e3) = all_57_6 & $i(all_57_6)))
% 159.61/25.96  | | | 
% 159.61/25.96  | | | ALPHA: (16) implies:
% 159.61/25.96  | | |   (17)  op(e3, e3) = e3
% 159.61/25.96  | | | 
% 159.61/25.96  | | | REF_CLOSE: (4), (10), (13), (17) are inconsistent by sub-proof #995.
% 159.61/25.96  | | | 
% 159.61/25.96  | | Case 2:
% 159.61/25.96  | | | 
% 159.61/25.96  | | |   (18)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 159.61/25.96  | | |             e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 159.61/25.96  | | |             $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 159.61/25.96  | | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 159.61/25.96  | | |         ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 159.61/25.96  | | |               e2) = all_57_7 & $i(all_57_7)))
% 159.61/25.96  | | | 
% 159.61/25.96  | | | ALPHA: (18) implies:
% 159.61/25.96  | | |   (19)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1,
% 159.61/25.96  | | |             e2) = all_57_3 & $i(all_57_3))
% 159.61/25.96  | | | 
% 159.61/25.96  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (11), (12), (14), (19) are
% 159.61/25.96  | | |            inconsistent by sub-proof #630.
% 159.61/25.96  | | | 
% 159.61/25.96  | | End of split
% 159.61/25.96  | | 
% 159.61/25.96  | Case 2:
% 159.61/25.96  | | 
% 159.61/25.96  | |   (20)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.61/25.96  | |               e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.61/25.96  | |               $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.61/25.96  | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.61/25.96  | |           ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.61/25.96  | |                 e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 159.61/25.96  | |             e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 159.61/25.96  | |                 e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 =
% 159.61/25.96  | |               e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 159.61/25.96  | |               all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 159.61/25.96  | |               e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.61/25.96  | |               $i(all_57_13))))
% 159.61/25.96  | | 
% 159.61/25.96  | | REF_CLOSE: (1), (2), (4), (9), (11), (20) are inconsistent by sub-proof
% 159.61/25.96  | |            #629.
% 159.61/25.96  | | 
% 159.61/25.96  | End of split
% 159.61/25.96  | 
% 159.61/25.96  End of proof
% 159.61/25.96  
% 159.61/25.96  Sub-proof #629 shows that the following formulas are inconsistent:
% 159.61/25.96  ----------------------------------------------------------------
% 159.61/25.96    (1)  op(e0, e0) = e1
% 159.61/25.96    (2)  op(e1, e1) = e0
% 159.61/25.96    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.96    (4)  op(e0, e0) = all_14_2
% 159.61/25.96    (5)   ~ (e1 = e0)
% 159.61/25.96    (6)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.61/25.96             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.61/25.96           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.61/25.96               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.61/25.96             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.61/25.96         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.61/25.96             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.61/25.96           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.61/25.96               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.61/25.96             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.61/25.96  
% 159.61/25.96  Begin of proof
% 159.61/25.96  | 
% 159.61/25.96  | BETA: splitting (6) gives:
% 159.61/25.96  | 
% 159.61/25.96  | Case 1:
% 159.61/25.96  | | 
% 159.61/25.96  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.61/25.96  | |            e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.61/25.96  | |            $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.61/25.96  | |            (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.61/25.96  | |        ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.61/25.96  | |              e1) = all_57_8 & $i(all_57_8)))
% 159.61/25.96  | | 
% 159.61/25.96  | | ALPHA: (7) implies:
% 159.61/25.96  | |   (8)  op(e1, e1) = e1
% 159.61/25.96  | | 
% 159.61/25.96  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #903.
% 159.61/25.96  | | 
% 159.61/25.96  | Case 2:
% 159.61/25.96  | | 
% 159.61/25.96  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 159.61/25.96  | |            e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.61/25.96  | |            $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 159.61/25.96  | |            (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 159.61/25.96  | |        ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 159.61/25.96  | |              e0) = all_57_13 & $i(all_57_13)))
% 159.61/25.96  | | 
% 159.61/25.96  | | ALPHA: (9) implies:
% 159.61/25.96  | |   (10)  op(e0, e0) = e0
% 159.61/25.96  | | 
% 159.61/25.96  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #991.
% 159.61/25.96  | | 
% 159.61/25.96  | End of split
% 159.61/25.96  | 
% 159.61/25.96  End of proof
% 159.61/25.96  
% 159.61/25.96  Sub-proof #630 shows that the following formulas are inconsistent:
% 159.61/25.96  ----------------------------------------------------------------
% 159.61/25.96    (1)  op(e1, e1) = e0
% 159.61/25.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.96    (3)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 159.61/25.96         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 159.61/25.96    (4)  op(e1, e3) = all_52_2
% 159.61/25.96    (5)   ~ (all_52_2 = e1)
% 159.61/25.96    (6)  op(e1, e0) = all_52_14
% 159.61/25.96    (7)  (all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 159.61/25.96           all_57_3 & $i(all_57_3))
% 159.61/25.96    (8)   ~ (e1 = e0)
% 159.61/25.96    (9)   ~ (all_52_14 = e1)
% 159.61/25.96    (10)   ~ (e2 = e0)
% 159.61/25.96  
% 159.61/25.96  Begin of proof
% 159.61/25.96  | 
% 159.61/25.96  | BETA: splitting (3) gives:
% 159.61/25.96  | 
% 159.61/25.96  | Case 1:
% 159.61/25.96  | | 
% 159.61/25.96  | |   (11)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 159.61/25.96  | |           e1)
% 159.61/25.96  | | 
% 159.61/25.96  | | BETA: splitting (11) gives:
% 159.61/25.96  | | 
% 159.61/25.96  | | Case 1:
% 159.61/25.96  | | | 
% 159.61/25.96  | | |   (12)  all_56_6 = e1 & op(e1, e3) = e1
% 159.61/25.96  | | | 
% 159.61/25.96  | | | ALPHA: (12) implies:
% 159.61/25.96  | | |   (13)  op(e1, e3) = e1
% 159.61/25.96  | | | 
% 159.61/25.96  | | | REF_CLOSE: (2), (4), (5), (13) are inconsistent by sub-proof #990.
% 159.61/25.96  | | | 
% 159.61/25.96  | | Case 2:
% 159.61/25.96  | | | 
% 159.61/25.96  | | |   (14)  all_56_7 = e1 & op(e1, e2) = e1
% 159.61/25.96  | | | 
% 159.61/25.96  | | | ALPHA: (14) implies:
% 159.61/25.96  | | |   (15)  op(e1, e2) = e1
% 159.61/25.96  | | | 
% 159.61/25.96  | | | BETA: splitting (7) gives:
% 159.61/25.96  | | | 
% 159.61/25.96  | | | Case 1:
% 159.61/25.96  | | | | 
% 159.61/25.96  | | | |   (16)  all_57_14 = e2 & op(e1, e1) = e2
% 159.61/25.96  | | | | 
% 159.61/25.96  | | | | ALPHA: (16) implies:
% 159.61/25.96  | | | |   (17)  op(e1, e1) = e2
% 159.61/25.96  | | | | 
% 159.61/25.96  | | | | REF_CLOSE: (1), (2), (10), (17) are inconsistent by sub-proof #914.
% 159.61/25.96  | | | | 
% 159.61/25.96  | | | Case 2:
% 159.61/25.96  | | | | 
% 159.61/25.96  | | | |   (18)   ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3)
% 159.61/25.96  | | | | 
% 159.61/25.96  | | | | ALPHA: (18) implies:
% 159.61/25.96  | | | |   (19)   ~ (all_57_3 = e1)
% 159.61/25.96  | | | |   (20)  op(e1, e2) = all_57_3
% 159.61/25.96  | | | | 
% 159.61/25.96  | | | | REF_CLOSE: (2), (15), (19), (20) are inconsistent by sub-proof #631.
% 159.61/25.96  | | | | 
% 159.61/25.96  | | | End of split
% 159.61/25.96  | | | 
% 159.61/25.96  | | End of split
% 159.61/25.96  | | 
% 159.61/25.96  | Case 2:
% 159.61/25.96  | | 
% 159.61/25.96  | |   (21)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 159.61/25.96  | |           e1)
% 159.61/25.96  | | 
% 159.61/25.96  | | REF_CLOSE: (1), (2), (6), (8), (9), (21) are inconsistent by sub-proof #902.
% 159.61/25.96  | | 
% 159.61/25.96  | End of split
% 159.61/25.96  | 
% 159.61/25.96  End of proof
% 159.61/25.96  
% 159.61/25.96  Sub-proof #631 shows that the following formulas are inconsistent:
% 159.61/25.96  ----------------------------------------------------------------
% 159.61/25.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.96    (2)  op(e1, e2) = all_57_3
% 159.61/25.96    (3)  op(e1, e2) = e1
% 159.61/25.96    (4)   ~ (all_57_3 = e1)
% 159.61/25.96  
% 159.61/25.96  Begin of proof
% 159.61/25.96  | 
% 159.61/25.96  | GROUND_INST: instantiating (1) with e1, all_57_3, e2, e1, simplifying with
% 159.61/25.96  |              (2), (3) gives:
% 159.61/25.96  |   (5)  all_57_3 = e1
% 159.61/25.96  | 
% 159.61/25.96  | REDUCE: (4), (5) imply:
% 159.61/25.96  |   (6)  $false
% 159.61/25.96  | 
% 159.61/25.96  | CLOSE: (6) is inconsistent.
% 159.61/25.96  | 
% 159.61/25.96  End of proof
% 159.61/25.96  
% 159.61/25.96  Sub-proof #632 shows that the following formulas are inconsistent:
% 159.61/25.96  ----------------------------------------------------------------
% 159.61/25.96    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.61/25.96         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.61/25.96    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.61/25.96         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.61/25.96    (3)   ~ (e3 = e2)
% 159.61/25.96    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.96    (5)  op(e3, e3) = e3
% 159.61/25.96    (6)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.61/25.96         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.61/25.96    (7)   ~ (e1 = e0)
% 159.61/25.96    (8)   ~ (e2 = e1)
% 159.61/25.96    (9)  all_56_9 = e3
% 159.61/25.96    (10)   ~ (e3 = e1)
% 159.61/25.96    (11)   ~ (e2 = e0)
% 159.61/25.96    (12)   ~ (e3 = e0)
% 159.61/25.96  
% 159.61/25.96  Begin of proof
% 159.61/25.96  | 
% 159.61/25.96  | BETA: splitting (1) gives:
% 159.61/25.96  | 
% 159.61/25.96  | Case 1:
% 159.61/25.96  | | 
% 159.61/25.96  | |   (13)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) =
% 159.61/25.96  | |           e2)
% 159.61/25.96  | | 
% 159.61/25.96  | | BETA: splitting (13) gives:
% 159.61/25.96  | | 
% 159.61/25.96  | | Case 1:
% 159.61/25.96  | | | 
% 159.61/25.96  | | |   (14)  all_56_0 = e2 & op(e3, e3) = e2
% 159.61/25.96  | | | 
% 159.61/25.96  | | | ALPHA: (14) implies:
% 159.61/25.96  | | |   (15)  op(e3, e3) = e2
% 159.61/25.96  | | | 
% 159.61/25.96  | | | GROUND_INST: instantiating (4) with e2, e3, e3, e3, simplifying with (5),
% 159.61/25.96  | | |              (15) gives:
% 159.61/25.96  | | |   (16)  e3 = e2
% 159.61/25.96  | | | 
% 159.61/25.96  | | | REDUCE: (3), (16) imply:
% 159.61/25.96  | | |   (17)  $false
% 159.61/25.96  | | | 
% 159.61/25.96  | | | CLOSE: (17) is inconsistent.
% 159.61/25.96  | | | 
% 159.61/25.96  | | Case 2:
% 159.61/25.96  | | | 
% 159.61/25.96  | | |   (18)  all_56_1 = e2 & op(e3, e2) = e2
% 159.61/25.96  | | | 
% 159.61/25.96  | | | ALPHA: (18) implies:
% 159.61/25.96  | | |   (19)  all_56_1 = e2
% 159.61/25.96  | | | 
% 159.61/25.96  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (19) are
% 159.61/25.96  | | |            inconsistent by sub-proof #633.
% 159.61/25.96  | | | 
% 159.61/25.96  | | End of split
% 159.61/25.96  | | 
% 159.61/25.96  | Case 2:
% 159.61/25.96  | | 
% 159.61/25.96  | |   (20)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 159.61/25.96  | |           e2)
% 159.61/25.96  | | 
% 159.61/25.96  | | BETA: splitting (20) gives:
% 159.61/25.96  | | 
% 159.61/25.96  | | Case 1:
% 159.61/25.96  | | | 
% 159.61/25.96  | | |   (21)  all_56_4 = e2 & op(e3, e1) = e2
% 159.61/25.96  | | | 
% 159.61/25.96  | | | ALPHA: (21) implies:
% 159.61/25.96  | | |   (22)  all_56_4 = e2
% 159.61/25.96  | | | 
% 159.61/25.96  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (22) are
% 159.61/25.96  | | |            inconsistent by sub-proof #757.
% 159.61/25.96  | | | 
% 159.61/25.96  | | Case 2:
% 159.61/25.96  | | | 
% 159.61/25.96  | | |   (23)  all_56_9 = e2 & op(e3, e0) = e2
% 159.61/25.96  | | | 
% 159.61/25.96  | | | ALPHA: (23) implies:
% 159.61/25.96  | | |   (24)  all_56_9 = e2
% 159.61/25.96  | | | 
% 159.61/25.96  | | | COMBINE_EQS: (9), (24) imply:
% 159.61/25.96  | | |   (25)  e3 = e2
% 159.61/25.96  | | | 
% 159.61/25.96  | | | REDUCE: (3), (25) imply:
% 159.61/25.96  | | |   (26)  $false
% 159.61/25.96  | | | 
% 159.61/25.96  | | | CLOSE: (26) is inconsistent.
% 159.61/25.96  | | | 
% 159.61/25.96  | | End of split
% 159.61/25.96  | | 
% 159.61/25.96  | End of split
% 159.61/25.96  | 
% 159.61/25.96  End of proof
% 159.61/25.96  
% 159.61/25.96  Sub-proof #633 shows that the following formulas are inconsistent:
% 159.61/25.96  ----------------------------------------------------------------
% 159.61/25.96    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.61/25.96         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.61/25.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.96    (3)  all_56_1 = e2
% 159.61/25.96    (4)  op(e3, e3) = e3
% 159.61/25.96    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.61/25.96         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.61/25.96    (6)   ~ (e1 = e0)
% 159.61/25.96    (7)   ~ (e2 = e1)
% 159.61/25.96    (8)  all_56_9 = e3
% 159.61/25.96    (9)   ~ (e3 = e1)
% 159.61/25.96    (10)   ~ (e2 = e0)
% 159.61/25.96    (11)   ~ (e3 = e0)
% 159.61/25.96  
% 159.61/25.96  Begin of proof
% 159.61/25.96  | 
% 159.61/25.96  | BETA: splitting (5) gives:
% 159.61/25.96  | 
% 159.61/25.96  | Case 1:
% 159.61/25.96  | | 
% 159.61/25.97  | |   (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 159.61/25.97  | |           e1)
% 159.61/25.97  | | 
% 159.61/25.97  | | REF_CLOSE: (2), (3), (4), (7), (9), (12) are inconsistent by sub-proof #635.
% 159.61/25.97  | | 
% 159.61/25.97  | Case 2:
% 159.61/25.97  | | 
% 159.61/25.97  | |   (13)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 159.61/25.97  | |           e1)
% 159.61/25.97  | | 
% 159.61/25.97  | | BETA: splitting (13) gives:
% 159.61/25.97  | | 
% 159.61/25.97  | | Case 1:
% 159.61/25.97  | | | 
% 159.61/25.97  | | |   (14)  all_56_4 = e1 & op(e3, e1) = e1
% 159.61/25.97  | | | 
% 159.61/25.97  | | | ALPHA: (14) implies:
% 159.61/25.97  | | |   (15)  all_56_4 = e1
% 159.61/25.97  | | | 
% 159.61/25.97  | | | BETA: splitting (1) gives:
% 159.61/25.97  | | | 
% 159.61/25.97  | | | Case 1:
% 159.61/25.97  | | | | 
% 159.61/25.97  | | | |   (16)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2)
% 159.61/25.97  | | | |           = e0)
% 159.61/25.97  | | | | 
% 159.61/25.97  | | | | REF_CLOSE: (2), (3), (4), (10), (11), (16) are inconsistent by sub-proof
% 159.61/25.97  | | | |            #634.
% 159.61/25.97  | | | | 
% 159.61/25.97  | | | Case 2:
% 159.61/25.97  | | | | 
% 159.61/25.97  | | | |   (17)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0)
% 159.61/25.97  | | | |           = e0)
% 159.61/25.97  | | | | 
% 159.61/25.97  | | | | BETA: splitting (17) gives:
% 159.61/25.97  | | | | 
% 159.61/25.97  | | | | Case 1:
% 159.61/25.97  | | | | | 
% 159.61/25.97  | | | | |   (18)  all_56_4 = e0 & op(e3, e1) = e0
% 159.61/25.97  | | | | | 
% 159.61/25.97  | | | | | REF_CLOSE: (6), (15), (18) are inconsistent by sub-proof #951.
% 159.61/25.97  | | | | | 
% 159.61/25.97  | | | | Case 2:
% 159.61/25.97  | | | | | 
% 159.61/25.97  | | | | |   (19)  all_56_9 = e0 & op(e3, e0) = e0
% 159.61/25.97  | | | | | 
% 159.61/25.97  | | | | | REF_CLOSE: (8), (11), (19) are inconsistent by sub-proof #759.
% 159.61/25.97  | | | | | 
% 159.61/25.97  | | | | End of split
% 159.61/25.97  | | | | 
% 159.61/25.97  | | | End of split
% 159.61/25.97  | | | 
% 159.61/25.97  | | Case 2:
% 159.61/25.97  | | | 
% 159.61/25.97  | | |   (20)  all_56_9 = e1 & op(e3, e0) = e1
% 159.61/25.97  | | | 
% 159.61/25.97  | | | REF_CLOSE: (8), (9), (20) are inconsistent by sub-proof #758.
% 159.61/25.97  | | | 
% 159.61/25.97  | | End of split
% 159.61/25.97  | | 
% 159.61/25.97  | End of split
% 159.61/25.97  | 
% 159.61/25.97  End of proof
% 159.61/25.97  
% 159.61/25.97  Sub-proof #634 shows that the following formulas are inconsistent:
% 159.61/25.97  ----------------------------------------------------------------
% 159.61/25.97    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.97    (2)  all_56_1 = e2
% 159.61/25.97    (3)  op(e3, e3) = e3
% 159.61/25.97    (4)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 159.61/25.97    (5)   ~ (e2 = e0)
% 159.61/25.97    (6)   ~ (e3 = e0)
% 159.61/25.97  
% 159.61/25.97  Begin of proof
% 159.61/25.97  | 
% 159.61/25.97  | BETA: splitting (4) gives:
% 159.61/25.97  | 
% 159.61/25.97  | Case 1:
% 159.61/25.97  | | 
% 159.61/25.97  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 159.61/25.97  | | 
% 159.61/25.97  | | ALPHA: (7) implies:
% 159.61/25.97  | |   (8)  op(e3, e3) = e0
% 159.61/25.97  | | 
% 159.61/25.97  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #971.
% 159.61/25.97  | | 
% 159.61/25.97  | Case 2:
% 159.61/25.97  | | 
% 159.61/25.97  | |   (9)  all_56_1 = e0 & op(e3, e2) = e0
% 159.61/25.97  | | 
% 159.61/25.97  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #910.
% 159.61/25.97  | | 
% 159.61/25.97  | End of split
% 159.61/25.97  | 
% 159.61/25.97  End of proof
% 159.61/25.97  
% 159.61/25.97  Sub-proof #635 shows that the following formulas are inconsistent:
% 159.61/25.97  ----------------------------------------------------------------
% 159.61/25.97    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.97    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1)
% 159.61/25.97    (3)  all_56_1 = e2
% 159.61/25.97    (4)  op(e3, e3) = e3
% 159.61/25.97    (5)   ~ (e2 = e1)
% 159.61/25.97    (6)   ~ (e3 = e1)
% 159.61/25.97  
% 159.61/25.97  Begin of proof
% 159.61/25.97  | 
% 159.61/25.97  | BETA: splitting (2) gives:
% 159.61/25.97  | 
% 159.61/25.97  | Case 1:
% 159.61/25.97  | | 
% 159.61/25.97  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 159.61/25.97  | | 
% 159.61/25.97  | | ALPHA: (7) implies:
% 159.61/25.97  | |   (8)  op(e3, e3) = e1
% 159.61/25.97  | | 
% 159.61/25.97  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #995.
% 159.61/25.97  | | 
% 159.61/25.97  | Case 2:
% 159.61/25.97  | | 
% 159.61/25.97  | |   (9)  all_56_1 = e1 & op(e3, e2) = e1
% 159.61/25.97  | | 
% 159.61/25.97  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #911.
% 159.61/25.97  | | 
% 159.61/25.97  | End of split
% 159.61/25.97  | 
% 159.61/25.97  End of proof
% 159.61/25.97  
% 159.61/25.97  Sub-proof #636 shows that the following formulas are inconsistent:
% 159.61/25.97  ----------------------------------------------------------------
% 159.61/25.97    (1)   ~ (all_52_7 = all_14_2)
% 159.61/25.97    (2)  all_54_5 = all_4_2
% 159.61/25.97    (3)   ~ (all_52_3 = all_14_2)
% 159.61/25.97    (4)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.61/25.97    (5)  op(e1, e1) = e3
% 159.61/25.97    (6)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.61/25.97             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.61/25.97           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.61/25.97               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.61/25.97             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.61/25.97         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.61/25.97             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.61/25.97           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.61/25.97               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.61/25.97             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.61/25.97         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.61/25.97             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.61/25.97           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.61/25.97               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.61/25.97             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.61/25.97         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.61/25.97             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.61/25.97           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.61/25.97               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.61/25.97             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.61/25.97    (7)  op(e0, e1) = all_52_11
% 159.61/25.97    (8)   ~ (e3 = e2)
% 159.61/25.97    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.61/25.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.61/25.97    (10)  op(e0, e3) = all_52_3
% 159.61/25.97    (11)  op(e3, e1) = all_52_8
% 159.61/25.97    (12)   ~ (all_52_9 = all_4_2)
% 159.61/25.97    (13)   ~ (all_4_2 = e3)
% 159.61/25.97    (14)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.61/25.97    (15)   ~ (all_52_11 = all_14_2)
% 159.61/25.97    (16)  op(e1, e3) = all_52_2
% 159.61/25.97    (17)  all_54_15 = all_14_2
% 159.61/25.97    (18)  op(e0, e2) = all_52_7
% 159.61/25.97    (19)   ~ (all_52_13 = all_4_2)
% 159.61/25.97    (20)   ~ (all_32_2 = e0) | ( ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 &
% 159.61/25.97            $i(all_32_0)) | ( ~ (all_32_1 = e1) & op(e0, e0) = all_32_1 &
% 159.61/25.97            $i(all_32_1))
% 159.61/25.97    (21)   ~ (all_52_2 = e1)
% 159.61/25.97    (22)  op(e1, e0) = all_52_14
% 159.61/25.97    (23)  op(e2, e2) = all_4_2
% 159.61/25.97    (24)   ~ (all_14_2 = e2)
% 159.61/25.97    (25)  all_32_2 = all_4_2
% 159.61/25.97    (26)  op(e0, e0) = all_14_2
% 159.61/25.97    (27)  op(e3, e3) = e1
% 159.61/25.97    (28)  op(e2, e3) = all_52_1
% 159.61/25.97    (29)   ~ (all_14_2 = e1)
% 159.61/25.97    (30)   ~ (all_4_2 = e1)
% 159.61/25.97    (31)   ~ (all_52_7 = all_4_2)
% 159.61/25.97    (32)  op(e2, e1) = all_52_9
% 159.61/25.97    (33)  op(e2, e0) = all_52_13
% 159.61/25.97    (34)   ~ (e2 = e1)
% 159.61/25.97    (35)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.61/25.97            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.61/25.97            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.61/25.97            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.61/25.97              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.61/25.97          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.61/25.97            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.61/25.97              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.61/25.97            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.61/25.97              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.61/25.97          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.61/25.97            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 159.61/25.97              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.61/25.97            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.61/25.97              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.61/25.97          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.61/25.97            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 159.61/25.97            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.61/25.97              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.61/25.97            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 159.61/25.97            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.61/25.97            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.61/25.97            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 159.61/25.97              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.61/25.97            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 159.61/25.97          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.61/25.97            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.61/25.97              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.61/25.97            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 159.61/25.97            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.61/25.97          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.61/25.97            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.61/25.97              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 159.61/25.97            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 159.61/25.97            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.61/25.97          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.61/25.97            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.61/25.97              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.61/25.97            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.61/25.97              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.61/25.97          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.61/25.97            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.61/25.97            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 159.61/25.97            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.61/25.97            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 159.61/25.97            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/25.97            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.61/25.97            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 159.61/25.97              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.61/25.97            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 159.61/25.97            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.61/25.97            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.61/25.97            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 159.61/25.97              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.61/25.97            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 159.61/25.97          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 159.61/25.97            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 159.61/25.97              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 159.61/25.97              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 159.61/25.97            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 159.61/25.97            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/25.97            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.61/25.97            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 159.61/25.97              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 159.61/25.97            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 159.61/25.97          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.61/25.97            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.61/25.97              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.61/25.97            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.61/25.97              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.61/25.97          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.61/25.97            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.61/25.97              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 159.61/25.97              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 159.61/25.97            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.61/25.97          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.61/25.97            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.61/25.97            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 159.61/25.97                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 159.61/25.97                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.61/25.97                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/25.97                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.61/25.97                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/25.97                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 159.61/25.97                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.61/25.97                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.61/25.97                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.61/25.97                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 159.61/25.97                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.61/25.97                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.61/25.97                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 159.61/25.97                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.61/25.97                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.61/25.97                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.61/25.97                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 159.61/25.97                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.61/25.97                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 159.61/25.97                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.61/25.97                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.61/25.97                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.61/25.97                op(e0, e1) = e0)))
% 159.61/25.97    (36)   ~ (e3 = e1)
% 159.61/25.97    (37)   ~ (all_52_1 = all_4_2)
% 159.61/25.97    (38)   ~ (all_52_8 = e3)
% 159.61/25.97    (39)   ~ (all_14_2 = e3)
% 159.61/25.97  
% 159.61/25.97  Begin of proof
% 159.61/25.97  | 
% 159.61/25.97  | BETA: splitting (14) gives:
% 159.61/25.97  | 
% 159.61/25.97  | Case 1:
% 159.61/25.97  | | 
% 159.61/25.97  | |   (40)  all_54_15 = e3
% 159.61/25.97  | | 
% 159.61/25.97  | | REF_CLOSE: (17), (39), (40) are inconsistent by sub-proof #1010.
% 159.61/25.97  | | 
% 159.61/25.97  | Case 2:
% 159.61/25.97  | | 
% 159.61/25.97  | |   (41)   ~ (all_54_15 = e3)
% 159.61/25.97  | |   (42)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.61/25.97  | | 
% 159.61/25.97  | | BETA: splitting (42) gives:
% 159.61/25.97  | | 
% 159.61/25.97  | | Case 1:
% 159.61/25.97  | | | 
% 159.61/25.97  | | |   (43)  all_54_15 = e2
% 159.61/25.97  | | | 
% 159.61/25.97  | | | REF_CLOSE: (17), (24), (43) are inconsistent by sub-proof #1009.
% 159.61/25.97  | | | 
% 159.61/25.97  | | Case 2:
% 159.61/25.97  | | | 
% 159.61/25.97  | | |   (44)   ~ (all_54_15 = e2)
% 159.61/25.98  | | |   (45)  all_54_15 = e1 | all_54_15 = e0
% 159.61/25.98  | | | 
% 159.61/25.98  | | | BETA: splitting (45) gives:
% 159.61/25.98  | | | 
% 159.61/25.98  | | | Case 1:
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | |   (46)  all_54_15 = e1
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | REF_CLOSE: (17), (29), (46) are inconsistent by sub-proof #1008.
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | Case 2:
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | |   (47)  all_54_15 = e0
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | COMBINE_EQS: (17), (47) imply:
% 159.61/25.98  | | | |   (48)  all_14_2 = e0
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | SIMP: (48) implies:
% 159.61/25.98  | | | |   (49)  all_14_2 = e0
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | REDUCE: (3), (49) imply:
% 159.61/25.98  | | | |   (50)   ~ (all_52_3 = e0)
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | REDUCE: (1), (49) imply:
% 159.61/25.98  | | | |   (51)   ~ (all_52_7 = e0)
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | REDUCE: (15), (49) imply:
% 159.61/25.98  | | | |   (52)   ~ (all_52_11 = e0)
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | REDUCE: (39), (49) imply:
% 159.61/25.98  | | | |   (53)   ~ (e3 = e0)
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | SIMP: (53) implies:
% 159.61/25.98  | | | |   (54)   ~ (e3 = e0)
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | REDUCE: (24), (49) imply:
% 159.61/25.98  | | | |   (55)   ~ (e2 = e0)
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | SIMP: (55) implies:
% 159.61/25.98  | | | |   (56)   ~ (e2 = e0)
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | REDUCE: (29), (49) imply:
% 159.61/25.98  | | | |   (57)   ~ (e1 = e0)
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | SIMP: (57) implies:
% 159.61/25.98  | | | |   (58)   ~ (e1 = e0)
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | REDUCE: (26), (49) imply:
% 159.61/25.98  | | | |   (59)  op(e0, e0) = e0
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | BETA: splitting (20) gives:
% 159.61/25.98  | | | | 
% 159.61/25.98  | | | | Case 1:
% 159.61/25.98  | | | | | 
% 159.61/25.98  | | | | |   (60)   ~ (all_32_2 = e0)
% 159.61/25.98  | | | | | 
% 159.61/25.98  | | | | | REDUCE: (25), (60) imply:
% 159.61/25.98  | | | | |   (61)   ~ (all_4_2 = e0)
% 159.61/25.98  | | | | | 
% 159.61/25.98  | | | | | BETA: splitting (4) gives:
% 159.61/25.98  | | | | | 
% 159.61/25.98  | | | | | Case 1:
% 159.61/25.98  | | | | | | 
% 159.61/25.98  | | | | | |   (62)  all_54_5 = e3
% 159.61/25.98  | | | | | | 
% 159.61/25.98  | | | | | | COMBINE_EQS: (2), (62) imply:
% 159.61/25.98  | | | | | |   (63)  all_4_2 = e3
% 159.61/25.98  | | | | | | 
% 159.61/25.98  | | | | | | REDUCE: (13), (63) imply:
% 159.61/25.98  | | | | | |   (64)  $false
% 159.61/25.98  | | | | | | 
% 159.61/25.98  | | | | | | CLOSE: (64) is inconsistent.
% 159.61/25.98  | | | | | | 
% 159.61/25.98  | | | | | Case 2:
% 159.61/25.98  | | | | | | 
% 159.61/25.98  | | | | | |   (65)   ~ (all_54_5 = e3)
% 159.61/25.98  | | | | | |   (66)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.61/25.98  | | | | | | 
% 159.61/25.98  | | | | | | BETA: splitting (66) gives:
% 159.61/25.98  | | | | | | 
% 159.61/25.98  | | | | | | Case 1:
% 159.61/25.98  | | | | | | | 
% 159.61/25.98  | | | | | | |   (67)  all_54_5 = e2
% 159.61/25.98  | | | | | | | 
% 159.61/25.98  | | | | | | | COMBINE_EQS: (2), (67) imply:
% 159.61/25.98  | | | | | | |   (68)  all_4_2 = e2
% 159.61/25.98  | | | | | | | 
% 159.61/25.98  | | | | | | | REDUCE: (37), (68) imply:
% 159.61/25.98  | | | | | | |   (69)   ~ (all_52_1 = e2)
% 159.61/25.98  | | | | | | | 
% 159.61/25.98  | | | | | | | REDUCE: (12), (68) imply:
% 159.61/25.98  | | | | | | |   (70)   ~ (all_52_9 = e2)
% 159.61/25.98  | | | | | | | 
% 159.61/25.98  | | | | | | | REDUCE: (19), (68) imply:
% 159.61/25.98  | | | | | | |   (71)   ~ (all_52_13 = e2)
% 159.61/25.98  | | | | | | | 
% 159.61/25.98  | | | | | | | REDUCE: (13), (68) imply:
% 159.61/25.98  | | | | | | |   (72)   ~ (e3 = e2)
% 159.61/25.98  | | | | | | | 
% 159.61/25.98  | | | | | | | REDUCE: (23), (68) imply:
% 159.61/25.98  | | | | | | |   (73)  op(e2, e2) = e2
% 159.61/25.98  | | | | | | | 
% 159.61/25.98  | | | | | | | BETA: splitting (35) gives:
% 159.61/25.98  | | | | | | | 
% 159.61/25.98  | | | | | | | Case 1:
% 159.61/25.98  | | | | | | | | 
% 159.61/25.98  | | | | | | | |   (74)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.61/25.98  | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.61/25.98  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.61/25.98  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.61/25.98  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.61/25.98  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 159.61/25.98  | | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.61/25.98  | | | | | | | |           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.61/25.98  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 159.61/25.98  | | | | | | | |           = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 =
% 159.61/25.98  | | | | | | | |           e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.61/25.98  | | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 159.61/25.98  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.61/25.98  | | | | | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.61/25.98  | | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.61/25.98  | | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.61/25.98  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.61/25.98  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.61/25.98  | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 159.61/25.98  | | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.61/25.98  | | | | | | | |           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.61/25.98  | | | | | | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 159.61/25.98  | | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.61/25.98  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 159.61/25.98  | | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.61/25.98  | | | | | | | |           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.61/25.98  | | | | | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.61/25.98  | | | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12)) |
% 159.61/25.98  | | | | | | | |         (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.61/25.98  | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2)
% 159.61/25.98  | | | | | | | |           = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.61/25.98  | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~
% 159.61/25.98  | | | | | | | |           (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 159.61/25.98  | | | | | | | |         (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 159.61/25.98  | | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.61/25.98  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.61/25.98  | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.61/25.98  | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1
% 159.61/25.98  | | | | | | | |           & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/25.98  | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_4
% 159.61/25.98  | | | | | | | |           = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 159.61/25.98  | | | | | | | |             e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1
% 159.61/25.98  | | | | | | | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 159.61/25.98  | | | | | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 159.61/25.98  | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 &
% 159.61/25.98  | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2 =
% 159.61/25.98  | | | | | | | |           e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.61/25.98  | | | | | | | |             e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.61/25.98  | | | | | | | |           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 159.61/25.98  | | | | | | | |         (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~
% 159.61/25.98  | | | | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0)
% 159.61/25.98  | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.61/25.98  | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~
% 159.61/25.98  | | | | | | | |           (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.61/25.98  | | | | | | | | 
% 159.61/25.98  | | | | | | | | BETA: splitting (74) gives:
% 159.61/25.98  | | | | | | | | 
% 159.61/25.98  | | | | | | | | Case 1:
% 159.61/25.98  | | | | | | | | | 
% 159.61/25.98  | | | | | | | | |   (75)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.61/25.98  | | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3
% 159.61/25.98  | | | | | | | | |           & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.61/25.98  | | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.61/25.98  | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.61/25.98  | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.61/25.98  | | | | | | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.61/25.98  | | | | | | | | |           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 159.61/25.98  | | | | | | | | |           & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1,
% 159.61/25.98  | | | | | | | | |             e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.61/25.98  | | | | | | | | |         (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 159.61/25.98  | | | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.61/25.98  | | | | | | | | |             e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.61/25.98  | | | | | | | | |           $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 159.61/25.98  | | | | | | | | |           all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 159.61/25.98  | | | | | | | | |           e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 159.61/25.98  | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.61/25.98  | | | | | | | | |           all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 159.61/25.98  | | | | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 159.61/25.98  | | | | | | | | |             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.61/25.98  | | | | | | | | |         (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.61/25.98  | | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3
% 159.61/25.98  | | | | | | | | |           & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.61/25.98  | | | | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.61/25.98  | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.61/25.98  | | | | | | | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 159.61/25.98  | | | | | | | | |           (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3
% 159.61/25.98  | | | | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.61/25.98  | | | | | | | | |           $i(all_57_12))
% 159.61/25.98  | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | REF_CLOSE: (9), (16), (21), (28), (32), (69), (70), (75) are
% 159.61/25.98  | | | | | | | | |            inconsistent by sub-proof #652.
% 159.61/25.98  | | | | | | | | | 
% 159.61/25.98  | | | | | | | | Case 2:
% 159.61/25.98  | | | | | | | | | 
% 159.61/25.98  | | | | | | | | |   (76)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.61/25.98  | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.61/25.98  | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.61/25.98  | | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 & 
% 159.61/25.98  | | | | | | | | |           ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 159.61/25.98  | | | | | | | | |         (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 159.61/25.98  | | | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3
% 159.61/25.98  | | | | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.61/25.98  | | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.61/25.98  | | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) =
% 159.61/25.98  | | | | | | | | |           e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.61/25.98  | | | | | | | | |           = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.61/25.98  | | | | | | | | |           all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 159.61/25.98  | | | | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1,
% 159.61/25.98  | | | | | | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.61/25.98  | | | | | | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.61/25.98  | | | | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2
% 159.61/25.98  | | | | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.61/25.98  | | | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 159.61/25.98  | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 159.61/25.98  | | | | | | | | |           e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.61/25.98  | | | | | | | | |           op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.61/25.98  | | | | | | | | |           all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 159.61/25.98  | | | | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1,
% 159.61/25.98  | | | | | | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.61/25.98  | | | | | | | | |         (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 159.61/25.98  | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.61/25.98  | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | BETA: splitting (76) gives:
% 159.61/25.98  | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | Case 1:
% 159.61/25.98  | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | |   (77)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.61/25.98  | | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.61/25.98  | | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.61/25.98  | | | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &
% 159.61/25.98  | | | | | | | | | |            ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 159.61/25.98  | | | | | | | | | |         | (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 159.61/25.98  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 159.61/25.98  | | | | | | | | | |           = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.61/25.98  | | | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.61/25.98  | | | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3)
% 159.61/25.98  | | | | | | | | | |           = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.61/25.98  | | | | | | | | | |             e1) = all_57_14 & $i(all_57_14))
% 159.61/25.98  | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | BETA: splitting (77) gives:
% 159.61/25.98  | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | Case 1:
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | |   (78)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.61/25.98  | | | | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.61/25.98  | | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.61/25.98  | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.61/25.98  | | | | | | | | | | |           = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.61/25.98  | | | | | | | | | | |             e2) = e3)
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | | REF_CLOSE: (9), (27), (36), (54), (59), (78) are inconsistent
% 159.61/25.98  | | | | | | | | | | |            by sub-proof #850.
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | Case 2:
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | |   (79)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 159.61/25.98  | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 159.61/25.98  | | | | | | | | | | |             e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.61/25.98  | | | | | | | | | | |           = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 159.61/25.98  | | | | | | | | | | |           all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 159.61/25.98  | | | | | | | | | | |             e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.61/25.98  | | | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.61/25.98  | | | | | | | | | | |           $i(all_57_14))
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | | REF_CLOSE: (9), (16), (21), (33), (71), (79) are inconsistent
% 159.61/25.98  | | | | | | | | | | |            by sub-proof #651.
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | End of split
% 159.61/25.98  | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | Case 2:
% 159.61/25.98  | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | |   (80)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 159.61/25.98  | | | | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.61/25.98  | | | | | | | | | |             e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.61/25.98  | | | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 159.61/25.98  | | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2)
% 159.61/25.98  | | | | | | | | | |           = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1,
% 159.61/25.98  | | | | | | | | | |             e1) = all_57_14 & $i(all_57_14)) | (all_57_2 =
% 159.61/25.98  | | | | | | | | | |           e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.61/25.98  | | | | | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/25.98  | | | | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.61/25.98  | | | | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.61/25.98  | | | | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 159.61/25.98  | | | | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 &
% 159.61/25.98  | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 159.61/25.98  | | | | | | | | | |           & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1
% 159.61/25.98  | | | | | | | | | |           & op(e1, e1) = e1)
% 159.61/25.98  | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | BETA: splitting (80) gives:
% 159.61/25.98  | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | Case 1:
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | |   (81)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.61/25.98  | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.61/25.98  | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/25.98  | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 159.61/25.98  | | | | | | | | | | |           = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 159.61/25.98  | | | | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 159.61/25.98  | | | | | | | | | | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | | REF_CLOSE: (9), (16), (21), (34), (73), (81) are inconsistent
% 159.61/25.98  | | | | | | | | | | |            by sub-proof #650.
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | Case 2:
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | |   (82)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.61/25.98  | | | | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 159.61/25.98  | | | | | | | | | | |             e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.61/25.98  | | | | | | | | | | |           = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.61/25.98  | | | | | | | | | | |           all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.61/25.98  | | | | | | | | | | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.61/25.98  | | | | | | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.61/25.98  | | | | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.61/25.98  | | | | | | | | | | |           &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/25.98  | | | | | | | | | | |           e1)
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | | REF_CLOSE: (5), (9), (16), (21), (26), (58), (59), (82) are
% 159.61/25.98  | | | | | | | | | | |            inconsistent by sub-proof #648.
% 159.61/25.98  | | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | | End of split
% 159.61/25.98  | | | | | | | | | | 
% 159.61/25.98  | | | | | | | | | End of split
% 159.61/25.98  | | | | | | | | | 
% 159.61/25.98  | | | | | | | | End of split
% 159.61/25.98  | | | | | | | | 
% 159.61/25.98  | | | | | | | Case 2:
% 159.61/25.98  | | | | | | | | 
% 159.61/25.99  | | | | | | | |   (83)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.61/25.99  | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.61/25.99  | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/25.99  | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.61/25.99  | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 159.61/25.99  | | | | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/25.99  | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5
% 159.61/25.99  | | | | | | | |           = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 159.61/25.99  | | | | | | | |             e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1
% 159.61/25.99  | | | | | | | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.61/25.99  | | | | | | | |           all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 159.61/25.99  | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1)
% 159.61/25.99  | | | | | | | |           = e0 & op(e0, e0) = e1 & $i(all_57_14)) | (all_57_3 =
% 159.61/25.99  | | | | | | | |           e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.61/25.99  | | | | | | | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.61/25.99  | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.61/25.99  | | | | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1,
% 159.61/25.99  | | | | | | | |             e2) = e1 & op(e1, e1) = e1) | (all_57_4 = e3 &
% 159.61/25.99  | | | | | | | |           all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 159.61/25.99  | | | | | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 159.61/25.99  | | | | | | | |           = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 =
% 159.61/25.99  | | | | | | | |           e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 159.61/25.99  | | | | | | | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 159.61/25.99  | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1
% 159.61/25.99  | | | | | | | |           & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 159.61/25.99  | | | | | | | |             e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 &
% 159.61/25.99  | | | | | | | |           all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.61/25.99  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2)
% 159.61/25.99  | | | | | | | |           = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 =
% 159.61/25.99  | | | | | | | |           e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 159.61/25.99  | | | | | | | |           op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 159.61/25.99  | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1
% 159.61/25.99  | | | | | | | |           & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.61/25.99  | | | | | | | |             e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 159.61/25.99  | | | | | | | |           all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 159.61/25.99  | | | | | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3)
% 159.61/25.99  | | | | | | | |           = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 =
% 159.61/25.99  | | | | | | | |           e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.61/25.99  | | | | | | | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.61/25.99  | | | | | | | |           op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.61/25.99  | | | | | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3,
% 159.61/25.99  | | | | | | | |             e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 159.61/25.99  | | | | | | | |           all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 &
% 159.61/25.99  | | | | | | | |           op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1 & 
% 159.61/25.99  | | | | | | | |           ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 159.61/25.99  | | | | | | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 =
% 159.61/25.99  | | | | | | | |               e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.61/25.99  | | | | | | | |               (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 159.61/25.99  | | | | | | | |               e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 159.61/25.99  | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.61/25.99  | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 159.61/25.99  | | | | | | | |               e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 159.61/25.99  | | | | | | | |               = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.61/25.99  | | | | | | | |               op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/25.99  | | | | | | | |               e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.61/25.99  | | | | | | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 =
% 159.61/25.99  | | | | | | | |               e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 &
% 159.61/25.99  | | | | | | | |               op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.61/25.99  | | | | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/25.99  | | | | | | | |               (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 159.61/25.99  | | | | | | | |               e2 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_13
% 159.61/25.99  | | | | | | | |               = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.61/25.99  | | | | | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.61/25.99  | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 =
% 159.61/25.99  | | | | | | | |                 e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.61/25.99  | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.99  | | | | | | | |                 e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.61/25.99  | | | | | | | |                 e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 159.61/25.99  | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2)
% 159.61/25.99  | | | | | | | |               = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.61/25.99  | | | | | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.61/25.99  | | | | | | | |               ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 159.61/25.99  | | | | | | | |               = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.61/25.99  | | | | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.61/25.99  | | | | | | | |                 e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/25.99  | | | | | | | |               op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0
% 159.61/25.99  | | | | | | | |               & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.61/25.99  | | | | | | | |               e0)))
% 159.61/25.99  | | | | | | | | 
% 159.61/25.99  | | | | | | | | BETA: splitting (83) gives:
% 159.61/25.99  | | | | | | | | 
% 159.61/25.99  | | | | | | | | Case 1:
% 159.61/25.99  | | | | | | | | | 
% 159.61/25.99  | | | | | | | | |   (84)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.61/25.99  | | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3
% 159.61/25.99  | | | | | | | | |           & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/25.99  | | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.61/25.99  | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 159.61/25.99  | | | | | | | | |           e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.61/25.99  | | | | | | | | |           = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.61/25.99  | | | | | | | | |           all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.61/25.99  | | | | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 159.61/25.99  | | | | | | | | |             e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.61/25.99  | | | | | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.61/25.99  | | | | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/25.99  | | | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.61/25.99  | | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 159.61/25.99  | | | | | | | | |           all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 159.61/25.99  | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 159.61/25.99  | | | | | | | | |           op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.61/25.99  | | | | | | | | |           all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 159.61/25.99  | | | | | | | | |           op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.61/25.99  | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.61/25.99  | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.61/25.99  | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 159.61/25.99  | | | | | | | | |           all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 159.61/25.99  | | | | | | | | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 159.61/25.99  | | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 159.61/25.99  | | | | | | | | |           e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 159.61/25.99  | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_14))
% 159.61/25.99  | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | BETA: splitting (84) gives:
% 159.61/25.99  | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | Case 1:
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | |   (85)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.61/25.99  | | | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) =
% 159.61/25.99  | | | | | | | | | |           e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/25.99  | | | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.61/25.99  | | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 159.61/25.99  | | | | | | | | | |           = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.61/25.99  | | | | | | | | | |             e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 159.61/25.99  | | | | | | | | | |           e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.61/25.99  | | | | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 159.61/25.99  | | | | | | | | | |             e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.61/25.99  | | | | | | | | | |           $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 &
% 159.61/25.99  | | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2)
% 159.61/25.99  | | | | | | | | | |           = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.61/25.99  | | | | | | | | | |           op(e0, e0) = e1 & $i(all_57_14))
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | BETA: splitting (85) gives:
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | Case 1:
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | |   (86)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.61/25.99  | | | | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 159.61/25.99  | | | | | | | | | | |             e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/25.99  | | | | | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.61/25.99  | | | | | | | | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 159.61/25.99  | | | | | | | | | | |             e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.61/25.99  | | | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/25.99  | | | | | | | | | | |           $i(all_57_14))
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | REF_CLOSE: (9), (11), (34), (38), (73), (86) are inconsistent
% 159.61/25.99  | | | | | | | | | | |            by sub-proof #647.
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | Case 2:
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | |   (87)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 159.61/25.99  | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.61/25.99  | | | | | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/25.99  | | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 159.61/25.99  | | | | | | | | | | |           = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 159.61/25.99  | | | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/25.99  | | | | | | | | | | |           op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.61/25.99  | | | | | | | | | | |           $i(all_57_14))
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (26), (58), (59), (87) are
% 159.61/25.99  | | | | | | | | | | |            inconsistent by sub-proof #645.
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | End of split
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | Case 2:
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | |   (88)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 159.61/25.99  | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.61/25.99  | | | | | | | | | |           op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/25.99  | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 =
% 159.61/25.99  | | | | | | | | | |           e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/25.99  | | | | | | | | | |           e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15 =
% 159.61/25.99  | | | | | | | | | |           e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 159.61/25.99  | | | | | | | | | |           & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.61/25.99  | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 =
% 159.61/25.99  | | | | | | | | | |           e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) =
% 159.61/25.99  | | | | | | | | | |           e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13
% 159.61/25.99  | | | | | | | | | |           = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 &
% 159.61/25.99  | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 159.61/25.99  | | | | | | | | | |             e0) = e1 & $i(all_57_14))
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | BETA: splitting (88) gives:
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | Case 1:
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | |   (89)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 159.61/25.99  | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.61/25.99  | | | | | | | | | | |           op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/25.99  | | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.61/25.99  | | | | | | | | | | |           = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.61/25.99  | | | | | | | | | | |             e1) = e1)
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (36), (89) are inconsistent by
% 159.61/25.99  | | | | | | | | | | |            sub-proof #644.
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | Case 2:
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | |   (90)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.61/25.99  | | | | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.61/25.99  | | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.61/25.99  | | | | | | | | | | |           e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 159.61/25.99  | | | | | | | | | | |           = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 159.61/25.99  | | | | | | | | | | |             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 159.61/25.99  | | | | | | | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 159.61/25.99  | | | | | | | | | | |             e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.61/25.99  | | | | | | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | BETA: splitting (90) gives:
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | Case 1:
% 159.61/25.99  | | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | |   (91)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.61/25.99  | | | | | | | | | | | |         ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.61/25.99  | | | | | | | | | | | |         op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.61/25.99  | | | | | | | | | | | |         e3 & $i(all_57_10)
% 159.61/25.99  | | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | | ALPHA: (91) implies:
% 159.61/25.99  | | | | | | | | | | | |   (92)  op(e0, e0) = e3
% 159.61/25.99  | | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | | REF_CLOSE: (9), (54), (59), (92) are inconsistent by
% 159.61/25.99  | | | | | | | | | | | |            sub-proof #999.
% 159.61/25.99  | | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | Case 2:
% 159.61/25.99  | | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | |   (93)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 159.61/25.99  | | | | | | | | | | | |           op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 159.61/25.99  | | | | | | | | | | | |           e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 159.61/25.99  | | | | | | | | | | | |           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 159.61/25.99  | | | | | | | | | | | |           = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 159.61/25.99  | | | | | | | | | | | |           & $i(all_57_14))
% 159.61/25.99  | | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | | REF_CLOSE: (9), (11), (27), (38), (93) are inconsistent by
% 159.61/25.99  | | | | | | | | | | | |            sub-proof #643.
% 159.61/25.99  | | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | End of split
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | End of split
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | End of split
% 159.61/25.99  | | | | | | | | | 
% 159.61/25.99  | | | | | | | | Case 2:
% 159.61/25.99  | | | | | | | | | 
% 159.61/25.99  | | | | | | | | |   (94)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.61/25.99  | | | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 159.61/25.99  | | | | | | | | |             e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.61/25.99  | | | | | | | | |           $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 & 
% 159.61/25.99  | | | | | | | | |           ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 159.61/25.99  | | | | | | | | |         (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 159.61/25.99  | | | | | | | | |           (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2
% 159.61/25.99  | | | | | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/25.99  | | | | | | | | |           $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.61/25.99  | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.61/25.99  | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 159.61/25.99  | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 &
% 159.61/25.99  | | | | | | | | |           all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.61/25.99  | | | | | | | | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.61/25.99  | | | | | | | | |           op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.61/25.99  | | | | | | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 159.61/25.99  | | | | | | | | |           op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2
% 159.61/25.99  | | | | | | | | |           & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 &
% 159.61/25.99  | | | | | | | | |           op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1
% 159.61/25.99  | | | | | | | | |           &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0) = e1)
% 159.61/25.99  | | | | | | | | |         | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6
% 159.61/25.99  | | | | | | | | |               = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.61/25.99  | | | | | | | | |               (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 159.61/25.99  | | | | | | | | |               = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.61/25.99  | | | | | | | | |               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.61/25.99  | | | | | | | | |                 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.61/25.99  | | | | | | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.61/25.99  | | | | | | | | |               e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.61/25.99  | | | | | | | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.61/25.99  | | | | | | | | |               e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.61/25.99  | | | | | | | | |                 e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.61/25.99  | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/25.99  | | | | | | | | |                 e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.61/25.99  | | | | | | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.61/25.99  | | | | | | | | |               e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.61/25.99  | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.61/25.99  | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.61/25.99  | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.61/25.99  | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 159.61/25.99  | | | | | | | | |             | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 159.61/25.99  | | | | | | | | |               op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 159.61/25.99  | | | | | | | | |               e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.61/25.99  | | | | | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.61/25.99  | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 159.61/25.99  | | | | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 159.61/25.99  | | | | | | | | |                 e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 159.61/25.99  | | | | | | | | |             | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 159.61/25.99  | | | | | | | | |               &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 159.61/25.99  | | | | | | | | |                 e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.61/25.99  | | | | | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 159.61/25.99  | | | | | | | | |                 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 159.61/25.99  | | | | | | | | |               e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 159.61/25.99  | | | | | | | | |             (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.61/25.99  | | | | | | | | |               op(e0, e1) = e0)))
% 159.61/25.99  | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | BETA: splitting (94) gives:
% 159.61/25.99  | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | Case 1:
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | |   (95)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.61/25.99  | | | | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 159.61/25.99  | | | | | | | | | |             e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.61/25.99  | | | | | | | | | |           $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &
% 159.61/25.99  | | | | | | | | | |            ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.61/25.99  | | | | | | | | | |         | (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 159.61/25.99  | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 159.61/25.99  | | | | | | | | | |           = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/25.99  | | | | | | | | | |           $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.61/25.99  | | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 159.61/25.99  | | | | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 159.61/25.99  | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_10))
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | BETA: splitting (95) gives:
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | Case 1:
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | |   (96)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.61/25.99  | | | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.61/25.99  | | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.61/25.99  | | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 159.61/25.99  | | | | | | | | | | |           = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 159.61/25.99  | | | | | | | | | | |             e1) = e2)
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | REF_CLOSE: (9), (32), (56), (59), (70), (96) are inconsistent
% 159.61/25.99  | | | | | | | | | | |            by sub-proof #978.
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | Case 2:
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | |   (97)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &
% 159.61/25.99  | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2,
% 159.61/25.99  | | | | | | | | | | |             e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 159.61/25.99  | | | | | | | | | | |           = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 159.61/25.99  | | | | | | | | | | |           all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 159.61/25.99  | | | | | | | | | | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.61/25.99  | | | | | | | | | | |           & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.61/25.99  | | | | | | | | | | |           $i(all_57_10))
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | | REF_CLOSE: (9), (34), (54), (59), (73), (97) are inconsistent
% 159.61/25.99  | | | | | | | | | | |            by sub-proof #977.
% 159.61/25.99  | | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | | End of split
% 159.61/25.99  | | | | | | | | | | 
% 159.61/25.99  | | | | | | | | | Case 2:
% 159.61/25.99  | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | |   (98)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 & 
% 159.61/26.00  | | | | | | | | | |           ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.61/26.00  | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.61/26.00  | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 =
% 159.61/26.00  | | | | | | | | | |           e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) =
% 159.61/26.00  | | | | | | | | | |           e3) | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 =
% 159.61/26.00  | | | | | | | | | |             e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.61/26.00  | | | | | | | | | |         (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.61/26.00  | | | | | | | | | |           op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.61/26.00  | | | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.61/26.00  | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/26.00  | | | | | | | | | |                 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.61/26.00  | | | | | | | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 159.61/26.00  | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.61/26.00  | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3)
% 159.61/26.00  | | | | | | | | | |               = e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 159.61/26.00  | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 159.61/26.00  | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.61/26.00  | | | | | | | | | |               e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3
% 159.61/26.00  | | | | | | | | | |                 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.61/26.00  | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/26.00  | | | | | | | | | |                 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.61/26.00  | | | | | | | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11
% 159.61/26.00  | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.00  | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2)
% 159.61/26.00  | | | | | | | | | |               = e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.61/26.00  | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.61/26.00  | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.61/26.00  | | | | | | | | | |               e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 159.61/26.00  | | | | | | | | | |                 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.61/26.00  | | | | | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/26.00  | | | | | | | | | |                 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.61/26.00  | | | | | | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 159.61/26.00  | | | | | | | | | |               = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.00  | | | | | | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 159.61/26.00  | | | | | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.61/26.00  | | | | | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 159.61/26.00  | | | | | | | | | |                 e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.61/26.00  | | | | | | | | | |               e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.61/26.00  | | | | | | | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 159.61/26.00  | | | | | | | | | |                 e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.61/26.00  | | | | | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.61/26.00  | | | | | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.61/26.00  | | | | | | | | | |               e0)))
% 159.61/26.00  | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | BETA: splitting (98) gives:
% 159.61/26.00  | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | Case 1:
% 159.61/26.00  | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | |   (99)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 159.61/26.00  | | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.61/26.00  | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.61/26.00  | | | | | | | | | | |           e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 159.61/26.00  | | | | | | | | | | |           = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 159.61/26.00  | | | | | | | | | | |             e0) = e3)
% 159.61/26.00  | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | REF_CLOSE: (9), (27), (36), (56), (59), (99) are inconsistent
% 159.61/26.00  | | | | | | | | | | |            by sub-proof #836.
% 159.61/26.00  | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | Case 2:
% 159.61/26.00  | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | |   (100)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.61/26.00  | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 159.61/26.00  | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 159.61/26.00  | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.61/26.00  | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.61/26.00  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.61/26.00  | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.00  | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.00  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.00  | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.61/26.00  | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.00  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/26.00  | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.61/26.00  | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.00  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.61/26.00  | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.61/26.00  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.00  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.61/26.00  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.61/26.00  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.00  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/26.00  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.61/26.00  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.00  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/26.00  | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.61/26.00  | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.61/26.00  | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.61/26.00  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.61/26.00  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.61/26.00  | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.61/26.00  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.61/26.00  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.61/26.00  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.61/26.00  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.61/26.00  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.61/26.00  | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.61/26.00  | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.61/26.00  | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.61/26.00  | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.61/26.00  | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.61/26.00  | | | | | | | | | | |                e0)))
% 159.61/26.00  | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | BETA: splitting (100) gives:
% 159.61/26.00  | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | Case 1:
% 159.61/26.00  | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | |   (101)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.61/26.00  | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 159.61/26.00  | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | ALPHA: (101) implies:
% 159.61/26.00  | | | | | | | | | | | |   (102)  op(e2, e0) = e2
% 159.61/26.00  | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | REF_CLOSE: (9), (33), (71), (102) are inconsistent by
% 159.61/26.00  | | | | | | | | | | | |            sub-proof #996.
% 159.61/26.00  | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | Case 2:
% 159.61/26.00  | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | |   (103)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.61/26.00  | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 159.61/26.00  | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.61/26.00  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.61/26.00  | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.00  | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.00  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.00  | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.61/26.00  | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.00  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/26.00  | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.61/26.00  | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.00  | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.61/26.00  | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.61/26.00  | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.00  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.61/26.00  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.61/26.00  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.00  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/26.00  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.61/26.00  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.00  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/26.00  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.61/26.00  | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.61/26.00  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.61/26.00  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.61/26.00  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.61/26.00  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.61/26.00  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.61/26.00  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.61/26.00  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.61/26.00  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.61/26.00  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.61/26.00  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.61/26.00  | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.61/26.00  | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.61/26.00  | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.61/26.00  | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.61/26.00  | | | | | | | | | | | |                e0)))
% 159.61/26.00  | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | BETA: splitting (103) gives:
% 159.61/26.00  | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | Case 1:
% 159.61/26.00  | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | |   (104)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.61/26.00  | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 159.61/26.00  | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | ALPHA: (104) implies:
% 159.61/26.00  | | | | | | | | | | | | |   (105)  op(e1, e1) = e1
% 159.61/26.00  | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (105) are inconsistent by
% 159.61/26.00  | | | | | | | | | | | | |            sub-proof #1003.
% 159.61/26.00  | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | Case 2:
% 159.61/26.00  | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | |   (106)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.61/26.00  | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.61/26.00  | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.00  | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.61/26.00  | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.00  | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.61/26.00  | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.61/26.00  | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/26.00  | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.61/26.00  | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.61/26.00  | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.61/26.00  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 159.61/26.00  | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 159.61/26.00  | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.61/26.00  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.61/26.00  | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.61/26.00  | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.61/26.00  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.61/26.00  | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.61/26.00  | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.61/26.00  | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 159.61/26.00  | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.61/26.00  | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/26.00  | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.61/26.00  | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 159.61/26.00  | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.00  | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 159.61/26.00  | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.61/26.00  | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 159.61/26.00  | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.61/26.00  | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.61/26.00  | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 159.61/26.00  | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.61/26.00  | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.61/26.00  | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.61/26.00  | | | | | | | | | | | | |              e0))
% 159.61/26.00  | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | ALPHA: (106) implies:
% 159.61/26.00  | | | | | | | | | | | | |   (107)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.61/26.00  | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.00  | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.61/26.00  | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.61/26.00  | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.61/26.00  | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.61/26.00  | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.61/26.00  | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.61/26.00  | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.61/26.00  | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.61/26.00  | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/26.00  | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.61/26.00  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.61/26.00  | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.00  | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.61/26.00  | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.61/26.00  | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.61/26.00  | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 159.61/26.00  | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 159.61/26.00  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 159.61/26.00  | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.00  | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.61/26.00  | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 159.61/26.00  | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 159.61/26.00  | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 159.61/26.00  | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 159.61/26.00  | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 159.61/26.00  | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.61/26.00  | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 159.61/26.00  | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 159.61/26.00  | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 159.61/26.00  | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.61/26.00  | | | | | | | | | | | | |            op(e0, e1) = e0)
% 159.61/26.00  | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | BETA: splitting (107) gives:
% 159.61/26.00  | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | Case 1:
% 159.61/26.00  | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | |   (108)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.61/26.00  | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.00  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.61/26.00  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.61/26.00  | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.61/26.00  | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.61/26.00  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.61/26.00  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.61/26.00  | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.61/26.00  | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.61/26.00  | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/26.00  | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.61/26.00  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.61/26.00  | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.00  | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.61/26.00  | | | | | | | | | | | | | |            e0)
% 159.61/26.00  | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 159.61/26.00  | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | Case 1:
% 159.61/26.00  | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | |   (109)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.61/26.00  | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.00  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.61/26.00  | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.61/26.00  | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.61/26.00  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.61/26.00  | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.61/26.00  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.61/26.00  | | | | | | | | | | | | | | |            e0)
% 159.61/26.00  | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (33), (50), (54), (71), (109) are
% 159.61/26.00  | | | | | | | | | | | | | | |            inconsistent by sub-proof #642.
% 159.61/26.00  | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | Case 2:
% 159.61/26.00  | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | |   (110)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.61/26.00  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 159.61/26.00  | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.00  | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.61/26.00  | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.61/26.00  | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.61/26.00  | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.61/26.00  | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 159.61/26.00  | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | Case 1:
% 159.61/26.00  | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | |   (111)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.61/26.00  | | | | | | | | | | | | | | | |          op(e0, e3) = e0
% 159.61/26.00  | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 159.61/26.00  | | | | | | | | | | | | | | | |   (112)  op(e0, e3) = e0
% 159.61/26.00  | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (50), (112) are inconsistent by
% 159.61/26.00  | | | | | | | | | | | | | | | |            sub-proof #973.
% 159.61/26.00  | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | Case 2:
% 159.61/26.00  | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | |   (113)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.61/26.00  | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.61/26.00  | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.61/26.00  | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.61/26.00  | | | | | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.61/26.00  | | | | | | | | | | | | | | | |            op(e0, e2) = e0)
% 159.61/26.00  | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 159.61/26.00  | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | Case 1:
% 159.61/26.00  | | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | |   (114)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.61/26.00  | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 159.61/26.00  | | | | | | | | | | | | | | | | |          = e3 & op(e0, e2) = e0
% 159.61/26.00  | | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 159.61/26.00  | | | | | | | | | | | | | | | | |   (115)  op(e3, e3) = e0
% 159.61/26.00  | | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (27), (58), (115) are inconsistent by
% 159.61/26.00  | | | | | | | | | | | | | | | | |            sub-proof #834.
% 159.61/26.00  | | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | Case 2:
% 159.61/26.00  | | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | |   (116)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 159.61/26.00  | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 159.61/26.00  | | | | | | | | | | | | | | | | |          = e2 & op(e0, e2) = e0
% 159.61/26.00  | | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 159.61/26.00  | | | | | | | | | | | | | | | | |   (117)  op(e2, e0) = e2
% 159.61/26.00  | | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (33), (71), (117) are inconsistent by
% 159.61/26.00  | | | | | | | | | | | | | | | | |            sub-proof #996.
% 159.61/26.00  | | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | | End of split
% 159.61/26.00  | | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | | End of split
% 159.61/26.00  | | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | | End of split
% 159.61/26.00  | | | | | | | | | | | | | | 
% 159.61/26.00  | | | | | | | | | | | | | Case 2:
% 159.61/26.00  | | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | | |   (118)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.61/26.01  | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.61/26.01  | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.61/26.01  | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.61/26.01  | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.61/26.01  | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.61/26.01  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.61/26.01  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.61/26.01  | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.61/26.01  | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.61/26.01  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.01  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.61/26.01  | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.61/26.01  | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 159.61/26.01  | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 159.61/26.01  | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.61/26.01  | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.61/26.01  | | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 159.61/26.01  | | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | | | Case 1:
% 159.61/26.01  | | | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | | | |   (119)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.61/26.01  | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.61/26.01  | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.61/26.01  | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.61/26.01  | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.61/26.01  | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.61/26.01  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 159.61/26.01  | | | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (18), (27), (51), (54), (58), (119) are
% 159.61/26.01  | | | | | | | | | | | | | | |            inconsistent by sub-proof #640.
% 159.61/26.01  | | | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | | | Case 2:
% 159.61/26.01  | | | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | | | |   (120)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.61/26.01  | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.61/26.01  | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.61/26.01  | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.61/26.01  | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.61/26.01  | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.61/26.01  | | | | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.61/26.01  | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/26.01  | | | | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 159.61/26.01  | | | | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 159.61/26.01  | | | | | | | | | | | | | | |            = e0)
% 159.61/26.01  | | | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (33), (52), (54), (71), (120) are
% 159.61/26.01  | | | | | | | | | | | | | | |            inconsistent by sub-proof #639.
% 159.61/26.01  | | | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | | | End of split
% 159.61/26.01  | | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | | End of split
% 159.61/26.01  | | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | End of split
% 159.61/26.01  | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | End of split
% 159.61/26.01  | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | End of split
% 159.61/26.01  | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | End of split
% 159.61/26.01  | | | | | | | | | 
% 159.61/26.01  | | | | | | | | End of split
% 159.61/26.01  | | | | | | | | 
% 159.61/26.01  | | | | | | | End of split
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | Case 2:
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | |   (121)  all_54_5 = e1 | all_54_5 = e0
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | | REF_CLOSE: (2), (30), (61), (121) are inconsistent by sub-proof
% 159.61/26.01  | | | | | | |            #962.
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | End of split
% 159.61/26.01  | | | | | | 
% 159.61/26.01  | | | | | End of split
% 159.61/26.01  | | | | | 
% 159.61/26.01  | | | | Case 2:
% 159.61/26.01  | | | | | 
% 159.61/26.01  | | | | |   (122)  all_32_2 = e0
% 159.61/26.01  | | | | | 
% 159.61/26.01  | | | | | COMBINE_EQS: (25), (122) imply:
% 159.61/26.01  | | | | |   (123)  all_4_2 = e0
% 159.61/26.01  | | | | | 
% 159.61/26.01  | | | | | REDUCE: (23), (123) imply:
% 159.61/26.01  | | | | |   (124)  op(e2, e2) = e0
% 159.61/26.01  | | | | | 
% 159.61/26.01  | | | | | BETA: splitting (6) gives:
% 159.61/26.01  | | | | | 
% 159.61/26.01  | | | | | Case 1:
% 159.61/26.01  | | | | | | 
% 159.61/26.01  | | | | | |   (125)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 &
% 159.61/26.01  | | | | | |                op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 159.61/26.01  | | | | | |                all_57_0 & $i(all_57_0))) & ((all_57_14 = e3 & op(e1,
% 159.61/26.01  | | | | | |                  e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 159.61/26.01  | | | | | |                all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0,
% 159.61/26.01  | | | | | |                  e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 159.61/26.01  | | | | | |                all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 159.61/26.01  | | | | | |              e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~
% 159.61/26.01  | | | | | |                (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 159.61/26.01  | | | | | |                $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2)
% 159.61/26.01  | | | | | |              | ( ~ (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 159.61/26.01  | | | | | |                $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2)
% 159.61/26.01  | | | | | |              | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 159.61/26.01  | | | | | |                $i(all_57_7))))
% 159.61/26.01  | | | | | | 
% 159.61/26.01  | | | | | | REF_CLOSE: (9), (27), (36), (56), (124), (125) are inconsistent by
% 159.61/26.01  | | | | | |            sub-proof #814.
% 159.61/26.01  | | | | | | 
% 159.61/26.01  | | | | | Case 2:
% 159.61/26.01  | | | | | | 
% 159.61/26.01  | | | | | |   (126)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 &
% 159.61/26.01  | | | | | |                op(e3, e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) =
% 159.61/26.01  | | | | | |                all_57_4 & $i(all_57_4))) & ((all_57_12 = e1 & op(e2,
% 159.61/26.01  | | | | | |                  e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 159.61/26.01  | | | | | |                all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 159.61/26.01  | | | | | |                  e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 159.61/26.01  | | | | | |                all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 159.61/26.01  | | | | | |              e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~
% 159.61/26.01  | | | | | |                (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.61/26.01  | | | | | |                $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0)
% 159.61/26.01  | | | | | |              | ( ~ (all_57_11 = e2) & op(e2, e0) = all_57_11 &
% 159.61/26.01  | | | | | |                $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.61/26.01  | | | | | |              | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.61/26.01  | | | | | |                $i(all_57_13))))
% 159.61/26.01  | | | | | | 
% 159.61/26.01  | | | | | | BETA: splitting (126) gives:
% 159.61/26.01  | | | | | | 
% 159.61/26.01  | | | | | | Case 1:
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | |   (127)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 &
% 159.61/26.01  | | | | | | |              op(e3, e3) = e1) | ( ~ (all_57_4 = e3) & op(e3, e1) =
% 159.61/26.01  | | | | | | |              all_57_4 & $i(all_57_4))) & ((all_57_12 = e1 & op(e2,
% 159.61/26.01  | | | | | | |                e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1) =
% 159.61/26.01  | | | | | | |              all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0,
% 159.61/26.01  | | | | | | |                e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 159.61/26.01  | | | | | | |              all_57_8 & $i(all_57_8)))
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | | ALPHA: (127) implies:
% 159.61/26.01  | | | | | | |   (128)  op(e1, e1) = e1
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | | REF_CLOSE: (5), (9), (36), (128) are inconsistent by sub-proof
% 159.61/26.01  | | | | | | |            #1003.
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | Case 2:
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | |   (129)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 &
% 159.61/26.01  | | | | | | |              op(e3, e3) = e0) | ( ~ (all_57_9 = e3) & op(e3, e0) =
% 159.61/26.01  | | | | | | |              all_57_9 & $i(all_57_9))) & ((all_57_12 = e0 & op(e2,
% 159.61/26.01  | | | | | | |                e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 159.61/26.01  | | | | | | |              all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 &
% 159.61/26.01  | | | | | | |              op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1, e0)
% 159.61/26.01  | | | | | | |              = all_57_13 & $i(all_57_13)))
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | | ALPHA: (129) implies:
% 159.61/26.01  | | | | | | |   (130)  (all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1)
% 159.61/26.01  | | | | | | |            & op(e1, e0) = all_57_13 & $i(all_57_13))
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | | BETA: splitting (130) gives:
% 159.61/26.01  | | | | | | | 
% 159.61/26.01  | | | | | | | Case 1:
% 159.61/26.01  | | | | | | | | 
% 159.61/26.01  | | | | | | | |   (131)  all_57_14 = e0 & op(e1, e1) = e0
% 159.61/26.01  | | | | | | | | 
% 159.61/26.01  | | | | | | | | ALPHA: (131) implies:
% 159.61/26.01  | | | | | | | |   (132)  op(e1, e1) = e0
% 159.61/26.01  | | | | | | | | 
% 159.61/26.01  | | | | | | | | REF_CLOSE: (5), (9), (54), (132) are inconsistent by sub-proof
% 159.61/26.01  | | | | | | | |            #912.
% 159.61/26.01  | | | | | | | | 
% 159.61/26.01  | | | | | | | Case 2:
% 159.61/26.01  | | | | | | | | 
% 159.61/26.01  | | | | | | | |   (133)   ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.61/26.01  | | | | | | | |          $i(all_57_13)
% 159.61/26.01  | | | | | | | | 
% 159.61/26.01  | | | | | | | | ALPHA: (133) implies:
% 159.61/26.01  | | | | | | | |   (134)   ~ (all_57_13 = e1)
% 159.61/26.01  | | | | | | | |   (135)  op(e1, e0) = all_57_13
% 159.61/26.01  | | | | | | | | 
% 159.61/26.01  | | | | | | | | BETA: splitting (35) gives:
% 159.61/26.01  | | | | | | | | 
% 159.61/26.01  | | | | | | | | Case 1:
% 159.61/26.01  | | | | | | | | | 
% 159.61/26.01  | | | | | | | | |   (136)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.61/26.01  | | | | | | | | |            (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) =
% 159.61/26.01  | | | | | | | | |            e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.61/26.01  | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.61/26.01  | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.61/26.01  | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.61/26.01  | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.61/26.01  | | | | | | | | |            all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.61/26.01  | | | | | | | | |              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.61/26.01  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 159.61/26.01  | | | | | | | | |          | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 159.61/26.01  | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.61/26.01  | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3
% 159.61/26.01  | | | | | | | | |            & $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 159.61/26.01  | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) =
% 159.61/26.01  | | | | | | | | |            e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 159.61/26.01  | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.61/26.01  | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.61/26.01  | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.61/26.01  | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.61/26.01  | | | | | | | | |          | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.61/26.01  | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3
% 159.61/26.01  | | | | | | | | |            & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.61/26.01  | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.61/26.01  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.61/26.01  | | | | | | | | |          | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 159.61/26.01  | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) =
% 159.61/26.01  | | | | | | | | |            e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.61/26.01  | | | | | | | | |            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 &
% 159.61/26.01  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.61/26.01  | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 159.61/26.01  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.61/26.01  | | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 159.61/26.01  | | | | | | | | |            op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2
% 159.61/26.01  | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3)
% 159.61/26.01  | | | | | | | | |            = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.61/26.01  | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 159.61/26.01  | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 159.61/26.01  | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 159.61/26.01  | | | | | | | | |              e3) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.01  | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.61/26.01  | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.61/26.01  | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 159.61/26.01  | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 159.61/26.01  | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 159.61/26.01  | | | | | | | | |              e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 159.61/26.01  | | | | | | | | |              e3) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.01  | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 159.61/26.01  | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) =
% 159.61/26.01  | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.61/26.01  | | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.61/26.01  | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.61/26.01  | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.61/26.01  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.61/26.01  | | | | | | | | |          | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) &
% 159.61/26.01  | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.61/26.01  | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | BETA: splitting (136) gives:
% 159.61/26.01  | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | Case 1:
% 159.61/26.01  | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | |   (137)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 159.61/26.01  | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2)
% 159.61/26.01  | | | | | | | | | |            = e3 & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.61/26.01  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.61/26.01  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 159.61/26.01  | | | | | | | | | |            = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.61/26.01  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 159.61/26.01  | | | | | | | | | |            & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12
% 159.61/26.01  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.61/26.01  | | | | | | | | | |            all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.61/26.01  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.61/26.01  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.61/26.01  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 &
% 159.61/26.01  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 159.61/26.01  | | | | | | | | | |            & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12
% 159.61/26.01  | | | | | | | | | |              = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.61/26.01  | | | | | | | | | |            all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.61/26.01  | | | | | | | | | |            $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.61/26.01  | | | | | | | | | |            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3)
% 159.61/26.01  | | | | | | | | | |            = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 159.61/26.01  | | | | | | | | | |            op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2
% 159.61/26.01  | | | | | | | | | |            & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 159.61/26.01  | | | | | | | | | |            & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 159.61/26.01  | | | | | | | | | |            e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.61/26.01  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.61/26.01  | | | | | | | | | |              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.61/26.01  | | | | | | | | | |          (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 159.61/26.01  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 159.61/26.01  | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.61/26.01  | | | | | | | | | |            $i(all_57_12))
% 159.61/26.01  | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | BETA: splitting (137) gives:
% 159.61/26.01  | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | Case 1:
% 159.61/26.01  | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | |   (138)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 159.61/26.01  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 159.61/26.01  | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.61/26.01  | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.61/26.01  | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.61/26.01  | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 159.61/26.01  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.61/26.01  | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1
% 159.61/26.01  | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2,
% 159.61/26.01  | | | | | | | | | | |              e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2)
% 159.61/26.01  | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.61/26.01  | | | | | | | | | | |          (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 & 
% 159.61/26.01  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.61/26.01  | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.61/26.01  | | | | | | | | | | |            e3 & $i(all_57_10))
% 159.61/26.01  | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | BETA: splitting (138) gives:
% 159.61/26.01  | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | Case 1:
% 159.61/26.01  | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | |   (139)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 & 
% 159.61/26.01  | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e3, e3) = e2 & op(e3,
% 159.61/26.01  | | | | | | | | | | | |              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.61/26.01  | | | | | | | | | | | |            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.61/26.01  | | | | | | | | | | | |            all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.61/26.01  | | | | | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 159.61/26.01  | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.61/26.01  | | | | | | | | | | | |            $i(all_57_10))
% 159.61/26.01  | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | REF_CLOSE: (9), (27), (34), (54), (124), (139) are
% 159.61/26.01  | | | | | | | | | | | |            inconsistent by sub-proof #827.
% 159.61/26.01  | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | Case 2:
% 159.61/26.01  | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | |   (140)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 159.61/26.01  | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 159.61/26.01  | | | | | | | | | | | |              e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 159.61/26.01  | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.61/26.01  | | | | | | | | | | | |            all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.61/26.01  | | | | | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 159.61/26.01  | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.61/26.01  | | | | | | | | | | | |            $i(all_57_10))
% 159.61/26.01  | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (54), (124), (140) are inconsistent
% 159.61/26.01  | | | | | | | | | | | |            by sub-proof #638.
% 159.61/26.01  | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | End of split
% 159.61/26.01  | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | Case 2:
% 159.61/26.01  | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | |   (141)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.61/26.01  | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 159.61/26.01  | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.61/26.01  | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.61/26.01  | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.61/26.01  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.61/26.01  | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.61/26.01  | | | | | | | | | | |            $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2
% 159.61/26.01  | | | | | | | | | | |            &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) =
% 159.61/26.01  | | | | | | | | | | |            e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14
% 159.61/26.01  | | | | | | | | | | |            = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.61/26.01  | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 159.61/26.01  | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 159.61/26.01  | | | | | | | | | | |            e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 159.61/26.01  | | | | | | | | | | |            (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 159.61/26.01  | | | | | | | | | | |            = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 159.61/26.01  | | | | | | | | | | |            & $i(all_57_12))
% 159.61/26.01  | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | BETA: splitting (141) gives:
% 159.61/26.01  | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | Case 1:
% 159.61/26.01  | | | | | | | | | | | | 
% 159.61/26.01  | | | | | | | | | | | |   (142)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.61/26.01  | | | | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 159.61/26.01  | | | | | | | | | | | |              e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.61/26.01  | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.61/26.01  | | | | | | | | | | | |            all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.61/26.01  | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.61/26.01  | | | | | | | | | | | |            & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.61/26.01  | | | | | | | | | | | |            $i(all_57_10))
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | REF_CLOSE: (9), (54), (56), (59), (124), (142) are
% 159.61/26.02  | | | | | | | | | | | |            inconsistent by sub-proof #826.
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | Case 2:
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | |   (143)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.61/26.02  | | | | | | | | | | | |            op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 =
% 159.61/26.02  | | | | | | | | | | | |            e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 159.61/26.02  | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.61/26.02  | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 159.61/26.02  | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.61/26.02  | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.61/26.02  | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | BETA: splitting (143) gives:
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | Case 1:
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | |   (144)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.61/26.02  | | | | | | | | | | | | |          op(e2, e3) = e2 & op(e2, e2) = e2
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | ALPHA: (144) implies:
% 159.61/26.02  | | | | | | | | | | | | |   (145)  op(e2, e2) = e2
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | REF_CLOSE: (9), (56), (124), (145) are inconsistent by
% 159.61/26.02  | | | | | | | | | | | | |            sub-proof #942.
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | Case 2:
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | |   (146)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 159.61/26.02  | | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.61/26.02  | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5
% 159.61/26.02  | | | | | | | | | | | | |            = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.61/26.02  | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.61/26.02  | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | BETA: splitting (146) gives:
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | Case 1:
% 159.61/26.02  | | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | |   (147)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 159.61/26.02  | | | | | | | | | | | | | |          ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.61/26.02  | | | | | | | | | | | | | |          op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 159.61/26.02  | | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | | ALPHA: (147) implies:
% 159.61/26.02  | | | | | | | | | | | | | |   (148)  op(e1, e3) = e1
% 159.61/26.02  | | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | | REF_CLOSE: (9), (16), (21), (148) are inconsistent by
% 159.61/26.02  | | | | | | | | | | | | | |            sub-proof #990.
% 159.61/26.02  | | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | Case 2:
% 159.61/26.02  | | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | |   (149)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 & 
% 159.61/26.02  | | | | | | | | | | | | | |          ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 159.61/26.02  | | | | | | | | | | | | | |          = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.61/26.02  | | | | | | | | | | | | | |          $i(all_57_12)
% 159.61/26.02  | | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | | ALPHA: (149) implies:
% 159.61/26.02  | | | | | | | | | | | | | |   (150)  op(e3, e3) = e2
% 159.61/26.02  | | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | | REF_CLOSE: (9), (27), (34), (150) are inconsistent by
% 159.61/26.02  | | | | | | | | | | | | | |            sub-proof #828.
% 159.61/26.02  | | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | End of split
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | End of split
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | End of split
% 159.61/26.02  | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | End of split
% 159.61/26.02  | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | Case 2:
% 159.61/26.02  | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | |   (151)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.61/26.02  | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.61/26.02  | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.61/26.02  | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.61/26.02  | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.61/26.02  | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 159.61/26.02  | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3)
% 159.61/26.02  | | | | | | | | | |            = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.61/26.02  | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1
% 159.61/26.02  | | | | | | | | | |            & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14
% 159.61/26.02  | | | | | | | | | |              = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.61/26.02  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.02  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.61/26.02  | | | | | | | | | |            all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.61/26.02  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 159.61/26.02  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1
% 159.61/26.02  | | | | | | | | | |            & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14
% 159.61/26.02  | | | | | | | | | |              = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.61/26.02  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.02  | | | | | | | | | |            $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 159.61/26.02  | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3)
% 159.61/26.02  | | | | | | | | | |            = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.61/26.02  | | | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1
% 159.61/26.02  | | | | | | | | | |            & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10
% 159.61/26.02  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 159.61/26.02  | | | | | | | | | |            e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.61/26.02  | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.61/26.02  | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | | |            e1)
% 159.61/26.02  | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | BETA: splitting (151) gives:
% 159.61/26.02  | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | Case 1:
% 159.61/26.02  | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | |   (152)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.61/26.02  | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.61/26.02  | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.61/26.02  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.61/26.02  | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.61/26.02  | | | | | | | | | | |              e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 159.61/26.02  | | | | | | | | | | |            all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3,
% 159.61/26.02  | | | | | | | | | | |              e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.61/26.02  | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 159.61/26.02  | | | | | | | | | | |          (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.61/26.02  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3,
% 159.61/26.02  | | | | | | | | | | |              e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | | | |            all_57_14 & $i(all_57_14))
% 159.61/26.02  | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | BETA: splitting (152) gives:
% 159.61/26.02  | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | Case 1:
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | |   (153)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.61/26.02  | | | | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.61/26.02  | | | | | | | | | | | |            op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.61/26.02  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10
% 159.61/26.02  | | | | | | | | | | | |            = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 159.61/26.02  | | | | | | | | | | | |              e2) = e3)
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | REF_CLOSE: (9), (27), (36), (54), (59), (153) are
% 159.61/26.02  | | | | | | | | | | | |            inconsistent by sub-proof #850.
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | Case 2:
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | |   (154)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 159.61/26.02  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3,
% 159.61/26.02  | | | | | | | | | | | |              e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.61/26.02  | | | | | | | | | | | |            = e2 & $i(all_57_12)) | (all_57_2 = e1 &
% 159.61/26.02  | | | | | | | | | | | |            all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 159.61/26.02  | | | | | | | | | | | |              e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.61/26.02  | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.02  | | | | | | | | | | | |            $i(all_57_14))
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | REF_CLOSE: (9), (16), (21), (27), (34), (154) are
% 159.61/26.02  | | | | | | | | | | | |            inconsistent by sub-proof #823.
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | End of split
% 159.61/26.02  | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | Case 2:
% 159.61/26.02  | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | |   (155)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.61/26.02  | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.61/26.02  | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 159.61/26.02  | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 159.61/26.02  | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 159.61/26.02  | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.61/26.02  | | | | | | | | | | |          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.61/26.02  | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 159.61/26.02  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.61/26.02  | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.61/26.02  | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.61/26.02  | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.61/26.02  | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.61/26.02  | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.61/26.02  | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | | | |            e1)
% 159.61/26.02  | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | BETA: splitting (155) gives:
% 159.61/26.02  | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | Case 1:
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | |   (156)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.61/26.02  | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.61/26.02  | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5
% 159.61/26.02  | | | | | | | | | | | |            = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3) &
% 159.61/26.02  | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 159.61/26.02  | | | | | | | | | | | |            e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | BETA: splitting (156) gives:
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | Case 1:
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | |   (157)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 & 
% 159.61/26.02  | | | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.61/26.02  | | | | | | | | | | | | |          op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | ALPHA: (157) implies:
% 159.61/26.02  | | | | | | | | | | | | |   (158)  op(e1, e3) = e1
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | REF_CLOSE: (9), (16), (21), (158) are inconsistent by
% 159.61/26.02  | | | | | | | | | | | | |            sub-proof #990.
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | Case 2:
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | |   (159)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 159.61/26.02  | | | | | | | | | | | | |          ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1)
% 159.61/26.02  | | | | | | | | | | | | |          = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.02  | | | | | | | | | | | | |          $i(all_57_14)
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | ALPHA: (159) implies:
% 159.61/26.02  | | | | | | | | | | | | |   (160)  op(e2, e2) = e1
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | | REF_CLOSE: (9), (58), (124), (160) are inconsistent by
% 159.61/26.02  | | | | | | | | | | | | |            sub-proof #960.
% 159.61/26.02  | | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | End of split
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | Case 2:
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | |   (161)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.61/26.02  | | | | | | | | | | | |            ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 159.61/26.02  | | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.61/26.02  | | | | | | | | | | | |            = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 159.61/26.02  | | | | | | | | | | | |            all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.61/26.02  | | | | | | | | | | | |              e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.61/26.02  | | | | | | | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.61/26.02  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1
% 159.61/26.02  | | | | | | | | | | | |            &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | | | | |            e1)
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | | REF_CLOSE: (5), (9), (16), (21), (26), (58), (59), (161) are
% 159.61/26.02  | | | | | | | | | | | |            inconsistent by sub-proof #648.
% 159.61/26.02  | | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | | End of split
% 159.61/26.02  | | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | | End of split
% 159.61/26.02  | | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | End of split
% 159.61/26.02  | | | | | | | | | 
% 159.61/26.02  | | | | | | | | Case 2:
% 159.61/26.02  | | | | | | | | | 
% 159.61/26.02  | | | | | | | | |   (162)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.61/26.02  | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) =
% 159.61/26.02  | | | | | | | | |            e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.02  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.61/26.02  | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) =
% 159.61/26.02  | | | | | | | | |            e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.61/26.02  | | | | | | | | |            = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.61/26.02  | | | | | | | | |            all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.61/26.02  | | | | | | | | |              e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.61/26.02  | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12))
% 159.61/26.02  | | | | | | | | |          | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.61/26.02  | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/26.02  | | | | | | | | |            all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.61/26.02  | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 159.61/26.02  | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 159.61/26.02  | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 159.61/26.02  | | | | | | | | |            op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.61/26.02  | | | | | | | | |            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 159.61/26.02  | | | | | | | | |            op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.61/26.02  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.61/26.02  | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.61/26.02  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 159.61/26.02  | | | | | | | | |            all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 159.61/26.02  | | | | | | | | |            op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 159.61/26.02  | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3)
% 159.61/26.02  | | | | | | | | |            = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 159.61/26.02  | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 &
% 159.61/26.02  | | | | | | | | |            all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.61/26.02  | | | | | | | | |              e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.61/26.02  | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 159.61/26.02  | | | | | | | | |          | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 159.61/26.02  | | | | | | | | |            op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2
% 159.61/26.02  | | | | | | | | |            & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 159.61/26.02  | | | | | | | | |              e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 159.61/26.02  | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/26.02  | | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.61/26.02  | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.61/26.02  | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 159.61/26.02  | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 &
% 159.61/26.02  | | | | | | | | |            all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.61/26.02  | | | | | | | | |              e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.61/26.02  | | | | | | | | |            op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12))
% 159.61/26.02  | | | | | | | | |          | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 159.61/26.02  | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 159.61/26.02  | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 159.61/26.02  | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14
% 159.61/26.02  | | | | | | | | |            = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0)
% 159.61/26.02  | | | | | | | | |            = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.61/26.02  | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.61/26.02  | | | | | | | | |                ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.02  | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.61/26.02  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.02  | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 159.61/26.02  | | | | | | | | |                = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.61/26.02  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.61/26.02  | | | | | | | | |                  = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.61/26.02  | | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 159.61/26.02  | | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.61/26.02  | | | | | | | | |              (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.61/26.02  | | | | | | | | |                 ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.61/26.02  | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 159.61/26.02  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.02  | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 159.61/26.02  | | | | | | | | |                = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.61/26.02  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.61/26.02  | | | | | | | | |                  = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.61/26.02  | | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.61/26.02  | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.61/26.02  | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.61/26.02  | | | | | | | | |                 ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.61/26.02  | | | | | | | | |                  e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.61/26.02  | | | | | | | | |                & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.02  | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 159.61/26.02  | | | | | | | | |                = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.61/26.02  | | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.61/26.02  | | | | | | | | |                  = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.61/26.02  | | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.61/26.02  | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.61/26.02  | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/26.02  | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 159.61/26.02  | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 159.61/26.02  | | | | | | | | |                = e0)))
% 159.61/26.02  | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | BETA: splitting (162) gives:
% 159.61/26.02  | | | | | | | | | 
% 159.61/26.02  | | | | | | | | | Case 1:
% 159.61/26.02  | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | |   (163)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.61/26.03  | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 159.61/26.03  | | | | | | | | | |            = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.03  | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.61/26.03  | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2)
% 159.61/26.03  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.61/26.03  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_14)) | (all_57_3 =
% 159.61/26.03  | | | | | | | | | |            e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.61/26.03  | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.61/26.03  | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/26.03  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 =
% 159.61/26.03  | | | | | | | | | |            e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 159.61/26.03  | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 159.61/26.03  | | | | | | | | | |              e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 159.61/26.03  | | | | | | | | | |          (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 & 
% 159.61/26.03  | | | | | | | | | |            ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.61/26.03  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/26.03  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.61/26.03  | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.61/26.03  | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.61/26.03  | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.61/26.03  | | | | | | | | | |            = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 159.61/26.03  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3
% 159.61/26.03  | | | | | | | | | |            & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3
% 159.61/26.03  | | | | | | | | | |            & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 =
% 159.61/26.03  | | | | | | | | | |            e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.61/26.03  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.61/26.03  | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.61/26.03  | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | BETA: splitting (163) gives:
% 159.61/26.03  | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | Case 1:
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | |   (164)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.61/26.03  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 159.61/26.03  | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/26.03  | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.61/26.03  | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 159.61/26.03  | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.61/26.03  | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.03  | | | | | | | | | | |            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2
% 159.61/26.03  | | | | | | | | | | |            & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2,
% 159.61/26.03  | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2)
% 159.61/26.03  | | | | | | | | | | |            = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.61/26.03  | | | | | | | | | | |          (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 & 
% 159.61/26.03  | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 159.61/26.03  | | | | | | | | | | |              e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.61/26.03  | | | | | | | | | | |            = e1 & $i(all_57_14))
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | BETA: splitting (164) gives:
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | Case 1:
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | |   (165)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.61/26.03  | | | | | | | | | | | |            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3,
% 159.61/26.03  | | | | | | | | | | | |              e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/26.03  | | | | | | | | | | | |            all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.61/26.03  | | | | | | | | | | | |            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 =
% 159.61/26.03  | | | | | | | | | | | |              e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.61/26.03  | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.03  | | | | | | | | | | | |            $i(all_57_14))
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | BETA: splitting (165) gives:
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | Case 1:
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | |   (166)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.61/26.03  | | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1)
% 159.61/26.03  | | | | | | | | | | | | |          = e3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.03  | | | | | | | | | | | | |          $i(all_57_14)
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | ALPHA: (166) implies:
% 159.61/26.03  | | | | | | | | | | | | |   (167)  op(e3, e1) = e3
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | REF_CLOSE: (9), (11), (38), (167) are inconsistent by
% 159.61/26.03  | | | | | | | | | | | | |            sub-proof #982.
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | Case 2:
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | |   (168)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 & 
% 159.61/26.03  | | | | | | | | | | | | |          ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 159.61/26.03  | | | | | | | | | | | | |          = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.03  | | | | | | | | | | | | |          $i(all_57_14)
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | ALPHA: (168) implies:
% 159.61/26.03  | | | | | | | | | | | | |   (169)  op(e2, e2) = e1
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | REF_CLOSE: (9), (58), (124), (169) are inconsistent by
% 159.61/26.03  | | | | | | | | | | | | |            sub-proof #960.
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | End of split
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | Case 2:
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | |   (170)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 & 
% 159.61/26.03  | | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.61/26.03  | | | | | | | | | | | |            op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/26.03  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 159.61/26.03  | | | | | | | | | | | |            = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) &
% 159.61/26.03  | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.61/26.03  | | | | | | | | | | | |            op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.61/26.03  | | | | | | | | | | | |            $i(all_57_14))
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (26), (58), (59), (170) are
% 159.61/26.03  | | | | | | | | | | | |            inconsistent by sub-proof #645.
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | End of split
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | Case 2:
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | |   (171)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 159.61/26.03  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.61/26.03  | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/26.03  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.61/26.03  | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.61/26.03  | | | | | | | | | | |              e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.61/26.03  | | | | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 159.61/26.03  | | | | | | | | | | |              e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3)
% 159.61/26.03  | | | | | | | | | | |            = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.61/26.03  | | | | | | | | | | |          (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 159.61/26.03  | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 159.61/26.03  | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 159.61/26.03  | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 159.61/26.03  | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 159.61/26.03  | | | | | | | | | | |            & $i(all_57_14))
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | BETA: splitting (171) gives:
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | Case 1:
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | |   (172)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &
% 159.61/26.03  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.61/26.03  | | | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.61/26.03  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14
% 159.61/26.03  | | | | | | | | | | | |            = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1,
% 159.61/26.03  | | | | | | | | | | | |              e1) = e1)
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (36), (172) are inconsistent by
% 159.61/26.03  | | | | | | | | | | | |            sub-proof #644.
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | Case 2:
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | |   (173)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.61/26.03  | | | | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.61/26.03  | | | | | | | | | | | |            op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.61/26.03  | | | | | | | | | | | |            e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10
% 159.61/26.03  | | | | | | | | | | | |            = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 159.61/26.03  | | | | | | | | | | | |              e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 &
% 159.61/26.03  | | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 159.61/26.03  | | | | | | | | | | | |              e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.61/26.03  | | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | BETA: splitting (173) gives:
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | Case 1:
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | |   (174)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 & 
% 159.61/26.03  | | | | | | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 159.61/26.03  | | | | | | | | | | | | |          op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.61/26.03  | | | | | | | | | | | | |          e3 & $i(all_57_10)
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | ALPHA: (174) implies:
% 159.61/26.03  | | | | | | | | | | | | |   (175)  op(e0, e0) = e3
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | REF_CLOSE: (9), (54), (59), (175) are inconsistent by
% 159.61/26.03  | | | | | | | | | | | | |            sub-proof #999.
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | Case 2:
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | |   (176)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 159.61/26.03  | | | | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 159.61/26.03  | | | | | | | | | | | | |            e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 159.61/26.03  | | | | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 159.61/26.03  | | | | | | | | | | | | |            = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 159.61/26.03  | | | | | | | | | | | | |            & $i(all_57_14))
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | BETA: splitting (176) gives:
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | Case 1:
% 159.61/26.03  | | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | |   (177)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) &
% 159.61/26.03  | | | | | | | | | | | | | |          op(e3, e3) = e3 & op(e3, e1) = e3
% 159.61/26.03  | | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | | ALPHA: (177) implies:
% 159.61/26.03  | | | | | | | | | | | | | |   (178)  op(e3, e3) = e3
% 159.61/26.03  | | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | | REF_CLOSE: (9), (27), (36), (178) are inconsistent by
% 159.61/26.03  | | | | | | | | | | | | | |            sub-proof #995.
% 159.61/26.03  | | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | Case 2:
% 159.61/26.03  | | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | |   (179)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 & 
% 159.61/26.03  | | | | | | | | | | | | | |          ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 159.61/26.03  | | | | | | | | | | | | | |          = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/26.03  | | | | | | | | | | | | | |          $i(all_57_14)
% 159.61/26.03  | | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | | ALPHA: (179) implies:
% 159.61/26.03  | | | | | | | | | | | | | |   (180)  op(e1, e0) = e1
% 159.61/26.03  | | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | | REF_CLOSE: (9), (22), (134), (135), (180) are inconsistent by
% 159.61/26.03  | | | | | | | | | | | | | |            sub-proof #637.
% 159.61/26.03  | | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | | End of split
% 159.61/26.03  | | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | End of split
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | End of split
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | End of split
% 159.61/26.03  | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | Case 2:
% 159.61/26.03  | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | |   (181)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.61/26.03  | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.61/26.03  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.61/26.03  | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 159.61/26.03  | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 159.61/26.03  | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 159.61/26.03  | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2)
% 159.61/26.03  | | | | | | | | | |            = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 &
% 159.61/26.03  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0
% 159.61/26.03  | | | | | | | | | |            & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10
% 159.61/26.03  | | | | | | | | | |              = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 159.61/26.03  | | | | | | | | | |            e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.61/26.03  | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2
% 159.61/26.03  | | | | | | | | | |            & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2,
% 159.61/26.03  | | | | | | | | | |              e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2)
% 159.61/26.03  | | | | | | | | | |            = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.61/26.03  | | | | | | | | | |          (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 159.61/26.03  | | | | | | | | | |            op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 =
% 159.61/26.03  | | | | | | | | | |            e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 159.61/26.03  | | | | | | | | | |            e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 159.61/26.03  | | | | | | | | | |            all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.61/26.03  | | | | | | | | | |            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 159.61/26.03  | | | | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 159.61/26.03  | | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3,
% 159.61/26.03  | | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 159.61/26.03  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_11 = e2 &
% 159.61/26.03  | | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2,
% 159.61/26.03  | | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 159.61/26.03  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 159.61/26.03  | | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 159.61/26.03  | | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.61/26.03  | | | | | | | | | |                e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.61/26.03  | | | | | | | | | |                (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0
% 159.61/26.03  | | | | | | | | | |                & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.61/26.03  | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.61/26.03  | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.61/26.03  | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.03  | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 159.61/26.03  | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 159.61/26.03  | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/26.03  | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.61/26.03  | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.61/26.03  | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 159.61/26.03  | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 159.61/26.03  | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.03  | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.61/26.03  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 = e2
% 159.61/26.03  | | | | | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.03  | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/26.03  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 159.61/26.03  | | | | | | | | | |                & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.03  | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/26.03  | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 159.61/26.03  | | | | | | | | | |                & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.61/26.03  | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/26.03  | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 159.61/26.03  | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0,
% 159.61/26.03  | | | | | | | | | |                  e1) = e0)))
% 159.61/26.03  | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | BETA: splitting (181) gives:
% 159.61/26.03  | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | Case 1:
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | |   (182)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 & 
% 159.61/26.03  | | | | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 159.61/26.03  | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.61/26.03  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12
% 159.61/26.03  | | | | | | | | | | |            = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2,
% 159.61/26.03  | | | | | | | | | | |              e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 159.61/26.03  | | | | | | | | | | |            all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2,
% 159.61/26.03  | | | | | | | | | | |              e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 159.61/26.03  | | | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 159.61/26.03  | | | | | | | | | | |          (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 & 
% 159.61/26.03  | | | | | | | | | | |            ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 159.61/26.03  | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.61/26.03  | | | | | | | | | | |            e3 & $i(all_57_10))
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | REF_CLOSE: (9), (54), (56), (58), (59), (124), (182) are
% 159.61/26.03  | | | | | | | | | | |            inconsistent by sub-proof #918.
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | Case 2:
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | |   (183)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 159.61/26.03  | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.61/26.03  | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.61/26.03  | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 159.61/26.03  | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 159.61/26.03  | | | | | | | | | | |              e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 &
% 159.61/26.03  | | | | | | | | | | |             ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 159.61/26.03  | | | | | | | | | | |            e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 159.61/26.03  | | | | | | | | | | |              = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 159.61/26.03  | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.61/26.03  | | | | | | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.61/26.03  | | | | | | | | | | |                &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 159.61/26.03  | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.61/26.03  | | | | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 =
% 159.61/26.03  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 159.61/26.03  | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.61/26.03  | | | | | | | | | | |              (all_57_6 = e0 & all_57_13 = e1 & all_57_14 =
% 159.61/26.03  | | | | | | | | | | |                e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 159.61/26.03  | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e3) = e0) |
% 159.61/26.03  | | | | | | | | | | |              (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 159.61/26.03  | | | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.61/26.03  | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.61/26.03  | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.61/26.03  | | | | | | | | | | |                  e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.61/26.03  | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.03  | | | | | | | | | | |                (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 159.61/26.03  | | | | | | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 159.61/26.03  | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/26.03  | | | | | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.61/26.03  | | | | | | | | | | |                  e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.61/26.03  | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 159.61/26.03  | | | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3
% 159.61/26.03  | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.03  | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.61/26.03  | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 159.61/26.03  | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.03  | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/26.03  | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.61/26.03  | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.03  | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/26.03  | | | | | | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.61/26.03  | | | | | | | | | | |                e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.61/26.03  | | | | | | | | | | |                op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.61/26.03  | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8
% 159.61/26.03  | | | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.61/26.03  | | | | | | | | | | |                op(e0, e1) = e0)))
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | BETA: splitting (183) gives:
% 159.61/26.03  | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | Case 1:
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | |   (184)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &
% 159.61/26.03  | | | | | | | | | | | |             ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 159.61/26.03  | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.61/26.03  | | | | | | | | | | | |            e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 159.61/26.03  | | | | | | | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3,
% 159.61/26.03  | | | | | | | | | | | |              e0) = e3)
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | | REF_CLOSE: (9), (27), (36), (56), (59), (184) are
% 159.61/26.03  | | | | | | | | | | | |            inconsistent by sub-proof #836.
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.03  | | | | | | | | | | | Case 2:
% 159.61/26.03  | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | |   (185)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.61/26.04  | | | | | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13
% 159.61/26.04  | | | | | | | | | | | |            = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 159.61/26.04  | | | | | | | | | | | |              e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.61/26.04  | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.61/26.04  | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.61/26.04  | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.04  | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.04  | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.04  | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.61/26.04  | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.04  | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/26.04  | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.61/26.04  | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.04  | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.61/26.04  | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.61/26.04  | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.04  | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.61/26.04  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.61/26.04  | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.04  | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/26.04  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.61/26.04  | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.04  | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/26.04  | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.61/26.04  | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.61/26.04  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.61/26.04  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.61/26.04  | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.61/26.04  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.61/26.04  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.61/26.04  | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.61/26.04  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.61/26.04  | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.61/26.04  | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.61/26.04  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.61/26.04  | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.61/26.04  | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.61/26.04  | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.61/26.04  | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.61/26.04  | | | | | | | | | | | |                e0)))
% 159.61/26.04  | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | BETA: splitting (185) gives:
% 159.61/26.04  | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | Case 1:
% 159.61/26.04  | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | |   (186)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.61/26.04  | | | | | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 159.61/26.04  | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | ALPHA: (186) implies:
% 159.61/26.04  | | | | | | | | | | | | |   (187)  op(e2, e2) = e2
% 159.61/26.04  | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | REF_CLOSE: (9), (56), (124), (187) are inconsistent by
% 159.61/26.04  | | | | | | | | | | | | |            sub-proof #942.
% 159.61/26.04  | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | Case 2:
% 159.61/26.04  | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | |   (188)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.61/26.04  | | | | | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0)
% 159.61/26.04  | | | | | | | | | | | | |            = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.61/26.04  | | | | | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.61/26.04  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.04  | | | | | | | | | | | | |                  e0) = e3 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.04  | | | | | | | | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.04  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.61/26.04  | | | | | | | | | | | | |                  e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.04  | | | | | | | | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/26.04  | | | | | | | | | | | | |                (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.61/26.04  | | | | | | | | | | | | |                  e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.61/26.04  | | | | | | | | | | | | |                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0,
% 159.61/26.04  | | | | | | | | | | | | |                  e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 159.61/26.04  | | | | | | | | | | | | |                & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.04  | | | | | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.61/26.04  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.61/26.04  | | | | | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.04  | | | | | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.61/26.04  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.61/26.04  | | | | | | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.04  | | | | | | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.61/26.04  | | | | | | | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_15 =
% 159.61/26.04  | | | | | | | | | | | | |                e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.61/26.04  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_9 = e3 & all_57_10 =
% 159.61/26.04  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.61/26.04  | | | | | | | | | | | | |                op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.61/26.04  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.61/26.04  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.61/26.04  | | | | | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.61/26.04  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.61/26.04  | | | | | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.61/26.04  | | | | | | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.61/26.04  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 159.61/26.04  | | | | | | | | | | | | |                e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 159.61/26.04  | | | | | | | | | | | | |                all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.61/26.04  | | | | | | | | | | | | |                e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.61/26.04  | | | | | | | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.61/26.04  | | | | | | | | | | | | |                e0)))
% 159.61/26.04  | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | BETA: splitting (188) gives:
% 159.61/26.04  | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | Case 1:
% 159.61/26.04  | | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | |   (189)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.61/26.04  | | | | | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 159.61/26.04  | | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | | ALPHA: (189) implies:
% 159.61/26.04  | | | | | | | | | | | | | |   (190)  op(e1, e1) = e1
% 159.61/26.04  | | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (190) are inconsistent by
% 159.61/26.04  | | | | | | | | | | | | | |            sub-proof #1003.
% 159.61/26.04  | | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | Case 2:
% 159.61/26.04  | | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | |   (191)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.61/26.04  | | | | | | | | | | | | | |          ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &
% 159.61/26.04  | | | | | | | | | | | | | |               ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.04  | | | | | | | | | | | | | |                e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.61/26.04  | | | | | | | | | | | | | |              & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.61/26.04  | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.61/26.04  | | | | | | | | | | | | | |                e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.61/26.04  | | | | | | | | | | | | | |              & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.61/26.04  | | | | | | | | | | | | | |              (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.61/26.04  | | | | | | | | | | | | | |                e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.61/26.04  | | | | | | | | | | | | | |              & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 159.61/26.04  | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 159.61/26.04  | | | | | | | | | | | | | |              all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 159.61/26.04  | | | | | | | | | | | | | |                e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.61/26.04  | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.61/26.04  | | | | | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.61/26.04  | | | | | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.61/26.04  | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.61/26.04  | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.61/26.04  | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.61/26.04  | | | | | | | | | | | | | |              e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2
% 159.61/26.04  | | | | | | | | | | | | | |                = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.61/26.04  | | | | | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.61/26.04  | | | | | | | | | | | | | |                = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.61/26.04  | | | | | | | | | | | | | |              op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 159.61/26.04  | | | | | | | | | | | | | |              = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.04  | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 159.61/26.04  | | | | | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.61/26.04  | | | | | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1,
% 159.61/26.04  | | | | | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.61/26.04  | | | | | | | | | | | | | |              e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.61/26.04  | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 159.61/26.04  | | | | | | | | | | | | | |                e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.61/26.04  | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.61/26.04  | | | | | | | | | | | | | |              all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) =
% 159.61/26.04  | | | | | | | | | | | | | |              e0))
% 159.61/26.04  | | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | | ALPHA: (191) implies:
% 159.61/26.04  | | | | | | | | | | | | | |   (192)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.61/26.04  | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.61/26.04  | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.61/26.04  | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.61/26.04  | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.61/26.04  | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.61/26.04  | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.61/26.04  | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.61/26.04  | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.61/26.04  | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.61/26.04  | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.61/26.04  | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.61/26.04  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.61/26.04  | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.61/26.04  | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.61/26.04  | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.61/26.04  | | | | | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.61/26.04  | | | | | | | | | | | | | |              e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 159.61/26.04  | | | | | | | | | | | | | |          | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 159.61/26.04  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 159.61/26.04  | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.61/26.04  | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 159.61/26.04  | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 159.61/26.04  | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 159.61/26.04  | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 159.61/26.04  | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0
% 159.61/26.04  | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 159.61/26.04  | | | | | | | | | | | | | |              e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.61/26.04  | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 159.61/26.04  | | | | | | | | | | | | | |              = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 159.61/26.04  | | | | | | | | | | | | | |            e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 159.61/26.04  | | | | | | | | | | | | | |          (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.61/26.04  | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 159.61/26.04  | | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 159.61/26.04  | | | | | | | | | | | | | | 
% 159.61/26.04  | | | | | | | | | | | | | | Case 1:
% 159.61/26.04  | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | |   (193)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.73/26.04  | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.73/26.04  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.73/26.04  | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.73/26.04  | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.73/26.04  | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.73/26.04  | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.73/26.04  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.73/26.04  | | | | | | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.73/26.04  | | | | | | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.73/26.04  | | | | | | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.73/26.04  | | | | | | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.73/26.04  | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.73/26.04  | | | | | | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.73/26.04  | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.73/26.04  | | | | | | | | | | | | | | |            e0)
% 159.73/26.04  | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 159.73/26.04  | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | Case 1:
% 159.73/26.04  | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | |   (194)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.73/26.04  | | | | | | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 159.73/26.04  | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.73/26.04  | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.73/26.04  | | | | | | | | | | | | | | | |              = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.73/26.04  | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.73/26.04  | | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.73/26.04  | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.73/26.04  | | | | | | | | | | | | | | | |            e0)
% 159.73/26.04  | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 159.73/26.04  | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | Case 1:
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | |   (195)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.73/26.04  | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 159.73/26.04  | | | | | | | | | | | | | | | | |          = e3 & op(e0, e3) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 159.73/26.04  | | | | | | | | | | | | | | | | |   (196)  op(e0, e3) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (50), (196) are inconsistent by
% 159.73/26.04  | | | | | | | | | | | | | | | | |            sub-proof #973.
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | Case 2:
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | |   (197)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.73/26.04  | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 159.73/26.04  | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.73/26.04  | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.73/26.04  | | | | | | | | | | | | | | | | |              = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.73/26.04  | | | | | | | | | | | | | | | | |            op(e0, e3) = e0)
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | Case 1:
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | |   (198)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 159.73/26.04  | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 159.73/26.04  | | | | | | | | | | | | | | | | | |          = e2 & op(e0, e3) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 159.73/26.04  | | | | | | | | | | | | | | | | | |   (199)  op(e0, e3) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (50), (199) are inconsistent by
% 159.73/26.04  | | | | | | | | | | | | | | | | | |            sub-proof #973.
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | Case 2:
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | |   (200)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.73/26.04  | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0)
% 159.73/26.04  | | | | | | | | | | | | | | | | | |          = e1 & op(e0, e3) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 159.73/26.04  | | | | | | | | | | | | | | | | | |   (201)  op(e1, e1) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (54), (201) are inconsistent by
% 159.73/26.04  | | | | | | | | | | | | | | | | | |            sub-proof #912.
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | End of split
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | End of split
% 159.73/26.04  | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | Case 2:
% 159.73/26.04  | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | |   (202)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.73/26.04  | | | | | | | | | | | | | | | |            op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 159.73/26.04  | | | | | | | | | | | | | | | |            e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.73/26.04  | | | | | | | | | | | | | | | |            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.73/26.04  | | | | | | | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.73/26.04  | | | | | | | | | | | | | | | |            all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.73/26.04  | | | | | | | | | | | | | | | |              e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.73/26.04  | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 159.73/26.04  | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | Case 1:
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | |   (203)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 159.73/26.04  | | | | | | | | | | | | | | | | |          op(e0, e3) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 159.73/26.04  | | | | | | | | | | | | | | | | |   (204)  op(e0, e3) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (50), (204) are inconsistent by
% 159.73/26.04  | | | | | | | | | | | | | | | | |            sub-proof #973.
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | Case 2:
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | |   (205)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.73/26.04  | | | | | | | | | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 159.73/26.04  | | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.73/26.04  | | | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.73/26.04  | | | | | | | | | | | | | | | | |              = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.73/26.04  | | | | | | | | | | | | | | | | |            op(e0, e2) = e0)
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | Case 1:
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | |   (206)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.73/26.04  | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0)
% 159.73/26.04  | | | | | | | | | | | | | | | | | |          = e3 & op(e0, e2) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 159.73/26.04  | | | | | | | | | | | | | | | | | |   (207)  op(e3, e3) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (27), (58), (207) are inconsistent by
% 159.73/26.04  | | | | | | | | | | | | | | | | | |            sub-proof #834.
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | Case 2:
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | |   (208)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 159.73/26.04  | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 159.73/26.04  | | | | | | | | | | | | | | | | | |          = e2 & op(e0, e2) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 159.73/26.04  | | | | | | | | | | | | | | | | | |   (209)  op(e0, e2) = e0
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18), (51), (209) are inconsistent by
% 159.73/26.04  | | | | | | | | | | | | | | | | | |            sub-proof #969.
% 159.73/26.04  | | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | | End of split
% 159.73/26.04  | | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | | End of split
% 159.73/26.04  | | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | | End of split
% 159.73/26.04  | | | | | | | | | | | | | | | 
% 159.73/26.04  | | | | | | | | | | | | | | Case 2:
% 159.73/26.04  | | | | | | | | | | | | | | | 
% 159.78/26.04  | | | | | | | | | | | | | | |   (210)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.78/26.04  | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.78/26.04  | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.78/26.04  | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.78/26.04  | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.78/26.04  | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.78/26.04  | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.78/26.04  | | | | | | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.78/26.04  | | | | | | | | | | | | | | |              = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.78/26.04  | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.78/26.04  | | | | | | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.78/26.04  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) =
% 159.78/26.04  | | | | | | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.78/26.04  | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1,
% 159.78/26.04  | | | | | | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1)
% 159.78/26.04  | | | | | | | | | | | | | | |            = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.78/26.04  | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.78/26.04  | | | | | | | | | | | | | | | 
% 159.78/26.04  | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 159.78/26.04  | | | | | | | | | | | | | | | 
% 159.78/26.04  | | | | | | | | | | | | | | | Case 1:
% 159.78/26.04  | | | | | | | | | | | | | | | | 
% 159.78/26.04  | | | | | | | | | | | | | | | |   (211)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.78/26.04  | | | | | | | | | | | | | | | |             ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 159.78/26.04  | | | | | | | | | | | | | | | |              e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.78/26.04  | | | | | | | | | | | | | | | |            all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.78/26.04  | | | | | | | | | | | | | | | |          | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0
% 159.78/26.04  | | | | | | | | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e0 & op(e3,
% 159.78/26.04  | | | | | | | | | | | | | | | |              e0) = e3 & op(e0, e1) = e0)
% 159.78/26.04  | | | | | | | | | | | | | | | | 
% 159.78/26.04  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (18), (27), (51), (54), (58), (211) are
% 159.78/26.04  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #640.
% 159.78/26.04  | | | | | | | | | | | | | | | | 
% 159.78/26.04  | | | | | | | | | | | | | | | Case 2:
% 159.78/26.04  | | | | | | | | | | | | | | | | 
% 159.78/26.04  | | | | | | | | | | | | | | | |   (212)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.78/26.04  | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.78/26.04  | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.78/26.04  | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.78/26.04  | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.78/26.04  | | | | | | | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.78/26.04  | | | | | | | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.78/26.04  | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.78/26.04  | | | | | | | | | | | | | | | |            op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 =
% 159.78/26.04  | | | | | | | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1)
% 159.78/26.04  | | | | | | | | | | | | | | | |            = e0)
% 159.78/26.04  | | | | | | | | | | | | | | | | 
% 159.78/26.04  | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 159.78/26.04  | | | | | | | | | | | | | | | | 
% 159.78/26.04  | | | | | | | | | | | | | | | | Case 1:
% 159.78/26.04  | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | |   (213)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 159.78/26.05  | | | | | | | | | | | | | | | | |             ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 159.78/26.05  | | | | | | | | | | | | | | | | |              e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.78/26.05  | | | | | | | | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.78/26.05  | | | | | | | | | | | | | | | | |              = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.78/26.05  | | | | | | | | | | | | | | | | |            op(e0, e1) = e0)
% 159.78/26.05  | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 159.78/26.05  | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | Case 1:
% 159.78/26.05  | | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | |   (214)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 159.78/26.05  | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 159.78/26.05  | | | | | | | | | | | | | | | | | |          = e2 & op(e0, e1) = e0
% 159.78/26.05  | | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 159.78/26.05  | | | | | | | | | | | | | | | | | |   (215)  op(e0, e1) = e0
% 159.78/26.05  | | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (52), (215) are inconsistent by
% 159.78/26.05  | | | | | | | | | | | | | | | | | |            sub-proof #966.
% 159.78/26.05  | | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | Case 2:
% 159.78/26.05  | | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | |   (216)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 159.78/26.05  | | | | | | | | | | | | | | | | | |          ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 159.78/26.05  | | | | | | | | | | | | | | | | | |          = e1 & op(e0, e1) = e0
% 159.78/26.05  | | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 159.78/26.05  | | | | | | | | | | | | | | | | | |   (217)  op(e1, e1) = e0
% 159.78/26.05  | | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (54), (217) are inconsistent by
% 159.78/26.05  | | | | | | | | | | | | | | | | | |            sub-proof #912.
% 159.78/26.05  | | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | End of split
% 159.78/26.05  | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | Case 2:
% 159.78/26.05  | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | |   (218)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 159.78/26.05  | | | | | | | | | | | | | | | | |             ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.78/26.05  | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.78/26.05  | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 159.78/26.05  | | | | | | | | | | | | | | | | |            &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.78/26.05  | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (52), (218) are inconsistent by
% 159.78/26.05  | | | | | | | | | | | | | | | | |            sub-proof #965.
% 159.78/26.05  | | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | | End of split
% 159.78/26.05  | | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | | End of split
% 159.78/26.05  | | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | | End of split
% 159.78/26.05  | | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | | End of split
% 159.78/26.05  | | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | | End of split
% 159.78/26.05  | | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | | End of split
% 159.78/26.05  | | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | | End of split
% 159.78/26.05  | | | | | | | | | | 
% 159.78/26.05  | | | | | | | | | End of split
% 159.78/26.05  | | | | | | | | | 
% 159.78/26.05  | | | | | | | | End of split
% 159.78/26.05  | | | | | | | | 
% 159.78/26.05  | | | | | | | End of split
% 159.78/26.05  | | | | | | | 
% 159.78/26.05  | | | | | | End of split
% 159.78/26.05  | | | | | | 
% 159.78/26.05  | | | | | End of split
% 159.78/26.05  | | | | | 
% 159.78/26.05  | | | | End of split
% 159.78/26.05  | | | | 
% 159.78/26.05  | | | End of split
% 159.78/26.05  | | | 
% 159.78/26.05  | | End of split
% 159.78/26.05  | | 
% 159.78/26.05  | End of split
% 159.78/26.05  | 
% 159.78/26.05  End of proof
% 159.78/26.05  
% 159.78/26.05  Sub-proof #637 shows that the following formulas are inconsistent:
% 159.78/26.05  ----------------------------------------------------------------
% 159.78/26.05    (1)  op(e1, e0) = all_57_13
% 159.78/26.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.05    (3)   ~ (all_57_13 = e1)
% 159.78/26.05    (4)  op(e1, e0) = all_52_14
% 159.78/26.05    (5)  op(e1, e0) = e1
% 159.78/26.05  
% 159.78/26.05  Begin of proof
% 159.78/26.05  | 
% 159.78/26.05  | GROUND_INST: instantiating (2) with all_52_14, all_57_13, e0, e1, simplifying
% 159.78/26.05  |              with (1), (4) gives:
% 159.78/26.05  |   (6)  all_57_13 = all_52_14
% 159.78/26.05  | 
% 159.78/26.05  | GROUND_INST: instantiating (2) with e1, all_57_13, e0, e1, simplifying with
% 159.78/26.05  |              (1), (5) gives:
% 159.78/26.05  |   (7)  all_57_13 = e1
% 159.78/26.05  | 
% 159.78/26.05  | COMBINE_EQS: (6), (7) imply:
% 159.78/26.05  |   (8)  all_52_14 = e1
% 159.78/26.05  | 
% 159.78/26.05  | REDUCE: (3), (7) imply:
% 159.78/26.05  |   (9)  $false
% 159.78/26.05  | 
% 159.78/26.05  | CLOSE: (9) is inconsistent.
% 159.78/26.05  | 
% 159.78/26.05  End of proof
% 159.78/26.05  
% 159.78/26.05  Sub-proof #638 shows that the following formulas are inconsistent:
% 159.78/26.05  ----------------------------------------------------------------
% 159.78/26.05    (1)  op(e1, e1) = e3
% 159.78/26.05    (2)   ~ (e3 = e2)
% 159.78/26.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.05    (4)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.78/26.05           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 159.78/26.05           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3
% 159.78/26.05           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 159.78/26.05           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.78/26.05    (5)  op(e2, e2) = e0
% 159.78/26.05    (6)   ~ (e3 = e0)
% 159.78/26.05  
% 159.78/26.05  Begin of proof
% 159.78/26.05  | 
% 159.78/26.05  | BETA: splitting (4) gives:
% 159.78/26.05  | 
% 159.78/26.05  | Case 1:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (7)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 159.78/26.05  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.78/26.05  | |          e1) = e2 & $i(all_57_12)
% 159.78/26.05  | | 
% 159.78/26.05  | | ALPHA: (7) implies:
% 159.78/26.05  | |   (8)  op(e1, e1) = e2
% 159.78/26.05  | | 
% 159.78/26.05  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #646.
% 159.78/26.05  | | 
% 159.78/26.05  | Case 2:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (9)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1)
% 159.78/26.05  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 159.78/26.05  | |          e2) = e3 & $i(all_57_10)
% 159.78/26.05  | | 
% 159.78/26.05  | | ALPHA: (9) implies:
% 159.78/26.05  | |   (10)  op(e2, e2) = e3
% 159.78/26.05  | | 
% 159.78/26.05  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #945.
% 159.78/26.05  | | 
% 159.78/26.05  | End of split
% 159.78/26.05  | 
% 159.78/26.05  End of proof
% 159.78/26.05  
% 159.78/26.05  Sub-proof #639 shows that the following formulas are inconsistent:
% 159.78/26.05  ----------------------------------------------------------------
% 159.78/26.05    (1)  op(e1, e1) = e3
% 159.78/26.05    (2)  op(e0, e1) = all_52_11
% 159.78/26.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.05    (4)  op(e2, e0) = all_52_13
% 159.78/26.05    (5)   ~ (all_52_11 = e0)
% 159.78/26.05    (6)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.78/26.05           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.78/26.05           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 159.78/26.05           & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 159.78/26.05           & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.78/26.05           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.78/26.05           all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.78/26.05    (7)   ~ (e3 = e0)
% 159.78/26.05    (8)   ~ (all_52_13 = e2)
% 159.78/26.05  
% 159.78/26.05  Begin of proof
% 159.78/26.05  | 
% 159.78/26.05  | BETA: splitting (6) gives:
% 159.78/26.05  | 
% 159.78/26.05  | Case 1:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (9)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.78/26.05  | |            e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.78/26.05  | |        (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.78/26.05  | |            e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0)
% 159.78/26.05  | | 
% 159.78/26.05  | | BETA: splitting (9) gives:
% 159.78/26.05  | | 
% 159.78/26.05  | | Case 1:
% 159.78/26.05  | | | 
% 159.78/26.05  | | |   (10)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.78/26.05  | | |           e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 159.78/26.05  | | | 
% 159.78/26.05  | | | ALPHA: (10) implies:
% 159.78/26.05  | | |   (11)  op(e2, e0) = e2
% 159.78/26.05  | | | 
% 159.78/26.05  | | | REF_CLOSE: (3), (4), (8), (11) are inconsistent by sub-proof #996.
% 159.78/26.05  | | | 
% 159.78/26.05  | | Case 2:
% 159.78/26.05  | | | 
% 159.78/26.05  | | |   (12)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.78/26.05  | | |           e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.78/26.05  | | | 
% 159.78/26.05  | | | ALPHA: (12) implies:
% 159.78/26.05  | | |   (13)  op(e1, e1) = e0
% 159.78/26.05  | | | 
% 159.78/26.05  | | | REF_CLOSE: (1), (3), (7), (13) are inconsistent by sub-proof #912.
% 159.78/26.05  | | | 
% 159.78/26.05  | | End of split
% 159.78/26.05  | | 
% 159.78/26.05  | Case 2:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (14)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.78/26.05  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.78/26.05  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 159.78/26.05  | |           & op(e0, e1) = e0)
% 159.78/26.05  | | 
% 159.78/26.05  | | REF_CLOSE: (2), (3), (5), (14) are inconsistent by sub-proof #965.
% 159.78/26.05  | | 
% 159.78/26.05  | End of split
% 159.78/26.05  | 
% 159.78/26.05  End of proof
% 159.78/26.05  
% 159.78/26.05  Sub-proof #640 shows that the following formulas are inconsistent:
% 159.78/26.05  ----------------------------------------------------------------
% 159.78/26.05    (1)   ~ (all_52_7 = e0)
% 159.78/26.05    (2)  op(e1, e1) = e3
% 159.78/26.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.05    (4)  op(e0, e2) = all_52_7
% 159.78/26.05    (5)  op(e3, e3) = e1
% 159.78/26.05    (6)   ~ (e1 = e0)
% 159.78/26.05    (7)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.78/26.05           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.78/26.05           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.78/26.05           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 159.78/26.05           & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.78/26.05    (8)   ~ (e3 = e0)
% 159.78/26.05  
% 159.78/26.05  Begin of proof
% 159.78/26.05  | 
% 159.78/26.05  | BETA: splitting (7) gives:
% 159.78/26.05  | 
% 159.78/26.05  | Case 1:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (9)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 159.78/26.05  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 159.78/26.05  | | 
% 159.78/26.05  | | ALPHA: (9) implies:
% 159.78/26.05  | |   (10)  op(e1, e1) = e0
% 159.78/26.05  | | 
% 159.78/26.05  | | REF_CLOSE: (2), (3), (8), (10) are inconsistent by sub-proof #912.
% 159.78/26.05  | | 
% 159.78/26.05  | Case 2:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (11)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.78/26.05  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.78/26.05  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.78/26.05  | | 
% 159.78/26.05  | | REF_CLOSE: (1), (3), (4), (5), (6), (11) are inconsistent by sub-proof #641.
% 159.78/26.05  | | 
% 159.78/26.05  | End of split
% 159.78/26.05  | 
% 159.78/26.05  End of proof
% 159.78/26.05  
% 159.78/26.05  Sub-proof #641 shows that the following formulas are inconsistent:
% 159.78/26.05  ----------------------------------------------------------------
% 159.78/26.05    (1)   ~ (all_52_7 = e0)
% 159.78/26.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.05    (3)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.78/26.05         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.78/26.05           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.78/26.05    (4)  op(e0, e2) = all_52_7
% 159.78/26.05    (5)  op(e3, e3) = e1
% 159.78/26.05    (6)   ~ (e1 = e0)
% 159.78/26.05  
% 159.78/26.05  Begin of proof
% 159.78/26.05  | 
% 159.78/26.05  | BETA: splitting (3) gives:
% 159.78/26.05  | 
% 159.78/26.05  | Case 1:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (7)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 159.78/26.05  | | 
% 159.78/26.05  | | ALPHA: (7) implies:
% 159.78/26.05  | |   (8)  op(e0, e2) = e0
% 159.78/26.05  | | 
% 159.78/26.05  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #969.
% 159.78/26.05  | | 
% 159.78/26.05  | Case 2:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (9)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 159.78/26.05  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 159.78/26.05  | | 
% 159.78/26.05  | | ALPHA: (9) implies:
% 159.78/26.05  | |   (10)  op(e3, e3) = e0
% 159.78/26.05  | | 
% 159.78/26.05  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #834.
% 159.78/26.05  | | 
% 159.78/26.05  | End of split
% 159.78/26.05  | 
% 159.78/26.05  End of proof
% 159.78/26.05  
% 159.78/26.05  Sub-proof #642 shows that the following formulas are inconsistent:
% 159.78/26.05  ----------------------------------------------------------------
% 159.78/26.05    (1)  op(e1, e1) = e3
% 159.78/26.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.05    (3)  op(e0, e3) = all_52_3
% 159.78/26.05    (4)   ~ (all_52_3 = e0)
% 159.78/26.05    (5)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.78/26.05           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.78/26.05           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 159.78/26.05           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 159.78/26.05           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 159.78/26.05           e1 & op(e0, e3) = e0)
% 159.78/26.05    (6)  op(e2, e0) = all_52_13
% 159.78/26.05    (7)   ~ (e3 = e0)
% 159.78/26.05    (8)   ~ (all_52_13 = e2)
% 159.78/26.05  
% 159.78/26.05  Begin of proof
% 159.78/26.05  | 
% 159.78/26.05  | BETA: splitting (5) gives:
% 159.78/26.05  | 
% 159.78/26.05  | Case 1:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 159.78/26.05  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 159.78/26.05  | | 
% 159.78/26.05  | | ALPHA: (9) implies:
% 159.78/26.05  | |   (10)  op(e0, e3) = e0
% 159.78/26.05  | | 
% 159.78/26.05  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #973.
% 159.78/26.05  | | 
% 159.78/26.05  | Case 2:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (11)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.78/26.05  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.78/26.05  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.78/26.05  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.78/26.05  | | 
% 159.78/26.05  | | BETA: splitting (11) gives:
% 159.78/26.05  | | 
% 159.78/26.05  | | Case 1:
% 159.78/26.05  | | | 
% 159.78/26.05  | | |   (12)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.78/26.05  | | |           e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 159.78/26.05  | | | 
% 159.78/26.05  | | | ALPHA: (12) implies:
% 159.78/26.05  | | |   (13)  op(e2, e0) = e2
% 159.78/26.05  | | | 
% 159.78/26.05  | | | REF_CLOSE: (2), (6), (8), (13) are inconsistent by sub-proof #996.
% 159.78/26.05  | | | 
% 159.78/26.05  | | Case 2:
% 159.78/26.05  | | | 
% 159.78/26.05  | | |   (14)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.78/26.05  | | |           e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 159.78/26.05  | | | 
% 159.78/26.05  | | | ALPHA: (14) implies:
% 159.78/26.05  | | |   (15)  op(e1, e1) = e0
% 159.78/26.05  | | | 
% 159.78/26.05  | | | REF_CLOSE: (1), (2), (7), (15) are inconsistent by sub-proof #912.
% 159.78/26.05  | | | 
% 159.78/26.05  | | End of split
% 159.78/26.05  | | 
% 159.78/26.05  | End of split
% 159.78/26.05  | 
% 159.78/26.05  End of proof
% 159.78/26.05  
% 159.78/26.05  Sub-proof #643 shows that the following formulas are inconsistent:
% 159.78/26.05  ----------------------------------------------------------------
% 159.78/26.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.05    (2)  op(e3, e1) = all_52_8
% 159.78/26.05    (3)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 159.78/26.05             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 159.78/26.05           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 159.78/26.05           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.78/26.05    (4)  op(e3, e3) = e1
% 159.78/26.05    (5)   ~ (all_52_8 = e3)
% 159.78/26.05  
% 159.78/26.05  Begin of proof
% 159.78/26.05  | 
% 159.78/26.05  | BETA: splitting (3) gives:
% 159.78/26.05  | 
% 159.78/26.05  | Case 1:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (6)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 159.78/26.05  | |        op(e3, e1) = e3
% 159.78/26.05  | | 
% 159.78/26.05  | | ALPHA: (6) implies:
% 159.78/26.05  | |   (7)   ~ (e3 = e1)
% 159.78/26.05  | |   (8)  op(e3, e3) = e3
% 159.78/26.05  | | 
% 159.78/26.05  | | REF_CLOSE: (1), (4), (7), (8) are inconsistent by sub-proof #995.
% 159.78/26.05  | | 
% 159.78/26.05  | Case 2:
% 159.78/26.05  | | 
% 159.78/26.05  | |   (9)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 159.78/26.05  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 159.78/26.05  | |          e0) = e1 & $i(all_57_14)
% 159.78/26.05  | | 
% 159.78/26.05  | | ALPHA: (9) implies:
% 159.78/26.05  | |   (10)  op(e3, e1) = e3
% 159.78/26.05  | | 
% 159.78/26.05  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #982.
% 159.78/26.05  | | 
% 159.78/26.05  | End of split
% 159.78/26.05  | 
% 159.78/26.05  End of proof
% 159.78/26.05  
% 159.78/26.05  Sub-proof #644 shows that the following formulas are inconsistent:
% 159.78/26.05  ----------------------------------------------------------------
% 159.78/26.05    (1)  op(e1, e1) = e3
% 159.78/26.05    (2)   ~ (e3 = e2)
% 159.78/26.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.06    (4)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 159.78/26.06           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.78/26.06           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1)
% 159.78/26.06           & op(e1, e2) = e1 & op(e1, e1) = e1)
% 159.78/26.06    (5)   ~ (e3 = e1)
% 159.78/26.06  
% 159.78/26.06  Begin of proof
% 159.78/26.06  | 
% 159.78/26.06  | BETA: splitting (4) gives:
% 159.78/26.06  | 
% 159.78/26.06  | Case 1:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (6)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0)
% 159.78/26.06  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1,
% 159.78/26.06  | |          e1) = e2 & $i(all_57_12)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (6) implies:
% 159.78/26.06  | |   (7)  op(e1, e1) = e2
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #646.
% 159.78/26.06  | | 
% 159.78/26.06  | Case 2:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (8)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 159.78/26.06  | |        op(e1, e1) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (8) implies:
% 159.78/26.06  | |   (9)  op(e1, e1) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1003.
% 159.78/26.06  | | 
% 159.78/26.06  | End of split
% 159.78/26.06  | 
% 159.78/26.06  End of proof
% 159.78/26.06  
% 159.78/26.06  Sub-proof #645 shows that the following formulas are inconsistent:
% 159.78/26.06  ----------------------------------------------------------------
% 159.78/26.06    (1)  op(e1, e1) = e3
% 159.78/26.06    (2)   ~ (e3 = e2)
% 159.78/26.06    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.06    (4)  op(e0, e0) = e0
% 159.78/26.06    (5)  op(e0, e0) = all_14_2
% 159.78/26.06    (6)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 159.78/26.06           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.78/26.06           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 159.78/26.06           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.78/26.06           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.78/26.06    (7)   ~ (e1 = e0)
% 159.78/26.06  
% 159.78/26.06  Begin of proof
% 159.78/26.06  | 
% 159.78/26.06  | BETA: splitting (6) gives:
% 159.78/26.06  | 
% 159.78/26.06  | Case 1:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (8)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.78/26.06  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.78/26.06  | |          e1) = e2 & $i(all_57_12)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (8) implies:
% 159.78/26.06  | |   (9)  op(e1, e1) = e2
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #646.
% 159.78/26.06  | | 
% 159.78/26.06  | Case 2:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (10)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 159.78/26.06  | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.78/26.06  | |         op(e0, e0) = e1 & $i(all_57_14)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (10) implies:
% 159.78/26.06  | |   (11)  op(e0, e0) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (3), (4), (5), (7), (11) are inconsistent by sub-proof #991.
% 159.78/26.06  | | 
% 159.78/26.06  | End of split
% 159.78/26.06  | 
% 159.78/26.06  End of proof
% 159.78/26.06  
% 159.78/26.06  Sub-proof #646 shows that the following formulas are inconsistent:
% 159.78/26.06  ----------------------------------------------------------------
% 159.78/26.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.06    (2)  op(e1, e1) = e3
% 159.78/26.06    (3)  op(e1, e1) = e2
% 159.78/26.06    (4)   ~ (e3 = e2)
% 159.78/26.06  
% 159.78/26.06  Begin of proof
% 159.78/26.06  | 
% 159.78/26.06  | GROUND_INST: instantiating (1) with e2, e3, e1, e1, simplifying with (2), (3)
% 159.78/26.06  |              gives:
% 159.78/26.06  |   (5)  e3 = e2
% 159.78/26.06  | 
% 159.78/26.06  | REDUCE: (4), (5) imply:
% 159.78/26.06  |   (6)  $false
% 159.78/26.06  | 
% 159.78/26.06  | CLOSE: (6) is inconsistent.
% 159.78/26.06  | 
% 159.78/26.06  End of proof
% 159.78/26.06  
% 159.78/26.06  Sub-proof #647 shows that the following formulas are inconsistent:
% 159.78/26.06  ----------------------------------------------------------------
% 159.78/26.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.06    (2)  op(e3, e1) = all_52_8
% 159.78/26.06    (3)  op(e2, e2) = e2
% 159.78/26.06    (4)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 159.78/26.06           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.78/26.06           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 159.78/26.06           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 159.78/26.06             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.78/26.06    (5)   ~ (e2 = e1)
% 159.78/26.06    (6)   ~ (all_52_8 = e3)
% 159.78/26.06  
% 159.78/26.06  Begin of proof
% 159.78/26.06  | 
% 159.78/26.06  | BETA: splitting (4) gives:
% 159.78/26.06  | 
% 159.78/26.06  | Case 1:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (7)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 159.78/26.06  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.78/26.06  | |        all_57_14 & $i(all_57_14)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (7) implies:
% 159.78/26.06  | |   (8)  op(e3, e1) = e3
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #982.
% 159.78/26.06  | | 
% 159.78/26.06  | Case 2:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 159.78/26.06  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.78/26.06  | |        all_57_14 & $i(all_57_14)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (9) implies:
% 159.78/26.06  | |   (10)  op(e2, e2) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #993.
% 159.78/26.06  | | 
% 159.78/26.06  | End of split
% 159.78/26.06  | 
% 159.78/26.06  End of proof
% 159.78/26.06  
% 159.78/26.06  Sub-proof #648 shows that the following formulas are inconsistent:
% 159.78/26.06  ----------------------------------------------------------------
% 159.78/26.06    (1)  op(e1, e1) = e3
% 159.78/26.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.06    (3)  op(e1, e3) = all_52_2
% 159.78/26.06    (4)   ~ (all_52_2 = e1)
% 159.78/26.06    (5)  op(e0, e0) = e0
% 159.78/26.06    (6)  op(e0, e0) = all_14_2
% 159.78/26.06    (7)   ~ (e1 = e0)
% 159.78/26.06    (8)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.78/26.06           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.78/26.06           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 159.78/26.06           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.78/26.06           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 159.78/26.06           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.78/26.06  
% 159.78/26.06  Begin of proof
% 159.78/26.06  | 
% 159.78/26.06  | BETA: splitting (8) gives:
% 159.78/26.06  | 
% 159.78/26.06  | Case 1:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (9)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 159.78/26.06  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.78/26.06  | |          e0) = e1 & $i(all_57_14)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (9) implies:
% 159.78/26.06  | |   (10)  op(e0, e0) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (2), (5), (6), (7), (10) are inconsistent by sub-proof #991.
% 159.78/26.06  | | 
% 159.78/26.06  | Case 2:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (11)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.78/26.06  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 159.78/26.06  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 159.78/26.06  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (1), (2), (3), (4), (11) are inconsistent by sub-proof #649.
% 159.78/26.06  | | 
% 159.78/26.06  | End of split
% 159.78/26.06  | 
% 159.78/26.06  End of proof
% 159.78/26.06  
% 159.78/26.06  Sub-proof #649 shows that the following formulas are inconsistent:
% 159.78/26.06  ----------------------------------------------------------------
% 159.78/26.06    (1)  op(e1, e1) = e3
% 159.78/26.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.06    (3)  op(e1, e3) = all_52_2
% 159.78/26.06    (4)   ~ (all_52_2 = e1)
% 159.78/26.06    (5)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) &
% 159.78/26.06           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.78/26.06           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1)
% 159.78/26.06           & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.78/26.06  
% 159.78/26.06  Begin of proof
% 159.78/26.06  | 
% 159.78/26.06  | BETA: splitting (5) gives:
% 159.78/26.06  | 
% 159.78/26.06  | Case 1:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (6)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 159.78/26.06  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 159.78/26.06  | |          e1) = e3 & $i(all_57_10)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (6) implies:
% 159.78/26.06  | |   (7)  op(e1, e3) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #990.
% 159.78/26.06  | | 
% 159.78/26.06  | Case 2:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (8)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.78/26.06  | |        op(e1, e1) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (8) implies:
% 159.78/26.06  | |   (9)   ~ (e3 = e1)
% 159.78/26.06  | |   (10)  op(e1, e1) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #1003.
% 159.78/26.06  | | 
% 159.78/26.06  | End of split
% 159.78/26.06  | 
% 159.78/26.06  End of proof
% 159.78/26.06  
% 159.78/26.06  Sub-proof #650 shows that the following formulas are inconsistent:
% 159.78/26.06  ----------------------------------------------------------------
% 159.78/26.06    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.78/26.06           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.78/26.06           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 159.78/26.06           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 159.78/26.06           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.78/26.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.06    (3)  op(e2, e2) = e2
% 159.78/26.06    (4)  op(e1, e3) = all_52_2
% 159.78/26.06    (5)   ~ (all_52_2 = e1)
% 159.78/26.06    (6)   ~ (e2 = e1)
% 159.78/26.06  
% 159.78/26.06  Begin of proof
% 159.78/26.06  | 
% 159.78/26.06  | BETA: splitting (1) gives:
% 159.78/26.06  | 
% 159.78/26.06  | Case 1:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 159.78/26.06  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.78/26.06  | |          e1) = e3 & $i(all_57_10)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (7) implies:
% 159.78/26.06  | |   (8)  op(e1, e3) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #990.
% 159.78/26.06  | | 
% 159.78/26.06  | Case 2:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 159.78/26.06  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 159.78/26.06  | |        all_57_14 & $i(all_57_14)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (9) implies:
% 159.78/26.06  | |   (10)  op(e2, e2) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #993.
% 159.78/26.06  | | 
% 159.78/26.06  | End of split
% 159.78/26.06  | 
% 159.78/26.06  End of proof
% 159.78/26.06  
% 159.78/26.06  Sub-proof #651 shows that the following formulas are inconsistent:
% 159.78/26.06  ----------------------------------------------------------------
% 159.78/26.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.06    (2)  op(e1, e3) = all_52_2
% 159.78/26.06    (3)   ~ (all_52_2 = e1)
% 159.78/26.06    (4)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.78/26.06           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.78/26.06           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 159.78/26.06           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 159.78/26.06           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.78/26.06    (5)  op(e2, e0) = all_52_13
% 159.78/26.06    (6)   ~ (all_52_13 = e2)
% 159.78/26.06  
% 159.78/26.06  Begin of proof
% 159.78/26.06  | 
% 159.78/26.06  | BETA: splitting (4) gives:
% 159.78/26.06  | 
% 159.78/26.06  | Case 1:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (7)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 159.78/26.06  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.78/26.06  | |          e0) = e2 & $i(all_57_12)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (7) implies:
% 159.78/26.06  | |   (8)  op(e2, e0) = e2
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #996.
% 159.78/26.06  | | 
% 159.78/26.06  | Case 2:
% 159.78/26.06  | | 
% 159.78/26.06  | |   (9)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 159.78/26.06  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.78/26.06  | |        all_57_14 & $i(all_57_14)
% 159.78/26.06  | | 
% 159.78/26.06  | | ALPHA: (9) implies:
% 159.78/26.06  | |   (10)  op(e1, e3) = e1
% 159.78/26.06  | | 
% 159.78/26.06  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #990.
% 159.78/26.06  | | 
% 159.78/26.06  | End of split
% 159.78/26.06  | 
% 159.78/26.06  End of proof
% 159.78/26.06  
% 159.78/26.06  Sub-proof #652 shows that the following formulas are inconsistent:
% 159.78/26.06  ----------------------------------------------------------------
% 159.78/26.06    (1)   ~ (all_52_1 = e2)
% 159.78/26.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.06    (3)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.78/26.06           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.78/26.06           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 159.78/26.06           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.78/26.06           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.78/26.06           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 159.78/26.06           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.78/26.06           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 159.78/26.06           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 159.78/26.06             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.78/26.06           all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 159.78/26.06           & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.78/26.06           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 159.78/26.06           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 159.78/26.06             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 159.78/26.06           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 159.78/26.06         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.78/26.06           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.78/26.06           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 159.78/26.06           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 159.78/26.06           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.78/26.06    (4)  op(e1, e3) = all_52_2
% 159.78/26.06    (5)   ~ (all_52_2 = e1)
% 159.78/26.06    (6)  op(e2, e3) = all_52_1
% 159.78/26.06    (7)  op(e2, e1) = all_52_9
% 159.78/26.06    (8)   ~ (all_52_9 = e2)
% 159.78/26.06  
% 159.78/26.06  Begin of proof
% 159.78/26.06  | 
% 159.78/26.06  | BETA: splitting (3) gives:
% 159.78/26.06  | 
% 159.78/26.06  | Case 1:
% 159.78/26.06  | | 
% 159.78/26.07  | |   (9)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 159.78/26.07  | |          & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 159.78/26.07  | |          = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.78/26.07  | |          all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 159.78/26.07  | |          op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.78/26.07  | |          $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 159.78/26.07  | |          ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.78/26.07  | |          op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 159.78/26.07  | |          & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.78/26.07  | |          = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.78/26.07  | |          $i(all_57_10))
% 159.78/26.07  | | 
% 159.78/26.07  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #1005.
% 159.78/26.07  | | 
% 159.78/26.07  | Case 2:
% 159.78/26.07  | | 
% 159.78/26.07  | |   (10)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.78/26.07  | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0
% 159.78/26.07  | |           & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 =
% 159.78/26.07  | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 159.78/26.07  | |           & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.78/26.07  | |           $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 159.78/26.07  | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 159.78/26.07  | |           e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 159.78/26.07  | |           & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.78/26.07  | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &
% 159.78/26.07  | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2,
% 159.78/26.07  | |             e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.78/26.07  | | 
% 159.78/26.07  | | BETA: splitting (10) gives:
% 159.78/26.07  | | 
% 159.78/26.07  | | Case 1:
% 159.78/26.07  | | | 
% 159.78/26.07  | | |   (11)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.78/26.07  | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) =
% 159.78/26.07  | | |           e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.78/26.07  | | |           all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 159.78/26.07  | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 159.78/26.07  | | |             e2) = e3 & $i(all_57_10))
% 159.78/26.07  | | | 
% 159.78/26.07  | | | REF_CLOSE: (1), (2), (6), (11) are inconsistent by sub-proof #1004.
% 159.78/26.07  | | | 
% 159.78/26.07  | | Case 2:
% 159.78/26.07  | | | 
% 159.78/26.07  | | |   (12)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.78/26.07  | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 =
% 159.78/26.07  | | |           e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 159.78/26.07  | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.78/26.07  | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 =
% 159.78/26.07  | | |             e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.78/26.07  | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.78/26.07  | | | 
% 159.78/26.07  | | | BETA: splitting (12) gives:
% 159.78/26.07  | | | 
% 159.78/26.07  | | | Case 1:
% 159.78/26.07  | | | | 
% 159.78/26.07  | | | |   (13)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 159.78/26.07  | | | |         & op(e2, e2) = e2
% 159.78/26.07  | | | | 
% 159.78/26.07  | | | | ALPHA: (13) implies:
% 159.78/26.07  | | | |   (14)  op(e2, e3) = e2
% 159.78/26.07  | | | | 
% 159.78/26.07  | | | | REF_CLOSE: (1), (2), (6), (14) are inconsistent by sub-proof #1007.
% 159.78/26.07  | | | | 
% 159.78/26.07  | | | Case 2:
% 159.78/26.07  | | | | 
% 159.78/26.07  | | | |   (15)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 159.78/26.07  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.78/26.07  | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 159.78/26.07  | | | |           & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 159.78/26.07  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.78/26.07  | | | |           op(e2, e1) = e2 & $i(all_57_12))
% 159.78/26.07  | | | | 
% 159.78/26.07  | | | | BETA: splitting (15) gives:
% 159.78/26.07  | | | | 
% 159.78/26.07  | | | | Case 1:
% 159.78/26.07  | | | | | 
% 159.78/26.07  | | | | |   (16)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 159.78/26.07  | | | | |           = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.78/26.07  | | | | |           e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)
% 159.78/26.07  | | | | | 
% 159.78/26.07  | | | | | ALPHA: (16) implies:
% 159.78/26.07  | | | | |   (17)  op(e1, e3) = e1
% 159.78/26.07  | | | | | 
% 159.78/26.07  | | | | | REF_CLOSE: (2), (4), (5), (17) are inconsistent by sub-proof #990.
% 159.78/26.07  | | | | | 
% 159.78/26.07  | | | | Case 2:
% 159.78/26.07  | | | | | 
% 159.78/26.07  | | | | |   (18)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12
% 159.78/26.07  | | | | |           = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.78/26.07  | | | | |         all_57_12 & op(e2, e1) = e2 & $i(all_57_12)
% 159.78/26.07  | | | | | 
% 159.78/26.07  | | | | | ALPHA: (18) implies:
% 159.78/26.07  | | | | |   (19)  op(e2, e1) = e2
% 159.78/26.07  | | | | | 
% 159.78/26.07  | | | | | REF_CLOSE: (2), (7), (8), (19) are inconsistent by sub-proof #1002.
% 159.78/26.07  | | | | | 
% 159.78/26.07  | | | | End of split
% 159.78/26.07  | | | | 
% 159.78/26.07  | | | End of split
% 159.78/26.07  | | | 
% 159.78/26.07  | | End of split
% 159.78/26.07  | | 
% 159.78/26.07  | End of split
% 159.78/26.07  | 
% 159.78/26.07  End of proof
% 159.78/26.07  
% 159.78/26.07  Sub-proof #653 shows that the following formulas are inconsistent:
% 159.78/26.07  ----------------------------------------------------------------
% 159.78/26.07    (1)  all_54_5 = all_4_2
% 159.78/26.07    (2)   ~ (all_52_1 = e3)
% 159.78/26.07    (3)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.78/26.07    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.07    (5)   ~ (all_4_2 = e3)
% 159.78/26.07    (6)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.78/26.07           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 159.78/26.07           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 159.78/26.07           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.78/26.07           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.78/26.07    (7)  op(e2, e2) = e2
% 159.78/26.07    (8)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 159.78/26.07    (9)  op(e2, e2) = all_4_2
% 159.78/26.07    (10)  op(e2, e3) = all_52_1
% 159.78/26.07    (11)   ~ (all_4_2 = e1)
% 159.78/26.07    (12)  all_54_4 = all_52_1
% 159.78/26.07    (13)   ~ (all_52_1 = all_4_2)
% 159.78/26.07  
% 159.78/26.07  Begin of proof
% 159.78/26.07  | 
% 159.78/26.07  | BETA: splitting (6) gives:
% 159.78/26.07  | 
% 159.78/26.07  | Case 1:
% 159.78/26.07  | | 
% 159.78/26.07  | |   (14)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 159.78/26.07  | |         & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 159.78/26.07  | |         op(e0, e0) = e2 & $i(all_57_12)
% 159.78/26.07  | | 
% 159.78/26.07  | | ALPHA: (14) implies:
% 159.78/26.07  | |   (15)  op(e2, e3) = e2
% 159.78/26.07  | | 
% 159.78/26.07  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 159.78/26.07  | |            (15) are inconsistent by sub-proof #925.
% 159.78/26.07  | | 
% 159.78/26.07  | Case 2:
% 159.78/26.07  | | 
% 159.78/26.07  | |   (16)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 159.78/26.07  | |         & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 159.78/26.07  | |         op(e2, e2) = e3 & $i(all_57_10)
% 159.78/26.07  | | 
% 159.78/26.07  | | ALPHA: (16) implies:
% 159.78/26.07  | |   (17)  op(e2, e3) = e2
% 159.78/26.07  | | 
% 159.78/26.07  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 159.78/26.07  | |            (17) are inconsistent by sub-proof #925.
% 159.78/26.07  | | 
% 159.78/26.07  | End of split
% 159.78/26.07  | 
% 159.78/26.07  End of proof
% 159.78/26.07  
% 159.78/26.07  Sub-proof #654 shows that the following formulas are inconsistent:
% 159.78/26.07  ----------------------------------------------------------------
% 159.78/26.07    (1)  all_54_5 = all_4_2
% 159.78/26.07    (2)   ~ (all_52_1 = e3)
% 159.78/26.07    (3)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.78/26.07    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.07    (5)   ~ (all_4_2 = e3)
% 159.78/26.07    (6)  op(e2, e2) = e2
% 159.78/26.07    (7)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 159.78/26.07    (8)  op(e2, e2) = all_4_2
% 159.78/26.07    (9)  op(e2, e3) = all_52_1
% 159.78/26.07    (10)   ~ (all_4_2 = e1)
% 159.78/26.07    (11)  all_54_4 = all_52_1
% 159.78/26.07    (12)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.78/26.07            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.78/26.07            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.78/26.07            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.78/26.07              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.78/26.07          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.78/26.07            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.78/26.07              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.78/26.07            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.78/26.07              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.78/26.07    (13)   ~ (all_52_1 = all_4_2)
% 159.78/26.07  
% 159.78/26.07  Begin of proof
% 159.78/26.07  | 
% 159.78/26.07  | BETA: splitting (12) gives:
% 159.78/26.07  | 
% 159.78/26.07  | Case 1:
% 159.78/26.07  | | 
% 159.78/26.07  | |   (14)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 =
% 159.78/26.07  | |             e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.78/26.07  | |           op(e2, e2) = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 159.78/26.07  | |           all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3)
% 159.78/26.07  | |           = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3
% 159.78/26.07  | |           & $i(all_57_10))
% 159.78/26.07  | | 
% 159.78/26.07  | | BETA: splitting (14) gives:
% 159.78/26.07  | | 
% 159.78/26.07  | | Case 1:
% 159.78/26.07  | | | 
% 159.78/26.07  | | |   (15)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 =
% 159.78/26.07  | | |           e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 159.78/26.07  | | |         op(e2, e2) = all_57_12 & $i(all_57_12)
% 159.78/26.07  | | | 
% 159.78/26.07  | | | ALPHA: (15) implies:
% 159.78/26.07  | | |   (16)  op(e2, e3) = e2
% 159.78/26.07  | | | 
% 159.78/26.07  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 159.78/26.07  | | |            (16) are inconsistent by sub-proof #925.
% 159.78/26.07  | | | 
% 159.78/26.07  | | Case 2:
% 159.78/26.07  | | | 
% 159.78/26.07  | | |   (17)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.78/26.07  | | |           e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2
% 159.78/26.07  | | |         & op(e2, e2) = e3 & $i(all_57_10)
% 159.78/26.07  | | | 
% 159.78/26.07  | | | ALPHA: (17) implies:
% 159.78/26.07  | | |   (18)  op(e2, e3) = e2
% 159.78/26.07  | | | 
% 159.78/26.07  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 159.78/26.07  | | |            (18) are inconsistent by sub-proof #925.
% 159.78/26.07  | | | 
% 159.78/26.07  | | End of split
% 159.78/26.07  | | 
% 159.78/26.07  | Case 2:
% 159.78/26.07  | | 
% 159.78/26.07  | |   (19)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.78/26.07  | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 159.78/26.07  | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 =
% 159.78/26.07  | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 159.78/26.07  | |           & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.78/26.07  | |           $i(all_57_10))
% 159.78/26.07  | | 
% 159.78/26.07  | | BETA: splitting (19) gives:
% 159.78/26.07  | | 
% 159.78/26.07  | | Case 1:
% 159.78/26.07  | | | 
% 159.78/26.07  | | |   (20)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 159.78/26.07  | | |           e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 159.78/26.07  | | |         & op(e1, e1) = e2 & $i(all_57_12)
% 159.78/26.07  | | | 
% 159.78/26.07  | | | ALPHA: (20) implies:
% 159.78/26.07  | | |   (21)  op(e2, e3) = e2
% 159.78/26.07  | | | 
% 159.78/26.07  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 159.78/26.07  | | |            (21) are inconsistent by sub-proof #925.
% 159.78/26.07  | | | 
% 159.78/26.07  | | Case 2:
% 159.78/26.07  | | | 
% 159.78/26.07  | | |   (22)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 159.78/26.07  | | |           e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2
% 159.78/26.07  | | |         & op(e2, e2) = e3 & $i(all_57_10)
% 159.78/26.07  | | | 
% 159.78/26.07  | | | ALPHA: (22) implies:
% 159.78/26.07  | | |   (23)  op(e2, e3) = e2
% 159.78/26.07  | | | 
% 159.78/26.07  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 159.78/26.07  | | |            (23) are inconsistent by sub-proof #925.
% 159.78/26.07  | | | 
% 159.78/26.07  | | End of split
% 159.78/26.07  | | 
% 159.78/26.07  | End of split
% 159.78/26.07  | 
% 159.78/26.07  End of proof
% 159.78/26.07  
% 159.78/26.07  Sub-proof #655 shows that the following formulas are inconsistent:
% 159.78/26.07  ----------------------------------------------------------------
% 159.78/26.07    (1)  all_54_11 = all_52_14
% 159.78/26.07    (2)  all_54_11 = e3
% 159.78/26.07    (3)   ~ (all_52_14 = e3)
% 159.78/26.07  
% 159.78/26.07  Begin of proof
% 159.78/26.07  | 
% 159.78/26.07  | COMBINE_EQS: (1), (2) imply:
% 159.78/26.07  |   (4)  all_52_14 = e3
% 159.78/26.07  | 
% 159.78/26.07  | SIMP: (4) implies:
% 159.78/26.07  |   (5)  all_52_14 = e3
% 159.78/26.07  | 
% 159.78/26.07  | REDUCE: (3), (5) imply:
% 159.78/26.07  |   (6)  $false
% 159.78/26.07  | 
% 159.78/26.07  | CLOSE: (6) is inconsistent.
% 159.78/26.07  | 
% 159.78/26.07  End of proof
% 159.78/26.07  
% 159.78/26.07  Sub-proof #656 shows that the following formulas are inconsistent:
% 159.78/26.07  ----------------------------------------------------------------
% 159.78/26.07    (1)  all_54_9 = all_52_6
% 159.78/26.07    (2)  all_54_9 = e3
% 159.78/26.07    (3)   ~ (all_52_6 = e3)
% 159.78/26.07  
% 159.78/26.07  Begin of proof
% 159.78/26.07  | 
% 159.78/26.07  | COMBINE_EQS: (1), (2) imply:
% 159.78/26.07  |   (4)  all_52_6 = e3
% 159.78/26.07  | 
% 159.78/26.07  | SIMP: (4) implies:
% 159.78/26.07  |   (5)  all_52_6 = e3
% 159.78/26.07  | 
% 159.78/26.07  | REDUCE: (3), (5) imply:
% 159.78/26.07  |   (6)  $false
% 159.78/26.07  | 
% 159.78/26.07  | CLOSE: (6) is inconsistent.
% 159.78/26.07  | 
% 159.78/26.07  End of proof
% 159.78/26.07  
% 159.78/26.07  Sub-proof #657 shows that the following formulas are inconsistent:
% 159.78/26.07  ----------------------------------------------------------------
% 159.78/26.07    (1)   ~ (e3 = e2)
% 159.78/26.07    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.07    (3)  all_56_6 = e3
% 159.78/26.07    (4)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 159.78/26.07         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.78/26.07    (5)  all_56_11 = e1
% 159.78/26.07    (6)  all_56_7 = e3
% 159.78/26.07    (7)  op(e1, e3) = e3
% 159.78/26.07    (8)   ~ (e1 = e0)
% 159.78/26.07    (9)   ~ (e2 = e1)
% 159.78/26.07    (10)   ~ (e2 = e0)
% 159.78/26.07    (11)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 159.78/26.07          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 159.78/26.07    (12)   ~ (e3 = e0)
% 159.78/26.07  
% 159.78/26.07  Begin of proof
% 159.78/26.07  | 
% 159.78/26.07  | BETA: splitting (11) gives:
% 159.78/26.07  | 
% 159.78/26.07  | Case 1:
% 159.78/26.07  | | 
% 159.78/26.07  | |   (13)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 159.78/26.07  | |           e2)
% 159.78/26.07  | | 
% 159.78/26.07  | | BETA: splitting (13) gives:
% 159.78/26.07  | | 
% 159.78/26.07  | | Case 1:
% 159.78/26.07  | | | 
% 159.78/26.07  | | |   (14)  all_56_6 = e2 & op(e1, e3) = e2
% 159.78/26.07  | | | 
% 159.78/26.07  | | | REF_CLOSE: (1), (3), (14) are inconsistent by sub-proof #662.
% 159.78/26.07  | | | 
% 159.78/26.07  | | Case 2:
% 159.78/26.07  | | | 
% 159.78/26.07  | | |   (15)  all_56_7 = e2 & op(e1, e2) = e2
% 159.78/26.07  | | | 
% 159.78/26.07  | | | ALPHA: (15) implies:
% 159.78/26.07  | | |   (16)  all_56_7 = e2
% 159.78/26.07  | | | 
% 159.78/26.07  | | | REF_CLOSE: (1), (6), (16) are inconsistent by sub-proof #661.
% 159.78/26.07  | | | 
% 159.78/26.07  | | End of split
% 159.78/26.07  | | 
% 159.78/26.07  | Case 2:
% 159.78/26.07  | | 
% 159.78/26.07  | |   (17)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 159.78/26.07  | |           e2)
% 159.78/26.07  | | 
% 159.78/26.07  | | BETA: splitting (17) gives:
% 159.78/26.07  | | 
% 159.78/26.07  | | Case 1:
% 159.78/26.07  | | | 
% 159.78/26.07  | | |   (18)  all_56_8 = e2 & op(e1, e1) = e2
% 159.78/26.07  | | | 
% 159.78/26.07  | | | ALPHA: (18) implies:
% 159.78/26.07  | | |   (19)  op(e1, e1) = e2
% 159.78/26.07  | | | 
% 159.78/26.07  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (10), (12), (19) are inconsistent
% 159.78/26.07  | | |            by sub-proof #659.
% 159.78/26.07  | | | 
% 159.78/26.07  | | Case 2:
% 159.78/26.07  | | | 
% 159.78/26.07  | | |   (20)  all_56_11 = e2 & op(e1, e0) = e2
% 159.78/26.07  | | | 
% 159.78/26.07  | | | REF_CLOSE: (5), (9), (20) are inconsistent by sub-proof #658.
% 159.78/26.07  | | | 
% 159.78/26.07  | | End of split
% 159.78/26.07  | | 
% 159.78/26.07  | End of split
% 159.78/26.07  | 
% 159.78/26.07  End of proof
% 159.78/26.07  
% 159.78/26.07  Sub-proof #658 shows that the following formulas are inconsistent:
% 159.78/26.07  ----------------------------------------------------------------
% 159.78/26.07    (1)  all_56_11 = e2 & op(e1, e0) = e2
% 159.78/26.07    (2)  all_56_11 = e1
% 159.78/26.07    (3)   ~ (e2 = e1)
% 159.78/26.07  
% 159.78/26.07  Begin of proof
% 159.78/26.07  | 
% 159.78/26.07  | ALPHA: (1) implies:
% 159.78/26.07  |   (4)  all_56_11 = e2
% 159.78/26.07  | 
% 159.78/26.07  | COMBINE_EQS: (2), (4) imply:
% 159.78/26.07  |   (5)  e2 = e1
% 159.78/26.07  | 
% 159.78/26.07  | REDUCE: (3), (5) imply:
% 159.78/26.07  |   (6)  $false
% 159.78/26.07  | 
% 159.78/26.07  | CLOSE: (6) is inconsistent.
% 159.78/26.07  | 
% 159.78/26.07  End of proof
% 159.78/26.07  
% 159.78/26.07  Sub-proof #659 shows that the following formulas are inconsistent:
% 159.78/26.07  ----------------------------------------------------------------
% 159.78/26.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.08    (2)  op(e1, e1) = e2
% 159.78/26.08    (3)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 159.78/26.08         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.78/26.08    (4)  all_56_11 = e1
% 159.78/26.08    (5)  all_56_7 = e3
% 159.78/26.08    (6)  op(e1, e3) = e3
% 159.78/26.08    (7)   ~ (e1 = e0)
% 159.78/26.08    (8)   ~ (e2 = e0)
% 159.78/26.08    (9)   ~ (e3 = e0)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | BETA: splitting (3) gives:
% 159.78/26.08  | 
% 159.78/26.08  | Case 1:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (10)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) =
% 159.78/26.08  | |           e0)
% 159.78/26.08  | | 
% 159.78/26.08  | | BETA: splitting (10) gives:
% 159.78/26.08  | | 
% 159.78/26.08  | | Case 1:
% 159.78/26.08  | | | 
% 159.78/26.08  | | |   (11)  all_56_6 = e0 & op(e1, e3) = e0
% 159.78/26.08  | | | 
% 159.78/26.08  | | | ALPHA: (11) implies:
% 159.78/26.08  | | |   (12)  op(e1, e3) = e0
% 159.78/26.08  | | | 
% 159.78/26.08  | | | REF_CLOSE: (1), (6), (9), (12) are inconsistent by sub-proof #913.
% 159.78/26.08  | | | 
% 159.78/26.08  | | Case 2:
% 159.78/26.08  | | | 
% 159.78/26.08  | | |   (13)  all_56_7 = e0 & op(e1, e2) = e0
% 159.78/26.08  | | | 
% 159.78/26.08  | | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #909.
% 159.78/26.08  | | | 
% 159.78/26.08  | | End of split
% 159.78/26.08  | | 
% 159.78/26.08  | Case 2:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (14)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.78/26.08  | |           e0)
% 159.78/26.08  | | 
% 159.78/26.08  | | BETA: splitting (14) gives:
% 159.78/26.08  | | 
% 159.78/26.08  | | Case 1:
% 159.78/26.08  | | | 
% 159.78/26.08  | | |   (15)  all_56_8 = e0 & op(e1, e1) = e0
% 159.78/26.08  | | | 
% 159.78/26.08  | | | ALPHA: (15) implies:
% 159.78/26.08  | | |   (16)  op(e1, e1) = e0
% 159.78/26.08  | | | 
% 159.78/26.08  | | | REF_CLOSE: (1), (2), (8), (16) are inconsistent by sub-proof #914.
% 159.78/26.08  | | | 
% 159.78/26.08  | | Case 2:
% 159.78/26.08  | | | 
% 159.78/26.08  | | |   (17)  all_56_11 = e0 & op(e1, e0) = e0
% 159.78/26.08  | | | 
% 159.78/26.08  | | | REF_CLOSE: (4), (7), (17) are inconsistent by sub-proof #660.
% 159.78/26.08  | | | 
% 159.78/26.08  | | End of split
% 159.78/26.08  | | 
% 159.78/26.08  | End of split
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #660 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  all_56_11 = e0 & op(e1, e0) = e0
% 159.78/26.08    (2)  all_56_11 = e1
% 159.78/26.08    (3)   ~ (e1 = e0)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | ALPHA: (1) implies:
% 159.78/26.08  |   (4)  all_56_11 = e0
% 159.78/26.08  | 
% 159.78/26.08  | COMBINE_EQS: (2), (4) imply:
% 159.78/26.08  |   (5)  e1 = e0
% 159.78/26.08  | 
% 159.78/26.08  | REDUCE: (3), (5) imply:
% 159.78/26.08  |   (6)  $false
% 159.78/26.08  | 
% 159.78/26.08  | CLOSE: (6) is inconsistent.
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #661 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  all_56_7 = e3
% 159.78/26.08    (2)  all_56_7 = e2
% 159.78/26.08    (3)   ~ (e3 = e2)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | COMBINE_EQS: (1), (2) imply:
% 159.78/26.08  |   (4)  e3 = e2
% 159.78/26.08  | 
% 159.78/26.08  | SIMP: (4) implies:
% 159.78/26.08  |   (5)  e3 = e2
% 159.78/26.08  | 
% 159.78/26.08  | REDUCE: (3), (5) imply:
% 159.78/26.08  |   (6)  $false
% 159.78/26.08  | 
% 159.78/26.08  | CLOSE: (6) is inconsistent.
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #662 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  all_56_6 = e2 & op(e1, e3) = e2
% 159.78/26.08    (2)  all_56_6 = e3
% 159.78/26.08    (3)   ~ (e3 = e2)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | ALPHA: (1) implies:
% 159.78/26.08  |   (4)  all_56_6 = e2
% 159.78/26.08  | 
% 159.78/26.08  | COMBINE_EQS: (2), (4) imply:
% 159.78/26.08  |   (5)  e3 = e2
% 159.78/26.08  | 
% 159.78/26.08  | REDUCE: (3), (5) imply:
% 159.78/26.08  |   (6)  $false
% 159.78/26.08  | 
% 159.78/26.08  | CLOSE: (6) is inconsistent.
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #663 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.08    (2)  op(e1, e3) = all_52_2
% 159.78/26.08    (3)   ~ (all_52_2 = e1)
% 159.78/26.08    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1)
% 159.78/26.08    (5)  op(e1, e2) = e3
% 159.78/26.08    (6)   ~ (e3 = e1)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | BETA: splitting (4) gives:
% 159.78/26.08  | 
% 159.78/26.08  | Case 1:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (7)  all_56_6 = e1 & op(e1, e3) = e1
% 159.78/26.08  | | 
% 159.78/26.08  | | ALPHA: (7) implies:
% 159.78/26.08  | |   (8)  op(e1, e3) = e1
% 159.78/26.08  | | 
% 159.78/26.08  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #990.
% 159.78/26.08  | | 
% 159.78/26.08  | Case 2:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (9)  all_56_7 = e1 & op(e1, e2) = e1
% 159.78/26.08  | | 
% 159.78/26.08  | | ALPHA: (9) implies:
% 159.78/26.08  | |   (10)  op(e1, e2) = e1
% 159.78/26.08  | | 
% 159.78/26.08  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #939.
% 159.78/26.08  | | 
% 159.78/26.08  | End of split
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #664 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  all_56_1 = e3 & op(e3, e2) = e3
% 159.78/26.08    (2)  all_56_1 = e0
% 159.78/26.08    (3)   ~ (e3 = e0)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | ALPHA: (1) implies:
% 159.78/26.08  |   (4)  all_56_1 = e3
% 159.78/26.08  | 
% 159.78/26.08  | COMBINE_EQS: (2), (4) imply:
% 159.78/26.08  |   (5)  e3 = e0
% 159.78/26.08  | 
% 159.78/26.08  | SIMP: (5) implies:
% 159.78/26.08  |   (6)  e3 = e0
% 159.78/26.08  | 
% 159.78/26.08  | REDUCE: (3), (6) imply:
% 159.78/26.08  |   (7)  $false
% 159.78/26.08  | 
% 159.78/26.08  | CLOSE: (7) is inconsistent.
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #665 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.78/26.08    (2)  op(e0, e0) = e2
% 159.78/26.08    (3)   ~ (all_52_3 = all_38_0)
% 159.78/26.08    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.08    (5)  op(e0, e3) = all_52_3
% 159.78/26.08    (6)  all_56_14 = e3
% 159.78/26.08    (7)  op(e0, e2) = all_52_7
% 159.78/26.08    (8)   ~ (all_38_0 = e3)
% 159.78/26.08    (9)   ~ (all_52_7 = all_38_0)
% 159.78/26.08    (10)  all_54_14 = all_38_0
% 159.78/26.08    (11)   ~ (all_38_0 = e2)
% 159.78/26.08    (12)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.78/26.08          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.78/26.08            e1)
% 159.78/26.08    (13)   ~ (all_38_0 = e0)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | BETA: splitting (1) gives:
% 159.78/26.08  | 
% 159.78/26.08  | Case 1:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (14)  all_54_14 = e3
% 159.78/26.08  | | 
% 159.78/26.08  | | COMBINE_EQS: (10), (14) imply:
% 159.78/26.08  | |   (15)  all_38_0 = e3
% 159.78/26.08  | | 
% 159.78/26.08  | | REDUCE: (8), (15) imply:
% 159.78/26.08  | |   (16)  $false
% 159.78/26.08  | | 
% 159.78/26.08  | | CLOSE: (16) is inconsistent.
% 159.78/26.08  | | 
% 159.78/26.08  | Case 2:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (17)   ~ (all_54_14 = e3)
% 159.78/26.08  | |   (18)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.78/26.08  | | 
% 159.78/26.08  | | BETA: splitting (18) gives:
% 159.78/26.08  | | 
% 159.78/26.08  | | Case 1:
% 159.78/26.08  | | | 
% 159.78/26.08  | | |   (19)  all_54_14 = e2
% 159.78/26.08  | | | 
% 159.78/26.08  | | | COMBINE_EQS: (10), (19) imply:
% 159.78/26.08  | | |   (20)  all_38_0 = e2
% 159.78/26.08  | | | 
% 159.78/26.08  | | | REDUCE: (11), (20) imply:
% 159.78/26.08  | | |   (21)  $false
% 159.78/26.08  | | | 
% 159.78/26.08  | | | CLOSE: (21) is inconsistent.
% 159.78/26.08  | | | 
% 159.78/26.08  | | Case 2:
% 159.78/26.08  | | | 
% 159.78/26.08  | | |   (22)   ~ (all_54_14 = e2)
% 159.78/26.08  | | |   (23)  all_54_14 = e1 | all_54_14 = e0
% 159.78/26.08  | | | 
% 159.78/26.08  | | | BETA: splitting (23) gives:
% 159.78/26.08  | | | 
% 159.78/26.08  | | | Case 1:
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | |   (24)  all_54_14 = e1
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | COMBINE_EQS: (10), (24) imply:
% 159.78/26.08  | | | |   (25)  all_38_0 = e1
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | REDUCE: (3), (25) imply:
% 159.78/26.08  | | | |   (26)   ~ (all_52_3 = e1)
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | REDUCE: (9), (25) imply:
% 159.78/26.08  | | | |   (27)   ~ (all_52_7 = e1)
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | REDUCE: (8), (25) imply:
% 159.78/26.08  | | | |   (28)   ~ (e3 = e1)
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | SIMP: (28) implies:
% 159.78/26.08  | | | |   (29)   ~ (e3 = e1)
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | REDUCE: (11), (25) imply:
% 159.78/26.08  | | | |   (30)   ~ (e2 = e1)
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | SIMP: (30) implies:
% 159.78/26.08  | | | |   (31)   ~ (e2 = e1)
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | REF_CLOSE: (2), (4), (5), (6), (7), (12), (26), (27), (29), (31) are
% 159.78/26.08  | | | |            inconsistent by sub-proof #666.
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | Case 2:
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | |   (32)  all_54_14 = e0
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | COMBINE_EQS: (10), (32) imply:
% 159.78/26.08  | | | |   (33)  all_38_0 = e0
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | REDUCE: (13), (33) imply:
% 159.78/26.08  | | | |   (34)  $false
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | | CLOSE: (34) is inconsistent.
% 159.78/26.08  | | | | 
% 159.78/26.08  | | | End of split
% 159.78/26.08  | | | 
% 159.78/26.08  | | End of split
% 159.78/26.08  | | 
% 159.78/26.08  | End of split
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #666 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  op(e0, e0) = e2
% 159.78/26.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.08    (3)  op(e0, e3) = all_52_3
% 159.78/26.08    (4)  all_56_14 = e3
% 159.78/26.08    (5)  op(e0, e2) = all_52_7
% 159.78/26.08    (6)   ~ (all_52_3 = e1)
% 159.78/26.08    (7)   ~ (e2 = e1)
% 159.78/26.08    (8)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1) |
% 159.78/26.08         (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.78/26.08    (9)   ~ (all_52_7 = e1)
% 159.78/26.08    (10)   ~ (e3 = e1)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | BETA: splitting (8) gives:
% 159.78/26.08  | 
% 159.78/26.08  | Case 1:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (11)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 159.78/26.08  | |           e1)
% 159.78/26.08  | | 
% 159.78/26.08  | | BETA: splitting (11) gives:
% 159.78/26.08  | | 
% 159.78/26.08  | | Case 1:
% 159.78/26.08  | | | 
% 159.78/26.08  | | |   (12)  all_56_12 = e1 & op(e0, e3) = e1
% 159.78/26.08  | | | 
% 159.78/26.08  | | | REF_CLOSE: (2), (3), (6), (12) are inconsistent by sub-proof #852.
% 159.78/26.08  | | | 
% 159.78/26.08  | | Case 2:
% 159.78/26.08  | | | 
% 159.78/26.08  | | |   (13)  all_56_13 = e1 & op(e0, e2) = e1
% 159.78/26.08  | | | 
% 159.78/26.08  | | | REF_CLOSE: (2), (5), (9), (13) are inconsistent by sub-proof #712.
% 159.78/26.08  | | | 
% 159.78/26.08  | | End of split
% 159.78/26.08  | | 
% 159.78/26.08  | Case 2:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (14)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.78/26.08  | |           e1)
% 159.78/26.08  | | 
% 159.78/26.08  | | BETA: splitting (14) gives:
% 159.78/26.08  | | 
% 159.78/26.08  | | Case 1:
% 159.78/26.08  | | | 
% 159.78/26.08  | | |   (15)  all_56_14 = e1 & op(e0, e1) = e1
% 159.78/26.08  | | | 
% 159.78/26.08  | | | REF_CLOSE: (4), (10), (15) are inconsistent by sub-proof #667.
% 159.78/26.08  | | | 
% 159.78/26.08  | | Case 2:
% 159.78/26.08  | | | 
% 159.78/26.08  | | |   (16)  all_56_15 = e1 & op(e0, e0) = e1
% 159.78/26.08  | | | 
% 159.78/26.08  | | | ALPHA: (16) implies:
% 159.78/26.08  | | |   (17)  op(e0, e0) = e1
% 159.78/26.08  | | | 
% 159.78/26.08  | | | REF_CLOSE: (1), (2), (7), (17) are inconsistent by sub-proof #875.
% 159.78/26.08  | | | 
% 159.78/26.08  | | End of split
% 159.78/26.08  | | 
% 159.78/26.08  | End of split
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #667 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  all_56_14 = e1 & op(e0, e1) = e1
% 159.78/26.08    (2)  all_56_14 = e3
% 159.78/26.08    (3)   ~ (e3 = e1)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | ALPHA: (1) implies:
% 159.78/26.08  |   (4)  all_56_14 = e1
% 159.78/26.08  | 
% 159.78/26.08  | COMBINE_EQS: (2), (4) imply:
% 159.78/26.08  |   (5)  e3 = e1
% 159.78/26.08  | 
% 159.78/26.08  | REDUCE: (3), (5) imply:
% 159.78/26.08  |   (6)  $false
% 159.78/26.08  | 
% 159.78/26.08  | CLOSE: (6) is inconsistent.
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #668 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  all_56_5 = e2 & op(e2, e1) = e2
% 159.78/26.08    (2)  all_56_5 = e3
% 159.78/26.08    (3)   ~ (e3 = e2)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | ALPHA: (1) implies:
% 159.78/26.08  |   (4)  all_56_5 = e2
% 159.78/26.08  | 
% 159.78/26.08  | COMBINE_EQS: (2), (4) imply:
% 159.78/26.08  |   (5)  e3 = e2
% 159.78/26.08  | 
% 159.78/26.08  | REDUCE: (3), (5) imply:
% 159.78/26.08  |   (6)  $false
% 159.78/26.08  | 
% 159.78/26.08  | CLOSE: (6) is inconsistent.
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #669 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  all_56_14 = e3
% 159.78/26.08    (2)  all_56_14 = e1
% 159.78/26.08    (3)   ~ (e3 = e1)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | COMBINE_EQS: (1), (2) imply:
% 159.78/26.08  |   (4)  e3 = e1
% 159.78/26.08  | 
% 159.78/26.08  | SIMP: (4) implies:
% 159.78/26.08  |   (5)  e3 = e1
% 159.78/26.08  | 
% 159.78/26.08  | REDUCE: (3), (5) imply:
% 159.78/26.08  |   (6)  $false
% 159.78/26.08  | 
% 159.78/26.08  | CLOSE: (6) is inconsistent.
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #670 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.08    (2)  op(e3, e1) = all_52_8
% 159.78/26.08    (3)  op(e3, e1) = e2
% 159.78/26.08    (4)   ~ (all_52_8 = e2)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | GROUND_INST: instantiating (1) with all_52_8, e2, e1, e3, simplifying with
% 159.78/26.08  |              (2), (3) gives:
% 159.78/26.08  |   (5)  all_52_8 = e2
% 159.78/26.08  | 
% 159.78/26.08  | REDUCE: (4), (5) imply:
% 159.78/26.08  |   (6)  $false
% 159.78/26.08  | 
% 159.78/26.08  | CLOSE: (6) is inconsistent.
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #671 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  op(e1, e1) = e0
% 159.78/26.08    (2)  op(e0, e0) = e2
% 159.78/26.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.08    (4)   ~ (e1 = e0)
% 159.78/26.08    (5)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.78/26.08             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.78/26.08           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.78/26.08               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.78/26.08             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.78/26.08         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.78/26.08             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.78/26.08           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.78/26.08               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.78/26.08             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.78/26.08    (6)   ~ (e2 = e0)
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | BETA: splitting (5) gives:
% 159.78/26.08  | 
% 159.78/26.08  | Case 1:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.78/26.08  | |            e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.78/26.08  | |            $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.78/26.08  | |            (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.78/26.08  | |        ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.78/26.08  | |              e1) = all_57_8 & $i(all_57_8)))
% 159.78/26.08  | | 
% 159.78/26.08  | | ALPHA: (7) implies:
% 159.78/26.08  | |   (8)  op(e1, e1) = e1
% 159.78/26.08  | | 
% 159.78/26.08  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #903.
% 159.78/26.08  | | 
% 159.78/26.08  | Case 2:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 159.78/26.08  | |            e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.78/26.08  | |            $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 159.78/26.08  | |            (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 159.78/26.08  | |        ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 159.78/26.08  | |              e0) = all_57_13 & $i(all_57_13)))
% 159.78/26.08  | | 
% 159.78/26.08  | | ALPHA: (9) implies:
% 159.78/26.08  | |   (10)  op(e0, e0) = e0
% 159.78/26.08  | | 
% 159.78/26.08  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #979.
% 159.78/26.08  | | 
% 159.78/26.08  | End of split
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #672 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.78/26.08    (2)  all_54_9 = all_52_6
% 159.78/26.08    (3)   ~ (all_52_6 = e1)
% 159.78/26.08    (4)  op(e1, e0) = e3
% 159.78/26.08    (5)   ~ (all_52_6 = e2)
% 159.78/26.08    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.08    (7)   ~ (all_52_6 = e0)
% 159.78/26.08    (8)   ~ (all_52_6 = all_52_14)
% 159.78/26.08    (9)  op(e1, e0) = all_52_14
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | BETA: splitting (1) gives:
% 159.78/26.08  | 
% 159.78/26.08  | Case 1:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (10)  all_54_9 = e3
% 159.78/26.08  | | 
% 159.78/26.08  | | COMBINE_EQS: (2), (10) imply:
% 159.78/26.08  | |   (11)  all_52_6 = e3
% 159.78/26.08  | | 
% 159.78/26.08  | | SIMP: (11) implies:
% 159.78/26.08  | |   (12)  all_52_6 = e3
% 159.78/26.08  | | 
% 159.78/26.08  | | REDUCE: (8), (12) imply:
% 159.78/26.08  | |   (13)   ~ (all_52_14 = e3)
% 159.78/26.08  | | 
% 159.78/26.08  | | SIMP: (13) implies:
% 159.78/26.08  | |   (14)   ~ (all_52_14 = e3)
% 159.78/26.08  | | 
% 159.78/26.08  | | REF_CLOSE: (4), (6), (9), (14) are inconsistent by sub-proof #677.
% 159.78/26.08  | | 
% 159.78/26.08  | Case 2:
% 159.78/26.08  | | 
% 159.78/26.08  | |   (15)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.78/26.08  | | 
% 159.78/26.08  | | REF_CLOSE: (2), (3), (5), (7), (15) are inconsistent by sub-proof #673.
% 159.78/26.08  | | 
% 159.78/26.08  | End of split
% 159.78/26.08  | 
% 159.78/26.08  End of proof
% 159.78/26.08  
% 159.78/26.08  Sub-proof #673 shows that the following formulas are inconsistent:
% 159.78/26.08  ----------------------------------------------------------------
% 159.78/26.08    (1)  all_54_9 = all_52_6
% 159.78/26.08    (2)   ~ (all_52_6 = e1)
% 159.78/26.08    (3)   ~ (all_52_6 = e2)
% 159.78/26.08    (4)   ~ (all_52_6 = e0)
% 159.78/26.08    (5)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.78/26.08  
% 159.78/26.08  Begin of proof
% 159.78/26.08  | 
% 159.78/26.08  | BETA: splitting (5) gives:
% 159.78/26.08  | 
% 159.78/26.08  | Case 1:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (6)  all_54_9 = e2
% 159.78/26.09  | | 
% 159.78/26.09  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #676.
% 159.78/26.09  | | 
% 159.78/26.09  | Case 2:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (7)  all_54_9 = e1 | all_54_9 = e0
% 159.78/26.09  | | 
% 159.78/26.09  | | BETA: splitting (7) gives:
% 159.78/26.09  | | 
% 159.78/26.09  | | Case 1:
% 159.78/26.09  | | | 
% 159.78/26.09  | | |   (8)  all_54_9 = e1
% 159.78/26.09  | | | 
% 159.78/26.09  | | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #675.
% 159.78/26.09  | | | 
% 159.78/26.09  | | Case 2:
% 159.78/26.09  | | | 
% 159.78/26.09  | | |   (9)  all_54_9 = e0
% 159.78/26.09  | | | 
% 159.78/26.09  | | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #674.
% 159.78/26.09  | | | 
% 159.78/26.09  | | End of split
% 159.78/26.09  | | 
% 159.78/26.09  | End of split
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #674 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  all_54_9 = all_52_6
% 159.78/26.09    (2)  all_54_9 = e0
% 159.78/26.09    (3)   ~ (all_52_6 = e0)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | COMBINE_EQS: (1), (2) imply:
% 159.78/26.09  |   (4)  all_52_6 = e0
% 159.78/26.09  | 
% 159.78/26.09  | SIMP: (4) implies:
% 159.78/26.09  |   (5)  all_52_6 = e0
% 159.78/26.09  | 
% 159.78/26.09  | REDUCE: (3), (5) imply:
% 159.78/26.09  |   (6)  $false
% 159.78/26.09  | 
% 159.78/26.09  | CLOSE: (6) is inconsistent.
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #675 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  all_54_9 = all_52_6
% 159.78/26.09    (2)  all_54_9 = e1
% 159.78/26.09    (3)   ~ (all_52_6 = e1)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | COMBINE_EQS: (1), (2) imply:
% 159.78/26.09  |   (4)  all_52_6 = e1
% 159.78/26.09  | 
% 159.78/26.09  | SIMP: (4) implies:
% 159.78/26.09  |   (5)  all_52_6 = e1
% 159.78/26.09  | 
% 159.78/26.09  | REDUCE: (3), (5) imply:
% 159.78/26.09  |   (6)  $false
% 159.78/26.09  | 
% 159.78/26.09  | CLOSE: (6) is inconsistent.
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #676 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  all_54_9 = all_52_6
% 159.78/26.09    (2)  all_54_9 = e2
% 159.78/26.09    (3)   ~ (all_52_6 = e2)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | COMBINE_EQS: (1), (2) imply:
% 159.78/26.09  |   (4)  all_52_6 = e2
% 159.78/26.09  | 
% 159.78/26.09  | SIMP: (4) implies:
% 159.78/26.09  |   (5)  all_52_6 = e2
% 159.78/26.09  | 
% 159.78/26.09  | REDUCE: (3), (5) imply:
% 159.78/26.09  |   (6)  $false
% 159.78/26.09  | 
% 159.78/26.09  | CLOSE: (6) is inconsistent.
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #677 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.09    (2)  op(e1, e0) = all_52_14
% 159.78/26.09    (3)  op(e1, e0) = e3
% 159.78/26.09    (4)   ~ (all_52_14 = e3)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | GROUND_INST: instantiating (1) with all_52_14, e3, e0, e1, simplifying with
% 159.78/26.09  |              (2), (3) gives:
% 159.78/26.09  |   (5)  all_52_14 = e3
% 159.78/26.09  | 
% 159.78/26.09  | REDUCE: (4), (5) imply:
% 159.78/26.09  |   (6)  $false
% 159.78/26.09  | 
% 159.78/26.09  | CLOSE: (6) is inconsistent.
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #678 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  all_54_5 = all_4_2
% 159.78/26.09    (2)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 159.78/26.09         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.78/26.09    (3)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 159.78/26.09         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 159.78/26.09    (4)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.78/26.09    (5)   ~ (e3 = e2)
% 159.78/26.09    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.09    (7)   ~ (all_4_2 = e3)
% 159.78/26.09    (8)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 159.78/26.09         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.78/26.09    (9)  op(e2, e2) = all_4_2
% 159.78/26.09    (10)  op(e1, e2) = e3
% 159.78/26.09    (11)  all_56_7 = e3
% 159.78/26.09    (12)   ~ (all_4_2 = e1)
% 159.78/26.09    (13)   ~ (e1 = e0)
% 159.78/26.09    (14)   ~ (e2 = e1)
% 159.78/26.09    (15)  all_56_13 = e3
% 159.78/26.09    (16)   ~ (e3 = e1)
% 159.78/26.09    (17)   ~ (e2 = e0)
% 159.78/26.09    (18)   ~ (e3 = e0)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | BETA: splitting (2) gives:
% 159.78/26.09  | 
% 159.78/26.09  | Case 1:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (19)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 159.78/26.09  | |           e1)
% 159.78/26.09  | | 
% 159.78/26.09  | | BETA: splitting (19) gives:
% 159.78/26.09  | | 
% 159.78/26.09  | | Case 1:
% 159.78/26.09  | | | 
% 159.78/26.09  | | |   (20)  all_56_1 = e1 & op(e3, e2) = e1
% 159.78/26.09  | | | 
% 159.78/26.09  | | | ALPHA: (20) implies:
% 159.78/26.09  | | |   (21)  all_56_1 = e1
% 159.78/26.09  | | | 
% 159.78/26.09  | | | BETA: splitting (8) gives:
% 159.78/26.09  | | | 
% 159.78/26.09  | | | Case 1:
% 159.78/26.09  | | | | 
% 159.78/26.09  | | | |   (22)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2)
% 159.78/26.09  | | | |           = e2)
% 159.78/26.09  | | | | 
% 159.78/26.09  | | | | BETA: splitting (22) gives:
% 159.78/26.09  | | | | 
% 159.78/26.09  | | | | Case 1:
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | |   (23)  all_56_1 = e2 & op(e3, e2) = e2
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | | ALPHA: (23) implies:
% 159.78/26.09  | | | | |   (24)  all_56_1 = e2
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | | REF_CLOSE: (14), (21), (24) are inconsistent by sub-proof #680.
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | Case 2:
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | |   (25)  all_56_3 = e2 & op(e2, e2) = e2
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | | ALPHA: (25) implies:
% 159.78/26.09  | | | | |   (26)  op(e2, e2) = e2
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | | BETA: splitting (3) gives:
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | | Case 1:
% 159.78/26.09  | | | | | | 
% 159.78/26.09  | | | | | |   (27)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2,
% 159.78/26.09  | | | | | |             e2) = e0)
% 159.78/26.09  | | | | | | 
% 159.78/26.09  | | | | | | BETA: splitting (27) gives:
% 159.78/26.09  | | | | | | 
% 159.78/26.09  | | | | | | Case 1:
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | |   (28)  all_56_1 = e0 & op(e3, e2) = e0
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | | REF_CLOSE: (13), (21), (28) are inconsistent by sub-proof #760.
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | Case 2:
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | |   (29)  all_56_3 = e0 & op(e2, e2) = e0
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | | ALPHA: (29) implies:
% 159.78/26.09  | | | | | | |   (30)  op(e2, e2) = e0
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | | REF_CLOSE: (6), (17), (26), (30) are inconsistent by sub-proof
% 159.78/26.09  | | | | | | |            #942.
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | End of split
% 159.78/26.09  | | | | | | 
% 159.78/26.09  | | | | | Case 2:
% 159.78/26.09  | | | | | | 
% 159.78/26.09  | | | | | |   (31)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0,
% 159.78/26.09  | | | | | |             e2) = e0)
% 159.78/26.09  | | | | | | 
% 159.78/26.09  | | | | | | BETA: splitting (31) gives:
% 159.78/26.09  | | | | | | 
% 159.78/26.09  | | | | | | Case 1:
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | |   (32)  all_56_7 = e0 & op(e1, e2) = e0
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | | REF_CLOSE: (11), (18), (32) are inconsistent by sub-proof #909.
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | Case 2:
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | |   (33)  all_56_13 = e0 & op(e0, e2) = e0
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | | REF_CLOSE: (15), (18), (33) are inconsistent by sub-proof #679.
% 159.78/26.09  | | | | | | | 
% 159.78/26.09  | | | | | | End of split
% 159.78/26.09  | | | | | | 
% 159.78/26.09  | | | | | End of split
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | End of split
% 159.78/26.09  | | | | 
% 159.78/26.09  | | | Case 2:
% 159.78/26.09  | | | | 
% 159.78/26.09  | | | |   (34)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2)
% 159.78/26.09  | | | |           = e2)
% 159.78/26.09  | | | | 
% 159.78/26.09  | | | | BETA: splitting (34) gives:
% 159.78/26.09  | | | | 
% 159.78/26.09  | | | | Case 1:
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | |   (35)  all_56_7 = e2 & op(e1, e2) = e2
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | | REF_CLOSE: (5), (11), (35) are inconsistent by sub-proof #940.
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | Case 2:
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | |   (36)  all_56_13 = e2 & op(e0, e2) = e2
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | | REF_CLOSE: (5), (15), (36) are inconsistent by sub-proof #904.
% 159.78/26.09  | | | | | 
% 159.78/26.09  | | | | End of split
% 159.78/26.09  | | | | 
% 159.78/26.09  | | | End of split
% 159.78/26.09  | | | 
% 159.78/26.09  | | Case 2:
% 159.78/26.09  | | | 
% 159.78/26.09  | | |   (37)  all_56_3 = e1 & op(e2, e2) = e1
% 159.78/26.09  | | | 
% 159.78/26.09  | | | ALPHA: (37) implies:
% 159.78/26.09  | | |   (38)  op(e2, e2) = e1
% 159.78/26.09  | | | 
% 159.78/26.09  | | | REF_CLOSE: (1), (4), (6), (7), (9), (12), (38) are inconsistent by
% 159.78/26.09  | | |            sub-proof #690.
% 159.78/26.09  | | | 
% 159.78/26.09  | | End of split
% 159.78/26.09  | | 
% 159.78/26.09  | Case 2:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (39)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 159.78/26.09  | |           e1)
% 159.78/26.09  | | 
% 159.78/26.09  | | BETA: splitting (39) gives:
% 159.78/26.09  | | 
% 159.78/26.09  | | Case 1:
% 159.78/26.09  | | | 
% 159.78/26.09  | | |   (40)  all_56_7 = e1 & op(e1, e2) = e1
% 159.78/26.09  | | | 
% 159.78/26.09  | | | ALPHA: (40) implies:
% 159.78/26.09  | | |   (41)  op(e1, e2) = e1
% 159.78/26.09  | | | 
% 159.78/26.09  | | | REF_CLOSE: (6), (10), (16), (41) are inconsistent by sub-proof #939.
% 159.78/26.09  | | | 
% 159.78/26.09  | | Case 2:
% 159.78/26.09  | | | 
% 159.78/26.09  | | |   (42)  all_56_13 = e1 & op(e0, e2) = e1
% 159.78/26.09  | | | 
% 159.78/26.09  | | | REF_CLOSE: (15), (16), (42) are inconsistent by sub-proof #728.
% 159.78/26.09  | | | 
% 159.78/26.09  | | End of split
% 159.78/26.09  | | 
% 159.78/26.09  | End of split
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #679 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  all_56_13 = e0 & op(e0, e2) = e0
% 159.78/26.09    (2)  all_56_13 = e3
% 159.78/26.09    (3)   ~ (e3 = e0)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | ALPHA: (1) implies:
% 159.78/26.09  |   (4)  all_56_13 = e0
% 159.78/26.09  | 
% 159.78/26.09  | COMBINE_EQS: (2), (4) imply:
% 159.78/26.09  |   (5)  e3 = e0
% 159.78/26.09  | 
% 159.78/26.09  | REDUCE: (3), (5) imply:
% 159.78/26.09  |   (6)  $false
% 159.78/26.09  | 
% 159.78/26.09  | CLOSE: (6) is inconsistent.
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #680 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  all_56_1 = e2
% 159.78/26.09    (2)  all_56_1 = e1
% 159.78/26.09    (3)   ~ (e2 = e1)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | COMBINE_EQS: (1), (2) imply:
% 159.78/26.09  |   (4)  e2 = e1
% 159.78/26.09  | 
% 159.78/26.09  | SIMP: (4) implies:
% 159.78/26.09  |   (5)  e2 = e1
% 159.78/26.09  | 
% 159.78/26.09  | REDUCE: (3), (5) imply:
% 159.78/26.09  |   (6)  $false
% 159.78/26.09  | 
% 159.78/26.09  | CLOSE: (6) is inconsistent.
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #681 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  all_56_6 = e3 & op(e1, e3) = e3
% 159.78/26.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.09    (3)  op(e1, e3) = all_52_2
% 159.78/26.09    (4)   ~ (all_52_2 = e3)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | ALPHA: (1) implies:
% 159.78/26.09  |   (5)  op(e1, e3) = e3
% 159.78/26.09  | 
% 159.78/26.09  | GROUND_INST: instantiating (2) with all_52_2, e3, e3, e1, simplifying with
% 159.78/26.09  |              (3), (5) gives:
% 159.78/26.09  |   (6)  all_52_2 = e3
% 159.78/26.09  | 
% 159.78/26.09  | REDUCE: (4), (6) imply:
% 159.78/26.09  |   (7)  $false
% 159.78/26.09  | 
% 159.78/26.09  | CLOSE: (7) is inconsistent.
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #682 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  op(e0, e1) = all_52_11
% 159.78/26.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.09    (3)  op(e2, e0) = all_52_13
% 159.78/26.09    (4)   ~ (all_52_11 = e0)
% 159.78/26.09    (5)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.78/26.09           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.78/26.09           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 159.78/26.09           & op(e1, e0) = e1 & op(e0, e1) = e0)
% 159.78/26.09    (6)   ~ (all_52_13 = e2)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | BETA: splitting (5) gives:
% 159.78/26.09  | 
% 159.78/26.09  | Case 1:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (7)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1)
% 159.78/26.09  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 159.78/26.09  | | 
% 159.78/26.09  | | ALPHA: (7) implies:
% 159.78/26.09  | |   (8)  op(e2, e0) = e2
% 159.78/26.09  | | 
% 159.78/26.09  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #996.
% 159.78/26.09  | | 
% 159.78/26.09  | Case 2:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (9)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1)
% 159.78/26.09  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.78/26.09  | | 
% 159.78/26.09  | | ALPHA: (9) implies:
% 159.78/26.09  | |   (10)  op(e0, e1) = e0
% 159.78/26.09  | | 
% 159.78/26.09  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #966.
% 159.78/26.09  | | 
% 159.78/26.09  | End of split
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #683 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.09    (2)   ~ (all_57_6 = e0)
% 159.78/26.09    (3)  op(e3, e3) = e3
% 159.78/26.09    (4)  op(e2, e0) = all_52_13
% 159.78/26.09    (5)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.78/26.09         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.78/26.09           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.78/26.09           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 159.78/26.09           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.78/26.09    (6)   ~ (e3 = e0)
% 159.78/26.09    (7)   ~ (all_52_13 = e2)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | BETA: splitting (5) gives:
% 159.78/26.09  | 
% 159.78/26.09  | Case 1:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (8)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 159.78/26.09  | | 
% 159.78/26.09  | | ALPHA: (8) implies:
% 159.78/26.09  | |   (9)  all_57_6 = e0
% 159.78/26.09  | | 
% 159.78/26.09  | | REDUCE: (2), (9) imply:
% 159.78/26.09  | |   (10)  $false
% 159.78/26.09  | | 
% 159.78/26.09  | | CLOSE: (10) is inconsistent.
% 159.78/26.09  | | 
% 159.78/26.09  | Case 2:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (11)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.78/26.09  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.78/26.09  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.78/26.09  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.78/26.09  | | 
% 159.78/26.09  | | REF_CLOSE: (1), (3), (4), (6), (7), (11) are inconsistent by sub-proof #864.
% 159.78/26.09  | | 
% 159.78/26.09  | End of split
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #684 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  (all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 159.78/26.09           all_57_6 & $i(all_57_6))
% 159.78/26.09    (2)   ~ (all_57_15 = e3)
% 159.78/26.09    (3)  all_57_6 = e0
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | BETA: splitting (1) gives:
% 159.78/26.09  | 
% 159.78/26.09  | Case 1:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (4)  all_57_15 = e3 & op(e0, e0) = e3
% 159.78/26.09  | | 
% 159.78/26.09  | | ALPHA: (4) implies:
% 159.78/26.09  | |   (5)  all_57_15 = e3
% 159.78/26.09  | | 
% 159.78/26.09  | | REDUCE: (2), (5) imply:
% 159.78/26.09  | |   (6)  $false
% 159.78/26.09  | | 
% 159.78/26.09  | | CLOSE: (6) is inconsistent.
% 159.78/26.09  | | 
% 159.78/26.09  | Case 2:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (7)   ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)
% 159.78/26.09  | | 
% 159.78/26.09  | | ALPHA: (7) implies:
% 159.78/26.09  | |   (8)   ~ (all_57_6 = e0)
% 159.78/26.09  | | 
% 159.78/26.09  | | REDUCE: (3), (8) imply:
% 159.78/26.09  | |   (9)  $false
% 159.78/26.09  | | 
% 159.78/26.09  | | CLOSE: (9) is inconsistent.
% 159.78/26.09  | | 
% 159.78/26.09  | End of split
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #685 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  op(e0, e0) = e1
% 159.78/26.09    (2)   ~ (e3 = e2)
% 159.78/26.09    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.09    (4)  op(e0, e3) = all_52_3
% 159.78/26.09    (5)  op(e0, e3) = e0
% 159.78/26.09    (6)  all_56_14 = e1
% 159.78/26.09    (7)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2) |
% 159.78/26.09         (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 159.78/26.09    (8)   ~ (e2 = e1)
% 159.78/26.09    (9)  all_56_13 = e3
% 159.78/26.09    (10)   ~ (e2 = e0)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | BETA: splitting (7) gives:
% 159.78/26.09  | 
% 159.78/26.09  | Case 1:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (11)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 159.78/26.09  | |           e2)
% 159.78/26.09  | | 
% 159.78/26.09  | | REF_CLOSE: (2), (3), (4), (5), (9), (10), (11) are inconsistent by sub-proof
% 159.78/26.09  | |            #687.
% 159.78/26.09  | | 
% 159.78/26.09  | Case 2:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (12)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 159.78/26.09  | |           e2)
% 159.78/26.09  | | 
% 159.78/26.09  | | BETA: splitting (12) gives:
% 159.78/26.09  | | 
% 159.78/26.09  | | Case 1:
% 159.78/26.09  | | | 
% 159.78/26.09  | | |   (13)  all_56_14 = e2 & op(e0, e1) = e2
% 159.78/26.09  | | | 
% 159.78/26.09  | | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #686.
% 159.78/26.09  | | | 
% 159.78/26.09  | | Case 2:
% 159.78/26.09  | | | 
% 159.78/26.09  | | |   (14)  all_56_15 = e2 & op(e0, e0) = e2
% 159.78/26.09  | | | 
% 159.78/26.09  | | | ALPHA: (14) implies:
% 159.78/26.09  | | |   (15)  op(e0, e0) = e2
% 159.78/26.09  | | | 
% 159.78/26.09  | | | REF_CLOSE: (1), (3), (8), (15) are inconsistent by sub-proof #875.
% 159.78/26.09  | | | 
% 159.78/26.09  | | End of split
% 159.78/26.09  | | 
% 159.78/26.09  | End of split
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #686 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  all_56_14 = e2 & op(e0, e1) = e2
% 159.78/26.09    (2)  all_56_14 = e1
% 159.78/26.09    (3)   ~ (e2 = e1)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | ALPHA: (1) implies:
% 159.78/26.09  |   (4)  all_56_14 = e2
% 159.78/26.09  | 
% 159.78/26.09  | COMBINE_EQS: (2), (4) imply:
% 159.78/26.09  |   (5)  e2 = e1
% 159.78/26.09  | 
% 159.78/26.09  | REDUCE: (3), (5) imply:
% 159.78/26.09  |   (6)  $false
% 159.78/26.09  | 
% 159.78/26.09  | CLOSE: (6) is inconsistent.
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #687 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)   ~ (e3 = e2)
% 159.78/26.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.78/26.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.78/26.09    (3)  op(e0, e3) = all_52_3
% 159.78/26.09    (4)  op(e0, e3) = e0
% 159.78/26.09    (5)  all_56_13 = e3
% 159.78/26.09    (6)   ~ (e2 = e0)
% 159.78/26.09    (7)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | BETA: splitting (7) gives:
% 159.78/26.09  | 
% 159.78/26.09  | Case 1:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (8)  all_56_12 = e2 & op(e0, e3) = e2
% 159.78/26.09  | | 
% 159.78/26.09  | | ALPHA: (8) implies:
% 159.78/26.09  | |   (9)  op(e0, e3) = e2
% 159.78/26.09  | | 
% 159.78/26.09  | | REF_CLOSE: (2), (3), (4), (6), (9) are inconsistent by sub-proof #689.
% 159.78/26.09  | | 
% 159.78/26.09  | Case 2:
% 159.78/26.09  | | 
% 159.78/26.09  | |   (10)  all_56_13 = e2 & op(e0, e2) = e2
% 159.78/26.09  | | 
% 159.78/26.09  | | ALPHA: (10) implies:
% 159.78/26.09  | |   (11)  all_56_13 = e2
% 159.78/26.09  | | 
% 159.78/26.09  | | REF_CLOSE: (1), (5), (11) are inconsistent by sub-proof #688.
% 159.78/26.09  | | 
% 159.78/26.09  | End of split
% 159.78/26.09  | 
% 159.78/26.09  End of proof
% 159.78/26.09  
% 159.78/26.09  Sub-proof #688 shows that the following formulas are inconsistent:
% 159.78/26.09  ----------------------------------------------------------------
% 159.78/26.09    (1)  all_56_13 = e3
% 159.78/26.09    (2)  all_56_13 = e2
% 159.78/26.09    (3)   ~ (e3 = e2)
% 159.78/26.09  
% 159.78/26.09  Begin of proof
% 159.78/26.09  | 
% 159.78/26.09  | COMBINE_EQS: (1), (2) imply:
% 159.78/26.09  |   (4)  e3 = e2
% 159.78/26.09  | 
% 159.78/26.09  | SIMP: (4) implies:
% 159.78/26.10  |   (5)  e3 = e2
% 159.78/26.10  | 
% 159.84/26.10  | REDUCE: (3), (5) imply:
% 159.84/26.10  |   (6)  $false
% 159.84/26.10  | 
% 159.84/26.10  | CLOSE: (6) is inconsistent.
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #689 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  op(e0, e3) = e2
% 159.84/26.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (3)  op(e0, e3) = all_52_3
% 159.84/26.10    (4)  op(e0, e3) = e0
% 159.84/26.10    (5)   ~ (e2 = e0)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | GROUND_INST: instantiating (2) with all_52_3, e0, e3, e0, simplifying with
% 159.84/26.10  |              (3), (4) gives:
% 159.84/26.10  |   (6)  all_52_3 = e0
% 159.84/26.10  | 
% 159.84/26.10  | GROUND_INST: instantiating (2) with all_52_3, e2, e3, e0, simplifying with
% 159.84/26.10  |              (1), (3) gives:
% 159.84/26.10  |   (7)  all_52_3 = e2
% 159.84/26.10  | 
% 159.84/26.10  | COMBINE_EQS: (6), (7) imply:
% 159.84/26.10  |   (8)  e2 = e0
% 159.84/26.10  | 
% 159.84/26.10  | REDUCE: (5), (8) imply:
% 159.84/26.10  |   (9)  $false
% 159.84/26.10  | 
% 159.84/26.10  | CLOSE: (9) is inconsistent.
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #690 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  all_54_5 = all_4_2
% 159.84/26.10    (2)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.84/26.10    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (4)   ~ (all_4_2 = e3)
% 159.84/26.10    (5)  op(e2, e2) = all_4_2
% 159.84/26.10    (6)   ~ (all_4_2 = e1)
% 159.84/26.10    (7)  op(e2, e2) = e1
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | BETA: splitting (2) gives:
% 159.84/26.10  | 
% 159.84/26.10  | Case 1:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (8)  all_54_5 = e3
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #930.
% 159.84/26.10  | | 
% 159.84/26.10  | Case 2:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (9)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (1), (3), (5), (6), (7), (9) are inconsistent by sub-proof #691.
% 159.84/26.10  | | 
% 159.84/26.10  | End of split
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #691 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  all_54_5 = all_4_2
% 159.84/26.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (3)  op(e2, e2) = all_4_2
% 159.84/26.10    (4)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 159.84/26.10    (5)   ~ (all_4_2 = e1)
% 159.84/26.10    (6)  op(e2, e2) = e1
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | BETA: splitting (4) gives:
% 159.84/26.10  | 
% 159.84/26.10  | Case 1:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (7)  all_54_5 = e2
% 159.84/26.10  | | 
% 159.84/26.10  | | COMBINE_EQS: (1), (7) imply:
% 159.84/26.10  | |   (8)  all_4_2 = e2
% 159.84/26.10  | | 
% 159.84/26.10  | | SIMP: (8) implies:
% 159.84/26.10  | |   (9)  all_4_2 = e2
% 159.84/26.10  | | 
% 159.84/26.10  | | REDUCE: (5), (9) imply:
% 159.84/26.10  | |   (10)   ~ (e2 = e1)
% 159.84/26.10  | | 
% 159.84/26.10  | | REDUCE: (3), (9) imply:
% 159.84/26.10  | |   (11)  op(e2, e2) = e2
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (2), (6), (10), (11) are inconsistent by sub-proof #993.
% 159.84/26.10  | | 
% 159.84/26.10  | Case 2:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (12)  all_54_5 = e1 | all_54_5 = e0
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (1), (2), (3), (5), (6), (12) are inconsistent by sub-proof #692.
% 159.84/26.10  | | 
% 159.84/26.10  | End of split
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #692 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  all_54_5 = all_4_2
% 159.84/26.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (3)  op(e2, e2) = all_4_2
% 159.84/26.10    (4)   ~ (all_4_2 = e1)
% 159.84/26.10    (5)  op(e2, e2) = e1
% 159.84/26.10    (6)  all_54_5 = e1 | all_54_5 = e0
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | BETA: splitting (6) gives:
% 159.84/26.10  | 
% 159.84/26.10  | Case 1:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (7)  all_54_5 = e1
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #693.
% 159.84/26.10  | | 
% 159.84/26.10  | Case 2:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (8)  all_54_5 = e0
% 159.84/26.10  | | 
% 159.84/26.10  | | COMBINE_EQS: (1), (8) imply:
% 159.84/26.10  | |   (9)  all_4_2 = e0
% 159.84/26.10  | | 
% 159.84/26.10  | | SIMP: (9) implies:
% 159.84/26.10  | |   (10)  all_4_2 = e0
% 159.84/26.10  | | 
% 159.84/26.10  | | REDUCE: (4), (10) imply:
% 159.84/26.10  | |   (11)   ~ (e1 = e0)
% 159.84/26.10  | | 
% 159.84/26.10  | | SIMP: (11) implies:
% 159.84/26.10  | |   (12)   ~ (e1 = e0)
% 159.84/26.10  | | 
% 159.84/26.10  | | REDUCE: (3), (10) imply:
% 159.84/26.10  | |   (13)  op(e2, e2) = e0
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (2), (5), (12), (13) are inconsistent by sub-proof #960.
% 159.84/26.10  | | 
% 159.84/26.10  | End of split
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #693 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  all_54_5 = all_4_2
% 159.84/26.10    (2)  all_54_5 = e1
% 159.84/26.10    (3)   ~ (all_4_2 = e1)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | COMBINE_EQS: (1), (2) imply:
% 159.84/26.10  |   (4)  all_4_2 = e1
% 159.84/26.10  | 
% 159.84/26.10  | SIMP: (4) implies:
% 159.84/26.10  |   (5)  all_4_2 = e1
% 159.84/26.10  | 
% 159.84/26.10  | REDUCE: (3), (5) imply:
% 159.84/26.10  |   (6)  $false
% 159.84/26.10  | 
% 159.84/26.10  | CLOSE: (6) is inconsistent.
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #694 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  op(e2, e3) = e2
% 159.84/26.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (3)   ~ (all_4_2 = e3)
% 159.84/26.10    (4)  op(e2, e2) = all_4_2
% 159.84/26.10    (5)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 159.84/26.10           all_57_0 & $i(all_57_0))
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | BETA: splitting (5) gives:
% 159.84/26.10  | 
% 159.84/26.10  | Case 1:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (6)  all_57_12 = e3 & op(e2, e2) = e3
% 159.84/26.10  | | 
% 159.84/26.10  | | ALPHA: (6) implies:
% 159.84/26.10  | |   (7)  op(e2, e2) = e3
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #711.
% 159.84/26.10  | | 
% 159.84/26.10  | Case 2:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (8)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0)
% 159.84/26.10  | | 
% 159.84/26.10  | | ALPHA: (8) implies:
% 159.84/26.10  | |   (9)   ~ (all_57_0 = e2)
% 159.84/26.10  | |   (10)  op(e2, e3) = all_57_0
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #783.
% 159.84/26.10  | | 
% 159.84/26.10  | End of split
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #695 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  all_54_12 = all_52_3
% 159.84/26.10    (2)  all_54_12 = e1
% 159.84/26.10    (3)   ~ (all_52_3 = e1)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | COMBINE_EQS: (1), (2) imply:
% 159.84/26.10  |   (4)  all_52_3 = e1
% 159.84/26.10  | 
% 159.84/26.10  | SIMP: (4) implies:
% 159.84/26.10  |   (5)  all_52_3 = e1
% 159.84/26.10  | 
% 159.84/26.10  | REDUCE: (3), (5) imply:
% 159.84/26.10  |   (6)  $false
% 159.84/26.10  | 
% 159.84/26.10  | CLOSE: (6) is inconsistent.
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #696 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  all_54_12 = all_52_3
% 159.84/26.10    (2)  all_54_12 = e2
% 159.84/26.10    (3)   ~ (all_52_3 = e2)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | COMBINE_EQS: (1), (2) imply:
% 159.84/26.10  |   (4)  all_52_3 = e2
% 159.84/26.10  | 
% 159.84/26.10  | SIMP: (4) implies:
% 159.84/26.10  |   (5)  all_52_3 = e2
% 159.84/26.10  | 
% 159.84/26.10  | REDUCE: (3), (5) imply:
% 159.84/26.10  |   (6)  $false
% 159.84/26.10  | 
% 159.84/26.10  | CLOSE: (6) is inconsistent.
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #697 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  all_54_12 = all_52_3
% 159.84/26.10    (2)  all_54_12 = e3
% 159.84/26.10    (3)   ~ (all_52_3 = e3)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | COMBINE_EQS: (1), (2) imply:
% 159.84/26.10  |   (4)  all_52_3 = e3
% 159.84/26.10  | 
% 159.84/26.10  | SIMP: (4) implies:
% 159.84/26.10  |   (5)  all_52_3 = e3
% 159.84/26.10  | 
% 159.84/26.10  | REDUCE: (3), (5) imply:
% 159.84/26.10  |   (6)  $false
% 159.84/26.10  | 
% 159.84/26.10  | CLOSE: (6) is inconsistent.
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #698 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (2)  op(e0, e3) = all_52_3
% 159.84/26.10    (3)   ~ (all_52_3 = e0)
% 159.84/26.10    (4)  op(e1, e3) = all_52_2
% 159.84/26.10    (5)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.84/26.10    (6)   ~ (all_52_2 = e0)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | BETA: splitting (5) gives:
% 159.84/26.10  | 
% 159.84/26.10  | Case 1:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (7)  all_56_6 = e0 & op(e1, e3) = e0
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (1), (4), (6), (7) are inconsistent by sub-proof #699.
% 159.84/26.10  | | 
% 159.84/26.10  | Case 2:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (8)  all_56_12 = e0 & op(e0, e3) = e0
% 159.84/26.10  | | 
% 159.84/26.10  | | ALPHA: (8) implies:
% 159.84/26.10  | |   (9)  op(e0, e3) = e0
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #973.
% 159.84/26.10  | | 
% 159.84/26.10  | End of split
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #699 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  all_56_6 = e0 & op(e1, e3) = e0
% 159.84/26.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (3)  op(e1, e3) = all_52_2
% 159.84/26.10    (4)   ~ (all_52_2 = e0)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | ALPHA: (1) implies:
% 159.84/26.10  |   (5)  op(e1, e3) = e0
% 159.84/26.10  | 
% 159.84/26.10  | GROUND_INST: instantiating (2) with all_52_2, e0, e3, e1, simplifying with
% 159.84/26.10  |              (3), (5) gives:
% 159.84/26.10  |   (6)  all_52_2 = e0
% 159.84/26.10  | 
% 159.84/26.10  | REDUCE: (4), (6) imply:
% 159.84/26.10  |   (7)  $false
% 159.84/26.10  | 
% 159.84/26.10  | CLOSE: (7) is inconsistent.
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #700 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  all_56_4 = e0 & op(e3, e1) = e0
% 159.84/26.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (3)  op(e3, e1) = all_52_8
% 159.84/26.10    (4)   ~ (all_52_8 = e0)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | ALPHA: (1) implies:
% 159.84/26.10  |   (5)  op(e3, e1) = e0
% 159.84/26.10  | 
% 159.84/26.10  | GROUND_INST: instantiating (2) with all_52_8, e0, e1, e3, simplifying with
% 159.84/26.10  |              (3), (5) gives:
% 159.84/26.10  |   (6)  all_52_8 = e0
% 159.84/26.10  | 
% 159.84/26.10  | REDUCE: (4), (6) imply:
% 159.84/26.10  |   (7)  $false
% 159.84/26.10  | 
% 159.84/26.10  | CLOSE: (7) is inconsistent.
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #701 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  op(e1, e1) = e0
% 159.84/26.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (3)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 159.84/26.10           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.84/26.10           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1)
% 159.84/26.10           & op(e1, e2) = e1 & op(e1, e1) = e1)
% 159.84/26.10    (4)   ~ (e1 = e0)
% 159.84/26.10    (5)   ~ (e2 = e0)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | BETA: splitting (3) gives:
% 159.84/26.10  | 
% 159.84/26.10  | Case 1:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (6)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0)
% 159.84/26.10  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1,
% 159.84/26.10  | |          e1) = e2 & $i(all_57_12)
% 159.84/26.10  | | 
% 159.84/26.10  | | ALPHA: (6) implies:
% 159.84/26.10  | |   (7)  op(e1, e1) = e2
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #914.
% 159.84/26.10  | | 
% 159.84/26.10  | Case 2:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (8)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 159.84/26.10  | |        op(e1, e1) = e1
% 159.84/26.10  | | 
% 159.84/26.10  | | ALPHA: (8) implies:
% 159.84/26.10  | |   (9)  op(e1, e1) = e1
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #903.
% 159.84/26.10  | | 
% 159.84/26.10  | End of split
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #702 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  op(e1, e1) = e0
% 159.84/26.10    (2)  all_54_15 = e1 | all_54_15 = e0
% 159.84/26.10    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (4)  all_54_15 = all_14_2
% 159.84/26.10    (5)  op(e0, e0) = all_14_2
% 159.84/26.10    (6)   ~ (all_14_2 = e1)
% 159.84/26.10    (7)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 159.84/26.10           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.84/26.10           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 159.84/26.10           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.84/26.10           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 159.84/26.10    (8)   ~ (e2 = e0)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | BETA: splitting (7) gives:
% 159.84/26.10  | 
% 159.84/26.10  | Case 1:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 159.84/26.10  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.84/26.10  | |          e1) = e2 & $i(all_57_12)
% 159.84/26.10  | | 
% 159.84/26.10  | | ALPHA: (9) implies:
% 159.84/26.10  | |   (10)  op(e1, e1) = e2
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (1), (3), (8), (10) are inconsistent by sub-proof #914.
% 159.84/26.10  | | 
% 159.84/26.10  | Case 2:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (11)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 159.84/26.10  | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.84/26.10  | |         op(e0, e0) = e1 & $i(all_57_14)
% 159.84/26.10  | | 
% 159.84/26.10  | | ALPHA: (11) implies:
% 159.84/26.10  | |   (12)  op(e0, e0) = e1
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (2), (3), (4), (5), (6), (12) are inconsistent by sub-proof #790.
% 159.84/26.10  | | 
% 159.84/26.10  | End of split
% 159.84/26.10  | 
% 159.84/26.10  End of proof
% 159.84/26.10  
% 159.84/26.10  Sub-proof #703 shows that the following formulas are inconsistent:
% 159.84/26.10  ----------------------------------------------------------------
% 159.84/26.10    (1)  op(e1, e1) = e0
% 159.84/26.10    (2)  all_54_15 = e1 | all_54_15 = e0
% 159.84/26.10    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.10    (4)  all_54_15 = all_14_2
% 159.84/26.10    (5)  op(e0, e0) = all_14_2
% 159.84/26.10    (6)   ~ (all_14_2 = e1)
% 159.84/26.10    (7)   ~ (e1 = e0)
% 159.84/26.10    (8)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.84/26.10           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 159.84/26.10           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 159.84/26.10           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.84/26.10           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 159.84/26.10           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.84/26.10    (9)   ~ (e3 = e0)
% 159.84/26.10  
% 159.84/26.10  Begin of proof
% 159.84/26.10  | 
% 159.84/26.10  | BETA: splitting (8) gives:
% 159.84/26.10  | 
% 159.84/26.10  | Case 1:
% 159.84/26.10  | | 
% 159.84/26.10  | |   (10)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 159.84/26.10  | |         & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.84/26.10  | |         op(e0, e0) = e1 & $i(all_57_14)
% 159.84/26.10  | | 
% 159.84/26.10  | | ALPHA: (10) implies:
% 159.84/26.10  | |   (11)  op(e0, e0) = e1
% 159.84/26.10  | | 
% 159.84/26.10  | | REF_CLOSE: (2), (3), (4), (5), (6), (11) are inconsistent by sub-proof #790.
% 159.84/26.10  | | 
% 159.84/26.10  | Case 2:
% 159.84/26.10  | | 
% 159.84/26.11  | |   (12)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.84/26.11  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 159.84/26.11  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 159.84/26.11  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (1), (3), (7), (9), (12) are inconsistent by sub-proof #704.
% 159.84/26.11  | | 
% 159.84/26.11  | End of split
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #704 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)  op(e1, e1) = e0
% 159.84/26.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (3)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) &
% 159.84/26.11           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.84/26.11           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1)
% 159.84/26.11           & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.84/26.11    (4)   ~ (e1 = e0)
% 159.84/26.11    (5)   ~ (e3 = e0)
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | BETA: splitting (3) gives:
% 159.84/26.11  | 
% 159.84/26.11  | Case 1:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (6)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 159.84/26.11  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 159.84/26.11  | |          e1) = e3 & $i(all_57_10)
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (6) implies:
% 159.84/26.11  | |   (7)  op(e1, e1) = e3
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #912.
% 159.84/26.11  | | 
% 159.84/26.11  | Case 2:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (8)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.84/26.11  | |        op(e1, e1) = e1
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (8) implies:
% 159.84/26.11  | |   (9)  op(e1, e1) = e1
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #903.
% 159.84/26.11  | | 
% 159.84/26.11  | End of split
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #705 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)  op(e1, e1) = e0
% 159.84/26.11    (2)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.84/26.11           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.84/26.11           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 159.84/26.11           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 159.84/26.11           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.84/26.11    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (4)  op(e2, e2) = e2
% 159.84/26.11    (5)   ~ (e2 = e1)
% 159.84/26.11    (6)   ~ (e3 = e0)
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | BETA: splitting (2) gives:
% 159.84/26.11  | 
% 159.84/26.11  | Case 1:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 159.84/26.11  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.84/26.11  | |          e1) = e3 & $i(all_57_10)
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (7) implies:
% 159.84/26.11  | |   (8)  op(e1, e1) = e3
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #912.
% 159.84/26.11  | | 
% 159.84/26.11  | Case 2:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 159.84/26.11  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 159.84/26.11  | |        all_57_14 & $i(all_57_14)
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (9) implies:
% 159.84/26.11  | |   (10)  op(e2, e2) = e1
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #993.
% 159.84/26.11  | | 
% 159.84/26.11  | End of split
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #706 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (2)  op(e2, e2) = e2
% 159.84/26.11    (3)   ~ (all_52_13 = all_4_2)
% 159.84/26.11    (4)  op(e2, e2) = all_4_2
% 159.84/26.11    (5)  op(e3, e3) = e3
% 159.84/26.11    (6)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.84/26.11           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.84/26.11           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 159.84/26.11           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 159.84/26.11           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.84/26.11    (7)  op(e2, e0) = all_52_13
% 159.84/26.11    (8)   ~ (e3 = e1)
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | BETA: splitting (6) gives:
% 159.84/26.11  | 
% 159.84/26.11  | Case 1:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (9)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 159.84/26.11  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.84/26.11  | |          e0) = e2 & $i(all_57_12)
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (9) implies:
% 159.84/26.11  | |   (10)  op(e2, e0) = e2
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (1), (2), (3), (4), (7), (10) are inconsistent by sub-proof #972.
% 159.84/26.11  | | 
% 159.84/26.11  | Case 2:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (11)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 159.84/26.11  | |         & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.84/26.11  | |         all_57_14 & $i(all_57_14)
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (11) implies:
% 159.84/26.11  | |   (12)  op(e3, e3) = e1
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (1), (5), (8), (12) are inconsistent by sub-proof #995.
% 159.84/26.11  | | 
% 159.84/26.11  | End of split
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #707 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)  op(e1, e1) = e0
% 159.84/26.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (3)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2,
% 159.84/26.11             e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 159.84/26.11           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.84/26.11             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.84/26.11           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 159.84/26.11           & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.84/26.11           $i(all_57_12))
% 159.84/26.11    (4)  op(e2, e3) = e0
% 159.84/26.11    (5)  op(e2, e1) = all_52_9
% 159.84/26.11    (6)   ~ (all_52_9 = e2)
% 159.84/26.11    (7)   ~ (e2 = e0)
% 159.84/26.11    (8)   ~ (e3 = e0)
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | BETA: splitting (3) gives:
% 159.84/26.11  | 
% 159.84/26.11  | Case 1:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (9)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.84/26.11  | |        op(e2, e2) = e2
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (9) implies:
% 159.84/26.11  | |   (10)  op(e2, e3) = e2
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (2), (4), (7), (10) are inconsistent by sub-proof #709.
% 159.84/26.11  | | 
% 159.84/26.11  | Case 2:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (11)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 159.84/26.11  | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1
% 159.84/26.11  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 =
% 159.84/26.11  | |           e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 159.84/26.11  | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.84/26.11  | |           $i(all_57_12))
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (1), (2), (5), (6), (8), (11) are inconsistent by sub-proof #708.
% 159.84/26.11  | | 
% 159.84/26.11  | End of split
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #708 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)  op(e1, e1) = e0
% 159.84/26.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (3)  op(e2, e1) = all_52_9
% 159.84/26.11    (4)   ~ (all_52_9 = e2)
% 159.84/26.11    (5)   ~ (e3 = e0)
% 159.84/26.11    (6)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.84/26.11           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.84/26.11           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 159.84/26.11           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 159.84/26.11           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | BETA: splitting (6) gives:
% 159.84/26.11  | 
% 159.84/26.11  | Case 1:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (7)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 159.84/26.11  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 159.84/26.11  | |          e1) = e3 & $i(all_57_10)
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (7) implies:
% 159.84/26.11  | |   (8)  op(e1, e1) = e3
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #912.
% 159.84/26.11  | | 
% 159.84/26.11  | Case 2:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (9)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 159.84/26.11  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.84/26.11  | |          e1) = e2 & $i(all_57_12)
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (9) implies:
% 159.84/26.11  | |   (10)  op(e2, e1) = e2
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #1002.
% 159.84/26.11  | | 
% 159.84/26.11  | End of split
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #709 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (2)  op(e2, e3) = e2
% 159.84/26.11    (3)  op(e2, e3) = e0
% 159.84/26.11    (4)   ~ (e2 = e0)
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | GROUND_INST: instantiating (1) with e0, e2, e3, e2, simplifying with (2), (3)
% 159.84/26.11  |              gives:
% 159.84/26.11  |   (5)  e2 = e0
% 159.84/26.11  | 
% 159.84/26.11  | REDUCE: (4), (5) imply:
% 159.84/26.11  |   (6)  $false
% 159.84/26.11  | 
% 159.84/26.11  | CLOSE: (6) is inconsistent.
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #710 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)   ~ (e3 = e2)
% 159.84/26.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (3)   ~ (all_4_2 = e3)
% 159.84/26.11    (4)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.84/26.11           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.84/26.11           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 159.84/26.11           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.84/26.11           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.84/26.11    (5)  op(e2, e2) = all_4_2
% 159.84/26.11    (6)  op(e3, e3) = e3
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | BETA: splitting (4) gives:
% 159.84/26.11  | 
% 159.84/26.11  | Case 1:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (7)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 159.84/26.11  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.84/26.11  | |        all_57_12 & $i(all_57_12)
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (7) implies:
% 159.84/26.11  | |   (8)  op(e3, e3) = e2
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #958.
% 159.84/26.11  | | 
% 159.84/26.11  | Case 2:
% 159.84/26.11  | | 
% 159.84/26.11  | |   (9)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2)
% 159.84/26.11  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 159.84/26.11  | |          e2) = e3 & $i(all_57_10)
% 159.84/26.11  | | 
% 159.84/26.11  | | ALPHA: (9) implies:
% 159.84/26.11  | |   (10)  op(e2, e2) = e3
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #711.
% 159.84/26.11  | | 
% 159.84/26.11  | End of split
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #711 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (2)  op(e2, e2) = all_4_2
% 159.84/26.11    (3)  op(e2, e2) = e3
% 159.84/26.11    (4)   ~ (all_4_2 = e3)
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | GROUND_INST: instantiating (1) with all_4_2, e3, e2, e2, simplifying with (2),
% 159.84/26.11  |              (3) gives:
% 159.84/26.11  |   (5)  all_4_2 = e3
% 159.84/26.11  | 
% 159.84/26.11  | REDUCE: (4), (5) imply:
% 159.84/26.11  |   (6)  $false
% 159.84/26.11  | 
% 159.84/26.11  | CLOSE: (6) is inconsistent.
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #712 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)  all_56_13 = e1 & op(e0, e2) = e1
% 159.84/26.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (3)  op(e0, e2) = all_52_7
% 159.84/26.11    (4)   ~ (all_52_7 = e1)
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | ALPHA: (1) implies:
% 159.84/26.11  |   (5)  op(e0, e2) = e1
% 159.84/26.11  | 
% 159.84/26.11  | GROUND_INST: instantiating (2) with all_52_7, e1, e2, e0, simplifying with
% 159.84/26.11  |              (3), (5) gives:
% 159.84/26.11  |   (6)  all_52_7 = e1
% 159.84/26.11  | 
% 159.84/26.11  | REDUCE: (4), (6) imply:
% 159.84/26.11  |   (7)  $false
% 159.84/26.11  | 
% 159.84/26.11  | CLOSE: (7) is inconsistent.
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #713 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)  all_56_10 = e1 & op(e2, e0) = e1
% 159.84/26.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (3)  op(e2, e0) = all_52_13
% 159.84/26.11    (4)   ~ (all_52_13 = e1)
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | ALPHA: (1) implies:
% 159.84/26.11  |   (5)  op(e2, e0) = e1
% 159.84/26.11  | 
% 159.84/26.11  | GROUND_INST: instantiating (2) with all_52_13, e1, e0, e2, simplifying with
% 159.84/26.11  |              (3), (5) gives:
% 159.84/26.11  |   (6)  all_52_13 = e1
% 159.84/26.11  | 
% 159.84/26.11  | REDUCE: (4), (6) imply:
% 159.84/26.11  |   (7)  $false
% 159.84/26.11  | 
% 159.84/26.11  | CLOSE: (7) is inconsistent.
% 159.84/26.11  | 
% 159.84/26.11  End of proof
% 159.84/26.11  
% 159.84/26.11  Sub-proof #714 shows that the following formulas are inconsistent:
% 159.84/26.11  ----------------------------------------------------------------
% 159.84/26.11    (1)  op(e0, e0) = e2
% 159.84/26.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.11    (3)  op(e1, e1) = e1
% 159.84/26.11    (4)  ( ~ (all_50_0 = e3) & op(e2, e0) = all_50_0 & $i(all_50_0)) | ( ~
% 159.84/26.11           (all_50_1 = e1) & op(e2, e2) = all_50_1 & $i(all_50_1))
% 159.84/26.11    (5)  op(e1, e0) = all_52_14
% 159.84/26.11    (6)  op(e0, e0) = all_57_15
% 159.84/26.11    (7)  op(e3, e3) = e3
% 159.84/26.11    (8)  op(e2, e2) = e1
% 159.84/26.11    (9)   ~ (e1 = e0)
% 159.84/26.11    (10)  op(e2, e0) = all_52_13
% 159.84/26.11    (11)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.84/26.11            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.84/26.11            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 159.84/26.11            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.84/26.11            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.84/26.11              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.84/26.11            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 159.84/26.11            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 159.84/26.11            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.84/26.11            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.84/26.11              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.84/26.11            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.84/26.11            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.84/26.11            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.84/26.11              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.84/26.11          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.84/26.11            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.84/26.11            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 159.84/26.11            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.84/26.11            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.84/26.11            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.84/26.11            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.84/26.11    (12)   ~ (all_52_14 = e1)
% 159.84/26.11    (13)   ~ (e2 = e0)
% 159.84/26.11    (14)   ~ (e3 = e0)
% 159.84/26.11    (15)   ~ (all_52_13 = e2)
% 159.84/26.11  
% 159.84/26.11  Begin of proof
% 159.84/26.11  | 
% 159.84/26.11  | BETA: splitting (4) gives:
% 159.84/26.11  | 
% 159.84/26.11  | Case 1:
% 159.84/26.11  | | 
% 159.84/26.11  | | 
% 159.84/26.11  | | GROUND_INST: instantiating (2) with e2, all_57_15, e0, e0, simplifying with
% 159.84/26.11  | |              (1), (6) gives:
% 159.84/26.11  | |   (16)  all_57_15 = e2
% 159.84/26.11  | | 
% 159.84/26.11  | | REF_CLOSE: (2), (3), (5), (7), (9), (10), (11), (12), (13), (14), (15), (16)
% 159.84/26.11  | |            are inconsistent by sub-proof #859.
% 159.84/26.11  | | 
% 159.84/26.11  | Case 2:
% 159.84/26.11  | | 
% 159.84/26.12  | |   (17)   ~ (all_50_1 = e1) & op(e2, e2) = all_50_1 & $i(all_50_1)
% 159.84/26.12  | | 
% 159.84/26.12  | | ALPHA: (17) implies:
% 159.84/26.12  | |   (18)   ~ (all_50_1 = e1)
% 159.84/26.12  | |   (19)  op(e2, e2) = all_50_1
% 159.84/26.12  | | 
% 159.84/26.12  | | GROUND_INST: instantiating (2) with e1, all_50_1, e2, e2, simplifying with
% 159.84/26.12  | |              (8), (19) gives:
% 159.84/26.12  | |   (20)  all_50_1 = e1
% 159.84/26.12  | | 
% 159.84/26.12  | | REDUCE: (18), (20) imply:
% 159.84/26.12  | |   (21)  $false
% 159.84/26.12  | | 
% 159.84/26.12  | | CLOSE: (21) is inconsistent.
% 159.84/26.12  | | 
% 159.84/26.12  | End of split
% 159.84/26.12  | 
% 159.84/26.12  End of proof
% 159.84/26.12  
% 159.84/26.12  Sub-proof #715 shows that the following formulas are inconsistent:
% 159.84/26.12  ----------------------------------------------------------------
% 159.84/26.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.12    (2)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.84/26.12           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.84/26.12           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 159.84/26.12           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 159.84/26.12    (3)  op(e3, e0) = e1
% 159.84/26.12    (4)  op(e2, e0) = all_52_13
% 159.84/26.12    (5)   ~ (e3 = e1)
% 159.84/26.12    (6)   ~ (all_52_13 = e2)
% 159.84/26.12  
% 159.84/26.12  Begin of proof
% 159.84/26.12  | 
% 159.84/26.12  | BETA: splitting (2) gives:
% 159.84/26.12  | 
% 159.84/26.12  | Case 1:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (7)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 159.84/26.12  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.84/26.12  | |          e0) = e2 & $i(all_57_12)
% 159.84/26.12  | | 
% 159.84/26.12  | | ALPHA: (7) implies:
% 159.84/26.12  | |   (8)  op(e2, e0) = e2
% 159.84/26.12  | | 
% 159.84/26.12  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #996.
% 159.84/26.12  | | 
% 159.84/26.12  | Case 2:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (9)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 159.84/26.12  | |        op(e3, e0) = e3
% 159.84/26.12  | | 
% 159.84/26.12  | | ALPHA: (9) implies:
% 159.84/26.12  | |   (10)  op(e3, e0) = e3
% 159.84/26.12  | | 
% 159.84/26.12  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #796.
% 159.84/26.12  | | 
% 159.84/26.12  | End of split
% 159.84/26.12  | 
% 159.84/26.12  End of proof
% 159.84/26.12  
% 159.84/26.12  Sub-proof #716 shows that the following formulas are inconsistent:
% 159.84/26.12  ----------------------------------------------------------------
% 159.84/26.12    (1)  op(e0, e0) = e2
% 159.84/26.12    (2)   ~ (e3 = e2)
% 159.84/26.12    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.12    (4)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 159.84/26.12           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 159.84/26.12           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 159.84/26.12           & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 159.84/26.12           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 159.84/26.12           e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 159.84/26.12         (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 159.84/26.12           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.84/26.12           = e3 & $i(all_57_10))
% 159.84/26.12    (5)  op(e1, e0) = all_52_14
% 159.84/26.12    (6)  op(e2, e2) = e1
% 159.84/26.12    (7)   ~ (all_52_14 = e1)
% 159.84/26.12  
% 159.84/26.12  Begin of proof
% 159.84/26.12  | 
% 159.84/26.12  | BETA: splitting (4) gives:
% 159.84/26.12  | 
% 159.84/26.12  | Case 1:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (8)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 159.84/26.12  | |          & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 &
% 159.84/26.12  | |          op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2
% 159.84/26.12  | |          &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.84/26.12  | | 
% 159.84/26.12  | | BETA: splitting (8) gives:
% 159.84/26.12  | | 
% 159.84/26.12  | | Case 1:
% 159.84/26.12  | | | 
% 159.84/26.12  | | |   (9)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 159.84/26.12  | | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0
% 159.84/26.12  | | |        & op(e0, e0) = e2 & $i(all_57_12)
% 159.84/26.12  | | | 
% 159.84/26.12  | | | ALPHA: (9) implies:
% 159.84/26.12  | | |   (10)   ~ (all_57_12 = e1)
% 159.84/26.12  | | |   (11)  op(e2, e2) = all_57_12
% 159.84/26.12  | | | 
% 159.84/26.12  | | | REF_CLOSE: (3), (6), (10), (11) are inconsistent by sub-proof #795.
% 159.84/26.12  | | | 
% 159.84/26.12  | | Case 2:
% 159.84/26.12  | | | 
% 159.84/26.12  | | |   (12)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 159.84/26.12  | | |         op(e2, e1) = e2
% 159.84/26.12  | | | 
% 159.84/26.12  | | | ALPHA: (12) implies:
% 159.84/26.12  | | |   (13)   ~ (e2 = e1)
% 159.84/26.12  | | |   (14)  op(e2, e2) = e2
% 159.84/26.12  | | | 
% 159.84/26.12  | | | REF_CLOSE: (3), (6), (13), (14) are inconsistent by sub-proof #993.
% 159.84/26.12  | | | 
% 159.84/26.12  | | End of split
% 159.84/26.12  | | 
% 159.84/26.12  | Case 2:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (15)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 159.84/26.12  | |             e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 159.84/26.12  | |           & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 159.84/26.12  | |           e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 159.84/26.12  | |           & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.84/26.12  | |           $i(all_57_10))
% 159.84/26.12  | | 
% 159.84/26.12  | | BETA: splitting (15) gives:
% 159.84/26.12  | | 
% 159.84/26.12  | | Case 1:
% 159.84/26.12  | | | 
% 159.84/26.12  | | |   (16)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 159.84/26.12  | | |           e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 159.84/26.12  | | |         & op(e1, e0) = e1 & $i(all_57_14)
% 159.84/26.12  | | | 
% 159.84/26.12  | | | ALPHA: (16) implies:
% 159.84/26.12  | | |   (17)  op(e1, e0) = e1
% 159.84/26.12  | | | 
% 159.84/26.12  | | | REF_CLOSE: (3), (5), (7), (17) are inconsistent by sub-proof #974.
% 159.84/26.12  | | | 
% 159.84/26.12  | | Case 2:
% 159.84/26.12  | | | 
% 159.84/26.12  | | |   (18)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 159.84/26.12  | | |           e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0
% 159.84/26.12  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 159.84/26.12  | | | 
% 159.84/26.12  | | | ALPHA: (18) implies:
% 159.84/26.12  | | |   (19)  op(e0, e0) = e3
% 159.84/26.12  | | | 
% 159.84/26.12  | | | REF_CLOSE: (1), (2), (3), (19) are inconsistent by sub-proof #878.
% 159.84/26.12  | | | 
% 159.84/26.12  | | End of split
% 159.84/26.12  | | 
% 159.84/26.12  | End of split
% 159.84/26.12  | 
% 159.84/26.12  End of proof
% 159.84/26.12  
% 159.84/26.12  Sub-proof #717 shows that the following formulas are inconsistent:
% 159.84/26.12  ----------------------------------------------------------------
% 159.84/26.12    (1)  all_56_12 = e1
% 159.84/26.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.12    (3)  op(e1, e3) = all_52_2
% 159.84/26.12    (4)   ~ (all_52_2 = e2)
% 159.84/26.12    (5)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.84/26.12    (6)   ~ (e2 = e1)
% 159.84/26.12  
% 159.84/26.12  Begin of proof
% 159.84/26.12  | 
% 159.84/26.12  | BETA: splitting (5) gives:
% 159.84/26.12  | 
% 159.84/26.12  | Case 1:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (7)  all_56_6 = e2 & op(e1, e3) = e2
% 159.84/26.12  | | 
% 159.84/26.12  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #761.
% 159.84/26.12  | | 
% 159.84/26.12  | Case 2:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (8)  all_56_12 = e2 & op(e0, e3) = e2
% 159.84/26.12  | | 
% 159.84/26.12  | | ALPHA: (8) implies:
% 159.84/26.12  | |   (9)  all_56_12 = e2
% 159.84/26.12  | | 
% 159.84/26.12  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #718.
% 159.84/26.12  | | 
% 159.84/26.12  | End of split
% 159.84/26.12  | 
% 159.84/26.12  End of proof
% 159.84/26.12  
% 159.84/26.12  Sub-proof #718 shows that the following formulas are inconsistent:
% 159.84/26.12  ----------------------------------------------------------------
% 159.84/26.12    (1)  all_56_12 = e2
% 159.84/26.12    (2)  all_56_12 = e1
% 159.84/26.12    (3)   ~ (e2 = e1)
% 159.84/26.12  
% 159.84/26.12  Begin of proof
% 159.84/26.12  | 
% 159.84/26.12  | COMBINE_EQS: (1), (2) imply:
% 159.84/26.12  |   (4)  e2 = e1
% 159.84/26.12  | 
% 159.84/26.12  | SIMP: (4) implies:
% 159.84/26.12  |   (5)  e2 = e1
% 159.84/26.12  | 
% 159.84/26.12  | REDUCE: (3), (5) imply:
% 159.84/26.12  |   (6)  $false
% 159.84/26.12  | 
% 159.84/26.12  | CLOSE: (6) is inconsistent.
% 159.84/26.12  | 
% 159.84/26.12  End of proof
% 159.84/26.12  
% 159.84/26.12  Sub-proof #719 shows that the following formulas are inconsistent:
% 159.84/26.12  ----------------------------------------------------------------
% 159.84/26.12    (1)  op(e0, e0) = e2
% 159.84/26.12    (2)  op(e0, e1) = all_52_11
% 159.84/26.12    (3)   ~ (e3 = e2)
% 159.84/26.12    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.12    (5)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.84/26.12    (6)   ~ (all_52_11 = e3)
% 159.84/26.12  
% 159.84/26.12  Begin of proof
% 159.84/26.12  | 
% 159.84/26.12  | BETA: splitting (5) gives:
% 159.84/26.12  | 
% 159.84/26.12  | Case 1:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (7)  all_56_14 = e3 & op(e0, e1) = e3
% 159.84/26.12  | | 
% 159.84/26.12  | | ALPHA: (7) implies:
% 159.84/26.12  | |   (8)  op(e0, e1) = e3
% 159.84/26.12  | | 
% 159.84/26.12  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #720.
% 159.84/26.12  | | 
% 159.84/26.12  | Case 2:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (9)  all_56_15 = e3 & op(e0, e0) = e3
% 159.84/26.12  | | 
% 159.84/26.12  | | ALPHA: (9) implies:
% 159.84/26.12  | |   (10)  op(e0, e0) = e3
% 159.84/26.12  | | 
% 159.84/26.12  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #878.
% 159.84/26.12  | | 
% 159.84/26.12  | End of split
% 159.84/26.12  | 
% 159.84/26.12  End of proof
% 159.84/26.12  
% 159.84/26.12  Sub-proof #720 shows that the following formulas are inconsistent:
% 159.84/26.12  ----------------------------------------------------------------
% 159.84/26.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.12    (2)  op(e0, e1) = all_52_11
% 159.84/26.12    (3)  op(e0, e1) = e3
% 159.84/26.12    (4)   ~ (all_52_11 = e3)
% 159.84/26.12  
% 159.84/26.12  Begin of proof
% 159.84/26.12  | 
% 159.84/26.12  | GROUND_INST: instantiating (1) with all_52_11, e3, e1, e0, simplifying with
% 159.84/26.12  |              (2), (3) gives:
% 159.84/26.12  |   (5)  all_52_11 = e3
% 159.84/26.12  | 
% 159.84/26.12  | REDUCE: (4), (5) imply:
% 159.84/26.12  |   (6)  $false
% 159.84/26.12  | 
% 159.84/26.12  | CLOSE: (6) is inconsistent.
% 159.84/26.12  | 
% 159.84/26.12  End of proof
% 159.84/26.12  
% 159.84/26.12  Sub-proof #721 shows that the following formulas are inconsistent:
% 159.84/26.12  ----------------------------------------------------------------
% 159.84/26.12    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.84/26.12         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.84/26.12    (2)  op(e0, e0) = e2
% 159.84/26.12    (3)   ~ (e3 = e2)
% 159.84/26.12    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.12    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.84/26.12             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.84/26.12               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.84/26.12               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.84/26.12    (6)  op(e3, e3) = e3
% 159.84/26.12    (7)  all_56_14 = e2 & op(e0, e1) = e2
% 159.84/26.12    (8)   ~ (e1 = e0)
% 159.84/26.12    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.84/26.12         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.84/26.12    (10)   ~ (e2 = e1)
% 159.84/26.12    (11)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 159.84/26.12          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 159.84/26.12            e3)
% 159.84/26.12    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.84/26.12          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.84/26.12    (13)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 159.84/26.12          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.84/26.12            e1)
% 159.84/26.12    (14)   ~ (e3 = e1)
% 159.84/26.12    (15)   ~ (e2 = e0)
% 159.84/26.12    (16)   ~ (e3 = e0)
% 159.84/26.12  
% 159.84/26.12  Begin of proof
% 159.84/26.12  | 
% 159.84/26.12  | ALPHA: (7) implies:
% 159.84/26.12  |   (17)  all_56_14 = e2
% 159.84/26.12  | 
% 159.84/26.12  | BETA: splitting (11) gives:
% 159.84/26.12  | 
% 159.84/26.12  | Case 1:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (18)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 159.84/26.12  | |           e3)
% 159.84/26.12  | | 
% 159.84/26.12  | | BETA: splitting (18) gives:
% 159.84/26.12  | | 
% 159.84/26.12  | | Case 1:
% 159.84/26.12  | | | 
% 159.84/26.12  | | |   (19)  all_56_12 = e3 & op(e0, e3) = e3
% 159.84/26.12  | | | 
% 159.84/26.12  | | | ALPHA: (19) implies:
% 159.84/26.12  | | |   (20)  all_56_12 = e3
% 159.84/26.12  | | | 
% 159.84/26.12  | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (12), (14), (15), (16),
% 159.84/26.12  | | |            (20) are inconsistent by sub-proof #729.
% 159.84/26.12  | | | 
% 159.84/26.12  | | Case 2:
% 159.84/26.12  | | | 
% 159.84/26.12  | | |   (21)  all_56_13 = e3 & op(e0, e2) = e3
% 159.84/26.12  | | | 
% 159.84/26.12  | | | ALPHA: (21) implies:
% 159.84/26.12  | | |   (22)  all_56_13 = e3
% 159.84/26.12  | | |   (23)  op(e0, e2) = e3
% 159.84/26.12  | | | 
% 159.84/26.12  | | | REF_CLOSE: (2), (4), (5), (8), (10), (13), (14), (15), (16), (17), (22),
% 159.84/26.12  | | |            (23) are inconsistent by sub-proof #724.
% 159.84/26.12  | | | 
% 159.84/26.12  | | End of split
% 159.84/26.12  | | 
% 159.84/26.12  | Case 2:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (24)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 159.84/26.12  | |           e3)
% 159.84/26.12  | | 
% 159.84/26.12  | | REF_CLOSE: (2), (3), (4), (17), (24) are inconsistent by sub-proof #722.
% 159.84/26.12  | | 
% 159.84/26.12  | End of split
% 159.84/26.12  | 
% 159.84/26.12  End of proof
% 159.84/26.12  
% 159.84/26.12  Sub-proof #722 shows that the following formulas are inconsistent:
% 159.84/26.12  ----------------------------------------------------------------
% 159.84/26.12    (1)  op(e0, e0) = e2
% 159.84/26.12    (2)   ~ (e3 = e2)
% 159.84/26.12    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.12    (4)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.84/26.12    (5)  all_56_14 = e2
% 159.84/26.12  
% 159.84/26.12  Begin of proof
% 159.84/26.12  | 
% 159.84/26.12  | BETA: splitting (4) gives:
% 159.84/26.12  | 
% 159.84/26.12  | Case 1:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (6)  all_56_14 = e3 & op(e0, e1) = e3
% 159.84/26.12  | | 
% 159.84/26.12  | | ALPHA: (6) implies:
% 159.84/26.12  | |   (7)  all_56_14 = e3
% 159.84/26.12  | | 
% 159.84/26.12  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #723.
% 159.84/26.12  | | 
% 159.84/26.12  | Case 2:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (8)  all_56_15 = e3 & op(e0, e0) = e3
% 159.84/26.12  | | 
% 159.84/26.12  | | ALPHA: (8) implies:
% 159.84/26.12  | |   (9)  op(e0, e0) = e3
% 159.84/26.12  | | 
% 159.84/26.12  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #878.
% 159.84/26.12  | | 
% 159.84/26.12  | End of split
% 159.84/26.12  | 
% 159.84/26.12  End of proof
% 159.84/26.12  
% 159.84/26.12  Sub-proof #723 shows that the following formulas are inconsistent:
% 159.84/26.12  ----------------------------------------------------------------
% 159.84/26.12    (1)  all_56_14 = e3
% 159.84/26.12    (2)  all_56_14 = e2
% 159.84/26.12    (3)   ~ (e3 = e2)
% 159.84/26.12  
% 159.84/26.12  Begin of proof
% 159.84/26.12  | 
% 159.84/26.12  | COMBINE_EQS: (1), (2) imply:
% 159.84/26.12  |   (4)  e3 = e2
% 159.84/26.12  | 
% 159.84/26.12  | SIMP: (4) implies:
% 159.84/26.12  |   (5)  e3 = e2
% 159.84/26.12  | 
% 159.84/26.12  | REDUCE: (3), (5) imply:
% 159.84/26.12  |   (6)  $false
% 159.84/26.12  | 
% 159.84/26.12  | CLOSE: (6) is inconsistent.
% 159.84/26.12  | 
% 159.84/26.12  End of proof
% 159.84/26.12  
% 159.84/26.12  Sub-proof #724 shows that the following formulas are inconsistent:
% 159.84/26.12  ----------------------------------------------------------------
% 159.84/26.12    (1)  op(e0, e0) = e2
% 159.84/26.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.12    (3)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.84/26.12             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.84/26.12               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.84/26.12               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.84/26.12    (4)   ~ (e1 = e0)
% 159.84/26.12    (5)  op(e0, e2) = e3
% 159.84/26.12    (6)  all_56_14 = e2
% 159.84/26.12    (7)   ~ (e2 = e1)
% 159.84/26.12    (8)  all_56_13 = e3
% 159.84/26.12    (9)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1) |
% 159.84/26.12         (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.84/26.12    (10)   ~ (e3 = e1)
% 159.84/26.12    (11)   ~ (e2 = e0)
% 159.84/26.12    (12)   ~ (e3 = e0)
% 159.84/26.12  
% 159.84/26.12  Begin of proof
% 159.84/26.12  | 
% 159.84/26.12  | BETA: splitting (3) gives:
% 159.84/26.12  | 
% 159.84/26.12  | Case 1:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (13)  all_56_15 = e0 & op(e0, e0) = e0
% 159.84/26.12  | | 
% 159.84/26.12  | | ALPHA: (13) implies:
% 159.84/26.12  | |   (14)  op(e0, e0) = e0
% 159.84/26.12  | | 
% 159.84/26.12  | | REF_CLOSE: (1), (2), (11), (14) are inconsistent by sub-proof #979.
% 159.84/26.12  | | 
% 159.84/26.12  | Case 2:
% 159.84/26.12  | | 
% 159.84/26.12  | |   (15)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 159.84/26.12  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 159.84/26.12  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 159.84/26.12  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 159.84/26.12  | | 
% 159.84/26.12  | | ALPHA: (15) implies:
% 159.84/26.12  | |   (16)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 159.84/26.12  | |           e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 159.84/26.12  | | 
% 159.84/26.12  | | BETA: splitting (16) gives:
% 159.84/26.12  | | 
% 159.84/26.12  | | Case 1:
% 159.84/26.12  | | | 
% 159.84/26.12  | | |   (17)  all_56_12 = e0 & op(e0, e3) = e0
% 159.84/26.12  | | | 
% 159.84/26.12  | | | ALPHA: (17) implies:
% 159.84/26.12  | | |   (18)  all_56_12 = e0
% 159.84/26.12  | | | 
% 159.84/26.12  | | | BETA: splitting (9) gives:
% 159.84/26.12  | | | 
% 159.84/26.12  | | | Case 1:
% 159.84/26.12  | | | | 
% 159.84/26.12  | | | |   (19)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0,
% 159.84/26.12  | | | |             e2) = e1)
% 159.84/26.12  | | | | 
% 159.84/26.12  | | | | BETA: splitting (19) gives:
% 159.84/26.12  | | | | 
% 159.84/26.12  | | | | Case 1:
% 159.84/26.12  | | | | | 
% 159.84/26.12  | | | | |   (20)  all_56_12 = e1 & op(e0, e3) = e1
% 159.84/26.12  | | | | | 
% 159.84/26.13  | | | | | ALPHA: (20) implies:
% 159.84/26.13  | | | | |   (21)  all_56_12 = e1
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | COMBINE_EQS: (18), (21) imply:
% 159.84/26.13  | | | | |   (22)  e1 = e0
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | REDUCE: (4), (22) imply:
% 159.84/26.13  | | | | |   (23)  $false
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | CLOSE: (23) is inconsistent.
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | Case 2:
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | |   (24)  all_56_13 = e1 & op(e0, e2) = e1
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | REF_CLOSE: (8), (10), (24) are inconsistent by sub-proof #728.
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | End of split
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | Case 2:
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | |   (25)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0,
% 159.84/26.13  | | | |             e0) = e1)
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | BETA: splitting (25) gives:
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | Case 1:
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | |   (26)  all_56_14 = e1 & op(e0, e1) = e1
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | REF_CLOSE: (6), (7), (26) are inconsistent by sub-proof #727.
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | Case 2:
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | |   (27)  all_56_15 = e1 & op(e0, e0) = e1
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | ALPHA: (27) implies:
% 159.84/26.13  | | | | |   (28)  op(e0, e0) = e1
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | REF_CLOSE: (1), (2), (7), (28) are inconsistent by sub-proof #875.
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | End of split
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | End of split
% 159.84/26.13  | | | 
% 159.84/26.13  | | Case 2:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (29)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1)
% 159.84/26.13  | | |           = e0)
% 159.84/26.13  | | | 
% 159.84/26.13  | | | BETA: splitting (29) gives:
% 159.84/26.13  | | | 
% 159.84/26.13  | | | Case 1:
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | |   (30)  all_56_13 = e0 & op(e0, e2) = e0
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | ALPHA: (30) implies:
% 159.84/26.13  | | | |   (31)  op(e0, e2) = e0
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | REF_CLOSE: (2), (5), (12), (31) are inconsistent by sub-proof #726.
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | Case 2:
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | |   (32)  all_56_14 = e0 & op(e0, e1) = e0
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | REF_CLOSE: (6), (11), (32) are inconsistent by sub-proof #725.
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | End of split
% 159.84/26.13  | | | 
% 159.84/26.13  | | End of split
% 159.84/26.13  | | 
% 159.84/26.13  | End of split
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #725 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  all_56_14 = e0 & op(e0, e1) = e0
% 159.84/26.13    (2)  all_56_14 = e2
% 159.84/26.13    (3)   ~ (e2 = e0)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | ALPHA: (1) implies:
% 159.84/26.13  |   (4)  all_56_14 = e0
% 159.84/26.13  | 
% 159.84/26.13  | COMBINE_EQS: (2), (4) imply:
% 159.84/26.13  |   (5)  e2 = e0
% 159.84/26.13  | 
% 159.84/26.13  | REDUCE: (3), (5) imply:
% 159.84/26.13  |   (6)  $false
% 159.84/26.13  | 
% 159.84/26.13  | CLOSE: (6) is inconsistent.
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #726 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.13    (2)  op(e0, e2) = e3
% 159.84/26.13    (3)  op(e0, e2) = e0
% 159.84/26.13    (4)   ~ (e3 = e0)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | GROUND_INST: instantiating (1) with e3, e0, e2, e0, simplifying with (2), (3)
% 159.84/26.13  |              gives:
% 159.84/26.13  |   (5)  e3 = e0
% 159.84/26.13  | 
% 159.84/26.13  | REDUCE: (4), (5) imply:
% 159.84/26.13  |   (6)  $false
% 159.84/26.13  | 
% 159.84/26.13  | CLOSE: (6) is inconsistent.
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #727 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  all_56_14 = e1 & op(e0, e1) = e1
% 159.84/26.13    (2)  all_56_14 = e2
% 159.84/26.13    (3)   ~ (e2 = e1)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | ALPHA: (1) implies:
% 159.84/26.13  |   (4)  all_56_14 = e1
% 159.84/26.13  | 
% 159.84/26.13  | COMBINE_EQS: (2), (4) imply:
% 159.84/26.13  |   (5)  e2 = e1
% 159.84/26.13  | 
% 159.84/26.13  | REDUCE: (3), (5) imply:
% 159.84/26.13  |   (6)  $false
% 159.84/26.13  | 
% 159.84/26.13  | CLOSE: (6) is inconsistent.
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #728 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  all_56_13 = e1 & op(e0, e2) = e1
% 159.84/26.13    (2)  all_56_13 = e3
% 159.84/26.13    (3)   ~ (e3 = e1)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | ALPHA: (1) implies:
% 159.84/26.13  |   (4)  all_56_13 = e1
% 159.84/26.13  | 
% 159.84/26.13  | COMBINE_EQS: (2), (4) imply:
% 159.84/26.13  |   (5)  e3 = e1
% 159.84/26.13  | 
% 159.84/26.13  | REDUCE: (3), (5) imply:
% 159.84/26.13  |   (6)  $false
% 159.84/26.13  | 
% 159.84/26.13  | CLOSE: (6) is inconsistent.
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #729 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.84/26.13         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.84/26.13    (2)   ~ (e3 = e2)
% 159.84/26.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.13    (4)  all_56_12 = e3
% 159.84/26.13    (5)  op(e3, e3) = e3
% 159.84/26.13    (6)   ~ (e1 = e0)
% 159.84/26.13    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.84/26.13         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.84/26.13    (8)   ~ (e2 = e1)
% 159.84/26.13    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.84/26.13         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.84/26.13    (10)   ~ (e3 = e1)
% 159.84/26.13    (11)   ~ (e2 = e0)
% 159.84/26.13    (12)   ~ (e3 = e0)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | BETA: splitting (1) gives:
% 159.84/26.13  | 
% 159.84/26.13  | Case 1:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (13)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 159.84/26.13  | |           e2)
% 159.84/26.13  | | 
% 159.84/26.13  | | BETA: splitting (13) gives:
% 159.84/26.13  | | 
% 159.84/26.13  | | Case 1:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (14)  all_56_0 = e2 & op(e3, e3) = e2
% 159.84/26.13  | | | 
% 159.84/26.13  | | | ALPHA: (14) implies:
% 159.84/26.13  | | |   (15)  op(e3, e3) = e2
% 159.84/26.13  | | | 
% 159.84/26.13  | | | REF_CLOSE: (2), (3), (5), (15) are inconsistent by sub-proof #958.
% 159.84/26.13  | | | 
% 159.84/26.13  | | Case 2:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (16)  all_56_2 = e2 & op(e2, e3) = e2
% 159.84/26.13  | | | 
% 159.84/26.13  | | | ALPHA: (16) implies:
% 159.84/26.13  | | |   (17)  all_56_2 = e2
% 159.84/26.13  | | | 
% 159.84/26.13  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (17) are
% 159.84/26.13  | | |            inconsistent by sub-proof #734.
% 159.84/26.13  | | | 
% 159.84/26.13  | | End of split
% 159.84/26.13  | | 
% 159.84/26.13  | Case 2:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (18)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 159.84/26.13  | |           e2)
% 159.84/26.13  | | 
% 159.84/26.13  | | BETA: splitting (18) gives:
% 159.84/26.13  | | 
% 159.84/26.13  | | Case 1:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (19)  all_56_6 = e2 & op(e1, e3) = e2
% 159.84/26.13  | | | 
% 159.84/26.13  | | | ALPHA: (19) implies:
% 159.84/26.13  | | |   (20)  all_56_6 = e2
% 159.84/26.13  | | | 
% 159.84/26.13  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (20) are
% 159.84/26.13  | | |            inconsistent by sub-proof #731.
% 159.84/26.13  | | | 
% 159.84/26.13  | | Case 2:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (21)  all_56_12 = e2 & op(e0, e3) = e2
% 159.84/26.13  | | | 
% 159.84/26.13  | | | REF_CLOSE: (2), (4), (21) are inconsistent by sub-proof #730.
% 159.84/26.13  | | | 
% 159.84/26.13  | | End of split
% 159.84/26.13  | | 
% 159.84/26.13  | End of split
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #730 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  all_56_12 = e2 & op(e0, e3) = e2
% 159.84/26.13    (2)  all_56_12 = e3
% 159.84/26.13    (3)   ~ (e3 = e2)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | ALPHA: (1) implies:
% 159.84/26.13  |   (4)  all_56_12 = e2
% 159.84/26.13  | 
% 159.84/26.13  | COMBINE_EQS: (2), (4) imply:
% 159.84/26.13  |   (5)  e3 = e2
% 159.84/26.13  | 
% 159.84/26.13  | REDUCE: (3), (5) imply:
% 159.84/26.13  |   (6)  $false
% 159.84/26.13  | 
% 159.84/26.13  | CLOSE: (6) is inconsistent.
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #731 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.13    (2)  all_56_6 = e2
% 159.84/26.13    (3)  all_56_12 = e3
% 159.84/26.13    (4)  op(e3, e3) = e3
% 159.84/26.13    (5)   ~ (e1 = e0)
% 159.84/26.13    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.84/26.13         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.84/26.13    (7)   ~ (e2 = e1)
% 159.84/26.13    (8)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.84/26.13         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.84/26.13    (9)   ~ (e3 = e1)
% 159.84/26.13    (10)   ~ (e2 = e0)
% 159.84/26.13    (11)   ~ (e3 = e0)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | BETA: splitting (6) gives:
% 159.84/26.13  | 
% 159.84/26.13  | Case 1:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 159.84/26.13  | |           e0)
% 159.84/26.13  | | 
% 159.84/26.13  | | BETA: splitting (12) gives:
% 159.84/26.13  | | 
% 159.84/26.13  | | Case 1:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (13)  all_56_0 = e0 & op(e3, e3) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | ALPHA: (13) implies:
% 159.84/26.13  | | |   (14)  op(e3, e3) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | REF_CLOSE: (1), (4), (11), (14) are inconsistent by sub-proof #971.
% 159.84/26.13  | | | 
% 159.84/26.13  | | Case 2:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (15)  all_56_2 = e0 & op(e2, e3) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | ALPHA: (15) implies:
% 159.84/26.13  | | |   (16)  all_56_2 = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | BETA: splitting (8) gives:
% 159.84/26.13  | | | 
% 159.84/26.13  | | | Case 1:
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | |   (17)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3)
% 159.84/26.13  | | | |           = e1)
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | REF_CLOSE: (1), (4), (5), (9), (16), (17) are inconsistent by sub-proof
% 159.84/26.13  | | | |            #732.
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | Case 2:
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | |   (18)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3)
% 159.84/26.13  | | | |           = e1)
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | BETA: splitting (18) gives:
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | Case 1:
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | |   (19)  all_56_6 = e1 & op(e1, e3) = e1
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | REF_CLOSE: (2), (7), (19) are inconsistent by sub-proof #772.
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | Case 2:
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | |   (20)  all_56_12 = e1 & op(e0, e3) = e1
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | REF_CLOSE: (3), (9), (20) are inconsistent by sub-proof #736.
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | End of split
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | End of split
% 159.84/26.13  | | | 
% 159.84/26.13  | | End of split
% 159.84/26.13  | | 
% 159.84/26.13  | Case 2:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (21)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 159.84/26.13  | |           e0)
% 159.84/26.13  | | 
% 159.84/26.13  | | BETA: splitting (21) gives:
% 159.84/26.13  | | 
% 159.84/26.13  | | Case 1:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (22)  all_56_6 = e0 & op(e1, e3) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | REF_CLOSE: (2), (10), (22) are inconsistent by sub-proof #775.
% 159.84/26.13  | | | 
% 159.84/26.13  | | Case 2:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (23)  all_56_12 = e0 & op(e0, e3) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | REF_CLOSE: (3), (11), (23) are inconsistent by sub-proof #735.
% 159.84/26.13  | | | 
% 159.84/26.13  | | End of split
% 159.84/26.13  | | 
% 159.84/26.13  | End of split
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #732 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  all_56_2 = e0
% 159.84/26.13    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 159.84/26.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.13    (4)  op(e3, e3) = e3
% 159.84/26.13    (5)   ~ (e1 = e0)
% 159.84/26.13    (6)   ~ (e3 = e1)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | BETA: splitting (2) gives:
% 159.84/26.13  | 
% 159.84/26.13  | Case 1:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 159.84/26.13  | | 
% 159.84/26.13  | | ALPHA: (7) implies:
% 159.84/26.13  | |   (8)  op(e3, e3) = e1
% 159.84/26.13  | | 
% 159.84/26.13  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #995.
% 159.84/26.13  | | 
% 159.84/26.13  | Case 2:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (9)  all_56_2 = e1 & op(e2, e3) = e1
% 159.84/26.13  | | 
% 159.84/26.13  | | ALPHA: (9) implies:
% 159.84/26.13  | |   (10)  all_56_2 = e1
% 159.84/26.13  | | 
% 159.84/26.13  | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #733.
% 159.84/26.13  | | 
% 159.84/26.13  | End of split
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #733 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  all_56_2 = e1
% 159.84/26.13    (2)  all_56_2 = e0
% 159.84/26.13    (3)   ~ (e1 = e0)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | COMBINE_EQS: (1), (2) imply:
% 159.84/26.13  |   (4)  e1 = e0
% 159.84/26.13  | 
% 159.84/26.13  | SIMP: (4) implies:
% 159.84/26.13  |   (5)  e1 = e0
% 159.84/26.13  | 
% 159.84/26.13  | REDUCE: (3), (5) imply:
% 159.84/26.13  |   (6)  $false
% 159.84/26.13  | 
% 159.84/26.13  | CLOSE: (6) is inconsistent.
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #734 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.13    (2)  all_56_2 = e2
% 159.84/26.13    (3)  all_56_12 = e3
% 159.84/26.13    (4)  op(e3, e3) = e3
% 159.84/26.13    (5)   ~ (e1 = e0)
% 159.84/26.13    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.84/26.13         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.84/26.13    (7)   ~ (e2 = e1)
% 159.84/26.13    (8)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.84/26.13         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.84/26.13    (9)   ~ (e3 = e1)
% 159.84/26.13    (10)   ~ (e2 = e0)
% 159.84/26.13    (11)   ~ (e3 = e0)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | BETA: splitting (6) gives:
% 159.84/26.13  | 
% 159.84/26.13  | Case 1:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 159.84/26.13  | |           e0)
% 159.84/26.13  | | 
% 159.84/26.13  | | BETA: splitting (12) gives:
% 159.84/26.13  | | 
% 159.84/26.13  | | Case 1:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (13)  all_56_0 = e0 & op(e3, e3) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | ALPHA: (13) implies:
% 159.84/26.13  | | |   (14)  op(e3, e3) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | REF_CLOSE: (1), (4), (11), (14) are inconsistent by sub-proof #971.
% 159.84/26.13  | | | 
% 159.84/26.13  | | Case 2:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (15)  all_56_2 = e0 & op(e2, e3) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | REF_CLOSE: (2), (10), (15) are inconsistent by sub-proof #846.
% 159.84/26.13  | | | 
% 159.84/26.13  | | End of split
% 159.84/26.13  | | 
% 159.84/26.13  | Case 2:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 159.84/26.13  | |           e0)
% 159.84/26.13  | | 
% 159.84/26.13  | | BETA: splitting (16) gives:
% 159.84/26.13  | | 
% 159.84/26.13  | | Case 1:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (17)  all_56_6 = e0 & op(e1, e3) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | ALPHA: (17) implies:
% 159.84/26.13  | | |   (18)  all_56_6 = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | BETA: splitting (8) gives:
% 159.84/26.13  | | | 
% 159.84/26.13  | | | Case 1:
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | |   (19)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3)
% 159.84/26.13  | | | |           = e1)
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | REF_CLOSE: (1), (2), (4), (7), (9), (19) are inconsistent by sub-proof
% 159.84/26.13  | | | |            #737.
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | Case 2:
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | |   (20)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3)
% 159.84/26.13  | | | |           = e1)
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | BETA: splitting (20) gives:
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | | Case 1:
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | |   (21)  all_56_6 = e1 & op(e1, e3) = e1
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | REF_CLOSE: (5), (18), (21) are inconsistent by sub-proof #917.
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | Case 2:
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | |   (22)  all_56_12 = e1 & op(e0, e3) = e1
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | | REF_CLOSE: (3), (9), (22) are inconsistent by sub-proof #736.
% 159.84/26.13  | | | | | 
% 159.84/26.13  | | | | End of split
% 159.84/26.13  | | | | 
% 159.84/26.13  | | | End of split
% 159.84/26.13  | | | 
% 159.84/26.13  | | Case 2:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (23)  all_56_12 = e0 & op(e0, e3) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | REF_CLOSE: (3), (11), (23) are inconsistent by sub-proof #735.
% 159.84/26.13  | | | 
% 159.84/26.13  | | End of split
% 159.84/26.13  | | 
% 159.84/26.13  | End of split
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #735 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  all_56_12 = e0 & op(e0, e3) = e0
% 159.84/26.13    (2)  all_56_12 = e3
% 159.84/26.13    (3)   ~ (e3 = e0)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | ALPHA: (1) implies:
% 159.84/26.13  |   (4)  all_56_12 = e0
% 159.84/26.13  | 
% 159.84/26.13  | COMBINE_EQS: (2), (4) imply:
% 159.84/26.13  |   (5)  e3 = e0
% 159.84/26.13  | 
% 159.84/26.13  | REDUCE: (3), (5) imply:
% 159.84/26.13  |   (6)  $false
% 159.84/26.13  | 
% 159.84/26.13  | CLOSE: (6) is inconsistent.
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #736 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  all_56_12 = e1 & op(e0, e3) = e1
% 159.84/26.13    (2)  all_56_12 = e3
% 159.84/26.13    (3)   ~ (e3 = e1)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | ALPHA: (1) implies:
% 159.84/26.13  |   (4)  all_56_12 = e1
% 159.84/26.13  | 
% 159.84/26.13  | COMBINE_EQS: (2), (4) imply:
% 159.84/26.13  |   (5)  e3 = e1
% 159.84/26.13  | 
% 159.84/26.13  | REDUCE: (3), (5) imply:
% 159.84/26.13  |   (6)  $false
% 159.84/26.13  | 
% 159.84/26.13  | CLOSE: (6) is inconsistent.
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #737 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 159.84/26.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.13    (3)  all_56_2 = e2
% 159.84/26.13    (4)  op(e3, e3) = e3
% 159.84/26.13    (5)   ~ (e2 = e1)
% 159.84/26.13    (6)   ~ (e3 = e1)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | BETA: splitting (1) gives:
% 159.84/26.13  | 
% 159.84/26.13  | Case 1:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 159.84/26.13  | | 
% 159.84/26.13  | | ALPHA: (7) implies:
% 159.84/26.13  | |   (8)  op(e3, e3) = e1
% 159.84/26.13  | | 
% 159.84/26.13  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #995.
% 159.84/26.13  | | 
% 159.84/26.13  | Case 2:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (9)  all_56_2 = e1 & op(e2, e3) = e1
% 159.84/26.13  | | 
% 159.84/26.13  | | ALPHA: (9) implies:
% 159.84/26.13  | |   (10)  all_56_2 = e1
% 159.84/26.13  | | 
% 159.84/26.13  | | COMBINE_EQS: (3), (10) imply:
% 159.84/26.13  | |   (11)  e2 = e1
% 159.84/26.13  | | 
% 159.84/26.13  | | REDUCE: (5), (11) imply:
% 159.84/26.13  | |   (12)  $false
% 159.84/26.13  | | 
% 159.84/26.13  | | CLOSE: (12) is inconsistent.
% 159.84/26.13  | | 
% 159.84/26.13  | End of split
% 159.84/26.13  | 
% 159.84/26.13  End of proof
% 159.84/26.13  
% 159.84/26.13  Sub-proof #738 shows that the following formulas are inconsistent:
% 159.84/26.13  ----------------------------------------------------------------
% 159.84/26.13    (1)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 159.84/26.13         (all_56_11 = e0 & op(e1, e0) = e0)
% 159.84/26.13    (2)  all_56_10 = e3
% 159.84/26.13    (3)  all_56_9 = e1
% 159.84/26.13    (4)  all_56_11 = e2
% 159.84/26.13    (5)   ~ (e1 = e0)
% 159.84/26.13    (6)   ~ (e2 = e0)
% 159.84/26.13    (7)   ~ (e3 = e0)
% 159.84/26.13  
% 159.84/26.13  Begin of proof
% 159.84/26.13  | 
% 159.84/26.13  | BETA: splitting (1) gives:
% 159.84/26.13  | 
% 159.84/26.13  | Case 1:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (8)  all_56_9 = e0 & op(e3, e0) = e0
% 159.84/26.13  | | 
% 159.84/26.13  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #952.
% 159.84/26.13  | | 
% 159.84/26.13  | Case 2:
% 159.84/26.13  | | 
% 159.84/26.13  | |   (9)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.84/26.13  | |          e0)
% 159.84/26.13  | | 
% 159.84/26.13  | | BETA: splitting (9) gives:
% 159.84/26.13  | | 
% 159.84/26.13  | | Case 1:
% 159.84/26.13  | | | 
% 159.84/26.13  | | |   (10)  all_56_10 = e0 & op(e2, e0) = e0
% 159.84/26.13  | | | 
% 159.84/26.13  | | | ALPHA: (10) implies:
% 159.84/26.14  | | |   (11)  all_56_10 = e0
% 159.84/26.14  | | | 
% 159.84/26.14  | | | REF_CLOSE: (2), (7), (11) are inconsistent by sub-proof #740.
% 159.84/26.14  | | | 
% 159.84/26.14  | | Case 2:
% 159.84/26.14  | | | 
% 159.84/26.14  | | |   (12)  all_56_11 = e0 & op(e1, e0) = e0
% 159.84/26.14  | | | 
% 159.84/26.14  | | | REF_CLOSE: (4), (6), (12) are inconsistent by sub-proof #739.
% 159.84/26.14  | | | 
% 159.84/26.14  | | End of split
% 159.84/26.14  | | 
% 159.84/26.14  | End of split
% 159.84/26.14  | 
% 159.84/26.14  End of proof
% 159.84/26.14  
% 159.84/26.14  Sub-proof #739 shows that the following formulas are inconsistent:
% 159.84/26.14  ----------------------------------------------------------------
% 159.84/26.14    (1)  all_56_11 = e0 & op(e1, e0) = e0
% 159.84/26.14    (2)  all_56_11 = e2
% 159.84/26.14    (3)   ~ (e2 = e0)
% 159.84/26.14  
% 159.84/26.14  Begin of proof
% 159.84/26.14  | 
% 159.84/26.14  | ALPHA: (1) implies:
% 159.84/26.14  |   (4)  all_56_11 = e0
% 159.84/26.14  | 
% 159.84/26.14  | COMBINE_EQS: (2), (4) imply:
% 159.84/26.14  |   (5)  e2 = e0
% 159.84/26.14  | 
% 159.84/26.14  | REDUCE: (3), (5) imply:
% 159.84/26.14  |   (6)  $false
% 159.84/26.14  | 
% 159.84/26.14  | CLOSE: (6) is inconsistent.
% 159.84/26.14  | 
% 159.84/26.14  End of proof
% 159.84/26.14  
% 159.84/26.14  Sub-proof #740 shows that the following formulas are inconsistent:
% 159.84/26.14  ----------------------------------------------------------------
% 159.84/26.14    (1)  all_56_10 = e3
% 159.84/26.14    (2)  all_56_10 = e0
% 159.84/26.14    (3)   ~ (e3 = e0)
% 159.84/26.14  
% 159.84/26.14  Begin of proof
% 159.84/26.14  | 
% 159.84/26.14  | COMBINE_EQS: (1), (2) imply:
% 159.84/26.14  |   (4)  e3 = e0
% 159.84/26.14  | 
% 159.84/26.14  | SIMP: (4) implies:
% 159.84/26.14  |   (5)  e3 = e0
% 159.84/26.14  | 
% 159.84/26.14  | REDUCE: (3), (5) imply:
% 159.84/26.14  |   (6)  $false
% 159.84/26.14  | 
% 159.84/26.14  | CLOSE: (6) is inconsistent.
% 159.84/26.14  | 
% 159.84/26.14  End of proof
% 159.84/26.14  
% 159.84/26.14  Sub-proof #741 shows that the following formulas are inconsistent:
% 159.84/26.14  ----------------------------------------------------------------
% 159.84/26.14    (1)   ~ (all_52_7 = all_14_2)
% 159.84/26.14    (2)   ~ (all_6_2 = e0)
% 159.84/26.14    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.84/26.14         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.84/26.14    (4)   ~ (all_52_8 = all_6_2)
% 159.84/26.14    (5)   ~ (all_52_6 = e1)
% 159.84/26.14    (6)   ~ (all_52_3 = all_14_2)
% 159.84/26.14    (7)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.84/26.14             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.84/26.14           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.84/26.14               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.84/26.14             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.84/26.14         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.84/26.14             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.84/26.14           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.84/26.14               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.84/26.14             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.84/26.14         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.84/26.14             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.84/26.14           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.84/26.14               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.84/26.14             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.84/26.14         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.84/26.14             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.84/26.14           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.84/26.14               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.84/26.14             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.84/26.14    (8)  op(e0, e1) = all_52_11
% 159.84/26.14    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.84/26.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.84/26.14    (10)  op(e0, e3) = all_52_3
% 159.84/26.14    (11)  op(e3, e1) = all_52_8
% 159.84/26.14    (12)   ~ (all_52_12 = all_6_2)
% 159.84/26.14    (13)  all_28_2 = all_14_2
% 159.84/26.14    (14)  op(e1, e1) = e2
% 159.84/26.14    (15)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.84/26.14    (16)   ~ (all_52_11 = all_14_2)
% 159.84/26.14    (17)  op(e1, e3) = all_52_2
% 159.84/26.14    (18)  all_54_15 = all_14_2
% 159.84/26.14    (19)  op(e0, e2) = all_52_7
% 159.84/26.14    (20)   ~ (all_52_2 = e2)
% 159.84/26.14    (21)  op(e1, e2) = all_52_6
% 159.84/26.14    (22)   ~ (all_28_2 = e2) | ( ~ (all_28_0 = e1) & op(e2, e0) = all_28_0 &
% 159.84/26.14            $i(all_28_0)) | ( ~ (all_28_1 = e3) & op(e2, e2) = all_28_1 &
% 159.84/26.14            $i(all_28_1))
% 159.84/26.14    (23)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.84/26.14    (24)   ~ (all_6_2 = e1)
% 159.84/26.14    (25)  op(e0, e0) = all_14_2
% 159.84/26.14    (26)   ~ (all_14_2 = e1)
% 159.84/26.14    (27)  op(e3, e2) = all_52_4
% 159.84/26.14    (28)  all_54_0 = all_6_2
% 159.84/26.14    (29)  op(e2, e2) = e1
% 159.84/26.14    (30)   ~ (e1 = e0)
% 159.84/26.14    (31)  op(e2, e1) = all_52_9
% 159.84/26.14    (32)   ~ (e2 = e1)
% 159.84/26.14    (33)  op(e3, e3) = all_6_2
% 159.84/26.14    (34)  op(e3, e0) = all_52_12
% 159.84/26.14    (35)   ~ (all_52_4 = all_6_2)
% 159.84/26.14    (36)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.84/26.14            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.84/26.14            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.84/26.14            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.84/26.14              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.84/26.14          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.84/26.14            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.84/26.14              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.84/26.14            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.84/26.14              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.84/26.14          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 159.84/26.14            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 159.84/26.14              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.84/26.14            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.84/26.14              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.84/26.14          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.84/26.14            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 159.84/26.14            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.84/26.14              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.84/26.14            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 159.84/26.14            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.84/26.14            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.84/26.14            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 159.84/26.14              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.84/26.14            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 159.84/26.14          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.84/26.14            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.84/26.14              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.84/26.14            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 159.84/26.14            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.84/26.14          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.84/26.14            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.84/26.14              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 159.84/26.14            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 159.84/26.14            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.84/26.14          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 159.84/26.14            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.84/26.14              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.84/26.14            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.84/26.14              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.84/26.14          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.84/26.14            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 159.84/26.14            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 159.84/26.14            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 159.84/26.14            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 159.84/26.14            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.84/26.14            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.84/26.14            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 159.84/26.14              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.84/26.14            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 159.84/26.14            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.84/26.14            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.84/26.14            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 159.84/26.14              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 159.84/26.14            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 159.84/26.14          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 159.84/26.14            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 159.84/26.14              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 159.84/26.14              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 159.84/26.14            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 159.84/26.14            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.84/26.14            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.84/26.14            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 159.84/26.14              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 159.84/26.14            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 159.84/26.14          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.84/26.14            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.84/26.14              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.84/26.14            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.84/26.14              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.84/26.14          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 159.84/26.14            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.84/26.14              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 159.84/26.14              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 159.84/26.14            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 159.84/26.14          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.84/26.14            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.84/26.14            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 159.84/26.14                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 159.84/26.14                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.84/26.14                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.84/26.14                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.84/26.14                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 159.84/26.14                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 159.84/26.14                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.84/26.14                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.84/26.14                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.84/26.14                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 159.84/26.14                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.84/26.14                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.84/26.14                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 159.84/26.14                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.84/26.14                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.84/26.14                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.84/26.14                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 159.84/26.14                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 159.84/26.14                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 159.84/26.14                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.84/26.14                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.84/26.14                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.84/26.14                op(e0, e1) = e0)))
% 159.84/26.14    (37)   ~ (all_52_9 = e2)
% 159.84/26.14    (38)   ~ (all_6_2 = e2)
% 159.84/26.14    (39)   ~ (e2 = e0)
% 159.84/26.14    (40)   ~ (all_14_2 = e3)
% 159.84/26.14  
% 159.84/26.14  Begin of proof
% 159.84/26.14  | 
% 159.84/26.14  | BETA: splitting (23) gives:
% 159.84/26.14  | 
% 159.84/26.14  | Case 1:
% 159.84/26.14  | | 
% 159.84/26.14  | |   (41)  all_54_0 = e3
% 159.84/26.14  | | 
% 159.84/26.14  | | COMBINE_EQS: (28), (41) imply:
% 159.84/26.14  | |   (42)  all_6_2 = e3
% 159.84/26.14  | | 
% 159.84/26.14  | | SIMP: (42) implies:
% 159.84/26.14  | |   (43)  all_6_2 = e3
% 159.84/26.14  | | 
% 159.84/26.14  | | REDUCE: (35), (43) imply:
% 159.84/26.14  | |   (44)   ~ (all_52_4 = e3)
% 159.84/26.14  | | 
% 159.84/26.14  | | REDUCE: (4), (43) imply:
% 159.84/26.14  | |   (45)   ~ (all_52_8 = e3)
% 159.84/26.14  | | 
% 159.84/26.14  | | REDUCE: (12), (43) imply:
% 159.84/26.14  | |   (46)   ~ (all_52_12 = e3)
% 159.84/26.14  | | 
% 159.84/26.14  | | REDUCE: (38), (43) imply:
% 159.84/26.14  | |   (47)   ~ (e3 = e2)
% 159.84/26.14  | | 
% 159.84/26.14  | | REDUCE: (24), (43) imply:
% 159.84/26.14  | |   (48)   ~ (e3 = e1)
% 159.84/26.14  | | 
% 159.84/26.14  | | REDUCE: (33), (43) imply:
% 159.84/26.14  | |   (49)  op(e3, e3) = e3
% 159.84/26.14  | | 
% 159.84/26.14  | | BETA: splitting (22) gives:
% 159.84/26.14  | | 
% 159.84/26.14  | | Case 1:
% 159.84/26.14  | | | 
% 159.84/26.14  | | |   (50)   ~ (all_28_2 = e2)
% 159.84/26.14  | | | 
% 159.84/26.14  | | | REDUCE: (13), (50) imply:
% 159.84/26.14  | | |   (51)   ~ (all_14_2 = e2)
% 159.84/26.14  | | | 
% 159.84/26.14  | | | BETA: splitting (15) gives:
% 159.84/26.14  | | | 
% 159.84/26.14  | | | Case 1:
% 159.84/26.14  | | | | 
% 159.84/26.14  | | | |   (52)  all_54_15 = e3
% 159.84/26.14  | | | | 
% 159.84/26.14  | | | | REF_CLOSE: (18), (40), (52) are inconsistent by sub-proof #1010.
% 159.84/26.14  | | | | 
% 159.84/26.14  | | | Case 2:
% 159.84/26.14  | | | | 
% 159.84/26.14  | | | |   (53)   ~ (all_54_15 = e3)
% 159.84/26.14  | | | |   (54)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.84/26.14  | | | | 
% 159.84/26.14  | | | | BETA: splitting (36) gives:
% 159.84/26.14  | | | | 
% 159.84/26.14  | | | | Case 1:
% 159.84/26.14  | | | | | 
% 159.84/26.14  | | | | |   (55)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.84/26.14  | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.84/26.14  | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12)) |
% 159.84/26.14  | | | | |         (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 159.84/26.14  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 159.84/26.14  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.84/26.14  | | | | |         (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 159.84/26.14  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 159.84/26.14  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.84/26.14  | | | | |         (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 159.84/26.14  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 159.84/26.14  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.84/26.14  | | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.84/26.14  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 159.84/26.14  | | | | |           & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.84/26.14  | | | | |         (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 159.84/26.14  | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 159.84/26.14  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.84/26.14  | | | | |         (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) =
% 159.84/26.14  | | | | |           e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 159.84/26.14  | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.84/26.14  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.84/26.14  | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 159.84/26.14  | | | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 159.84/26.15  | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.84/26.15  | | | | |           $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15
% 159.84/26.15  | | | | |           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.84/26.15  | | | | |             e2) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.84/26.15  | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 =
% 159.84/26.15  | | | | |             e2) & op(e3, e3) = e3 & op(e3, e2) = e3) | (all_57_1 = e3
% 159.84/26.15  | | | | |           & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.84/26.15  | | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.84/26.15  | | | | |           op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4
% 159.84/26.15  | | | | |           = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) =
% 159.84/26.15  | | | | |           e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.84/26.15  | | | | |           all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3
% 159.84/26.15  | | | | |           & all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.84/26.15  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.84/26.15  | | | | |           e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 159.84/26.15  | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 &
% 159.84/26.15  | | | | |           op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.84/26.15  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 & all_57_15
% 159.84/26.15  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 159.84/26.15  | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.84/26.15  | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14
% 159.84/26.15  | | | | |           = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.84/26.15  | | | | |             e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.84/26.15  | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 =
% 159.84/26.15  | | | | |             e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.84/26.15  | | | | | 
% 159.84/26.15  | | | | | BETA: splitting (55) gives:
% 159.84/26.15  | | | | | 
% 159.84/26.15  | | | | | Case 1:
% 159.84/26.15  | | | | | | 
% 159.84/26.15  | | | | | |   (56)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.84/26.15  | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.84/26.15  | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12))
% 159.84/26.15  | | | | | |         | (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 159.84/26.15  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 159.84/26.15  | | | | | |           e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 159.84/26.15  | | | | | |         (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 159.84/26.15  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.84/26.15  | | | | | |           all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.84/26.15  | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.84/26.15  | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.84/26.15  | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 159.84/26.15  | | | | | |           = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_7 = e0 &
% 159.84/26.15  | | | | | |           all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 159.84/26.15  | | | | | |           op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2
% 159.84/26.15  | | | | | |           & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.84/26.15  | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.84/26.15  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 159.84/26.15  | | | | | |           = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 & 
% 159.84/26.15  | | | | | |           ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 159.84/26.15  | | | | | |         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 159.84/26.15  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 159.84/26.15  | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 159.84/26.15  | | | | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 159.84/26.15  | | | | | |           (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.84/26.15  | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.84/26.15  | | | | | | 
% 159.84/26.15  | | | | | | BETA: splitting (56) gives:
% 159.84/26.15  | | | | | | 
% 159.84/26.15  | | | | | | Case 1:
% 159.84/26.15  | | | | | | | 
% 159.84/26.15  | | | | | | |   (57)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.84/26.15  | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.84/26.15  | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.84/26.15  | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.84/26.15  | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.84/26.15  | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 159.84/26.15  | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_3
% 159.84/26.15  | | | | | | |           = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3)
% 159.84/26.15  | | | | | | |           = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.84/26.15  | | | | | | |             e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4
% 159.84/26.15  | | | | | | |           = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 159.84/26.15  | | | | | | |           = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 159.84/26.15  | | | | | | |             e2) = e3 & $i(all_57_10))
% 159.84/26.15  | | | | | | | 
% 159.84/26.15  | | | | | | | BETA: splitting (57) gives:
% 159.84/26.15  | | | | | | | 
% 159.84/26.15  | | | | | | | Case 1:
% 159.84/26.15  | | | | | | | | 
% 159.84/26.15  | | | | | | | |   (58)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 159.84/26.15  | | | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.84/26.15  | | | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 159.84/26.15  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 159.84/26.15  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 159.84/26.15  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 159.84/26.15  | | | | | | | |             e2) = e3 & $i(all_57_10))
% 159.84/26.15  | | | | | | | | 
% 159.84/26.15  | | | | | | | | REF_CLOSE: (9), (29), (47), (48), (49), (58) are inconsistent by
% 159.84/26.15  | | | | | | | |            sub-proof #801.
% 159.84/26.15  | | | | | | | | 
% 159.84/26.15  | | | | | | | Case 2:
% 159.84/26.15  | | | | | | | | 
% 159.84/26.15  | | | | | | | |   (59)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 159.84/26.15  | | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.84/26.15  | | | | | | | |           all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.84/26.15  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 159.84/26.15  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.84/26.15  | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 159.84/26.15  | | | | | | | |             e2) = e3 & $i(all_57_10))
% 159.84/26.15  | | | | | | | | 
% 159.84/26.15  | | | | | | | | REF_CLOSE: (5), (9), (21), (29), (48), (59) are inconsistent by
% 159.84/26.15  | | | | | | | |            sub-proof #751.
% 159.84/26.15  | | | | | | | | 
% 159.84/26.15  | | | | | | | End of split
% 159.84/26.15  | | | | | | | 
% 159.84/26.15  | | | | | | Case 2:
% 159.84/26.15  | | | | | | | 
% 159.84/26.15  | | | | | | |   (60)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.84/26.15  | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.84/26.15  | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.84/26.15  | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.84/26.15  | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.84/26.15  | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 159.84/26.15  | | | | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_12
% 159.84/26.15  | | | | | | |           = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2)
% 159.84/26.15  | | | | | | |         | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 159.84/26.15  | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 159.84/26.15  | | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.84/26.15  | | | | | | |         | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~
% 159.84/26.15  | | | | | | |           (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.84/26.15  | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.84/26.15  | | | | | | |           $i(all_57_12))
% 159.84/26.15  | | | | | | | 
% 159.84/26.15  | | | | | | | BETA: splitting (60) gives:
% 159.84/26.15  | | | | | | | 
% 159.84/26.15  | | | | | | | Case 1:
% 159.84/26.15  | | | | | | | | 
% 159.84/26.15  | | | | | | | |   (61)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.84/26.15  | | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.84/26.15  | | | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.84/26.15  | | | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 159.84/26.15  | | | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.84/26.15  | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 159.84/26.15  | | | | | | | |             e2) = e3 & $i(all_57_10))
% 159.84/26.15  | | | | | | | | 
% 159.84/26.15  | | | | | | | | BETA: splitting (61) gives:
% 159.84/26.15  | | | | | | | | 
% 159.84/26.15  | | | | | | | | Case 1:
% 159.84/26.15  | | | | | | | | | 
% 159.84/26.15  | | | | | | | | |   (62)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.84/26.15  | | | | | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 159.84/26.15  | | | | | | | | |         all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.84/26.15  | | | | | | | | |         $i(all_57_12)
% 159.84/26.15  | | | | | | | | | 
% 159.84/26.15  | | | | | | | | | ALPHA: (62) implies:
% 159.84/26.15  | | | | | | | | |   (63)  op(e0, e0) = e2
% 159.84/26.15  | | | | | | | | | 
% 159.84/26.15  | | | | | | | | | REF_CLOSE: (9), (18), (25), (26), (51), (54), (63) are
% 159.84/26.15  | | | | | | | | |            inconsistent by sub-proof #798.
% 159.84/26.15  | | | | | | | | | 
% 159.84/26.15  | | | | | | | | Case 2:
% 159.84/26.15  | | | | | | | | | 
% 159.84/26.15  | | | | | | | | |   (64)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 159.84/26.15  | | | | | | | | |         (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0)
% 159.84/26.15  | | | | | | | | |         = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 159.84/26.15  | | | | | | | | |         $i(all_57_10)
% 159.84/26.15  | | | | | | | | | 
% 159.84/26.15  | | | | | | | | | ALPHA: (64) implies:
% 159.84/26.15  | | | | | | | | |   (65)  op(e3, e0) = e3
% 159.84/26.15  | | | | | | | | | 
% 159.84/26.15  | | | | | | | | | REF_CLOSE: (9), (34), (46), (65) are inconsistent by sub-proof
% 159.91/26.15  | | | | | | | | |            #976.
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | End of split
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | Case 2:
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | |   (66)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2,
% 159.91/26.15  | | | | | | | |             e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 &
% 159.91/26.15  | | | | | | | |           all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.91/26.15  | | | | | | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3)
% 159.91/26.15  | | | | | | | |           = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 =
% 159.91/26.15  | | | | | | | |           e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 =
% 159.91/26.15  | | | | | | | |             e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 159.91/26.15  | | | | | | | |           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | | BETA: splitting (66) gives:
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | | Case 1:
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | |   (67)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2,
% 159.91/26.15  | | | | | | | | |           e3) = e2 & op(e2, e2) = e2
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | | ALPHA: (67) implies:
% 159.91/26.15  | | | | | | | | |   (68)  op(e2, e2) = e2
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | | REF_CLOSE: (9), (29), (32), (68) are inconsistent by sub-proof
% 159.91/26.15  | | | | | | | | |            #993.
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | Case 2:
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | |   (69)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 159.91/26.15  | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 159.91/26.15  | | | | | | | | |             e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.91/26.15  | | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 159.91/26.15  | | | | | | | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) =
% 159.91/26.15  | | | | | | | | |           e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 159.91/26.15  | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_12))
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | | REF_CLOSE: (9), (27), (31), (37), (44), (69) are inconsistent
% 159.91/26.15  | | | | | | | | |            by sub-proof #750.
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | End of split
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | End of split
% 159.91/26.15  | | | | | | | 
% 159.91/26.15  | | | | | | End of split
% 159.91/26.15  | | | | | | 
% 159.91/26.15  | | | | | Case 2:
% 159.91/26.15  | | | | | | 
% 159.91/26.15  | | | | | |   (70)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.91/26.15  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 159.91/26.15  | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.91/26.15  | | | | | |         (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3)
% 159.91/26.15  | | | | | |           = e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2
% 159.91/26.15  | | | | | |           & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 &
% 159.91/26.15  | | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 159.91/26.15  | | | | | |           & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.91/26.15  | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 159.91/26.15  | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 159.91/26.15  | | | | | |           & $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.91/26.15  | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.91/26.15  | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.91/26.15  | | | | | |           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 159.91/26.15  | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 &
% 159.91/26.15  | | | | | |           op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 159.91/26.15  | | | | | |           & $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 159.91/26.15  | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 159.91/26.15  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1
% 159.91/26.15  | | | | | |           & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.91/26.15  | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.91/26.15  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.91/26.15  | | | | | |           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 & 
% 159.91/26.15  | | | | | |           ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.91/26.15  | | | | | | 
% 159.91/26.15  | | | | | | BETA: splitting (70) gives:
% 159.91/26.15  | | | | | | 
% 159.91/26.15  | | | | | | Case 1:
% 159.91/26.15  | | | | | | | 
% 159.91/26.15  | | | | | | |   (71)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.91/26.15  | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 159.91/26.15  | | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 159.91/26.15  | | | | | | |         | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3,
% 159.91/26.15  | | | | | | |             e3) = e3 & op(e3, e2) = e3) | (all_57_1 = e3 &
% 159.91/26.15  | | | | | | |           all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 159.91/26.15  | | | | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 159.91/26.15  | | | | | | |           all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2
% 159.91/26.15  | | | | | | |           = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 159.91/26.15  | | | | | | |             e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) =
% 159.91/26.15  | | | | | | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.91/26.15  | | | | | | | 
% 159.91/26.15  | | | | | | | BETA: splitting (71) gives:
% 159.91/26.15  | | | | | | | 
% 159.91/26.15  | | | | | | | Case 1:
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | |   (72)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.91/26.15  | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2)
% 159.91/26.15  | | | | | | | |           = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.91/26.15  | | | | | | | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~
% 159.91/26.15  | | | | | | | |           (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | | REF_CLOSE: (9), (27), (44), (72) are inconsistent by sub-proof
% 159.91/26.15  | | | | | | | |            #792.
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | Case 2:
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | |   (73)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 159.91/26.15  | | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 159.91/26.15  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 159.91/26.15  | | | | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 159.91/26.15  | | | | | | | |           all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1
% 159.91/26.15  | | | | | | | |           & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 159.91/26.15  | | | | | | | |           all_57_14 & $i(all_57_14))
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | | REF_CLOSE: (9), (47), (48), (49), (73) are inconsistent by
% 159.91/26.15  | | | | | | | |            sub-proof #922.
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | End of split
% 159.91/26.15  | | | | | | | 
% 159.91/26.15  | | | | | | Case 2:
% 159.91/26.15  | | | | | | | 
% 159.91/26.15  | | | | | | |   (74)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 159.91/26.15  | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 159.91/26.15  | | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10))
% 159.91/26.15  | | | | | | |         | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.91/26.15  | | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.91/26.15  | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.91/26.15  | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 &
% 159.91/26.15  | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 159.91/26.15  | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) =
% 159.91/26.15  | | | | | | |           e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.91/26.15  | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.91/26.15  | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 159.91/26.15  | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14
% 159.91/26.15  | | | | | | |           = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.91/26.15  | | | | | | | 
% 159.91/26.15  | | | | | | | BETA: splitting (74) gives:
% 159.91/26.15  | | | | | | | 
% 159.91/26.15  | | | | | | | Case 1:
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | |   (75)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 159.91/26.15  | | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 159.91/26.15  | | | | | | | |           = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.91/26.15  | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 159.91/26.15  | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1
% 159.91/26.15  | | | | | | | |           & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 159.91/26.15  | | | | | | | |           all_57_14 & $i(all_57_14))
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | | BETA: splitting (75) gives:
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | | Case 1:
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | |   (76)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 159.91/26.15  | | | | | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 159.91/26.15  | | | | | | | | |         = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.91/26.15  | | | | | | | | |         $i(all_57_10)
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | | ALPHA: (76) implies:
% 159.91/26.15  | | | | | | | | |   (77)  op(e3, e1) = e3
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | | REF_CLOSE: (9), (11), (45), (77) are inconsistent by sub-proof
% 159.91/26.15  | | | | | | | | |            #982.
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | Case 2:
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | |   (78)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.91/26.15  | | | | | | | | |         (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.91/26.15  | | | | | | | | |         op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 159.91/26.15  | | | | | | | | |         $i(all_57_14)
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | | ALPHA: (78) implies:
% 159.91/26.15  | | | | | | | | |   (79)  op(e2, e1) = e2
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | | REF_CLOSE: (9), (31), (37), (79) are inconsistent by sub-proof
% 159.91/26.15  | | | | | | | | |            #1002.
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.15  | | | | | | | | End of split
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | Case 2:
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | |   (80)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.91/26.15  | | | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 159.91/26.15  | | | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.91/26.15  | | | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 159.91/26.15  | | | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.91/26.15  | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 159.91/26.15  | | | | | | | |             e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 159.91/26.15  | | | | | | | |           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.91/26.15  | | | | | | | |           op(e1, e1) = e1)
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | | BETA: splitting (80) gives:
% 159.91/26.15  | | | | | | | | 
% 159.91/26.15  | | | | | | | | Case 1:
% 159.91/26.15  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | |   (81)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.91/26.16  | | | | | | | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 159.91/26.16  | | | | | | | | |         all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.91/26.16  | | | | | | | | |         $i(all_57_14)
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | ALPHA: (81) implies:
% 159.91/26.16  | | | | | | | | |   (82)  all_57_2 = e1
% 159.91/26.16  | | | | | | | | |   (83)   ~ (all_57_14 = e3)
% 159.91/26.16  | | | | | | | | |   (84)  op(e0, e0) = e1
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | BETA: splitting (7) gives:
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | Case 1:
% 159.91/26.16  | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | |   (85)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3
% 159.91/26.16  | | | | | | | | | |               & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 159.91/26.16  | | | | | | | | | |               op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.91/26.16  | | | | | | | | | |           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.91/26.16  | | | | | | | | | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 159.91/26.16  | | | | | | | | | |               $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 159.91/26.16  | | | | | | | | | |               = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 159.91/26.16  | | | | | | | | | |               all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 &
% 159.91/26.16  | | | | | | | | | |           op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 159.91/26.16  | | | | | | | | | |               e2) | ( ~ (all_57_1 = e3) & op(e3, e2) =
% 159.91/26.16  | | | | | | | | | |               all_57_1 & $i(all_57_1))) & ((all_57_14 = e2 &
% 159.91/26.16  | | | | | | | | | |               op(e1, e1) = e2) | ( ~ (all_57_3 = e1) &
% 159.91/26.16  | | | | | | | | | |               op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 159.91/26.16  | | | | | | | | | |           ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~
% 159.91/26.16  | | | | | | | | | |               (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 159.91/26.16  | | | | | | | | | |               $i(all_57_7))))
% 159.91/26.16  | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | BETA: splitting (85) gives:
% 159.91/26.16  | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | Case 1:
% 159.91/26.16  | | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | |   (86)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 =
% 159.91/26.16  | | | | | | | | | | |             e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) &
% 159.91/26.16  | | | | | | | | | | |             op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.91/26.16  | | | | | | | | | | |         ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.91/26.16  | | | | | | | | | | |             (all_57_2 = e1) & op(e1, e3) = all_57_2 &
% 159.91/26.16  | | | | | | | | | | |             $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0)
% 159.91/26.16  | | | | | | | | | | |             = e3) | ( ~ (all_57_6 = e0) & op(e0, e3) =
% 159.91/26.16  | | | | | | | | | | |             all_57_6 & $i(all_57_6)))
% 159.91/26.16  | | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | | ALPHA: (86) implies:
% 159.91/26.16  | | | | | | | | | | |   (87)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2
% 159.91/26.16  | | | | | | | | | | |             = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))
% 159.91/26.16  | | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | | REF_CLOSE: (82), (83), (87) are inconsistent by sub-proof
% 159.91/26.16  | | | | | | | | | | |            #749.
% 159.91/26.16  | | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | Case 2:
% 159.91/26.16  | | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | |   (88)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 =
% 159.91/26.16  | | | | | | | | | | |             e2 & op(e3, e3) = e2) | ( ~ (all_57_1 = e3) &
% 159.91/26.16  | | | | | | | | | | |             op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.91/26.16  | | | | | | | | | | |         ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 159.91/26.16  | | | | | | | | | | |             (all_57_3 = e1) & op(e1, e2) = all_57_3 &
% 159.91/26.16  | | | | | | | | | | |             $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0)
% 159.91/26.16  | | | | | | | | | | |             = e2) | ( ~ (all_57_7 = e0) & op(e0, e2) =
% 159.91/26.16  | | | | | | | | | | |             all_57_7 & $i(all_57_7)))
% 159.91/26.16  | | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | | ALPHA: (88) implies:
% 159.91/26.16  | | | | | | | | | | |   (89)  op(e2, e2) = e2
% 159.91/26.16  | | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (89) are inconsistent by
% 159.91/26.16  | | | | | | | | | | |            sub-proof #993.
% 159.91/26.16  | | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | End of split
% 159.91/26.16  | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | Case 2:
% 159.91/26.16  | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | |   (90)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1
% 159.91/26.16  | | | | | | | | | |               & op(e3, e3) = e1) | ( ~ (all_57_4 = e3) &
% 159.91/26.16  | | | | | | | | | |               op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.91/26.16  | | | | | | | | | |           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.91/26.16  | | | | | | | | | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 &
% 159.91/26.16  | | | | | | | | | |               $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0)
% 159.91/26.16  | | | | | | | | | |               = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 159.91/26.16  | | | | | | | | | |               all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 &
% 159.91/26.16  | | | | | | | | | |           op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 159.91/26.16  | | | | | | | | | |               e0) | ( ~ (all_57_9 = e3) & op(e3, e0) =
% 159.91/26.16  | | | | | | | | | |               all_57_9 & $i(all_57_9))) & ((all_57_12 = e0 &
% 159.91/26.16  | | | | | | | | | |               op(e2, e2) = e0) | ( ~ (all_57_11 = e2) &
% 159.91/26.16  | | | | | | | | | |               op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 159.91/26.16  | | | | | | | | | |           ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~
% 159.91/26.16  | | | | | | | | | |               (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.91/26.16  | | | | | | | | | |               $i(all_57_13))))
% 159.91/26.16  | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | | REF_CLOSE: (9), (14), (25), (30), (32), (84), (90) are
% 159.91/26.16  | | | | | | | | | |            inconsistent by sub-proof #748.
% 159.91/26.16  | | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | End of split
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | Case 2:
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | |   (91)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~
% 159.91/26.16  | | | | | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 159.91/26.16  | | | | | | | | |             e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 159.91/26.16  | | | | | | | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 & 
% 159.91/26.16  | | | | | | | | |           ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | REF_CLOSE: (9), (14), (32), (34), (46), (91) are inconsistent
% 159.91/26.16  | | | | | | | | |            by sub-proof #747.
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | End of split
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | End of split
% 159.91/26.16  | | | | | | | 
% 159.91/26.16  | | | | | | End of split
% 159.91/26.16  | | | | | | 
% 159.91/26.16  | | | | | End of split
% 159.91/26.16  | | | | | 
% 159.91/26.16  | | | | Case 2:
% 159.91/26.16  | | | | | 
% 159.91/26.16  | | | | |   (92)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.91/26.16  | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.91/26.16  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.91/26.16  | | | | |         (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.91/26.16  | | | | |           (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.91/26.16  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 159.91/26.16  | | | | |         (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.91/26.16  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 159.91/26.16  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.91/26.16  | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.91/26.16  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 159.91/26.16  | | | | |           & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 159.91/26.16  | | | | |         (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.91/26.16  | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 159.91/26.16  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.91/26.16  | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) =
% 159.91/26.16  | | | | |           e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 159.91/26.16  | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 159.91/26.16  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.91/26.16  | | | | |           e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~
% 159.91/26.16  | | | | |           (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 159.91/26.16  | | | | |           e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.91/26.16  | | | | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 159.91/26.16  | | | | |           op(e1, e0) = e1 & $i(all_57_14)) | (all_57_5 = e2 & all_57_7
% 159.91/26.16  | | | | |           = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) =
% 159.91/26.16  | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.91/26.16  | | | | |           e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~
% 159.91/26.16  | | | | |           (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 =
% 159.91/26.16  | | | | |           e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.91/26.16  | | | | |           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 &
% 159.91/26.16  | | | | |           op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9
% 159.91/26.16  | | | | |           = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.91/26.16  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 159.91/26.16  | | | | |           e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.91/26.16  | | | | |           all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 159.91/26.16  | | | | |           all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) =
% 159.91/26.16  | | | | |           e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~
% 159.91/26.16  | | | | |           (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11
% 159.91/26.16  | | | | |           = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 &
% 159.91/26.16  | | | | |           op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1
% 159.91/26.16  | | | | |             = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.91/26.16  | | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3
% 159.91/26.16  | | | | |               & all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0
% 159.91/26.16  | | | | |               & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.91/26.16  | | | | |               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.91/26.16  | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.91/26.16  | | | | |             (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.91/26.16  | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.91/26.16  | | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.91/26.16  | | | | |               (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9
% 159.91/26.16  | | | | |               = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3)
% 159.91/26.16  | | | | |               = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 159.91/26.16  | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.16  | | | | |                 e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.91/26.16  | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 159.91/26.16  | | | | |                ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1
% 159.91/26.16  | | | | |               & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 & 
% 159.91/26.16  | | | | |               ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.91/26.16  | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.91/26.16  | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.91/26.16  | | | | |             (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.91/26.16  | | | | |               (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.91/26.16  | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.91/26.16  | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.91/26.16  | | | | |               op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.91/26.16  | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.91/26.16  | | | | |               op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.91/26.16  | | | | |               e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 159.91/26.16  | | | | |               ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.91/26.16  | | | | | 
% 159.91/26.16  | | | | | BETA: splitting (92) gives:
% 159.91/26.16  | | | | | 
% 159.91/26.16  | | | | | Case 1:
% 159.91/26.16  | | | | | | 
% 159.91/26.16  | | | | | |   (93)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.91/26.16  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.91/26.16  | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.91/26.16  | | | | | |         | (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.91/26.16  | | | | | |           (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.91/26.16  | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.91/26.16  | | | | | |         | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.91/26.16  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 159.91/26.16  | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 159.91/26.16  | | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.91/26.16  | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.91/26.16  | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.91/26.16  | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 &
% 159.91/26.16  | | | | | |           all_57_14 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) =
% 159.91/26.16  | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 159.91/26.16  | | | | | |           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 & 
% 159.91/26.16  | | | | | |           ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 159.91/26.16  | | | | | |         (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.91/26.16  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 159.91/26.16  | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 159.91/26.16  | | | | | |         (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 159.91/26.16  | | | | | |           = e3 & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 159.91/26.16  | | | | | |           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 &
% 159.91/26.16  | | | | | |           op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 159.91/26.16  | | | | | |           & $i(all_57_14))
% 159.91/26.16  | | | | | | 
% 159.91/26.16  | | | | | | BETA: splitting (93) gives:
% 159.91/26.16  | | | | | | 
% 159.91/26.16  | | | | | | Case 1:
% 159.91/26.16  | | | | | | | 
% 159.91/26.16  | | | | | | |   (94)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.91/26.16  | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.91/26.16  | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.91/26.16  | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.91/26.16  | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 &
% 159.91/26.16  | | | | | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.91/26.16  | | | | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 =
% 159.91/26.16  | | | | | | |           e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) =
% 159.91/26.16  | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 159.91/26.16  | | | | | | |             e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8
% 159.91/26.16  | | | | | | |           = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2)
% 159.91/26.16  | | | | | | |           = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 159.91/26.16  | | | | | | |             e0) = e1 & $i(all_57_14))
% 159.91/26.16  | | | | | | | 
% 159.91/26.16  | | | | | | | BETA: splitting (94) gives:
% 159.91/26.16  | | | | | | | 
% 159.91/26.16  | | | | | | | Case 1:
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | |   (95)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.91/26.16  | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.91/26.16  | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.91/26.16  | | | | | | | |           $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 159.91/26.16  | | | | | | | |           all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 159.91/26.16  | | | | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.91/26.16  | | | | | | | |           all_57_14 & $i(all_57_14))
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | | BETA: splitting (95) gives:
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | | Case 1:
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | |   (96)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 159.91/26.16  | | | | | | | | |         (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.91/26.16  | | | | | | | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.91/26.16  | | | | | | | | |         $i(all_57_14)
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | ALPHA: (96) implies:
% 159.91/26.16  | | | | | | | | |   (97)  op(e3, e3) = e1
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | REF_CLOSE: (9), (48), (49), (97) are inconsistent by sub-proof
% 159.91/26.16  | | | | | | | | |            #995.
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | Case 2:
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | |   (98)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 159.91/26.16  | | | | | | | | |         (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.91/26.16  | | | | | | | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 159.91/26.16  | | | | | | | | |         $i(all_57_14)
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | ALPHA: (98) implies:
% 159.91/26.16  | | | | | | | | |   (99)  op(e2, e1) = e2
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | REF_CLOSE: (9), (31), (37), (99) are inconsistent by sub-proof
% 159.91/26.16  | | | | | | | | |            #1002.
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | End of split
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | Case 2:
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | |   (100)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.91/26.16  | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 159.91/26.16  | | | | | | | |              e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.91/26.16  | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 &
% 159.91/26.16  | | | | | | | |            all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) =
% 159.91/26.16  | | | | | | | |            e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 159.91/26.16  | | | | | | | |            op(e0, e0) = e1 & $i(all_57_14))
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | | BETA: splitting (100) gives:
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | | Case 1:
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | |   (101)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 159.91/26.16  | | | | | | | | |          (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 159.91/26.16  | | | | | | | | |            e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.91/26.16  | | | | | | | | |          $i(all_57_12)
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | ALPHA: (101) implies:
% 159.91/26.16  | | | | | | | | |   (102)  op(e2, e1) = e2
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | REF_CLOSE: (9), (31), (37), (102) are inconsistent by
% 159.91/26.16  | | | | | | | | |            sub-proof #1002.
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | Case 2:
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | |   (103)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 159.91/26.16  | | | | | | | | |          (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 159.91/26.16  | | | | | | | | |          all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 159.91/26.16  | | | | | | | | |          $i(all_57_14)
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | ALPHA: (103) implies:
% 159.91/26.16  | | | | | | | | |   (104)  op(e1, e2) = e1
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | REF_CLOSE: (5), (9), (21), (104) are inconsistent by sub-proof
% 159.91/26.16  | | | | | | | | |            #984.
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | End of split
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | End of split
% 159.91/26.16  | | | | | | | 
% 159.91/26.16  | | | | | | Case 2:
% 159.91/26.16  | | | | | | | 
% 159.91/26.16  | | | | | | |   (105)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.91/26.16  | | | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.91/26.16  | | | | | | |            = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.91/26.16  | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~
% 159.91/26.16  | | | | | | |            (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 159.91/26.16  | | | | | | |          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.91/26.16  | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 159.91/26.16  | | | | | | |            = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.91/26.16  | | | | | | |            $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~
% 159.91/26.16  | | | | | | |            (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) |
% 159.91/26.16  | | | | | | |          (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 159.91/26.16  | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 159.91/26.16  | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.91/26.16  | | | | | | |            $i(all_57_14))
% 159.91/26.16  | | | | | | | 
% 159.91/26.16  | | | | | | | BETA: splitting (105) gives:
% 159.91/26.16  | | | | | | | 
% 159.91/26.16  | | | | | | | Case 1:
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | |   (106)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.91/26.16  | | | | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 159.91/26.16  | | | | | | | |              e0) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.91/26.16  | | | | | | | |            $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~
% 159.91/26.16  | | | | | | | |            (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1)
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | | BETA: splitting (106) gives:
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | | Case 1:
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | |   (107)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 159.91/26.16  | | | | | | | | |          (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 159.91/26.16  | | | | | | | | |            e0) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 159.91/26.16  | | | | | | | | |          $i(all_57_12)
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | ALPHA: (107) implies:
% 159.91/26.16  | | | | | | | | |   (108)  op(e1, e2) = e1
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | REF_CLOSE: (5), (9), (21), (108) are inconsistent by sub-proof
% 159.91/26.16  | | | | | | | | |            #984.
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | Case 2:
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | |   (109)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) &
% 159.91/26.16  | | | | | | | | |          op(e1, e2) = e1 & op(e1, e1) = e1
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | ALPHA: (109) implies:
% 159.91/26.16  | | | | | | | | |   (110)  op(e1, e1) = e1
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | | REF_CLOSE: (9), (14), (32), (110) are inconsistent by
% 159.91/26.16  | | | | | | | | |            sub-proof #986.
% 159.91/26.16  | | | | | | | | | 
% 159.91/26.16  | | | | | | | | End of split
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | Case 2:
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | |   (111)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 159.91/26.16  | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 159.91/26.16  | | | | | | | |              e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 159.91/26.16  | | | | | | | |            $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~
% 159.91/26.16  | | | | | | | |            (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) |
% 159.91/26.16  | | | | | | | |          (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 159.91/26.16  | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3
% 159.91/26.16  | | | | | | | |            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.91/26.16  | | | | | | | |            $i(all_57_14))
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | | REF_CLOSE: (9), (11), (45), (48), (49), (111) are inconsistent
% 159.91/26.16  | | | | | | | |            by sub-proof #787.
% 159.91/26.16  | | | | | | | | 
% 159.91/26.16  | | | | | | | End of split
% 159.91/26.16  | | | | | | | 
% 159.91/26.16  | | | | | | End of split
% 159.91/26.16  | | | | | | 
% 159.91/26.16  | | | | | Case 2:
% 159.91/26.16  | | | | | | 
% 159.91/26.17  | | | | | |   (112)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.91/26.17  | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 159.91/26.17  | | | | | |            e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 159.91/26.17  | | | | | |          (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2)
% 159.91/26.17  | | | | | |            = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 159.91/26.17  | | | | | |            & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1
% 159.91/26.17  | | | | | |            & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 159.91/26.17  | | | | | |            e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.91/26.17  | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.91/26.17  | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 159.91/26.17  | | | | | |              e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11
% 159.91/26.17  | | | | | |            = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2, e2)
% 159.91/26.17  | | | | | |            = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 159.91/26.17  | | | | | |              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 159.91/26.17  | | | | | |            = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3)
% 159.91/26.17  | | | | | |          | (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 159.91/26.17  | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 159.91/26.17  | | | | | |            all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1,
% 159.91/26.17  | | | | | |              e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 159.91/26.17  | | | | | |            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.91/26.17  | | | | | |                (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3
% 159.91/26.17  | | | | | |                & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2
% 159.91/26.17  | | | | | |                & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 159.91/26.17  | | | | | |                e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 159.91/26.17  | | | | | |                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.91/26.17  | | | | | |                  = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.91/26.17  | | | | | |                  e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.91/26.17  | | | | | |                (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.91/26.17  | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 159.91/26.17  | | | | | |                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 159.91/26.17  | | | | | |                e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.91/26.17  | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 159.91/26.17  | | | | | |                  e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.91/26.17  | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 159.91/26.17  | | | | | |                & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.91/26.17  | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 159.91/26.17  | | | | | |                & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 159.91/26.17  | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) =
% 159.91/26.17  | | | | | |                e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.91/26.17  | | | | | |                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.91/26.17  | | | | | |                  = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.91/26.17  | | | | | |                  e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 159.91/26.17  | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 159.91/26.17  | | | | | |                e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 159.91/26.17  | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 159.91/26.17  | | | | | |                  = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.91/26.17  | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.91/26.17  | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.91/26.17  | | | | | | 
% 159.91/26.17  | | | | | | BETA: splitting (112) gives:
% 159.91/26.17  | | | | | | 
% 159.91/26.17  | | | | | | Case 1:
% 159.91/26.17  | | | | | | | 
% 159.91/26.17  | | | | | | |   (113)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.91/26.17  | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1)
% 159.91/26.17  | | | | | | |            = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.91/26.17  | | | | | | |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~
% 159.91/26.17  | | | | | | |            (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 159.91/26.17  | | | | | | |          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 159.91/26.17  | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 159.91/26.17  | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.91/26.17  | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.91/26.17  | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.91/26.17  | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 159.91/26.17  | | | | | | |              e0) = e3 & $i(all_57_10))
% 159.91/26.17  | | | | | | | 
% 159.91/26.17  | | | | | | | BETA: splitting (113) gives:
% 159.91/26.17  | | | | | | | 
% 159.91/26.17  | | | | | | | Case 1:
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | |   (114)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.91/26.17  | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 159.91/26.17  | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.91/26.17  | | | | | | | |            $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~
% 159.91/26.17  | | | | | | | |            (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | | BETA: splitting (114) gives:
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | | Case 1:
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | |   (115)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 159.91/26.17  | | | | | | | | |          (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 159.91/26.17  | | | | | | | | |            e1) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.91/26.17  | | | | | | | | |          $i(all_57_12)
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | ALPHA: (115) implies:
% 159.91/26.17  | | | | | | | | |   (116)  op(e2, e1) = e2
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | REF_CLOSE: (9), (31), (37), (116) are inconsistent by
% 159.91/26.17  | | | | | | | | |            sub-proof #1002.
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | Case 2:
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | |   (117)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) &
% 159.91/26.17  | | | | | | | | |          op(e2, e2) = e2 & op(e2, e1) = e2
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | ALPHA: (117) implies:
% 159.91/26.17  | | | | | | | | |   (118)  op(e2, e2) = e2
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | REF_CLOSE: (9), (29), (32), (118) are inconsistent by
% 159.91/26.17  | | | | | | | | |            sub-proof #993.
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | End of split
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | Case 2:
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | |   (119)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 159.91/26.17  | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2
% 159.91/26.17  | | | | | | | |            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.91/26.17  | | | | | | | |            $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 159.91/26.17  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 159.91/26.17  | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 &
% 159.91/26.17  | | | | | | | |            op(e0, e0) = e3 & $i(all_57_10))
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | | REF_CLOSE: (9), (31), (34), (37), (46), (119) are inconsistent
% 159.91/26.17  | | | | | | | |            by sub-proof #746.
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | End of split
% 159.91/26.17  | | | | | | | 
% 159.91/26.17  | | | | | | Case 2:
% 159.91/26.17  | | | | | | | 
% 159.91/26.17  | | | | | | |   (120)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 159.91/26.17  | | | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0)
% 159.91/26.17  | | | | | | |            = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.91/26.17  | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~
% 159.91/26.17  | | | | | | |            (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) |
% 159.91/26.17  | | | | | | |          (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 159.91/26.17  | | | | | | |              e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1 &
% 159.91/26.17  | | | | | | |            all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.91/26.17  | | | | | | |            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 159.91/26.17  | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 159.91/26.17  | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) =
% 159.91/26.17  | | | | | | |                e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 159.91/26.17  | | | | | | |                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.91/26.17  | | | | | | |                (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) =
% 159.91/26.17  | | | | | | |                e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13
% 159.91/26.17  | | | | | | |                = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.91/26.17  | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.91/26.17  | | | | | | |                e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.91/26.17  | | | | | | |                  e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.91/26.17  | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.91/26.17  | | | | | | |                  e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.91/26.17  | | | | | | |                  e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.91/26.17  | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) =
% 159.91/26.17  | | | | | | |                e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7
% 159.91/26.17  | | | | | | |                = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.91/26.17  | | | | | | |                (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) =
% 159.91/26.17  | | | | | | |                e1 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15
% 159.91/26.17  | | | | | | |                = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 159.91/26.17  | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.91/26.17  | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) =
% 159.91/26.17  | | | | | | |                e3 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11
% 159.91/26.17  | | | | | | |                = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.91/26.17  | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) =
% 159.91/26.17  | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.91/26.17  | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 159.91/26.17  | | | | | | |                  e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.91/26.17  | | | | | | |                all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.91/26.17  | | | | | | |                  e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 159.91/26.17  | | | | | | |                op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.91/26.17  | | | | | | |                all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.91/26.17  | | | | | | | 
% 159.91/26.17  | | | | | | | BETA: splitting (120) gives:
% 159.91/26.17  | | | | | | | 
% 159.91/26.17  | | | | | | | Case 1:
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | |   (121)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 159.91/26.17  | | | | | | | |            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 159.91/26.17  | | | | | | | |              e0) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.91/26.17  | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~
% 159.91/26.17  | | | | | | | |            (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3)
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | | BETA: splitting (121) gives:
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | | Case 1:
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | |   (122)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 159.91/26.17  | | | | | | | | |          (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2,
% 159.91/26.17  | | | | | | | | |            e0) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 159.91/26.17  | | | | | | | | |          $i(all_57_12)
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | ALPHA: (122) implies:
% 159.91/26.17  | | | | | | | | |   (123)  op(e0, e0) = e2
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | REF_CLOSE: (9), (18), (25), (26), (51), (54), (123) are
% 159.91/26.17  | | | | | | | | |            inconsistent by sub-proof #798.
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | Case 2:
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | |   (124)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) &
% 159.91/26.17  | | | | | | | | |          op(e3, e3) = e3 & op(e3, e0) = e3
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | ALPHA: (124) implies:
% 159.91/26.17  | | | | | | | | |   (125)  op(e3, e0) = e3
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | REF_CLOSE: (9), (34), (46), (125) are inconsistent by
% 159.91/26.17  | | | | | | | | |            sub-proof #976.
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | End of split
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | Case 2:
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | |   (126)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.91/26.17  | | | | | | | |            op(e2, e2) = e2 & op(e2, e0) = e2) | (all_57_13 = e1
% 159.91/26.17  | | | | | | | |            & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 159.91/26.17  | | | | | | | |            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 159.91/26.17  | | | | | | | |            $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 159.91/26.17  | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3)
% 159.91/26.17  | | | | | | | |                = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.91/26.17  | | | | | | | |              (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 159.91/26.17  | | | | | | | |                ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0)
% 159.91/26.17  | | | | | | | |                = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.91/26.17  | | | | | | | |                all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.91/26.17  | | | | | | | |                  e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.91/26.17  | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 =
% 159.91/26.17  | | | | | | | |                e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 159.91/26.17  | | | | | | | |                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.91/26.17  | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 159.91/26.17  | | | | | | | |                e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.91/26.17  | | | | | | | |                all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.17  | | | | | | | |                  e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.91/26.17  | | | | | | | |                op(e0, e2) = e0) | (all_57_7 = e0 & all_57_13 =
% 159.91/26.17  | | | | | | | |                e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.91/26.17  | | | | | | | |                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.91/26.17  | | | | | | | |                e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 =
% 159.91/26.17  | | | | | | | |                  e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.91/26.17  | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.91/26.17  | | | | | | | |                  e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.91/26.17  | | | | | | | |                op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 =
% 159.91/26.17  | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.91/26.17  | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) =
% 159.91/26.17  | | | | | | | |                e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14
% 159.91/26.17  | | | | | | | |                = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.91/26.17  | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 159.91/26.17  | | | | | | | |                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 159.91/26.17  | | | | | | | |                (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.91/26.17  | | | | | | | |                op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.91/26.17  | | | | | | | |                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 159.91/26.17  | | | | | | | |                &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | | BETA: splitting (126) gives:
% 159.91/26.17  | | | | | | | | 
% 159.91/26.17  | | | | | | | | Case 1:
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | |   (127)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) &
% 159.91/26.17  | | | | | | | | |          op(e2, e2) = e2 & op(e2, e0) = e2
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | ALPHA: (127) implies:
% 159.91/26.17  | | | | | | | | |   (128)  op(e2, e2) = e2
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | REF_CLOSE: (9), (29), (32), (128) are inconsistent by
% 159.91/26.17  | | | | | | | | |            sub-proof #993.
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | Case 2:
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | |   (129)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.91/26.17  | | | | | | | | |            op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 159.91/26.17  | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 159.91/26.17  | | | | | | | | |                all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.91/26.17  | | | | | | | | |                  = e3) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.91/26.17  | | | | | | | | |                op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 =
% 159.91/26.17  | | | | | | | | |                e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.91/26.17  | | | | | | | | |                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3)
% 159.91/26.17  | | | | | | | | |                = e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 159.91/26.17  | | | | | | | | |                all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1,
% 159.91/26.17  | | | | | | | | |                  e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.91/26.17  | | | | | | | | |              | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 159.91/26.17  | | | | | | | | |                & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9
% 159.91/26.17  | | | | | | | | |                = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.91/26.17  | | | | | | | | |                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2)
% 159.91/26.17  | | | | | | | | |                = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 159.91/26.17  | | | | | | | | |                all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2,
% 159.91/26.17  | | | | | | | | |                  e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.91/26.17  | | | | | | | | |              | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 159.91/26.17  | | | | | | | | |                e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 159.91/26.17  | | | | | | | | |                op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7
% 159.91/26.17  | | | | | | | | |                = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0,
% 159.91/26.17  | | | | | | | | |                  e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 159.91/26.17  | | | | | | | | |                all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3,
% 159.91/26.17  | | | | | | | | |                  e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.91/26.17  | | | | | | | | |              | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 159.91/26.17  | | | | | | | | |                e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 159.91/26.17  | | | | | | | | |                op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8
% 159.91/26.17  | | | | | | | | |                = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.91/26.17  | | | | | | | | |                (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 159.91/26.17  | | | | | | | | |                = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.91/26.17  | | | | | | | | |                all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 159.91/26.17  | | | | | | | | |                  = e0) & op(e1, e1) = all_57_14 & op(e1, e0) =
% 159.91/26.17  | | | | | | | | |                e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 159.91/26.17  | | | | | | | | |              (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 159.91/26.17  | | | | | | | | |                op(e0, e1) = e0)))
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | BETA: splitting (129) gives:
% 159.91/26.17  | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | Case 1:
% 159.91/26.17  | | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | |   (130)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) &
% 159.91/26.17  | | | | | | | | | |          op(e1, e1) = e1 & op(e1, e0) = e1
% 159.91/26.17  | | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | | ALPHA: (130) implies:
% 159.91/26.17  | | | | | | | | | |   (131)  op(e1, e1) = e1
% 159.91/26.17  | | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | | REF_CLOSE: (9), (14), (32), (131) are inconsistent by
% 159.91/26.17  | | | | | | | | | |            sub-proof #986.
% 159.91/26.17  | | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | Case 2:
% 159.91/26.17  | | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | |   (132)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6
% 159.91/26.17  | | | | | | | | | |              = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.91/26.17  | | | | | | | | | |              (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 159.91/26.17  | | | | | | | | | |              = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.91/26.17  | | | | | | | | | |              all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.91/26.17  | | | | | | | | | |                = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.91/26.17  | | | | | | | | | |              op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.91/26.17  | | | | | | | | | |              e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.91/26.17  | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3)
% 159.91/26.17  | | | | | | | | | |              = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.91/26.17  | | | | | | | | | |              (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.91/26.17  | | | | | | | | | |              all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.91/26.17  | | | | | | | | | |                = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.91/26.17  | | | | | | | | | |              op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.91/26.17  | | | | | | | | | |              e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.91/26.17  | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2)
% 159.91/26.17  | | | | | | | | | |              = e0) | (all_57_7 = e0 & all_57_13 = e1 &
% 159.91/26.17  | | | | | | | | | |              all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1,
% 159.91/26.17  | | | | | | | | | |                e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0)
% 159.91/26.17  | | | | | | | | | |            | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 159.91/26.17  | | | | | | | | | |              & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9
% 159.91/26.17  | | | | | | | | | |              = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 159.91/26.17  | | | | | | | | | |              op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1)
% 159.91/26.17  | | | | | | | | | |              = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 159.91/26.17  | | | | | | | | | |              all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2,
% 159.91/26.17  | | | | | | | | | |                e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 159.91/26.17  | | | | | | | | | |            | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 159.91/26.17  | | | | | | | | | |              e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 159.91/26.17  | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8
% 159.91/26.17  | | | | | | | | | |              = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 159.91/26.17  | | | | | | | | | |              (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.91/26.17  | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e0 &
% 159.91/26.17  | | | | | | | | | |              $i(all_57_14)) | (all_57_8 = e0 & all_57_15 =
% 159.91/26.17  | | | | | | | | | |              e0 &  ~ (e1 = e0) & op(e0, e1) = e0))
% 159.91/26.17  | | | | | | | | | | 
% 159.91/26.17  | | | | | | | | | | ALPHA: (132) implies:
% 159.91/26.18  | | | | | | | | | |   (133)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 159.91/26.18  | | | | | | | | | |            ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 159.91/26.18  | | | | | | | | | |            = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.91/26.18  | | | | | | | | | |            all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | | | | | | | | | |              e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 159.91/26.18  | | | | | | | | | |            op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.91/26.18  | | | | | | | | | |            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 159.91/26.18  | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 159.91/26.18  | | | | | | | | | |            e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 =
% 159.91/26.18  | | | | | | | | | |              e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 159.91/26.18  | | | | | | | | | |            all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | | | | | | | | | |              e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 159.91/26.18  | | | | | | | | | |            op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 =
% 159.91/26.18  | | | | | | | | | |            e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 159.91/26.18  | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 159.91/26.18  | | | | | | | | | |            e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14
% 159.91/26.18  | | | | | | | | | |            = e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 &
% 159.91/26.18  | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 159.91/26.18  | | | | | | | | | |            e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.91/26.18  | | | | | | | | | |            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10
% 159.91/26.18  | | | | | | | | | |            = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0 &
% 159.91/26.18  | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 159.91/26.18  | | | | | | | | | |            e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 159.91/26.18  | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 159.91/26.18  | | | | | | | | | |            e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.91/26.18  | | | | | | | | | |            all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | | | | | | | | | |              e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 159.91/26.18  | | | | | | | | | |            op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.91/26.18  | | | | | | | | | |            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 159.91/26.18  | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 159.91/26.18  | | | | | | | | | |              e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.91/26.18  | | | | | | | | | |            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.91/26.18  | | | | | | | | | | 
% 159.91/26.18  | | | | | | | | | | REF_CLOSE: (1), (6), (8), (9), (10), (14), (16), (18), (19),
% 159.91/26.18  | | | | | | | | | |            (26), (40), (49), (51), (54), (133) are
% 159.91/26.18  | | | | | | | | | |            inconsistent by sub-proof #742.
% 159.91/26.18  | | | | | | | | | | 
% 159.91/26.18  | | | | | | | | | End of split
% 159.91/26.18  | | | | | | | | | 
% 159.91/26.18  | | | | | | | | End of split
% 159.91/26.18  | | | | | | | | 
% 159.91/26.18  | | | | | | | End of split
% 159.91/26.18  | | | | | | | 
% 159.91/26.18  | | | | | | End of split
% 159.91/26.18  | | | | | | 
% 159.91/26.18  | | | | | End of split
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | End of split
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | End of split
% 159.91/26.18  | | | 
% 159.91/26.18  | | Case 2:
% 159.91/26.18  | | | 
% 159.91/26.18  | | |   (134)  all_28_2 = e2
% 159.91/26.18  | | | 
% 159.91/26.18  | | | COMBINE_EQS: (13), (134) imply:
% 159.91/26.18  | | |   (135)  all_14_2 = e2
% 159.91/26.18  | | | 
% 159.91/26.18  | | | SIMP: (135) implies:
% 159.91/26.18  | | |   (136)  all_14_2 = e2
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REDUCE: (6), (136) imply:
% 159.91/26.18  | | |   (137)   ~ (all_52_3 = e2)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REDUCE: (40), (136) imply:
% 159.91/26.18  | | |   (138)   ~ (e3 = e2)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REDUCE: (25), (136) imply:
% 159.91/26.18  | | |   (139)  op(e0, e0) = e2
% 159.91/26.18  | | | 
% 159.91/26.18  | | | BETA: splitting (3) gives:
% 159.91/26.18  | | | 
% 159.91/26.18  | | | Case 1:
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | |   (140)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3)
% 159.91/26.18  | | | |            = e2)
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | | BETA: splitting (140) gives:
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | | Case 1:
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | |   (141)  all_56_0 = e2 & op(e3, e3) = e2
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | | ALPHA: (141) implies:
% 159.91/26.18  | | | | |   (142)  op(e3, e3) = e2
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | | REF_CLOSE: (9), (47), (49), (142) are inconsistent by sub-proof #958.
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | Case 2:
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | |   (143)  all_56_2 = e2 & op(e2, e3) = e2
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | | ALPHA: (143) implies:
% 159.91/26.18  | | | | |   (144)  op(e2, e3) = e2
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | | REF_CLOSE: (7), (9), (14), (29), (32), (39), (48), (139), (144) are
% 159.91/26.18  | | | | |            inconsistent by sub-proof #779.
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | End of split
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | Case 2:
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | |   (145)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0,
% 159.91/26.18  | | | |              e3) = e2)
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | | BETA: splitting (145) gives:
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | | Case 1:
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | |   (146)  all_56_6 = e2 & op(e1, e3) = e2
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | | REF_CLOSE: (9), (17), (20), (146) are inconsistent by sub-proof #761.
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | Case 2:
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | |   (147)  all_56_12 = e2 & op(e0, e3) = e2
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | | REF_CLOSE: (9), (10), (137), (147) are inconsistent by sub-proof #858.
% 159.91/26.18  | | | | | 
% 159.91/26.18  | | | | End of split
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | End of split
% 159.91/26.18  | | | 
% 159.91/26.18  | | End of split
% 159.91/26.18  | | 
% 159.91/26.18  | Case 2:
% 159.91/26.18  | | 
% 159.91/26.18  | |   (148)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.91/26.18  | | 
% 159.91/26.18  | | REF_CLOSE: (2), (24), (28), (38), (148) are inconsistent by sub-proof #853.
% 159.91/26.18  | | 
% 159.91/26.18  | End of split
% 159.91/26.18  | 
% 159.91/26.18  End of proof
% 159.91/26.18  
% 159.91/26.18  Sub-proof #742 shows that the following formulas are inconsistent:
% 159.91/26.18  ----------------------------------------------------------------
% 159.91/26.18    (1)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.91/26.18    (2)   ~ (all_52_7 = all_14_2)
% 159.91/26.18    (3)   ~ (all_52_3 = all_14_2)
% 159.91/26.18    (4)  op(e0, e1) = all_52_11
% 159.91/26.18    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.91/26.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.91/26.18    (6)  op(e0, e3) = all_52_3
% 159.91/26.18    (7)  op(e1, e1) = e2
% 159.91/26.18    (8)   ~ (all_52_11 = all_14_2)
% 159.91/26.18    (9)  all_54_15 = all_14_2
% 159.91/26.18    (10)  op(e0, e2) = all_52_7
% 159.91/26.18    (11)  op(e3, e3) = e3
% 159.91/26.18    (12)   ~ (all_14_2 = e2)
% 159.91/26.18    (13)   ~ (all_14_2 = e1)
% 159.91/26.18    (14)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.91/26.18            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.91/26.18            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 159.91/26.18            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.91/26.18            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.91/26.18              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.91/26.18            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 159.91/26.18            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 159.91/26.18            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.91/26.18            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.91/26.18              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.91/26.18            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.91/26.18            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.91/26.18            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.91/26.18              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.91/26.18          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.91/26.18            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.91/26.18            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 159.91/26.18            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.91/26.18            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.91/26.18            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.91/26.18            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.91/26.18    (15)   ~ (all_14_2 = e3)
% 159.91/26.18  
% 159.91/26.18  Begin of proof
% 159.91/26.18  | 
% 159.91/26.18  | BETA: splitting (1) gives:
% 159.91/26.18  | 
% 159.91/26.18  | Case 1:
% 159.91/26.18  | | 
% 159.91/26.18  | |   (16)  all_54_15 = e2
% 159.91/26.18  | | 
% 159.91/26.18  | | REF_CLOSE: (9), (12), (16) are inconsistent by sub-proof #1009.
% 159.91/26.18  | | 
% 159.91/26.18  | Case 2:
% 159.91/26.18  | | 
% 159.91/26.18  | |   (17)   ~ (all_54_15 = e2)
% 159.91/26.18  | |   (18)  all_54_15 = e1 | all_54_15 = e0
% 159.91/26.18  | | 
% 159.91/26.18  | | BETA: splitting (18) gives:
% 159.91/26.18  | | 
% 159.91/26.18  | | Case 1:
% 159.91/26.18  | | | 
% 159.91/26.18  | | |   (19)  all_54_15 = e1
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REF_CLOSE: (9), (13), (19) are inconsistent by sub-proof #1008.
% 159.91/26.18  | | | 
% 159.91/26.18  | | Case 2:
% 159.91/26.18  | | | 
% 159.91/26.18  | | |   (20)  all_54_15 = e0
% 159.91/26.18  | | | 
% 159.91/26.18  | | | COMBINE_EQS: (9), (20) imply:
% 159.91/26.18  | | |   (21)  all_14_2 = e0
% 159.91/26.18  | | | 
% 159.91/26.18  | | | SIMP: (21) implies:
% 159.91/26.18  | | |   (22)  all_14_2 = e0
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REDUCE: (3), (22) imply:
% 159.91/26.18  | | |   (23)   ~ (all_52_3 = e0)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REDUCE: (2), (22) imply:
% 159.91/26.18  | | |   (24)   ~ (all_52_7 = e0)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REDUCE: (8), (22) imply:
% 159.91/26.18  | | |   (25)   ~ (all_52_11 = e0)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REDUCE: (15), (22) imply:
% 159.91/26.18  | | |   (26)   ~ (e3 = e0)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | SIMP: (26) implies:
% 159.91/26.18  | | |   (27)   ~ (e3 = e0)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REDUCE: (12), (22) imply:
% 159.91/26.18  | | |   (28)   ~ (e2 = e0)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | SIMP: (28) implies:
% 159.91/26.18  | | |   (29)   ~ (e2 = e0)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REF_CLOSE: (4), (5), (6), (7), (10), (11), (14), (23), (24), (25), (27),
% 159.91/26.18  | | |            (29) are inconsistent by sub-proof #743.
% 159.91/26.18  | | | 
% 159.91/26.18  | | End of split
% 159.91/26.18  | | 
% 159.91/26.18  | End of split
% 159.91/26.18  | 
% 159.91/26.18  End of proof
% 159.91/26.18  
% 159.91/26.18  Sub-proof #743 shows that the following formulas are inconsistent:
% 159.91/26.18  ----------------------------------------------------------------
% 159.91/26.18    (1)   ~ (all_52_7 = e0)
% 159.91/26.18    (2)  op(e0, e1) = all_52_11
% 159.91/26.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.91/26.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.91/26.18    (4)  op(e0, e3) = all_52_3
% 159.91/26.18    (5)  op(e1, e1) = e2
% 159.91/26.18    (6)   ~ (all_52_3 = e0)
% 159.91/26.18    (7)  op(e0, e2) = all_52_7
% 159.91/26.18    (8)  op(e3, e3) = e3
% 159.91/26.18    (9)   ~ (all_52_11 = e0)
% 159.91/26.18    (10)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 159.91/26.18            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 159.91/26.18            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 159.91/26.18            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 159.91/26.18            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 159.91/26.18              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 159.91/26.18            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 159.91/26.18            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 159.91/26.18            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 159.91/26.18            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 159.91/26.18              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.91/26.18            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 159.91/26.18            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.91/26.18            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.91/26.18              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.91/26.18          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.91/26.18            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 159.91/26.18            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 159.91/26.18            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 159.91/26.18            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.91/26.18            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.91/26.18            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.91/26.18    (11)   ~ (e2 = e0)
% 159.91/26.18    (12)   ~ (e3 = e0)
% 159.91/26.18  
% 159.91/26.18  Begin of proof
% 159.91/26.18  | 
% 159.91/26.18  | BETA: splitting (10) gives:
% 159.91/26.18  | 
% 159.91/26.18  | Case 1:
% 159.91/26.18  | | 
% 159.91/26.18  | |   (13)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.91/26.18  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.91/26.18  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 159.91/26.18  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.91/26.18  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.91/26.18  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.91/26.18  | | 
% 159.91/26.18  | | BETA: splitting (13) gives:
% 159.91/26.18  | | 
% 159.91/26.18  | | Case 1:
% 159.91/26.18  | | | 
% 159.91/26.18  | | |   (14)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 159.91/26.18  | | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 159.91/26.18  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | BETA: splitting (14) gives:
% 159.91/26.18  | | | 
% 159.91/26.18  | | | Case 1:
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | |   (15)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | | | |           e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | | ALPHA: (15) implies:
% 159.91/26.18  | | | |   (16)  op(e3, e3) = e0
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | | REF_CLOSE: (3), (8), (12), (16) are inconsistent by sub-proof #971.
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | Case 2:
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | |   (17)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 159.91/26.18  | | | |             = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0)
% 159.91/26.18  | | | |         | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 159.91/26.18  | | | |           (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 159.91/26.18  | | | |             e3) = e0)
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | | REF_CLOSE: (3), (4), (5), (6), (11), (17) are inconsistent by sub-proof
% 159.91/26.18  | | | |            #745.
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | End of split
% 159.91/26.18  | | | 
% 159.91/26.18  | | Case 2:
% 159.91/26.18  | | | 
% 159.91/26.18  | | |   (18)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0)
% 159.91/26.18  | | |         | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.91/26.18  | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.91/26.18  | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (12), (18) are inconsistent by
% 159.91/26.18  | | |            sub-proof #899.
% 159.91/26.18  | | | 
% 159.91/26.18  | | End of split
% 159.91/26.18  | | 
% 159.91/26.18  | Case 2:
% 159.91/26.18  | | 
% 159.91/26.18  | |   (19)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 159.91/26.18  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.91/26.18  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 159.91/26.18  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.91/26.18  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.91/26.18  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.91/26.18  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.91/26.18  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 159.91/26.18  | |           & op(e0, e1) = e0)
% 159.91/26.18  | | 
% 159.91/26.18  | | BETA: splitting (19) gives:
% 159.91/26.18  | | 
% 159.91/26.18  | | Case 1:
% 159.91/26.18  | | | 
% 159.91/26.18  | | |   (20)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.91/26.18  | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 159.91/26.18  | | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 159.91/26.18  | | |         | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 159.91/26.18  | | |             = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.91/26.18  | | | 
% 159.91/26.18  | | | BETA: splitting (20) gives:
% 159.91/26.18  | | | 
% 159.91/26.18  | | | Case 1:
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | |   (21)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 159.91/26.18  | | | |           = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | | ALPHA: (21) implies:
% 159.91/26.18  | | | |   (22)  op(e1, e1) = e0
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | | REF_CLOSE: (3), (5), (11), (22) are inconsistent by sub-proof #914.
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | Case 2:
% 159.91/26.18  | | | | 
% 159.91/26.18  | | | |   (23)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 159.91/26.18  | | | |           e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 159.91/26.18  | | | |           (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 159.91/26.18  | | | |             e1) = e0)
% 159.91/26.18  | | | | 
% 159.91/26.19  | | | | REF_CLOSE: (1), (3), (7), (8), (12), (23) are inconsistent by sub-proof
% 159.91/26.19  | | | |            #968.
% 159.91/26.19  | | | | 
% 159.91/26.19  | | | End of split
% 159.91/26.19  | | | 
% 159.91/26.19  | | Case 2:
% 159.91/26.19  | | | 
% 159.91/26.19  | | |   (24)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.19  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.91/26.19  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.91/26.19  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 159.91/26.19  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.91/26.19  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 159.91/26.19  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 159.91/26.19  | | |             e0) & op(e0, e1) = e0)
% 159.91/26.19  | | | 
% 159.91/26.19  | | | REF_CLOSE: (2), (3), (9), (24) are inconsistent by sub-proof #744.
% 159.91/26.19  | | | 
% 159.91/26.19  | | End of split
% 159.91/26.19  | | 
% 159.91/26.19  | End of split
% 159.91/26.19  | 
% 159.91/26.19  End of proof
% 159.91/26.19  
% 159.91/26.19  Sub-proof #744 shows that the following formulas are inconsistent:
% 159.91/26.19  ----------------------------------------------------------------
% 159.91/26.19    (1)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 159.91/26.19           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 159.91/26.19           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 159.91/26.19           & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 159.91/26.19           & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 159.91/26.19           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 159.91/26.19           all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 159.91/26.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.91/26.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.91/26.19    (3)  op(e0, e1) = all_52_11
% 159.91/26.19    (4)   ~ (all_52_11 = e0)
% 159.91/26.19  
% 159.91/26.19  Begin of proof
% 159.91/26.19  | 
% 159.91/26.19  | BETA: splitting (1) gives:
% 159.91/26.19  | 
% 159.91/26.19  | Case 1:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (5)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.19  | |            e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 159.91/26.19  | |        (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.91/26.19  | |            e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0)
% 159.91/26.19  | | 
% 159.91/26.19  | | BETA: splitting (5) gives:
% 159.91/26.19  | | 
% 159.91/26.19  | | Case 1:
% 159.91/26.19  | | | 
% 159.91/26.19  | | |   (6)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.91/26.19  | | |          e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 159.91/26.19  | | | 
% 159.91/26.19  | | | ALPHA: (6) implies:
% 159.91/26.19  | | |   (7)  op(e0, e1) = e0
% 159.91/26.19  | | | 
% 159.91/26.19  | | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #966.
% 159.91/26.19  | | | 
% 159.91/26.19  | | Case 2:
% 159.91/26.19  | | | 
% 159.91/26.19  | | |   (8)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 159.91/26.19  | | |          e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.91/26.19  | | | 
% 159.91/26.19  | | | ALPHA: (8) implies:
% 159.91/26.19  | | |   (9)  op(e0, e1) = e0
% 159.91/26.19  | | | 
% 159.91/26.19  | | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #966.
% 159.91/26.19  | | | 
% 159.91/26.19  | | End of split
% 159.91/26.19  | | 
% 159.91/26.19  | Case 2:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (10)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 159.91/26.19  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 159.91/26.19  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 159.91/26.19  | |           & op(e0, e1) = e0)
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #965.
% 159.91/26.19  | | 
% 159.91/26.19  | End of split
% 159.91/26.19  | 
% 159.91/26.19  End of proof
% 159.91/26.19  
% 159.91/26.19  Sub-proof #745 shows that the following formulas are inconsistent:
% 159.91/26.19  ----------------------------------------------------------------
% 159.91/26.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.91/26.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.91/26.19    (2)  op(e0, e3) = all_52_3
% 159.91/26.19    (3)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 159.91/26.19           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 159.91/26.19           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 159.91/26.19           & op(e1, e0) = e1 & op(e0, e3) = e0)
% 159.91/26.19    (4)  op(e1, e1) = e2
% 159.91/26.19    (5)   ~ (all_52_3 = e0)
% 159.91/26.19    (6)   ~ (e2 = e0)
% 159.91/26.19  
% 159.91/26.19  Begin of proof
% 159.91/26.19  | 
% 159.91/26.19  | BETA: splitting (3) gives:
% 159.91/26.19  | 
% 159.91/26.19  | Case 1:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (7)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3)
% 159.91/26.19  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (7) implies:
% 159.91/26.19  | |   (8)  op(e0, e3) = e0
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #973.
% 159.91/26.19  | | 
% 159.91/26.19  | Case 2:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (9)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3)
% 159.91/26.19  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (9) implies:
% 159.91/26.19  | |   (10)  op(e1, e1) = e0
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #914.
% 159.91/26.19  | | 
% 159.91/26.19  | End of split
% 159.91/26.19  | 
% 159.91/26.19  End of proof
% 159.91/26.19  
% 159.91/26.19  Sub-proof #746 shows that the following formulas are inconsistent:
% 159.91/26.19  ----------------------------------------------------------------
% 159.91/26.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.91/26.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.91/26.19    (2)   ~ (all_52_12 = e3)
% 159.91/26.19    (3)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 159.91/26.19           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 159.91/26.19           = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3
% 159.91/26.19           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 159.91/26.19           op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 159.91/26.19    (4)  op(e2, e1) = all_52_9
% 159.91/26.19    (5)  op(e3, e0) = all_52_12
% 159.91/26.19    (6)   ~ (all_52_9 = e2)
% 159.91/26.19  
% 159.91/26.19  Begin of proof
% 159.91/26.19  | 
% 159.91/26.19  | BETA: splitting (3) gives:
% 159.91/26.19  | 
% 159.91/26.19  | Case 1:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (7)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 159.91/26.19  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 159.91/26.19  | |          e0) = e1 & $i(all_57_14)
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (7) implies:
% 159.91/26.19  | |   (8)  op(e2, e1) = e2
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #1002.
% 159.91/26.19  | | 
% 159.91/26.19  | Case 2:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0)
% 159.91/26.19  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 159.91/26.19  | |          e0) = e3 & $i(all_57_10)
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (9) implies:
% 159.91/26.19  | |   (10)  op(e3, e0) = e3
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #976.
% 159.91/26.19  | | 
% 159.91/26.19  | End of split
% 159.91/26.19  | 
% 159.91/26.19  End of proof
% 159.91/26.19  
% 159.91/26.19  Sub-proof #747 shows that the following formulas are inconsistent:
% 159.91/26.19  ----------------------------------------------------------------
% 159.91/26.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.91/26.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.91/26.19    (2)   ~ (all_52_12 = e3)
% 159.91/26.19    (3)  op(e1, e1) = e2
% 159.91/26.19    (4)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) &
% 159.91/26.19           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.91/26.19           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1)
% 159.91/26.19           & op(e1, e3) = e1 & op(e1, e1) = e1)
% 159.91/26.19    (5)   ~ (e2 = e1)
% 159.91/26.19    (6)  op(e3, e0) = all_52_12
% 159.91/26.19  
% 159.91/26.19  Begin of proof
% 159.91/26.19  | 
% 159.91/26.19  | BETA: splitting (4) gives:
% 159.91/26.19  | 
% 159.91/26.19  | Case 1:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (7)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 159.91/26.19  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 159.91/26.19  | |          e1) = e3 & $i(all_57_10)
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (7) implies:
% 159.91/26.19  | |   (8)  op(e3, e0) = e3
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #976.
% 159.91/26.19  | | 
% 159.91/26.19  | Case 2:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (9)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 159.91/26.19  | |        op(e1, e1) = e1
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (9) implies:
% 159.91/26.19  | |   (10)  op(e1, e1) = e1
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #986.
% 159.91/26.19  | | 
% 159.91/26.19  | End of split
% 159.91/26.19  | 
% 159.91/26.19  End of proof
% 159.91/26.19  
% 159.91/26.19  Sub-proof #748 shows that the following formulas are inconsistent:
% 159.91/26.19  ----------------------------------------------------------------
% 159.91/26.19    (1)  op(e0, e0) = e1
% 159.91/26.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.91/26.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.91/26.19    (3)  op(e1, e1) = e2
% 159.91/26.19    (4)  op(e0, e0) = all_14_2
% 159.91/26.19    (5)   ~ (e1 = e0)
% 159.91/26.19    (6)   ~ (e2 = e1)
% 159.91/26.19    (7)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.91/26.19             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.91/26.19           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.91/26.19               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.91/26.19             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.91/26.19         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.91/26.19             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.91/26.19           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.91/26.19               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.91/26.19             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.91/26.19  
% 159.91/26.19  Begin of proof
% 159.91/26.19  | 
% 159.91/26.19  | BETA: splitting (7) gives:
% 159.91/26.19  | 
% 159.91/26.19  | Case 1:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (8)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.91/26.19  | |            e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.91/26.19  | |            $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.91/26.19  | |            (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.91/26.19  | |        ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.91/26.19  | |              e1) = all_57_8 & $i(all_57_8)))
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (8) implies:
% 159.91/26.19  | |   (9)  op(e1, e1) = e1
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #986.
% 159.91/26.19  | | 
% 159.91/26.19  | Case 2:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (10)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 159.91/26.19  | |             e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.91/26.19  | |             $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 159.91/26.19  | |             (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 159.91/26.19  | |         ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 159.91/26.19  | |               e0) = all_57_13 & $i(all_57_13)))
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (10) implies:
% 159.91/26.19  | |   (11)  op(e0, e0) = e0
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (1), (2), (4), (5), (11) are inconsistent by sub-proof #991.
% 159.91/26.19  | | 
% 159.91/26.19  | End of split
% 159.91/26.19  | 
% 159.91/26.19  End of proof
% 159.91/26.19  
% 159.91/26.19  Sub-proof #749 shows that the following formulas are inconsistent:
% 159.91/26.19  ----------------------------------------------------------------
% 159.91/26.19    (1)  (all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3) =
% 159.91/26.19           all_57_2 & $i(all_57_2))
% 159.91/26.19    (2)   ~ (all_57_14 = e3)
% 159.91/26.19    (3)  all_57_2 = e1
% 159.91/26.19  
% 159.91/26.19  Begin of proof
% 159.91/26.19  | 
% 159.91/26.19  | BETA: splitting (1) gives:
% 159.91/26.19  | 
% 159.91/26.19  | Case 1:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (4)  all_57_14 = e3 & op(e1, e1) = e3
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (4) implies:
% 159.91/26.19  | |   (5)  all_57_14 = e3
% 159.91/26.19  | | 
% 159.91/26.19  | | REDUCE: (2), (5) imply:
% 159.91/26.19  | |   (6)  $false
% 159.91/26.19  | | 
% 159.91/26.19  | | CLOSE: (6) is inconsistent.
% 159.91/26.19  | | 
% 159.91/26.19  | Case 2:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (7)   ~ (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2)
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (7) implies:
% 159.91/26.19  | |   (8)   ~ (all_57_2 = e1)
% 159.91/26.19  | | 
% 159.91/26.19  | | REDUCE: (3), (8) imply:
% 159.91/26.19  | |   (9)  $false
% 159.91/26.19  | | 
% 159.91/26.19  | | CLOSE: (9) is inconsistent.
% 159.91/26.19  | | 
% 159.91/26.19  | End of split
% 159.91/26.19  | 
% 159.91/26.19  End of proof
% 159.91/26.19  
% 159.91/26.19  Sub-proof #750 shows that the following formulas are inconsistent:
% 159.91/26.19  ----------------------------------------------------------------
% 159.91/26.19    (1)   ~ (all_52_4 = e3)
% 159.91/26.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.91/26.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.91/26.19    (3)  op(e3, e2) = all_52_4
% 159.91/26.19    (4)  op(e2, e1) = all_52_9
% 159.91/26.19    (5)   ~ (all_52_9 = e2)
% 159.91/26.19    (6)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.91/26.19           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.91/26.19           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 159.91/26.19           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 159.91/26.19           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.91/26.19  
% 159.91/26.19  Begin of proof
% 159.91/26.19  | 
% 159.91/26.19  | BETA: splitting (6) gives:
% 159.91/26.19  | 
% 159.91/26.19  | Case 1:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (7)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 159.91/26.19  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 159.91/26.19  | |          e1) = e3 & $i(all_57_10)
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (7) implies:
% 159.91/26.19  | |   (8)  op(e3, e2) = e3
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #998.
% 159.91/26.19  | | 
% 159.91/26.19  | Case 2:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (9)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 159.91/26.19  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.91/26.19  | |          e1) = e2 & $i(all_57_12)
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (9) implies:
% 159.91/26.19  | |   (10)  op(e2, e1) = e2
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #1002.
% 159.91/26.19  | | 
% 159.91/26.19  | End of split
% 159.91/26.19  | 
% 159.91/26.19  End of proof
% 159.91/26.19  
% 159.91/26.19  Sub-proof #751 shows that the following formulas are inconsistent:
% 159.91/26.19  ----------------------------------------------------------------
% 159.91/26.19    (1)   ~ (all_52_6 = e1)
% 159.91/26.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.91/26.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.91/26.19    (3)  op(e1, e2) = all_52_6
% 159.91/26.19    (4)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.91/26.19           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 159.91/26.19           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3
% 159.91/26.19           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 159.91/26.19           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.91/26.19    (5)  op(e2, e2) = e1
% 159.91/26.19    (6)   ~ (e3 = e1)
% 159.91/26.19  
% 159.91/26.19  Begin of proof
% 159.91/26.19  | 
% 159.91/26.19  | BETA: splitting (4) gives:
% 159.91/26.19  | 
% 159.91/26.19  | Case 1:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (7)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 159.91/26.19  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.91/26.19  | |          e1) = e2 & $i(all_57_12)
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (7) implies:
% 159.91/26.19  | |   (8)  op(e1, e2) = e1
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #984.
% 159.91/26.19  | | 
% 159.91/26.19  | Case 2:
% 159.91/26.19  | | 
% 159.91/26.19  | |   (9)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1)
% 159.91/26.19  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 159.91/26.19  | |          e2) = e3 & $i(all_57_10)
% 159.91/26.19  | | 
% 159.91/26.19  | | ALPHA: (9) implies:
% 159.91/26.19  | |   (10)  op(e2, e2) = e3
% 159.91/26.19  | | 
% 159.91/26.19  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #847.
% 159.91/26.19  | | 
% 159.91/26.19  | End of split
% 159.91/26.19  | 
% 159.91/26.19  End of proof
% 159.91/26.19  
% 159.91/26.19  Sub-proof #752 shows that the following formulas are inconsistent:
% 159.91/26.19  ----------------------------------------------------------------
% 159.91/26.19    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.91/26.19         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.91/26.19    (2)  op(e0, e0) = e2
% 159.91/26.20    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.91/26.20         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.91/26.20    (4)   ~ (e3 = e2)
% 159.91/26.20    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.91/26.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.91/26.20    (6)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.91/26.20             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.91/26.20               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.91/26.20               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.91/26.20    (7)  all_56_10 = e2
% 159.91/26.20    (8)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 159.91/26.20         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 159.91/26.20    (9)  all_56_4 = e2
% 159.91/26.20    (10)  op(e3, e3) = e3
% 159.91/26.20    (11)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.91/26.20          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.91/26.20    (12)   ~ (e1 = e0)
% 159.91/26.20    (13)   ~ (e2 = e1)
% 159.91/26.20    (14)   ~ (e3 = e1)
% 159.91/26.20    (15)   ~ (e2 = e0)
% 159.91/26.20    (16)   ~ (e3 = e0)
% 159.91/26.20  
% 159.91/26.20  Begin of proof
% 159.91/26.20  | 
% 159.91/26.20  | BETA: splitting (8) gives:
% 159.91/26.20  | 
% 159.91/26.20  | Case 1:
% 159.91/26.20  | | 
% 159.91/26.20  | |   (17)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 159.91/26.20  | |           e3)
% 159.91/26.20  | | 
% 159.91/26.20  | | BETA: splitting (17) gives:
% 159.91/26.20  | | 
% 159.91/26.20  | | Case 1:
% 159.91/26.20  | | | 
% 159.91/26.20  | | |   (18)  all_56_9 = e3 & op(e3, e0) = e3
% 159.91/26.20  | | | 
% 159.91/26.20  | | | ALPHA: (18) implies:
% 159.91/26.20  | | |   (19)  all_56_9 = e3
% 159.91/26.20  | | | 
% 159.91/26.20  | | | REF_CLOSE: (3), (5), (9), (10), (11), (12), (13), (14), (15), (16), (19)
% 159.91/26.20  | | |            are inconsistent by sub-proof #757.
% 159.91/26.20  | | | 
% 159.91/26.20  | | Case 2:
% 159.91/26.20  | | | 
% 159.91/26.20  | | |   (20)  all_56_10 = e3 & op(e2, e0) = e3
% 159.91/26.20  | | | 
% 159.91/26.20  | | | REF_CLOSE: (4), (7), (20) are inconsistent by sub-proof #894.
% 159.91/26.20  | | | 
% 159.91/26.20  | | End of split
% 159.91/26.20  | | 
% 159.91/26.20  | Case 2:
% 159.91/26.20  | | 
% 159.91/26.20  | |   (21)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 159.91/26.20  | |           e3)
% 159.91/26.20  | | 
% 159.91/26.20  | | BETA: splitting (21) gives:
% 159.91/26.20  | | 
% 159.91/26.20  | | Case 1:
% 159.91/26.20  | | | 
% 159.91/26.20  | | |   (22)  all_56_11 = e3 & op(e1, e0) = e3
% 159.91/26.20  | | | 
% 159.91/26.20  | | | ALPHA: (22) implies:
% 159.91/26.20  | | |   (23)  all_56_11 = e3
% 159.91/26.20  | | | 
% 159.91/26.20  | | | REF_CLOSE: (1), (2), (5), (6), (7), (12), (13), (14), (15), (16), (23) are
% 159.91/26.20  | | |            inconsistent by sub-proof #753.
% 159.91/26.20  | | | 
% 159.91/26.20  | | Case 2:
% 159.91/26.20  | | | 
% 159.91/26.20  | | |   (24)  all_56_15 = e3 & op(e0, e0) = e3
% 159.91/26.20  | | | 
% 159.91/26.20  | | | ALPHA: (24) implies:
% 159.91/26.20  | | |   (25)  op(e0, e0) = e3
% 159.91/26.20  | | | 
% 159.91/26.20  | | | REF_CLOSE: (2), (4), (5), (25) are inconsistent by sub-proof #878.
% 159.91/26.20  | | | 
% 159.91/26.20  | | End of split
% 159.91/26.20  | | 
% 159.91/26.20  | End of split
% 159.91/26.20  | 
% 159.91/26.20  End of proof
% 159.91/26.20  
% 159.91/26.20  Sub-proof #753 shows that the following formulas are inconsistent:
% 159.91/26.20  ----------------------------------------------------------------
% 159.96/26.20    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 159.96/26.20         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.96/26.20    (2)  op(e0, e0) = e2
% 159.96/26.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.20    (4)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 159.96/26.20             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 159.96/26.20               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 159.96/26.20               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 159.96/26.20    (5)  all_56_10 = e2
% 159.96/26.20    (6)   ~ (e1 = e0)
% 159.96/26.20    (7)  all_56_11 = e3
% 159.96/26.20    (8)   ~ (e2 = e1)
% 159.96/26.20    (9)   ~ (e3 = e1)
% 159.96/26.20    (10)   ~ (e2 = e0)
% 159.96/26.20    (11)   ~ (e3 = e0)
% 159.96/26.20  
% 159.96/26.20  Begin of proof
% 159.96/26.20  | 
% 159.96/26.20  | BETA: splitting (1) gives:
% 159.96/26.20  | 
% 159.96/26.20  | Case 1:
% 159.96/26.20  | | 
% 159.96/26.20  | |   (12)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 159.96/26.20  | |           e1)
% 159.96/26.20  | | 
% 159.96/26.20  | | BETA: splitting (12) gives:
% 159.96/26.20  | | 
% 159.96/26.20  | | Case 1:
% 159.96/26.20  | | | 
% 159.96/26.20  | | |   (13)  all_56_9 = e1 & op(e3, e0) = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | ALPHA: (13) implies:
% 159.96/26.20  | | |   (14)  all_56_9 = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | BETA: splitting (4) gives:
% 159.96/26.20  | | | 
% 159.96/26.20  | | | Case 1:
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | |   (15)  all_56_15 = e0 & op(e0, e0) = e0
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | | ALPHA: (15) implies:
% 159.96/26.20  | | | |   (16)  op(e0, e0) = e0
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | | REF_CLOSE: (2), (3), (10), (16) are inconsistent by sub-proof #979.
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | Case 2:
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | |   (17)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 159.96/26.20  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 159.96/26.20  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 159.96/26.20  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | | ALPHA: (17) implies:
% 159.96/26.20  | | | |   (18)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0)
% 159.96/26.20  | | | |           = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | | BETA: splitting (18) gives:
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | | Case 1:
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | |   (19)  all_56_9 = e0 & op(e3, e0) = e0
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | ALPHA: (19) implies:
% 159.96/26.20  | | | | |   (20)  all_56_9 = e0
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | REF_CLOSE: (6), (14), (20) are inconsistent by sub-proof #756.
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | Case 2:
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | |   (21)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 159.96/26.20  | | | | |             e0) = e0)
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | BETA: splitting (21) gives:
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | Case 1:
% 159.96/26.20  | | | | | | 
% 159.96/26.20  | | | | | |   (22)  all_56_10 = e0 & op(e2, e0) = e0
% 159.96/26.20  | | | | | | 
% 159.96/26.20  | | | | | | ALPHA: (22) implies:
% 159.96/26.20  | | | | | |   (23)  all_56_10 = e0
% 159.96/26.20  | | | | | | 
% 159.96/26.20  | | | | | | REF_CLOSE: (5), (10), (23) are inconsistent by sub-proof #755.
% 159.96/26.20  | | | | | | 
% 159.96/26.20  | | | | | Case 2:
% 159.96/26.20  | | | | | | 
% 159.96/26.20  | | | | | |   (24)  all_56_11 = e0 & op(e1, e0) = e0
% 159.96/26.20  | | | | | | 
% 159.96/26.20  | | | | | | ALPHA: (24) implies:
% 159.96/26.20  | | | | | |   (25)  all_56_11 = e0
% 159.96/26.20  | | | | | | 
% 159.96/26.20  | | | | | | REF_CLOSE: (7), (11), (25) are inconsistent by sub-proof #893.
% 159.96/26.20  | | | | | | 
% 159.96/26.20  | | | | | End of split
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | End of split
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | End of split
% 159.96/26.20  | | | 
% 159.96/26.20  | | Case 2:
% 159.96/26.20  | | | 
% 159.96/26.20  | | |   (26)  all_56_10 = e1 & op(e2, e0) = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | ALPHA: (26) implies:
% 159.96/26.20  | | |   (27)  all_56_10 = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | COMBINE_EQS: (5), (27) imply:
% 159.96/26.20  | | |   (28)  e2 = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | REDUCE: (8), (28) imply:
% 159.96/26.20  | | |   (29)  $false
% 159.96/26.20  | | | 
% 159.96/26.20  | | | CLOSE: (29) is inconsistent.
% 159.96/26.20  | | | 
% 159.96/26.20  | | End of split
% 159.96/26.20  | | 
% 159.96/26.20  | Case 2:
% 159.96/26.20  | | 
% 159.96/26.20  | |   (30)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 159.96/26.20  | |           e1)
% 159.96/26.20  | | 
% 159.96/26.20  | | BETA: splitting (30) gives:
% 159.96/26.20  | | 
% 159.96/26.20  | | Case 1:
% 159.96/26.20  | | | 
% 159.96/26.20  | | |   (31)  all_56_11 = e1 & op(e1, e0) = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | REF_CLOSE: (7), (9), (31) are inconsistent by sub-proof #754.
% 159.96/26.20  | | | 
% 159.96/26.20  | | Case 2:
% 159.96/26.20  | | | 
% 159.96/26.20  | | |   (32)  all_56_15 = e1 & op(e0, e0) = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | ALPHA: (32) implies:
% 159.96/26.20  | | |   (33)  op(e0, e0) = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | REF_CLOSE: (2), (3), (8), (33) are inconsistent by sub-proof #875.
% 159.96/26.20  | | | 
% 159.96/26.20  | | End of split
% 159.96/26.20  | | 
% 159.96/26.20  | End of split
% 159.96/26.20  | 
% 159.96/26.20  End of proof
% 159.96/26.20  
% 159.96/26.20  Sub-proof #754 shows that the following formulas are inconsistent:
% 159.96/26.20  ----------------------------------------------------------------
% 159.96/26.20    (1)  all_56_11 = e1 & op(e1, e0) = e1
% 159.96/26.20    (2)  all_56_11 = e3
% 159.96/26.20    (3)   ~ (e3 = e1)
% 159.96/26.20  
% 159.96/26.20  Begin of proof
% 159.96/26.20  | 
% 159.96/26.20  | ALPHA: (1) implies:
% 159.96/26.20  |   (4)  all_56_11 = e1
% 159.96/26.20  | 
% 159.96/26.20  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.20  |   (5)  e3 = e1
% 159.96/26.20  | 
% 159.96/26.20  | REDUCE: (3), (5) imply:
% 159.96/26.20  |   (6)  $false
% 159.96/26.20  | 
% 159.96/26.20  | CLOSE: (6) is inconsistent.
% 159.96/26.20  | 
% 159.96/26.20  End of proof
% 159.96/26.20  
% 159.96/26.20  Sub-proof #755 shows that the following formulas are inconsistent:
% 159.96/26.20  ----------------------------------------------------------------
% 159.96/26.20    (1)  all_56_10 = e2
% 159.96/26.20    (2)  all_56_10 = e0
% 159.96/26.20    (3)   ~ (e2 = e0)
% 159.96/26.20  
% 159.96/26.20  Begin of proof
% 159.96/26.20  | 
% 159.96/26.20  | COMBINE_EQS: (1), (2) imply:
% 159.96/26.20  |   (4)  e2 = e0
% 159.96/26.20  | 
% 159.96/26.20  | SIMP: (4) implies:
% 159.96/26.20  |   (5)  e2 = e0
% 159.96/26.20  | 
% 159.96/26.20  | REDUCE: (3), (5) imply:
% 159.96/26.20  |   (6)  $false
% 159.96/26.20  | 
% 159.96/26.20  | CLOSE: (6) is inconsistent.
% 159.96/26.20  | 
% 159.96/26.20  End of proof
% 159.96/26.20  
% 159.96/26.20  Sub-proof #756 shows that the following formulas are inconsistent:
% 159.96/26.20  ----------------------------------------------------------------
% 159.96/26.20    (1)  all_56_9 = e1
% 159.96/26.20    (2)  all_56_9 = e0
% 159.96/26.20    (3)   ~ (e1 = e0)
% 159.96/26.20  
% 159.96/26.20  Begin of proof
% 159.96/26.20  | 
% 159.96/26.20  | COMBINE_EQS: (1), (2) imply:
% 159.96/26.20  |   (4)  e1 = e0
% 159.96/26.20  | 
% 159.96/26.20  | SIMP: (4) implies:
% 159.96/26.20  |   (5)  e1 = e0
% 159.96/26.20  | 
% 159.96/26.20  | REDUCE: (3), (5) imply:
% 159.96/26.20  |   (6)  $false
% 159.96/26.20  | 
% 159.96/26.20  | CLOSE: (6) is inconsistent.
% 159.96/26.20  | 
% 159.96/26.20  End of proof
% 159.96/26.20  
% 159.96/26.20  Sub-proof #757 shows that the following formulas are inconsistent:
% 159.96/26.20  ----------------------------------------------------------------
% 159.96/26.20    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.96/26.20         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.96/26.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.20    (3)  all_56_4 = e2
% 159.96/26.20    (4)  op(e3, e3) = e3
% 159.96/26.20    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.96/26.20         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.96/26.20    (6)   ~ (e1 = e0)
% 159.96/26.20    (7)   ~ (e2 = e1)
% 159.96/26.20    (8)  all_56_9 = e3
% 159.96/26.20    (9)   ~ (e3 = e1)
% 159.96/26.20    (10)   ~ (e2 = e0)
% 159.96/26.20    (11)   ~ (e3 = e0)
% 159.96/26.20  
% 159.96/26.20  Begin of proof
% 159.96/26.20  | 
% 159.96/26.20  | BETA: splitting (5) gives:
% 159.96/26.20  | 
% 159.96/26.20  | Case 1:
% 159.96/26.20  | | 
% 159.96/26.20  | |   (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 159.96/26.20  | |           e1)
% 159.96/26.20  | | 
% 159.96/26.20  | | BETA: splitting (12) gives:
% 159.96/26.20  | | 
% 159.96/26.20  | | Case 1:
% 159.96/26.20  | | | 
% 159.96/26.20  | | |   (13)  all_56_0 = e1 & op(e3, e3) = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | ALPHA: (13) implies:
% 159.96/26.20  | | |   (14)  op(e3, e3) = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | REF_CLOSE: (2), (4), (9), (14) are inconsistent by sub-proof #995.
% 159.96/26.20  | | | 
% 159.96/26.20  | | Case 2:
% 159.96/26.20  | | | 
% 159.96/26.20  | | |   (15)  all_56_1 = e1 & op(e3, e2) = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | ALPHA: (15) implies:
% 159.96/26.20  | | |   (16)  all_56_1 = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | BETA: splitting (1) gives:
% 159.96/26.20  | | | 
% 159.96/26.20  | | | Case 1:
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | |   (17)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2)
% 159.96/26.20  | | | |           = e0)
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | | BETA: splitting (17) gives:
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | | Case 1:
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | |   (18)  all_56_0 = e0 & op(e3, e3) = e0
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | ALPHA: (18) implies:
% 159.96/26.20  | | | | |   (19)  op(e3, e3) = e0
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | GROUND_INST: instantiating (2) with e0, e3, e3, e3, simplifying with
% 159.96/26.20  | | | | |              (4), (19) gives:
% 159.96/26.20  | | | | |   (20)  e3 = e0
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | REDUCE: (11), (20) imply:
% 159.96/26.20  | | | | |   (21)  $false
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | CLOSE: (21) is inconsistent.
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | Case 2:
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | |   (22)  all_56_1 = e0 & op(e3, e2) = e0
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | REF_CLOSE: (6), (16), (22) are inconsistent by sub-proof #760.
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | End of split
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | Case 2:
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | |   (23)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0)
% 159.96/26.20  | | | |           = e0)
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | | BETA: splitting (23) gives:
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | | Case 1:
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | |   (24)  all_56_4 = e0 & op(e3, e1) = e0
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | REF_CLOSE: (3), (10), (24) are inconsistent by sub-proof #953.
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | Case 2:
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | |   (25)  all_56_9 = e0 & op(e3, e0) = e0
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | | REF_CLOSE: (8), (11), (25) are inconsistent by sub-proof #759.
% 159.96/26.20  | | | | | 
% 159.96/26.20  | | | | End of split
% 159.96/26.20  | | | | 
% 159.96/26.20  | | | End of split
% 159.96/26.20  | | | 
% 159.96/26.20  | | End of split
% 159.96/26.20  | | 
% 159.96/26.20  | Case 2:
% 159.96/26.20  | | 
% 159.96/26.20  | |   (26)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 159.96/26.20  | |           e1)
% 159.96/26.20  | | 
% 159.96/26.20  | | BETA: splitting (26) gives:
% 159.96/26.20  | | 
% 159.96/26.20  | | Case 1:
% 159.96/26.20  | | | 
% 159.96/26.20  | | |   (27)  all_56_4 = e1 & op(e3, e1) = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | REF_CLOSE: (3), (7), (27) are inconsistent by sub-proof #956.
% 159.96/26.20  | | | 
% 159.96/26.20  | | Case 2:
% 159.96/26.20  | | | 
% 159.96/26.20  | | |   (28)  all_56_9 = e1 & op(e3, e0) = e1
% 159.96/26.20  | | | 
% 159.96/26.20  | | | REF_CLOSE: (8), (9), (28) are inconsistent by sub-proof #758.
% 159.96/26.20  | | | 
% 159.96/26.20  | | End of split
% 159.96/26.20  | | 
% 159.96/26.20  | End of split
% 159.96/26.20  | 
% 159.96/26.20  End of proof
% 159.96/26.20  
% 159.96/26.20  Sub-proof #758 shows that the following formulas are inconsistent:
% 159.96/26.20  ----------------------------------------------------------------
% 159.96/26.20    (1)  all_56_9 = e1 & op(e3, e0) = e1
% 159.96/26.20    (2)  all_56_9 = e3
% 159.96/26.20    (3)   ~ (e3 = e1)
% 159.96/26.20  
% 159.96/26.20  Begin of proof
% 159.96/26.20  | 
% 159.96/26.20  | ALPHA: (1) implies:
% 159.96/26.20  |   (4)  all_56_9 = e1
% 159.96/26.20  | 
% 159.96/26.20  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.20  |   (5)  e3 = e1
% 159.96/26.20  | 
% 159.96/26.20  | REDUCE: (3), (5) imply:
% 159.96/26.20  |   (6)  $false
% 159.96/26.20  | 
% 159.96/26.20  | CLOSE: (6) is inconsistent.
% 159.96/26.20  | 
% 159.96/26.20  End of proof
% 159.96/26.20  
% 159.96/26.20  Sub-proof #759 shows that the following formulas are inconsistent:
% 159.96/26.20  ----------------------------------------------------------------
% 159.96/26.20    (1)  all_56_9 = e0 & op(e3, e0) = e0
% 159.96/26.20    (2)  all_56_9 = e3
% 159.96/26.20    (3)   ~ (e3 = e0)
% 159.96/26.20  
% 159.96/26.20  Begin of proof
% 159.96/26.20  | 
% 159.96/26.20  | ALPHA: (1) implies:
% 159.96/26.20  |   (4)  all_56_9 = e0
% 159.96/26.20  | 
% 159.96/26.20  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.20  |   (5)  e3 = e0
% 159.96/26.20  | 
% 159.96/26.20  | REDUCE: (3), (5) imply:
% 159.96/26.20  |   (6)  $false
% 159.96/26.20  | 
% 159.96/26.20  | CLOSE: (6) is inconsistent.
% 159.96/26.20  | 
% 159.96/26.20  End of proof
% 159.96/26.20  
% 159.96/26.20  Sub-proof #760 shows that the following formulas are inconsistent:
% 159.96/26.20  ----------------------------------------------------------------
% 159.96/26.20    (1)  all_56_1 = e0 & op(e3, e2) = e0
% 159.96/26.20    (2)  all_56_1 = e1
% 159.96/26.20    (3)   ~ (e1 = e0)
% 159.96/26.20  
% 159.96/26.20  Begin of proof
% 159.96/26.20  | 
% 159.96/26.20  | ALPHA: (1) implies:
% 159.96/26.20  |   (4)  all_56_1 = e0
% 159.96/26.20  | 
% 159.96/26.20  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.20  |   (5)  e1 = e0
% 159.96/26.20  | 
% 159.96/26.20  | REDUCE: (3), (5) imply:
% 159.96/26.20  |   (6)  $false
% 159.96/26.20  | 
% 159.96/26.20  | CLOSE: (6) is inconsistent.
% 159.96/26.20  | 
% 159.96/26.20  End of proof
% 159.96/26.20  
% 159.96/26.20  Sub-proof #761 shows that the following formulas are inconsistent:
% 159.96/26.20  ----------------------------------------------------------------
% 159.96/26.20    (1)  all_56_6 = e2 & op(e1, e3) = e2
% 159.96/26.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.20    (3)  op(e1, e3) = all_52_2
% 159.96/26.20    (4)   ~ (all_52_2 = e2)
% 159.96/26.20  
% 159.96/26.20  Begin of proof
% 159.96/26.20  | 
% 159.96/26.20  | ALPHA: (1) implies:
% 159.96/26.20  |   (5)  op(e1, e3) = e2
% 159.96/26.20  | 
% 159.96/26.20  | GROUND_INST: instantiating (2) with all_52_2, e2, e3, e1, simplifying with
% 159.96/26.20  |              (3), (5) gives:
% 159.96/26.20  |   (6)  all_52_2 = e2
% 159.96/26.20  | 
% 159.96/26.20  | REDUCE: (4), (6) imply:
% 159.96/26.20  |   (7)  $false
% 159.96/26.20  | 
% 159.96/26.20  | CLOSE: (7) is inconsistent.
% 159.96/26.20  | 
% 159.96/26.20  End of proof
% 159.96/26.20  
% 159.96/26.20  Sub-proof #762 shows that the following formulas are inconsistent:
% 159.96/26.20  ----------------------------------------------------------------
% 159.96/26.20    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 159.96/26.20         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 159.96/26.20    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 159.96/26.20         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 159.96/26.20    (3)   ~ (e3 = e2)
% 159.96/26.20    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.20    (5)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 159.96/26.20    (6)  op(e3, e3) = e3
% 159.96/26.20    (7)  op(e2, e2) = e1
% 159.96/26.20    (8)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 159.96/26.20         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 159.96/26.20    (9)   ~ (e1 = e0)
% 159.96/26.20    (10)   ~ (e2 = e1)
% 159.96/26.20    (11)   ~ (e3 = e1)
% 159.96/26.20    (12)   ~ (e2 = e0)
% 159.96/26.20    (13)   ~ (e3 = e0)
% 159.96/26.20  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | BETA: splitting (5) gives:
% 159.96/26.21  | 
% 159.96/26.21  | Case 1:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (14)  all_56_1 = e3 & op(e3, e2) = e3
% 159.96/26.21  | | 
% 159.96/26.21  | | ALPHA: (14) implies:
% 159.96/26.21  | |   (15)  all_56_1 = e3
% 159.96/26.21  | | 
% 159.96/26.21  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (15)
% 159.96/26.21  | |            are inconsistent by sub-proof #946.
% 159.96/26.21  | | 
% 159.96/26.21  | Case 2:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (16)  all_56_3 = e3 & op(e2, e2) = e3
% 159.96/26.21  | | 
% 159.96/26.21  | | ALPHA: (16) implies:
% 159.96/26.21  | |   (17)  op(e2, e2) = e3
% 159.96/26.21  | | 
% 159.96/26.21  | | REF_CLOSE: (4), (7), (11), (17) are inconsistent by sub-proof #847.
% 159.96/26.21  | | 
% 159.96/26.21  | End of split
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #763 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.21    (2)  op(e2, e1) = all_52_9
% 159.96/26.21    (3)  op(e2, e1) = e3
% 159.96/26.21    (4)   ~ (all_52_9 = e3)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | GROUND_INST: instantiating (1) with all_52_9, e3, e1, e2, simplifying with
% 159.96/26.21  |              (2), (3) gives:
% 159.96/26.21  |   (5)  all_52_9 = e3
% 159.96/26.21  | 
% 159.96/26.21  | REDUCE: (4), (5) imply:
% 159.96/26.21  |   (6)  $false
% 159.96/26.21  | 
% 159.96/26.21  | CLOSE: (6) is inconsistent.
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #764 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.96/26.21         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.96/26.21    (2)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 159.96/26.21    (3)   ~ (e3 = e2)
% 159.96/26.21    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.21    (5)  op(e3, e3) = e3
% 159.96/26.21    (6)  op(e2, e2) = e1
% 159.96/26.21    (7)   ~ (e1 = e0)
% 159.96/26.21    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.96/26.21         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.96/26.21    (9)   ~ (e2 = e1)
% 159.96/26.21    (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.96/26.21          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.96/26.21    (11)   ~ (e3 = e1)
% 159.96/26.21    (12)   ~ (e2 = e0)
% 159.96/26.21    (13)   ~ (e3 = e0)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | BETA: splitting (2) gives:
% 159.96/26.21  | 
% 159.96/26.21  | Case 1:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (14)  all_56_2 = e3 & op(e2, e3) = e3
% 159.96/26.21  | | 
% 159.96/26.21  | | ALPHA: (14) implies:
% 159.96/26.21  | |   (15)  all_56_2 = e3
% 159.96/26.21  | | 
% 159.96/26.21  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (15)
% 159.96/26.21  | |            are inconsistent by sub-proof #765.
% 159.96/26.21  | | 
% 159.96/26.21  | Case 2:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (16)  all_56_3 = e3 & op(e2, e2) = e3
% 159.96/26.21  | | 
% 159.96/26.21  | | ALPHA: (16) implies:
% 159.96/26.21  | |   (17)  op(e2, e2) = e3
% 159.96/26.21  | | 
% 159.96/26.21  | | REF_CLOSE: (4), (6), (11), (17) are inconsistent by sub-proof #847.
% 159.96/26.21  | | 
% 159.96/26.21  | End of split
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #765 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 159.96/26.21         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 159.96/26.21    (2)  all_56_2 = e3
% 159.96/26.21    (3)   ~ (e3 = e2)
% 159.96/26.21    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.21    (5)  op(e3, e3) = e3
% 159.96/26.21    (6)   ~ (e1 = e0)
% 159.96/26.21    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.96/26.21         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.96/26.21    (8)   ~ (e2 = e1)
% 159.96/26.21    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.96/26.21         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.96/26.21    (10)   ~ (e3 = e1)
% 159.96/26.21    (11)   ~ (e2 = e0)
% 159.96/26.21    (12)   ~ (e3 = e0)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | BETA: splitting (1) gives:
% 159.96/26.21  | 
% 159.96/26.21  | Case 1:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (13)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 159.96/26.21  | |           e2)
% 159.96/26.21  | | 
% 159.96/26.21  | | BETA: splitting (13) gives:
% 159.96/26.21  | | 
% 159.96/26.21  | | Case 1:
% 159.96/26.21  | | | 
% 159.96/26.21  | | |   (14)  all_56_0 = e2 & op(e3, e3) = e2
% 159.96/26.21  | | | 
% 159.96/26.21  | | | ALPHA: (14) implies:
% 159.96/26.21  | | |   (15)  op(e3, e3) = e2
% 159.96/26.21  | | | 
% 159.96/26.21  | | | REF_CLOSE: (3), (4), (5), (15) are inconsistent by sub-proof #958.
% 159.96/26.21  | | | 
% 159.96/26.21  | | Case 2:
% 159.96/26.21  | | | 
% 159.96/26.21  | | |   (16)  all_56_2 = e2 & op(e2, e3) = e2
% 159.96/26.21  | | | 
% 159.96/26.21  | | | REF_CLOSE: (2), (3), (16) are inconsistent by sub-proof #778.
% 159.96/26.21  | | | 
% 159.96/26.21  | | End of split
% 159.96/26.21  | | 
% 159.96/26.21  | Case 2:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (17)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 159.96/26.21  | |           e2)
% 159.96/26.21  | | 
% 159.96/26.21  | | BETA: splitting (17) gives:
% 159.96/26.21  | | 
% 159.96/26.21  | | Case 1:
% 159.96/26.21  | | | 
% 159.96/26.21  | | |   (18)  all_56_6 = e2 & op(e1, e3) = e2
% 159.96/26.21  | | | 
% 159.96/26.21  | | | ALPHA: (18) implies:
% 159.96/26.21  | | |   (19)  all_56_6 = e2
% 159.96/26.21  | | | 
% 159.96/26.21  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (19) are
% 159.96/26.21  | | |            inconsistent by sub-proof #770.
% 159.96/26.21  | | | 
% 159.96/26.21  | | Case 2:
% 159.96/26.21  | | | 
% 159.96/26.21  | | |   (20)  all_56_12 = e2 & op(e0, e3) = e2
% 159.96/26.21  | | | 
% 159.96/26.21  | | | ALPHA: (20) implies:
% 159.96/26.21  | | |   (21)  all_56_12 = e2
% 159.96/26.21  | | | 
% 159.96/26.21  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (21) are
% 159.96/26.21  | | |            inconsistent by sub-proof #766.
% 159.96/26.21  | | | 
% 159.96/26.21  | | End of split
% 159.96/26.21  | | 
% 159.96/26.21  | End of split
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #766 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  all_56_2 = e3
% 159.96/26.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.21    (3)  all_56_12 = e2
% 159.96/26.21    (4)  op(e3, e3) = e3
% 159.96/26.21    (5)   ~ (e1 = e0)
% 159.96/26.21    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.96/26.21         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.96/26.21    (7)   ~ (e2 = e1)
% 159.96/26.21    (8)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.96/26.21         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.96/26.21    (9)   ~ (e3 = e1)
% 159.96/26.21    (10)   ~ (e2 = e0)
% 159.96/26.21    (11)   ~ (e3 = e0)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | BETA: splitting (6) gives:
% 159.96/26.21  | 
% 159.96/26.21  | Case 1:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 159.96/26.21  | |           e0)
% 159.96/26.21  | | 
% 159.96/26.21  | | REF_CLOSE: (1), (2), (4), (11), (12) are inconsistent by sub-proof #776.
% 159.96/26.21  | | 
% 159.96/26.21  | Case 2:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (13)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 159.96/26.21  | |           e0)
% 159.96/26.21  | | 
% 159.96/26.21  | | BETA: splitting (13) gives:
% 159.96/26.21  | | 
% 159.96/26.21  | | Case 1:
% 159.96/26.21  | | | 
% 159.96/26.21  | | |   (14)  all_56_6 = e0 & op(e1, e3) = e0
% 159.96/26.21  | | | 
% 159.96/26.21  | | | ALPHA: (14) implies:
% 159.96/26.21  | | |   (15)  all_56_6 = e0
% 159.96/26.21  | | | 
% 159.96/26.21  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (15) are inconsistent
% 159.96/26.21  | | |            by sub-proof #768.
% 159.96/26.21  | | | 
% 159.96/26.21  | | Case 2:
% 159.96/26.21  | | | 
% 159.96/26.21  | | |   (16)  all_56_12 = e0 & op(e0, e3) = e0
% 159.96/26.21  | | | 
% 159.96/26.21  | | | REF_CLOSE: (3), (10), (16) are inconsistent by sub-proof #767.
% 159.96/26.21  | | | 
% 159.96/26.21  | | End of split
% 159.96/26.21  | | 
% 159.96/26.21  | End of split
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #767 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  all_56_12 = e0 & op(e0, e3) = e0
% 159.96/26.21    (2)  all_56_12 = e2
% 159.96/26.21    (3)   ~ (e2 = e0)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | ALPHA: (1) implies:
% 159.96/26.21  |   (4)  all_56_12 = e0
% 159.96/26.21  | 
% 159.96/26.21  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.21  |   (5)  e2 = e0
% 159.96/26.21  | 
% 159.96/26.21  | REDUCE: (3), (5) imply:
% 159.96/26.21  |   (6)  $false
% 159.96/26.21  | 
% 159.96/26.21  | CLOSE: (6) is inconsistent.
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #768 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  all_56_2 = e3
% 159.96/26.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.21    (3)  all_56_12 = e2
% 159.96/26.21    (4)  op(e3, e3) = e3
% 159.96/26.21    (5)  all_56_6 = e0
% 159.96/26.21    (6)   ~ (e1 = e0)
% 159.96/26.21    (7)   ~ (e2 = e1)
% 159.96/26.21    (8)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.96/26.21         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.96/26.21    (9)   ~ (e3 = e1)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | BETA: splitting (8) gives:
% 159.96/26.21  | 
% 159.96/26.21  | Case 1:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 159.96/26.21  | |           e1)
% 159.96/26.21  | | 
% 159.96/26.21  | | REF_CLOSE: (1), (2), (4), (9), (10) are inconsistent by sub-proof #773.
% 159.96/26.21  | | 
% 159.96/26.21  | Case 2:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (11)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 159.96/26.21  | |           e1)
% 159.96/26.21  | | 
% 159.96/26.21  | | BETA: splitting (11) gives:
% 159.96/26.21  | | 
% 159.96/26.21  | | Case 1:
% 159.96/26.21  | | | 
% 159.96/26.21  | | |   (12)  all_56_6 = e1 & op(e1, e3) = e1
% 159.96/26.21  | | | 
% 159.96/26.21  | | | REF_CLOSE: (5), (6), (12) are inconsistent by sub-proof #917.
% 159.96/26.21  | | | 
% 159.96/26.21  | | Case 2:
% 159.96/26.21  | | | 
% 159.96/26.21  | | |   (13)  all_56_12 = e1 & op(e0, e3) = e1
% 159.96/26.21  | | | 
% 159.96/26.21  | | | REF_CLOSE: (3), (7), (13) are inconsistent by sub-proof #769.
% 159.96/26.21  | | | 
% 159.96/26.21  | | End of split
% 159.96/26.21  | | 
% 159.96/26.21  | End of split
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #769 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  all_56_12 = e1 & op(e0, e3) = e1
% 159.96/26.21    (2)  all_56_12 = e2
% 159.96/26.21    (3)   ~ (e2 = e1)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | ALPHA: (1) implies:
% 159.96/26.21  |   (4)  all_56_12 = e1
% 159.96/26.21  | 
% 159.96/26.21  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.21  |   (5)  e2 = e1
% 159.96/26.21  | 
% 159.96/26.21  | REDUCE: (3), (5) imply:
% 159.96/26.21  |   (6)  $false
% 159.96/26.21  | 
% 159.96/26.21  | CLOSE: (6) is inconsistent.
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #770 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  all_56_2 = e3
% 159.96/26.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.21    (3)  all_56_6 = e2
% 159.96/26.21    (4)  op(e3, e3) = e3
% 159.96/26.21    (5)   ~ (e1 = e0)
% 159.96/26.21    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 159.96/26.21         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 159.96/26.21    (7)   ~ (e2 = e1)
% 159.96/26.21    (8)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 159.96/26.21         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 159.96/26.21    (9)   ~ (e3 = e1)
% 159.96/26.21    (10)   ~ (e2 = e0)
% 159.96/26.21    (11)   ~ (e3 = e0)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | BETA: splitting (6) gives:
% 159.96/26.21  | 
% 159.96/26.21  | Case 1:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 159.96/26.21  | |           e0)
% 159.96/26.21  | | 
% 159.96/26.21  | | REF_CLOSE: (1), (2), (4), (11), (12) are inconsistent by sub-proof #776.
% 159.96/26.21  | | 
% 159.96/26.21  | Case 2:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (13)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 159.96/26.21  | |           e0)
% 159.96/26.21  | | 
% 159.96/26.21  | | BETA: splitting (13) gives:
% 159.96/26.21  | | 
% 159.96/26.21  | | Case 1:
% 159.96/26.21  | | | 
% 159.96/26.21  | | |   (14)  all_56_6 = e0 & op(e1, e3) = e0
% 159.96/26.21  | | | 
% 159.96/26.21  | | | REF_CLOSE: (3), (10), (14) are inconsistent by sub-proof #775.
% 159.96/26.21  | | | 
% 159.96/26.21  | | Case 2:
% 159.96/26.21  | | | 
% 159.96/26.21  | | |   (15)  all_56_12 = e0 & op(e0, e3) = e0
% 159.96/26.21  | | | 
% 159.96/26.21  | | | ALPHA: (15) implies:
% 159.96/26.21  | | |   (16)  all_56_12 = e0
% 159.96/26.21  | | | 
% 159.96/26.21  | | | BETA: splitting (8) gives:
% 159.96/26.21  | | | 
% 159.96/26.21  | | | Case 1:
% 159.96/26.21  | | | | 
% 159.96/26.21  | | | |   (17)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3)
% 159.96/26.21  | | | |           = e1)
% 159.96/26.21  | | | | 
% 159.96/26.21  | | | | REF_CLOSE: (1), (2), (4), (9), (17) are inconsistent by sub-proof #773.
% 159.96/26.21  | | | | 
% 159.96/26.21  | | | Case 2:
% 159.96/26.21  | | | | 
% 159.96/26.21  | | | |   (18)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3)
% 159.96/26.21  | | | |           = e1)
% 159.96/26.21  | | | | 
% 159.96/26.21  | | | | BETA: splitting (18) gives:
% 159.96/26.21  | | | | 
% 159.96/26.21  | | | | Case 1:
% 159.96/26.21  | | | | | 
% 159.96/26.21  | | | | |   (19)  all_56_6 = e1 & op(e1, e3) = e1
% 159.96/26.21  | | | | | 
% 159.96/26.21  | | | | | REF_CLOSE: (3), (7), (19) are inconsistent by sub-proof #772.
% 159.96/26.21  | | | | | 
% 159.96/26.21  | | | | Case 2:
% 159.96/26.21  | | | | | 
% 159.96/26.21  | | | | |   (20)  all_56_12 = e1 & op(e0, e3) = e1
% 159.96/26.21  | | | | | 
% 159.96/26.21  | | | | | REF_CLOSE: (5), (16), (20) are inconsistent by sub-proof #771.
% 159.96/26.21  | | | | | 
% 159.96/26.21  | | | | End of split
% 159.96/26.21  | | | | 
% 159.96/26.21  | | | End of split
% 159.96/26.21  | | | 
% 159.96/26.21  | | End of split
% 159.96/26.21  | | 
% 159.96/26.21  | End of split
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #771 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  all_56_12 = e1 & op(e0, e3) = e1
% 159.96/26.21    (2)  all_56_12 = e0
% 159.96/26.21    (3)   ~ (e1 = e0)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | ALPHA: (1) implies:
% 159.96/26.21  |   (4)  all_56_12 = e1
% 159.96/26.21  | 
% 159.96/26.21  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.21  |   (5)  e1 = e0
% 159.96/26.21  | 
% 159.96/26.21  | SIMP: (5) implies:
% 159.96/26.21  |   (6)  e1 = e0
% 159.96/26.21  | 
% 159.96/26.21  | REDUCE: (3), (6) imply:
% 159.96/26.21  |   (7)  $false
% 159.96/26.21  | 
% 159.96/26.21  | CLOSE: (7) is inconsistent.
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #772 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  all_56_6 = e1 & op(e1, e3) = e1
% 159.96/26.21    (2)  all_56_6 = e2
% 159.96/26.21    (3)   ~ (e2 = e1)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | ALPHA: (1) implies:
% 159.96/26.21  |   (4)  all_56_6 = e1
% 159.96/26.21  | 
% 159.96/26.21  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.21  |   (5)  e2 = e1
% 159.96/26.21  | 
% 159.96/26.21  | REDUCE: (3), (5) imply:
% 159.96/26.21  |   (6)  $false
% 159.96/26.21  | 
% 159.96/26.21  | CLOSE: (6) is inconsistent.
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #773 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 159.96/26.21    (2)  all_56_2 = e3
% 159.96/26.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.21    (4)  op(e3, e3) = e3
% 159.96/26.21    (5)   ~ (e3 = e1)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | BETA: splitting (1) gives:
% 159.96/26.21  | 
% 159.96/26.21  | Case 1:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (6)  all_56_0 = e1 & op(e3, e3) = e1
% 159.96/26.21  | | 
% 159.96/26.21  | | ALPHA: (6) implies:
% 159.96/26.21  | |   (7)  op(e3, e3) = e1
% 159.96/26.21  | | 
% 159.96/26.21  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #995.
% 159.96/26.21  | | 
% 159.96/26.21  | Case 2:
% 159.96/26.21  | | 
% 159.96/26.21  | |   (8)  all_56_2 = e1 & op(e2, e3) = e1
% 159.96/26.21  | | 
% 159.96/26.21  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #774.
% 159.96/26.21  | | 
% 159.96/26.21  | End of split
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #774 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  all_56_2 = e1 & op(e2, e3) = e1
% 159.96/26.21    (2)  all_56_2 = e3
% 159.96/26.21    (3)   ~ (e3 = e1)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | ALPHA: (1) implies:
% 159.96/26.21  |   (4)  all_56_2 = e1
% 159.96/26.21  | 
% 159.96/26.21  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.21  |   (5)  e3 = e1
% 159.96/26.21  | 
% 159.96/26.21  | REDUCE: (3), (5) imply:
% 159.96/26.21  |   (6)  $false
% 159.96/26.21  | 
% 159.96/26.21  | CLOSE: (6) is inconsistent.
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #775 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  all_56_6 = e0 & op(e1, e3) = e0
% 159.96/26.21    (2)  all_56_6 = e2
% 159.96/26.21    (3)   ~ (e2 = e0)
% 159.96/26.21  
% 159.96/26.21  Begin of proof
% 159.96/26.21  | 
% 159.96/26.21  | ALPHA: (1) implies:
% 159.96/26.21  |   (4)  all_56_6 = e0
% 159.96/26.21  | 
% 159.96/26.21  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.21  |   (5)  e2 = e0
% 159.96/26.21  | 
% 159.96/26.21  | REDUCE: (3), (5) imply:
% 159.96/26.21  |   (6)  $false
% 159.96/26.21  | 
% 159.96/26.21  | CLOSE: (6) is inconsistent.
% 159.96/26.21  | 
% 159.96/26.21  End of proof
% 159.96/26.21  
% 159.96/26.21  Sub-proof #776 shows that the following formulas are inconsistent:
% 159.96/26.21  ----------------------------------------------------------------
% 159.96/26.21    (1)  all_56_2 = e3
% 159.96/26.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.22    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 159.96/26.22    (4)  op(e3, e3) = e3
% 159.96/26.22    (5)   ~ (e3 = e0)
% 159.96/26.22  
% 159.96/26.22  Begin of proof
% 159.96/26.22  | 
% 159.96/26.22  | BETA: splitting (3) gives:
% 159.96/26.22  | 
% 159.96/26.22  | Case 1:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (6)  all_56_0 = e0 & op(e3, e3) = e0
% 159.96/26.22  | | 
% 159.96/26.22  | | ALPHA: (6) implies:
% 159.96/26.22  | |   (7)  op(e3, e3) = e0
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #971.
% 159.96/26.22  | | 
% 159.96/26.22  | Case 2:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (8)  all_56_2 = e0 & op(e2, e3) = e0
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #777.
% 159.96/26.22  | | 
% 159.96/26.22  | End of split
% 159.96/26.22  | 
% 159.96/26.22  End of proof
% 159.96/26.22  
% 159.96/26.22  Sub-proof #777 shows that the following formulas are inconsistent:
% 159.96/26.22  ----------------------------------------------------------------
% 159.96/26.22    (1)  all_56_2 = e0 & op(e2, e3) = e0
% 159.96/26.22    (2)  all_56_2 = e3
% 159.96/26.22    (3)   ~ (e3 = e0)
% 159.96/26.22  
% 159.96/26.22  Begin of proof
% 159.96/26.22  | 
% 159.96/26.22  | ALPHA: (1) implies:
% 159.96/26.22  |   (4)  all_56_2 = e0
% 159.96/26.22  | 
% 159.96/26.22  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.22  |   (5)  e3 = e0
% 159.96/26.22  | 
% 159.96/26.22  | REDUCE: (3), (5) imply:
% 159.96/26.22  |   (6)  $false
% 159.96/26.22  | 
% 159.96/26.22  | CLOSE: (6) is inconsistent.
% 159.96/26.22  | 
% 159.96/26.22  End of proof
% 159.96/26.22  
% 159.96/26.22  Sub-proof #778 shows that the following formulas are inconsistent:
% 159.96/26.22  ----------------------------------------------------------------
% 159.96/26.22    (1)  all_56_2 = e2 & op(e2, e3) = e2
% 159.96/26.22    (2)  all_56_2 = e3
% 159.96/26.22    (3)   ~ (e3 = e2)
% 159.96/26.22  
% 159.96/26.22  Begin of proof
% 159.96/26.22  | 
% 159.96/26.22  | ALPHA: (1) implies:
% 159.96/26.22  |   (4)  all_56_2 = e2
% 159.96/26.22  | 
% 159.96/26.22  | COMBINE_EQS: (2), (4) imply:
% 159.96/26.22  |   (5)  e3 = e2
% 159.96/26.22  | 
% 159.96/26.22  | REDUCE: (3), (5) imply:
% 159.96/26.22  |   (6)  $false
% 159.96/26.22  | 
% 159.96/26.22  | CLOSE: (6) is inconsistent.
% 159.96/26.22  | 
% 159.96/26.22  End of proof
% 159.96/26.22  
% 159.96/26.22  Sub-proof #779 shows that the following formulas are inconsistent:
% 159.96/26.22  ----------------------------------------------------------------
% 159.96/26.22    (1)  op(e2, e3) = e2
% 159.96/26.22    (2)  op(e0, e0) = e2
% 159.96/26.22    (3)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.96/26.22             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.96/26.22           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.96/26.22               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.96/26.22             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.96/26.22         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.96/26.22             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.96/26.22           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.96/26.22               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.96/26.22             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7)))) |
% 159.96/26.22         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.96/26.22             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.96/26.22           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.96/26.22               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.96/26.22             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.96/26.22         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.96/26.22             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.96/26.22           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.96/26.22               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.96/26.22             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.96/26.22    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.22    (5)  op(e1, e1) = e2
% 159.96/26.22    (6)  op(e2, e2) = e1
% 159.96/26.22    (7)   ~ (e2 = e1)
% 159.96/26.22    (8)   ~ (e3 = e1)
% 159.96/26.22    (9)   ~ (e2 = e0)
% 159.96/26.22  
% 159.96/26.22  Begin of proof
% 159.96/26.22  | 
% 159.96/26.22  | BETA: splitting (3) gives:
% 159.96/26.22  | 
% 159.96/26.22  | Case 1:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (10)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.96/26.22  | |               e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.96/26.22  | |               $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.96/26.22  | |               (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.96/26.22  | |           ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.96/26.22  | |                 e3) = all_57_6 & $i(all_57_6)))) | (all_57_12 = e2 & op(e2,
% 159.96/26.22  | |             e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) | ( ~ (all_57_1 =
% 159.96/26.22  | |                 e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) & ((all_57_14 =
% 159.96/26.22  | |               e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2) =
% 159.96/26.22  | |               all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) =
% 159.96/26.22  | |               e2) | ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 &
% 159.96/26.22  | |               $i(all_57_7))))
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (1), (4), (6), (7), (8), (10) are inconsistent by sub-proof #781.
% 159.96/26.22  | | 
% 159.96/26.22  | Case 2:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (11)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.96/26.22  | |               e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.96/26.22  | |               $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.96/26.22  | |               (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.96/26.22  | |           ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.96/26.22  | |                 e1) = all_57_8 & $i(all_57_8)))) | (all_57_15 = e0 & op(e0,
% 159.96/26.22  | |             e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) | ( ~ (all_57_9 =
% 159.96/26.22  | |                 e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) & ((all_57_12 =
% 159.96/26.22  | |               e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0) =
% 159.96/26.22  | |               all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) =
% 159.96/26.22  | |               e0) | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 &
% 159.96/26.22  | |               $i(all_57_13))))
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (2), (4), (5), (7), (9), (11) are inconsistent by sub-proof #780.
% 159.96/26.22  | | 
% 159.96/26.22  | End of split
% 159.96/26.22  | 
% 159.96/26.22  End of proof
% 159.96/26.22  
% 159.96/26.22  Sub-proof #780 shows that the following formulas are inconsistent:
% 159.96/26.22  ----------------------------------------------------------------
% 159.96/26.22    (1)  op(e0, e0) = e2
% 159.96/26.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.22    (3)  op(e1, e1) = e2
% 159.96/26.22    (4)   ~ (e2 = e1)
% 159.96/26.22    (5)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) = e1) |
% 159.96/26.22             ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 & $i(all_57_4))) &
% 159.96/26.22           ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~ (all_57_5 = e2) & op(e2, e1)
% 159.96/26.22               = all_57_5 & $i(all_57_5))) & ((all_57_15 = e1 & op(e0, e0) = e1) |
% 159.96/26.22             ( ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)))) |
% 159.96/26.22         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) = e0) |
% 159.96/26.22             ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 & $i(all_57_9))) &
% 159.96/26.22           ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~ (all_57_11 = e2) & op(e2, e0)
% 159.96/26.22               = all_57_11 & $i(all_57_11))) & ((all_57_14 = e0 & op(e1, e1) = e0)
% 159.96/26.22             | ( ~ (all_57_13 = e1) & op(e1, e0) = all_57_13 & $i(all_57_13))))
% 159.96/26.22    (6)   ~ (e2 = e0)
% 159.96/26.22  
% 159.96/26.22  Begin of proof
% 159.96/26.22  | 
% 159.96/26.22  | BETA: splitting (5) gives:
% 159.96/26.22  | 
% 159.96/26.22  | Case 1:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_10 = e1 & op(e3, e3) =
% 159.96/26.22  | |            e1) | ( ~ (all_57_4 = e3) & op(e3, e1) = all_57_4 &
% 159.96/26.22  | |            $i(all_57_4))) & ((all_57_12 = e1 & op(e2, e2) = e1) | ( ~
% 159.96/26.22  | |            (all_57_5 = e2) & op(e2, e1) = all_57_5 & $i(all_57_5))) &
% 159.96/26.22  | |        ((all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0,
% 159.96/26.22  | |              e1) = all_57_8 & $i(all_57_8)))
% 159.96/26.22  | | 
% 159.96/26.22  | | ALPHA: (7) implies:
% 159.96/26.22  | |   (8)  op(e1, e1) = e1
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #986.
% 159.96/26.22  | | 
% 159.96/26.22  | Case 2:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_10 = e0 & op(e3, e3) =
% 159.96/26.22  | |            e0) | ( ~ (all_57_9 = e3) & op(e3, e0) = all_57_9 &
% 159.96/26.22  | |            $i(all_57_9))) & ((all_57_12 = e0 & op(e2, e2) = e0) | ( ~
% 159.96/26.22  | |            (all_57_11 = e2) & op(e2, e0) = all_57_11 & $i(all_57_11))) &
% 159.96/26.22  | |        ((all_57_14 = e0 & op(e1, e1) = e0) | ( ~ (all_57_13 = e1) & op(e1,
% 159.96/26.22  | |              e0) = all_57_13 & $i(all_57_13)))
% 159.96/26.22  | | 
% 159.96/26.22  | | ALPHA: (9) implies:
% 159.96/26.22  | |   (10)  op(e0, e0) = e0
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #979.
% 159.96/26.22  | | 
% 159.96/26.22  | End of split
% 159.96/26.22  | 
% 159.96/26.22  End of proof
% 159.96/26.22  
% 159.96/26.22  Sub-proof #781 shows that the following formulas are inconsistent:
% 159.96/26.22  ----------------------------------------------------------------
% 159.96/26.22    (1)  op(e2, e3) = e2
% 159.96/26.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.22    (3)  op(e2, e2) = e1
% 159.96/26.22    (4)   ~ (e2 = e1)
% 159.96/26.22    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 159.96/26.22             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 159.96/26.22           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 159.96/26.22               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 159.96/26.22             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 159.96/26.22         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 159.96/26.22             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 159.96/26.22           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 159.96/26.22               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 159.96/26.22             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 159.96/26.22    (6)   ~ (e3 = e1)
% 159.96/26.22  
% 159.96/26.22  Begin of proof
% 159.96/26.22  | 
% 159.96/26.22  | BETA: splitting (5) gives:
% 159.96/26.22  | 
% 159.96/26.22  | Case 1:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 159.96/26.22  | |            e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 159.96/26.22  | |            $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 159.96/26.22  | |            (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 159.96/26.22  | |        ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 159.96/26.22  | |              e3) = all_57_6 & $i(all_57_6)))
% 159.96/26.22  | | 
% 159.96/26.22  | | ALPHA: (7) implies:
% 159.96/26.22  | |   (8)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3)
% 159.96/26.22  | |          = all_57_0 & $i(all_57_0))
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (1), (2), (3), (6), (8) are inconsistent by sub-proof #782.
% 159.96/26.22  | | 
% 159.96/26.22  | Case 2:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 159.96/26.22  | |            e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 159.96/26.22  | |            $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 159.96/26.22  | |            (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 159.96/26.22  | |        ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 159.96/26.22  | |              e2) = all_57_7 & $i(all_57_7)))
% 159.96/26.22  | | 
% 159.96/26.22  | | ALPHA: (9) implies:
% 159.96/26.22  | |   (10)  op(e2, e2) = e2
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #993.
% 159.96/26.22  | | 
% 159.96/26.22  | End of split
% 159.96/26.22  | 
% 159.96/26.22  End of proof
% 159.96/26.22  
% 159.96/26.22  Sub-proof #782 shows that the following formulas are inconsistent:
% 159.96/26.22  ----------------------------------------------------------------
% 159.96/26.22    (1)  op(e2, e3) = e2
% 159.96/26.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.22    (3)  op(e2, e2) = e1
% 159.96/26.22    (4)  (all_57_12 = e3 & op(e2, e2) = e3) | ( ~ (all_57_0 = e2) & op(e2, e3) =
% 159.96/26.22           all_57_0 & $i(all_57_0))
% 159.96/26.22    (5)   ~ (e3 = e1)
% 159.96/26.22  
% 159.96/26.22  Begin of proof
% 159.96/26.22  | 
% 159.96/26.22  | BETA: splitting (4) gives:
% 159.96/26.22  | 
% 159.96/26.22  | Case 1:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (6)  all_57_12 = e3 & op(e2, e2) = e3
% 159.96/26.22  | | 
% 159.96/26.22  | | ALPHA: (6) implies:
% 159.96/26.22  | |   (7)  op(e2, e2) = e3
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #847.
% 159.96/26.22  | | 
% 159.96/26.22  | Case 2:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (8)   ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0)
% 159.96/26.22  | | 
% 159.96/26.22  | | ALPHA: (8) implies:
% 159.96/26.22  | |   (9)   ~ (all_57_0 = e2)
% 159.96/26.22  | |   (10)  op(e2, e3) = all_57_0
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #783.
% 159.96/26.22  | | 
% 159.96/26.22  | End of split
% 159.96/26.22  | 
% 159.96/26.22  End of proof
% 159.96/26.22  
% 159.96/26.22  Sub-proof #783 shows that the following formulas are inconsistent:
% 159.96/26.22  ----------------------------------------------------------------
% 159.96/26.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.22    (2)  op(e2, e3) = all_57_0
% 159.96/26.22    (3)  op(e2, e3) = e2
% 159.96/26.22    (4)   ~ (all_57_0 = e2)
% 159.96/26.22  
% 159.96/26.22  Begin of proof
% 159.96/26.22  | 
% 159.96/26.22  | GROUND_INST: instantiating (1) with e2, all_57_0, e3, e2, simplifying with
% 159.96/26.22  |              (2), (3) gives:
% 159.96/26.22  |   (5)  all_57_0 = e2
% 159.96/26.22  | 
% 159.96/26.22  | REDUCE: (4), (5) imply:
% 159.96/26.22  |   (6)  $false
% 159.96/26.22  | 
% 159.96/26.22  | CLOSE: (6) is inconsistent.
% 159.96/26.22  | 
% 159.96/26.22  End of proof
% 159.96/26.22  
% 159.96/26.22  Sub-proof #784 shows that the following formulas are inconsistent:
% 159.96/26.22  ----------------------------------------------------------------
% 159.96/26.22    (1)   ~ (all_52_7 = e0)
% 159.96/26.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.22    (3)  op(e1, e1) = e1
% 159.96/26.22    (4)  op(e0, e2) = all_52_7
% 159.96/26.22    (5)  op(e3, e3) = e3
% 159.96/26.22    (6)   ~ (e1 = e0)
% 159.96/26.22    (7)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 159.96/26.22           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.96/26.22           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 159.96/26.22           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 159.96/26.22           & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.96/26.22    (8)   ~ (e3 = e0)
% 159.96/26.22  
% 159.96/26.22  Begin of proof
% 159.96/26.22  | 
% 159.96/26.22  | BETA: splitting (7) gives:
% 159.96/26.22  | 
% 159.96/26.22  | Case 1:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (9)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 159.96/26.22  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 159.96/26.22  | | 
% 159.96/26.22  | | ALPHA: (9) implies:
% 159.96/26.22  | |   (10)  op(e1, e1) = e0
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #903.
% 159.96/26.22  | | 
% 159.96/26.22  | Case 2:
% 159.96/26.22  | | 
% 159.96/26.22  | |   (11)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 159.96/26.22  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.96/26.22  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 159.96/26.22  | | 
% 159.96/26.22  | | REF_CLOSE: (1), (2), (4), (5), (8), (11) are inconsistent by sub-proof #968.
% 159.96/26.22  | | 
% 159.96/26.22  | End of split
% 159.96/26.22  | 
% 159.96/26.22  End of proof
% 159.96/26.22  
% 159.96/26.22  Sub-proof #785 shows that the following formulas are inconsistent:
% 159.96/26.22  ----------------------------------------------------------------
% 159.96/26.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.22    (2)  op(e3, e3) = e3
% 159.96/26.22    (3)  op(e0, e3) = e1
% 159.96/26.22    (4)  op(e2, e2) = e1
% 159.96/26.22    (5)   ~ (e1 = e0)
% 159.96/26.23    (6)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 159.96/26.23         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 159.96/26.23           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 159.96/26.23           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 159.96/26.23           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.96/26.23    (7)   ~ (e3 = e0)
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.23  | BETA: splitting (6) gives:
% 159.96/26.23  | 
% 159.96/26.23  | Case 1:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (8)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (8) implies:
% 159.96/26.23  | |   (9)  op(e0, e3) = e0
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #786.
% 159.96/26.23  | | 
% 159.96/26.23  | Case 2:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (10)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.96/26.23  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 159.96/26.23  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.96/26.23  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 159.96/26.23  | | 
% 159.96/26.23  | | BETA: splitting (10) gives:
% 159.96/26.23  | | 
% 159.96/26.23  | | Case 1:
% 159.96/26.23  | | | 
% 159.96/26.23  | | |   (11)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 159.96/26.23  | | |           e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 159.96/26.23  | | | 
% 159.96/26.23  | | | ALPHA: (11) implies:
% 159.96/26.23  | | |   (12)  op(e3, e3) = e0
% 159.96/26.23  | | | 
% 159.96/26.23  | | | REF_CLOSE: (1), (2), (7), (12) are inconsistent by sub-proof #971.
% 159.96/26.23  | | | 
% 159.96/26.23  | | Case 2:
% 159.96/26.23  | | | 
% 159.96/26.23  | | |   (13)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 159.96/26.23  | | |           e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 159.96/26.23  | | | 
% 159.96/26.23  | | | ALPHA: (13) implies:
% 159.96/26.23  | | |   (14)  op(e2, e2) = e0
% 159.96/26.23  | | | 
% 159.96/26.23  | | | REF_CLOSE: (1), (4), (5), (14) are inconsistent by sub-proof #960.
% 159.96/26.23  | | | 
% 159.96/26.23  | | End of split
% 159.96/26.23  | | 
% 159.96/26.23  | End of split
% 159.96/26.23  | 
% 159.96/26.23  End of proof
% 159.96/26.23  
% 159.96/26.23  Sub-proof #786 shows that the following formulas are inconsistent:
% 159.96/26.23  ----------------------------------------------------------------
% 159.96/26.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.23    (2)  op(e0, e3) = e1
% 159.96/26.23    (3)  op(e0, e3) = e0
% 159.96/26.23    (4)   ~ (e1 = e0)
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.23  | GROUND_INST: instantiating (1) with e1, e0, e3, e0, simplifying with (2), (3)
% 159.96/26.23  |              gives:
% 159.96/26.23  |   (5)  e1 = e0
% 159.96/26.23  | 
% 159.96/26.23  | REDUCE: (4), (5) imply:
% 159.96/26.23  |   (6)  $false
% 159.96/26.23  | 
% 159.96/26.23  | CLOSE: (6) is inconsistent.
% 159.96/26.23  | 
% 159.96/26.23  End of proof
% 159.96/26.23  
% 159.96/26.23  Sub-proof #787 shows that the following formulas are inconsistent:
% 159.96/26.23  ----------------------------------------------------------------
% 159.96/26.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.23    (2)  op(e3, e1) = all_52_8
% 159.96/26.23    (3)  op(e3, e3) = e3
% 159.96/26.23    (4)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 159.96/26.23           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.96/26.23           = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1)
% 159.96/26.23           & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 159.96/26.23           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 159.96/26.23           e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.96/26.23    (5)   ~ (e3 = e1)
% 159.96/26.23    (6)   ~ (all_52_8 = e3)
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.23  | BETA: splitting (4) gives:
% 159.96/26.23  | 
% 159.96/26.23  | Case 1:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (7)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1)
% 159.96/26.23  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 159.96/26.23  | |          e0) = e3 & $i(all_57_10)
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (7) implies:
% 159.96/26.23  | |   (8)  op(e3, e1) = e3
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #982.
% 159.96/26.23  | | 
% 159.96/26.23  | Case 2:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (9)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 159.96/26.23  | |          op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1
% 159.96/26.23  | |          &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 159.96/26.23  | |            e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (1), (2), (3), (5), (6), (9) are inconsistent by sub-proof #981.
% 159.96/26.23  | | 
% 159.96/26.23  | End of split
% 159.96/26.23  | 
% 159.96/26.23  End of proof
% 159.96/26.23  
% 159.96/26.23  Sub-proof #788 shows that the following formulas are inconsistent:
% 159.96/26.23  ----------------------------------------------------------------
% 159.96/26.23    (1)   ~ (all_52_6 = e1)
% 159.96/26.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.23    (3)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 159.96/26.23           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.96/26.23           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 159.96/26.23           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 159.96/26.23             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.96/26.23    (4)  op(e1, e2) = all_52_6
% 159.96/26.23    (5)  op(e3, e3) = e3
% 159.96/26.23    (6)   ~ (e3 = e1)
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.23  | BETA: splitting (3) gives:
% 159.96/26.23  | 
% 159.96/26.23  | Case 1:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (7)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 159.96/26.23  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 159.96/26.23  | |        all_57_14 & $i(all_57_14)
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (7) implies:
% 159.96/26.23  | |   (8)  op(e3, e3) = e1
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #995.
% 159.96/26.23  | | 
% 159.96/26.23  | Case 2:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 159.96/26.23  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 159.96/26.23  | |        all_57_14 & $i(all_57_14)
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (9) implies:
% 159.96/26.23  | |   (10)  op(e1, e2) = e1
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #984.
% 159.96/26.23  | | 
% 159.96/26.23  | End of split
% 159.96/26.23  | 
% 159.96/26.23  End of proof
% 159.96/26.23  
% 159.96/26.23  Sub-proof #789 shows that the following formulas are inconsistent:
% 159.96/26.23  ----------------------------------------------------------------
% 159.96/26.23    (1)  op(e0, e0) = e1
% 159.96/26.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.23    (3)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.96/26.23    (4)  all_54_15 = all_14_2
% 159.96/26.23    (5)   ~ (all_14_2 = e2)
% 159.96/26.23    (6)  op(e0, e0) = all_14_2
% 159.96/26.23    (7)   ~ (all_14_2 = e1)
% 159.96/26.23    (8)   ~ (all_14_2 = e3)
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.23  | BETA: splitting (3) gives:
% 159.96/26.23  | 
% 159.96/26.23  | Case 1:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (9)  all_54_15 = e3
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #1010.
% 159.96/26.23  | | 
% 159.96/26.23  | Case 2:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (10)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.96/26.23  | | 
% 159.96/26.23  | | BETA: splitting (10) gives:
% 159.96/26.23  | | 
% 159.96/26.23  | | Case 1:
% 159.96/26.23  | | | 
% 159.96/26.23  | | |   (11)  all_54_15 = e2
% 159.96/26.23  | | | 
% 159.96/26.23  | | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #1009.
% 159.96/26.23  | | | 
% 159.96/26.23  | | Case 2:
% 159.96/26.23  | | | 
% 159.96/26.23  | | |   (12)  all_54_15 = e1 | all_54_15 = e0
% 159.96/26.23  | | | 
% 159.96/26.23  | | | REF_CLOSE: (1), (2), (4), (6), (7), (12) are inconsistent by sub-proof
% 159.96/26.23  | | |            #790.
% 159.96/26.23  | | | 
% 159.96/26.23  | | End of split
% 159.96/26.23  | | 
% 159.96/26.23  | End of split
% 159.96/26.23  | 
% 159.96/26.23  End of proof
% 159.96/26.23  
% 159.96/26.23  Sub-proof #790 shows that the following formulas are inconsistent:
% 159.96/26.23  ----------------------------------------------------------------
% 159.96/26.23    (1)  op(e0, e0) = e1
% 159.96/26.23    (2)  all_54_15 = e1 | all_54_15 = e0
% 159.96/26.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.23    (4)  all_54_15 = all_14_2
% 159.96/26.23    (5)  op(e0, e0) = all_14_2
% 159.96/26.23    (6)   ~ (all_14_2 = e1)
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.23  | BETA: splitting (2) gives:
% 159.96/26.23  | 
% 159.96/26.23  | Case 1:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (7)  all_54_15 = e1
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #1008.
% 159.96/26.23  | | 
% 159.96/26.23  | Case 2:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (8)  all_54_15 = e0
% 159.96/26.23  | | 
% 159.96/26.23  | | COMBINE_EQS: (4), (8) imply:
% 159.96/26.23  | |   (9)  all_14_2 = e0
% 159.96/26.23  | | 
% 159.96/26.23  | | SIMP: (9) implies:
% 159.96/26.23  | |   (10)  all_14_2 = e0
% 159.96/26.23  | | 
% 159.96/26.23  | | REDUCE: (6), (10) imply:
% 159.96/26.23  | |   (11)   ~ (e1 = e0)
% 159.96/26.23  | | 
% 159.96/26.23  | | SIMP: (11) implies:
% 159.96/26.23  | |   (12)   ~ (e1 = e0)
% 159.96/26.23  | | 
% 159.96/26.23  | | REDUCE: (5), (10) imply:
% 159.96/26.23  | |   (13)  op(e0, e0) = e0
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (1), (3), (5), (12), (13) are inconsistent by sub-proof #991.
% 159.96/26.23  | | 
% 159.96/26.23  | End of split
% 159.96/26.23  | 
% 159.96/26.23  End of proof
% 159.96/26.23  
% 159.96/26.23  Sub-proof #791 shows that the following formulas are inconsistent:
% 159.96/26.23  ----------------------------------------------------------------
% 159.96/26.23    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 159.96/26.23           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.96/26.23           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 159.96/26.23           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 159.96/26.23           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 159.96/26.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.23    (3)  op(e1, e1) = e1
% 159.96/26.23    (4)  op(e1, e3) = all_52_2
% 159.96/26.23    (5)   ~ (all_52_2 = e1)
% 159.96/26.23    (6)   ~ (e3 = e1)
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.23  | BETA: splitting (1) gives:
% 159.96/26.23  | 
% 159.96/26.23  | Case 1:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 159.96/26.23  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 159.96/26.23  | |          e1) = e3 & $i(all_57_10)
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (7) implies:
% 159.96/26.23  | |   (8)  op(e1, e1) = e3
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1003.
% 159.96/26.23  | | 
% 159.96/26.23  | Case 2:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 159.96/26.23  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 159.96/26.23  | |        all_57_14 & $i(all_57_14)
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (9) implies:
% 159.96/26.23  | |   (10)  op(e1, e3) = e1
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #990.
% 159.96/26.23  | | 
% 159.96/26.23  | End of split
% 159.96/26.23  | 
% 159.96/26.23  End of proof
% 159.96/26.23  
% 159.96/26.23  Sub-proof #792 shows that the following formulas are inconsistent:
% 159.96/26.23  ----------------------------------------------------------------
% 159.96/26.23    (1)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 159.96/26.23           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 159.96/26.23           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 159.96/26.23           & op(e3, e3) = e3 & op(e3, e2) = e3)
% 159.96/26.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.23    (3)  op(e3, e2) = all_52_4
% 159.96/26.23    (4)   ~ (all_52_4 = e3)
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.23  | BETA: splitting (1) gives:
% 159.96/26.23  | 
% 159.96/26.23  | Case 1:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (5)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 159.96/26.23  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 159.96/26.23  | |          e0) = e3 & $i(all_57_10)
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (5) implies:
% 159.96/26.23  | |   (6)  op(e3, e2) = e3
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #998.
% 159.96/26.23  | | 
% 159.96/26.23  | Case 2:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (7)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 159.96/26.23  | |        op(e3, e2) = e3
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (7) implies:
% 159.96/26.23  | |   (8)  op(e3, e2) = e3
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #998.
% 159.96/26.23  | | 
% 159.96/26.23  | End of split
% 159.96/26.23  | 
% 159.96/26.23  End of proof
% 159.96/26.23  
% 159.96/26.23  Sub-proof #793 shows that the following formulas are inconsistent:
% 159.96/26.23  ----------------------------------------------------------------
% 159.96/26.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.23    (2)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2,
% 159.96/26.23             e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 159.96/26.23           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 159.96/26.23             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 159.96/26.23           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 159.96/26.23           & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 159.96/26.23           $i(all_57_12))
% 159.96/26.23    (3)  op(e1, e1) = e1
% 159.96/26.23    (4)  op(e2, e2) = e1
% 159.96/26.23    (5)   ~ (e2 = e1)
% 159.96/26.23    (6)   ~ (e3 = e1)
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.23  | BETA: splitting (2) gives:
% 159.96/26.23  | 
% 159.96/26.23  | Case 1:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (7)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 159.96/26.23  | |        op(e2, e2) = e2
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (7) implies:
% 159.96/26.23  | |   (8)  op(e2, e2) = e2
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #993.
% 159.96/26.23  | | 
% 159.96/26.23  | Case 2:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (9)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 159.96/26.23  | |          & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 &
% 159.96/26.23  | |          op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 159.96/26.23  | |          all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2)
% 159.96/26.23  | |          = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (1), (3), (4), (6), (9) are inconsistent by sub-proof #794.
% 159.96/26.23  | | 
% 159.96/26.23  | End of split
% 159.96/26.23  | 
% 159.96/26.23  End of proof
% 159.96/26.23  
% 159.96/26.23  Sub-proof #794 shows that the following formulas are inconsistent:
% 159.96/26.23  ----------------------------------------------------------------
% 159.96/26.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.23    (2)  op(e1, e1) = e1
% 159.96/26.23    (3)  op(e2, e2) = e1
% 159.96/26.23    (4)   ~ (e3 = e1)
% 159.96/26.23    (5)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 159.96/26.23           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 159.96/26.23           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 159.96/26.23           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 159.96/26.23           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.23  | BETA: splitting (5) gives:
% 159.96/26.23  | 
% 159.96/26.23  | Case 1:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (6)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 159.96/26.23  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 159.96/26.23  | |          e1) = e3 & $i(all_57_10)
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (6) implies:
% 159.96/26.23  | |   (7)  op(e1, e1) = e3
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #1003.
% 159.96/26.23  | | 
% 159.96/26.23  | Case 2:
% 159.96/26.23  | | 
% 159.96/26.23  | |   (8)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 159.96/26.23  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 159.96/26.23  | |          e1) = e2 & $i(all_57_12)
% 159.96/26.23  | | 
% 159.96/26.23  | | ALPHA: (8) implies:
% 159.96/26.23  | |   (9)   ~ (all_57_12 = e1)
% 159.96/26.23  | |   (10)  op(e2, e2) = all_57_12
% 159.96/26.23  | | 
% 159.96/26.23  | | REF_CLOSE: (1), (3), (9), (10) are inconsistent by sub-proof #795.
% 159.96/26.23  | | 
% 159.96/26.23  | End of split
% 159.96/26.23  | 
% 159.96/26.23  End of proof
% 159.96/26.23  
% 159.96/26.23  Sub-proof #795 shows that the following formulas are inconsistent:
% 159.96/26.23  ----------------------------------------------------------------
% 159.96/26.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.23    (2)  op(e2, e2) = all_57_12
% 159.96/26.23    (3)  op(e2, e2) = e1
% 159.96/26.23    (4)   ~ (all_57_12 = e1)
% 159.96/26.23  
% 159.96/26.23  Begin of proof
% 159.96/26.23  | 
% 159.96/26.24  | GROUND_INST: instantiating (1) with e1, all_57_12, e2, e2, simplifying with
% 159.96/26.24  |              (2), (3) gives:
% 159.96/26.24  |   (5)  all_57_12 = e1
% 159.96/26.24  | 
% 159.96/26.24  | REDUCE: (4), (5) imply:
% 159.96/26.24  |   (6)  $false
% 159.96/26.24  | 
% 159.96/26.24  | CLOSE: (6) is inconsistent.
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #796 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (2)  op(e3, e0) = e3
% 159.96/26.24    (3)  op(e3, e0) = e1
% 159.96/26.24    (4)   ~ (e3 = e1)
% 159.96/26.24  
% 159.96/26.24  Begin of proof
% 159.96/26.24  | 
% 159.96/26.24  | GROUND_INST: instantiating (1) with e1, e3, e0, e3, simplifying with (2), (3)
% 159.96/26.24  |              gives:
% 159.96/26.24  |   (5)  e3 = e1
% 159.96/26.24  | 
% 159.96/26.24  | REDUCE: (4), (5) imply:
% 159.96/26.24  |   (6)  $false
% 159.96/26.24  | 
% 159.96/26.24  | CLOSE: (6) is inconsistent.
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #797 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)  op(e0, e0) = e2
% 159.96/26.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (3)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.96/26.24    (4)  all_54_15 = all_14_2
% 159.96/26.24    (5)   ~ (all_14_2 = e2)
% 159.96/26.24    (6)  op(e0, e0) = all_14_2
% 159.96/26.24    (7)   ~ (all_14_2 = e1)
% 159.96/26.24    (8)   ~ (all_14_2 = e3)
% 159.96/26.24  
% 159.96/26.24  Begin of proof
% 159.96/26.24  | 
% 159.96/26.24  | BETA: splitting (3) gives:
% 159.96/26.24  | 
% 159.96/26.24  | Case 1:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (9)  all_54_15 = e3
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #1010.
% 159.96/26.24  | | 
% 159.96/26.24  | Case 2:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (10)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10) are inconsistent by sub-proof
% 159.96/26.24  | |            #798.
% 159.96/26.24  | | 
% 159.96/26.24  | End of split
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #798 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.96/26.24    (2)  op(e0, e0) = e2
% 159.96/26.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (4)  all_54_15 = all_14_2
% 159.96/26.24    (5)   ~ (all_14_2 = e2)
% 159.96/26.24    (6)  op(e0, e0) = all_14_2
% 159.96/26.24    (7)   ~ (all_14_2 = e1)
% 159.96/26.24  
% 159.96/26.24  Begin of proof
% 159.96/26.24  | 
% 159.96/26.24  | BETA: splitting (1) gives:
% 159.96/26.24  | 
% 159.96/26.24  | Case 1:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (8)  all_54_15 = e2
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1009.
% 159.96/26.24  | | 
% 159.96/26.24  | Case 2:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (9)   ~ (all_54_15 = e2)
% 159.96/26.24  | |   (10)  all_54_15 = e1 | all_54_15 = e0
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10) are inconsistent by sub-proof
% 159.96/26.24  | |            #799.
% 159.96/26.24  | | 
% 159.96/26.24  | End of split
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #799 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)  op(e0, e0) = e2
% 159.96/26.24    (2)  all_54_15 = e1 | all_54_15 = e0
% 159.96/26.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (4)  all_54_15 = all_14_2
% 159.96/26.24    (5)   ~ (all_14_2 = e2)
% 159.96/26.24    (6)  op(e0, e0) = all_14_2
% 159.96/26.24    (7)   ~ (all_14_2 = e1)
% 159.96/26.24  
% 159.96/26.24  Begin of proof
% 159.96/26.24  | 
% 159.96/26.24  | BETA: splitting (2) gives:
% 159.96/26.24  | 
% 159.96/26.24  | Case 1:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (8)  all_54_15 = e1
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (4), (7), (8) are inconsistent by sub-proof #1008.
% 159.96/26.24  | | 
% 159.96/26.24  | Case 2:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (9)  all_54_15 = e0
% 159.96/26.24  | | 
% 159.96/26.24  | | COMBINE_EQS: (4), (9) imply:
% 159.96/26.24  | |   (10)  all_14_2 = e0
% 159.96/26.24  | | 
% 159.96/26.24  | | SIMP: (10) implies:
% 159.96/26.24  | |   (11)  all_14_2 = e0
% 159.96/26.24  | | 
% 159.96/26.24  | | REDUCE: (5), (11) imply:
% 159.96/26.24  | |   (12)   ~ (e2 = e0)
% 159.96/26.24  | | 
% 159.96/26.24  | | SIMP: (12) implies:
% 159.96/26.24  | |   (13)   ~ (e2 = e0)
% 159.96/26.24  | | 
% 159.96/26.24  | | REDUCE: (6), (11) imply:
% 159.96/26.24  | |   (14)  op(e0, e0) = e0
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (1), (3), (13), (14) are inconsistent by sub-proof #979.
% 159.96/26.24  | | 
% 159.96/26.24  | End of split
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #800 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (2)  op(e1, e1) = e1
% 159.96/26.24    (3)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 159.96/26.24           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 159.96/26.24           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3
% 159.96/26.24           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 159.96/26.24           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.96/26.24    (4)  op(e2, e2) = e1
% 159.96/26.24    (5)   ~ (e2 = e1)
% 159.96/26.24    (6)   ~ (e3 = e1)
% 159.96/26.24  
% 159.96/26.24  Begin of proof
% 159.96/26.24  | 
% 159.96/26.24  | BETA: splitting (3) gives:
% 159.96/26.24  | 
% 159.96/26.24  | Case 1:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (7)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 159.96/26.24  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 159.96/26.24  | |          e1) = e2 & $i(all_57_12)
% 159.96/26.24  | | 
% 159.96/26.24  | | ALPHA: (7) implies:
% 159.96/26.24  | |   (8)  op(e1, e1) = e2
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #986.
% 159.96/26.24  | | 
% 159.96/26.24  | Case 2:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (9)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1)
% 159.96/26.24  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 159.96/26.24  | |          e2) = e3 & $i(all_57_10)
% 159.96/26.24  | | 
% 159.96/26.24  | | ALPHA: (9) implies:
% 159.96/26.24  | |   (10)  op(e2, e2) = e3
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #847.
% 159.96/26.24  | | 
% 159.96/26.24  | End of split
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #801 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)   ~ (e3 = e2)
% 159.96/26.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (3)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 159.96/26.24           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.96/26.24           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 159.96/26.24           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 159.96/26.24           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 159.96/26.24    (4)  op(e3, e3) = e3
% 159.96/26.24    (5)  op(e2, e2) = e1
% 159.96/26.24    (6)   ~ (e3 = e1)
% 159.96/26.24  
% 159.96/26.24  Begin of proof
% 159.96/26.24  | 
% 159.96/26.24  | BETA: splitting (3) gives:
% 159.96/26.24  | 
% 159.96/26.24  | Case 1:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (7)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 159.96/26.24  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 159.96/26.24  | |        all_57_12 & $i(all_57_12)
% 159.96/26.24  | | 
% 159.96/26.24  | | ALPHA: (7) implies:
% 159.96/26.24  | |   (8)  op(e3, e3) = e2
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #958.
% 159.96/26.24  | | 
% 159.96/26.24  | Case 2:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (9)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2)
% 159.96/26.24  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 159.96/26.24  | |          e2) = e3 & $i(all_57_10)
% 159.96/26.24  | | 
% 159.96/26.24  | | ALPHA: (9) implies:
% 159.96/26.24  | |   (10)  op(e2, e2) = e3
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #847.
% 159.96/26.24  | | 
% 159.96/26.24  | End of split
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #802 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)  op(e0, e1) = all_52_11
% 159.96/26.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (3)   ~ (all_52_11 = e1)
% 159.96/26.24    (4)  op(e0, e0) = all_14_2
% 159.96/26.24    (5)   ~ (all_14_2 = e1)
% 159.96/26.24    (6)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.96/26.24  
% 159.96/26.24  Begin of proof
% 159.96/26.24  | 
% 159.96/26.24  | BETA: splitting (6) gives:
% 159.96/26.24  | 
% 159.96/26.24  | Case 1:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (7)  all_56_14 = e1 & op(e0, e1) = e1
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #803.
% 159.96/26.24  | | 
% 159.96/26.24  | Case 2:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (8)  all_56_15 = e1 & op(e0, e0) = e1
% 159.96/26.24  | | 
% 159.96/26.24  | | ALPHA: (8) implies:
% 159.96/26.24  | |   (9)  op(e0, e0) = e1
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #805.
% 159.96/26.24  | | 
% 159.96/26.24  | End of split
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #803 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)  all_56_14 = e1 & op(e0, e1) = e1
% 159.96/26.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (3)  op(e0, e1) = all_52_11
% 159.96/26.24    (4)   ~ (all_52_11 = e1)
% 159.96/26.24  
% 159.96/26.24  Begin of proof
% 159.96/26.24  | 
% 159.96/26.24  | ALPHA: (1) implies:
% 159.96/26.24  |   (5)  op(e0, e1) = e1
% 159.96/26.24  | 
% 159.96/26.24  | GROUND_INST: instantiating (2) with all_52_11, e1, e1, e0, simplifying with
% 159.96/26.24  |              (3), (5) gives:
% 159.96/26.24  |   (6)  all_52_11 = e1
% 159.96/26.24  | 
% 159.96/26.24  | REDUCE: (4), (6) imply:
% 159.96/26.24  |   (7)  $false
% 159.96/26.24  | 
% 159.96/26.24  | CLOSE: (7) is inconsistent.
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #804 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (2)  op(e1, e0) = all_52_14
% 159.96/26.24    (3)  op(e0, e0) = all_14_2
% 159.96/26.24    (4)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 159.96/26.24    (5)   ~ (all_14_2 = e1)
% 159.96/26.24    (6)   ~ (all_52_14 = e1)
% 159.96/26.24  
% 159.96/26.24  Begin of proof
% 159.96/26.24  | 
% 159.96/26.24  | BETA: splitting (4) gives:
% 159.96/26.24  | 
% 159.96/26.24  | Case 1:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (7)  all_56_11 = e1 & op(e1, e0) = e1
% 159.96/26.24  | | 
% 159.96/26.24  | | ALPHA: (7) implies:
% 159.96/26.24  | |   (8)  op(e1, e0) = e1
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #974.
% 159.96/26.24  | | 
% 159.96/26.24  | Case 2:
% 159.96/26.24  | | 
% 159.96/26.24  | |   (9)  all_56_15 = e1 & op(e0, e0) = e1
% 159.96/26.24  | | 
% 159.96/26.24  | | ALPHA: (9) implies:
% 159.96/26.24  | |   (10)  op(e0, e0) = e1
% 159.96/26.24  | | 
% 159.96/26.24  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #805.
% 159.96/26.24  | | 
% 159.96/26.24  | End of split
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #805 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (2)  op(e0, e0) = all_14_2
% 159.96/26.24    (3)  op(e0, e0) = e1
% 159.96/26.24    (4)   ~ (all_14_2 = e1)
% 159.96/26.24  
% 159.96/26.24  Begin of proof
% 159.96/26.24  | 
% 159.96/26.24  | GROUND_INST: instantiating (1) with all_14_2, e1, e0, e0, simplifying with
% 159.96/26.24  |              (2), (3) gives:
% 159.96/26.24  |   (5)  all_14_2 = e1
% 159.96/26.24  | 
% 159.96/26.24  | REDUCE: (4), (5) imply:
% 159.96/26.24  |   (6)  $false
% 159.96/26.24  | 
% 159.96/26.24  | CLOSE: (6) is inconsistent.
% 159.96/26.24  | 
% 159.96/26.24  End of proof
% 159.96/26.24  
% 159.96/26.24  Sub-proof #806 shows that the following formulas are inconsistent:
% 159.96/26.24  ----------------------------------------------------------------
% 159.96/26.24    (1)   ~ (all_52_6 = e1)
% 159.96/26.24    (2)  op(e0, e0) = e2
% 159.96/26.24    (3)   ~ (e3 = e2)
% 159.96/26.24    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 159.96/26.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 159.96/26.24    (5)  op(e1, e1) = e1
% 159.96/26.24    (6)  op(e1, e3) = all_52_2
% 159.96/26.24    (7)   ~ (all_52_2 = e1)
% 159.96/26.24    (8)  op(e1, e2) = all_52_6
% 159.96/26.24    (9)  op(e1, e0) = all_52_14
% 159.96/26.24    (10)  op(e2, e2) = e0
% 159.96/26.24    (11)  op(e3, e3) = e1
% 159.96/26.24    (12)  (all_57_15 = e1 & op(e0, e0) = e1) | ( ~ (all_57_8 = e0) & op(e0, e1) =
% 159.96/26.24            all_57_8 & $i(all_57_8))
% 159.96/26.24    (13)   ~ (e1 = e0)
% 159.96/26.24    (14)  op(e0, e2) = e1
% 159.96/26.24    (15)   ~ (e2 = e1)
% 159.96/26.24    (16)   ~ (all_52_14 = e1)
% 160.01/26.25    (17)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 160.01/26.25            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 160.01/26.25            all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 160.01/26.25            all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 160.01/26.25              e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 160.01/26.25          (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 160.01/26.25            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 160.01/26.25              e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 160.01/26.25            all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 160.01/26.25              e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 160.01/26.25          (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 160.01/26.25            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 160.01/26.25              e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 160.01/26.25            all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 160.01/26.25              e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 160.01/26.25          (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 160.01/26.25            op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 & 
% 160.01/26.25            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 160.01/26.25              e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 160.01/26.25            all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 160.01/26.25            & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 160.01/26.25            $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 160.01/26.25            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 160.01/26.25              e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 160.01/26.25            all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) |
% 160.01/26.25          (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 160.01/26.25            op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 160.01/26.25              e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 &
% 160.01/26.25            all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 160.01/26.25            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 160.01/26.25          (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 160.01/26.25            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 160.01/26.25              e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 160.01/26.25            all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) =
% 160.01/26.25            e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 160.01/26.25          (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 160.01/26.25            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 160.01/26.25              e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 160.01/26.25            all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 160.01/26.25              e0) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 160.01/26.25          (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 160.01/26.25            op(e1, e1) = e1) | (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 & 
% 160.01/26.25            ~ (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) =
% 160.01/26.25            e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 160.01/26.25            all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1
% 160.01/26.25            & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 160.01/26.25            $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 160.01/26.25            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1,
% 160.01/26.25              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 160.01/26.25            all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 160.01/26.25            & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 160.01/26.25            $i(all_57_14)) | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 160.01/26.25            (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 160.01/26.25              e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 &
% 160.01/26.25            all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 160.01/26.25          (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 160.01/26.25            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 160.01/26.25              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 160.01/26.25              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 160.01/26.25            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 160.01/26.25            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 160.01/26.25            $i(all_57_14)) | (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 160.01/26.25            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 160.01/26.25              e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 &
% 160.01/26.25            all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 160.01/26.25          (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 160.01/26.25            op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 160.01/26.25              e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 &
% 160.01/26.25            all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 160.01/26.25              e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 160.01/26.25          (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 160.01/26.25            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 160.01/26.25              e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3
% 160.01/26.25              = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 160.01/26.25            all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 160.01/26.25          (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) = e1 &
% 160.01/26.25            op(e1, e0) = e1) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 160.01/26.25            ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 160.01/26.25                & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 160.01/26.25                = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.25                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 =
% 160.01/26.25                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.25                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 =
% 160.01/26.25                e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7
% 160.01/26.25                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 160.01/26.25                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 160.01/26.25                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 160.01/26.25                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 =
% 160.01/26.25                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 160.01/26.25                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 =
% 160.01/26.25                e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8
% 160.01/26.25                = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.25                op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 =
% 160.01/26.25                e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.25                op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 =
% 160.01/26.25                e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.25                op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 =
% 160.01/26.25                e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 160.01/26.25                op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.01/26.25                $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 160.01/26.25                op(e0, e1) = e0)))
% 160.01/26.25    (18)   ~ (e3 = e1)
% 160.01/26.25    (19)   ~ (e2 = e0)
% 160.01/26.25    (20)   ~ (e3 = e0)
% 160.01/26.25    (21)  op(e2, e0) = e1
% 160.01/26.25  
% 160.01/26.25  Begin of proof
% 160.01/26.25  | 
% 160.01/26.25  | BETA: splitting (12) gives:
% 160.01/26.25  | 
% 160.01/26.25  | Case 1:
% 160.01/26.25  | | 
% 160.01/26.25  | |   (22)  all_57_15 = e1 & op(e0, e0) = e1
% 160.01/26.25  | | 
% 160.01/26.25  | | ALPHA: (22) implies:
% 160.01/26.25  | |   (23)  op(e0, e0) = e1
% 160.01/26.25  | | 
% 160.01/26.25  | | REF_CLOSE: (2), (4), (15), (23) are inconsistent by sub-proof #875.
% 160.01/26.25  | | 
% 160.01/26.25  | Case 2:
% 160.01/26.25  | | 
% 160.01/26.25  | |   (24)   ~ (all_57_8 = e0) & op(e0, e1) = all_57_8 & $i(all_57_8)
% 160.01/26.25  | | 
% 160.01/26.25  | | ALPHA: (24) implies:
% 160.01/26.25  | |   (25)   ~ (all_57_8 = e0)
% 160.01/26.25  | | 
% 160.01/26.25  | | BETA: splitting (17) gives:
% 160.01/26.25  | | 
% 160.01/26.25  | | Case 1:
% 160.01/26.25  | | | 
% 160.01/26.25  | | |   (26)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 =
% 160.01/26.25  | | |             e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 &
% 160.01/26.25  | | |           op(e2, e2) = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 160.01/26.25  | | |           all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3,
% 160.01/26.25  | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 160.01/26.25  | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 &
% 160.01/26.25  | | |           all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 160.01/26.25  | | |             e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 160.01/26.25  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3
% 160.01/26.25  | | |           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 160.01/26.25  | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0
% 160.01/26.25  | | |           = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 160.01/26.25  | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 &
% 160.01/26.25  | | |           op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 =
% 160.01/26.25  | | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 160.01/26.25  | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3
% 160.01/26.25  | | |           & $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 =
% 160.01/26.25  | | |             e2) & op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 &
% 160.01/26.25  | | |           all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3,
% 160.01/26.25  | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 160.01/26.25  | | |             e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 160.01/26.25  | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3,
% 160.01/26.25  | | |             e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 160.01/26.25  | | |           $i(all_57_12)) | (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3
% 160.01/26.25  | | |           &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 160.01/26.25  | | |           & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1
% 160.01/26.25  | | |           = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3,
% 160.01/26.25  | | |             e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &
% 160.01/26.25  | | |            ~ (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2,
% 160.01/26.25  | | |             e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2
% 160.01/26.25  | | |           = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3) &
% 160.01/26.25  | | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.01/26.25  | | |           = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 & all_57_4 = e3 &
% 160.01/26.25  | | |           all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 160.01/26.25  | | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 160.01/26.25  | | |           $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 160.01/26.25  | | |           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 160.01/26.25  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 160.01/26.25  | | |         (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 =
% 160.01/26.25  | | |             e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) =
% 160.01/26.25  | | |           e0 & op(e0, e0) = e1 & $i(all_57_14)) | (all_57_2 = e1 &
% 160.01/26.25  | | |           all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 160.01/26.25  | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 160.01/26.25  | | |             e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 & 
% 160.01/26.25  | | |           ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 160.01/26.25  | | | 
% 160.01/26.25  | | | BETA: splitting (26) gives:
% 160.01/26.25  | | | 
% 160.01/26.25  | | | Case 1:
% 160.01/26.25  | | | | 
% 160.01/26.25  | | | |   (27)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12
% 160.01/26.25  | | | |             = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2
% 160.01/26.25  | | | |           & op(e2, e2) = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 &
% 160.01/26.25  | | | |           all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3,
% 160.01/26.25  | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 160.01/26.25  | | | |             e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 &
% 160.01/26.25  | | | |           all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 160.01/26.25  | | | |           op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 160.01/26.25  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 =
% 160.01/26.25  | | | |           e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1)
% 160.01/26.25  | | | |           = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 160.01/26.25  | | | |         (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12
% 160.01/26.25  | | | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0,
% 160.01/26.25  | | | |             e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 160.01/26.25  | | | |           & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) &
% 160.01/26.25  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 &
% 160.01/26.25  | | | |           op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 & all_57_12
% 160.01/26.25  | | | |           = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 160.01/26.25  | | | |         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 160.01/26.25  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 160.01/26.25  | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 160.01/26.25  | | | |           & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 160.01/26.25  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 160.01/26.25  | | | |           op(e2, e1) = e2 & $i(all_57_12))
% 160.01/26.25  | | | | 
% 160.01/26.25  | | | | BETA: splitting (27) gives:
% 160.01/26.25  | | | | 
% 160.01/26.25  | | | | Case 1:
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | |   (28)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 160.01/26.25  | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 160.01/26.25  | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12)) |
% 160.01/26.25  | | | | |         (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 160.01/26.25  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 160.01/26.25  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 160.01/26.25  | | | | |         (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 160.01/26.25  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 160.01/26.25  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 160.01/26.25  | | | | |         (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 160.01/26.25  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 160.01/26.25  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | | BETA: splitting (28) gives:
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | | Case 1:
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | |   (29)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~
% 160.01/26.25  | | | | | |           (all_57_12 = e3) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 160.01/26.25  | | | | | |           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & $i(all_57_12))
% 160.01/26.25  | | | | | |         | (all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~
% 160.01/26.25  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 160.01/26.25  | | | | | |           e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | | REF_CLOSE: (4), (10), (11), (15), (20), (29) are inconsistent by
% 160.01/26.25  | | | | | |            sub-proof #827.
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | Case 2:
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | |   (30)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~
% 160.01/26.25  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 160.01/26.25  | | | | | |           all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 160.01/26.25  | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 160.01/26.25  | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 160.01/26.25  | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 160.01/26.25  | | | | | |           = e3 & $i(all_57_10))
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | | REF_CLOSE: (4), (5), (10), (15), (20), (30) are inconsistent by
% 160.01/26.25  | | | | | |            sub-proof #933.
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | End of split
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | Case 2:
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | |   (31)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 160.01/26.25  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 160.01/26.25  | | | | |           & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 160.01/26.25  | | | | |         (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 160.01/26.25  | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 160.01/26.25  | | | | |           & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) |
% 160.01/26.25  | | | | |         (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) =
% 160.01/26.25  | | | | |           e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 160.01/26.25  | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 160.01/26.25  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 160.01/26.25  | | | | |           e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 160.01/26.25  | | | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 160.01/26.25  | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 160.01/26.25  | | | | |           $i(all_57_12))
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | | BETA: splitting (31) gives:
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | | Case 1:
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | |   (32)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 160.01/26.25  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 160.01/26.25  | | | | | |           all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 160.01/26.25  | | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 &
% 160.01/26.25  | | | | | |           all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 160.01/26.25  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 160.01/26.25  | | | | | |           = e3 & $i(all_57_10))
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | | BETA: splitting (32) gives:
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | | Case 1:
% 160.01/26.25  | | | | | | | 
% 160.01/26.25  | | | | | | |   (33)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 160.01/26.25  | | | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 160.01/26.25  | | | | | | |         all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 160.01/26.25  | | | | | | |         $i(all_57_12)
% 160.01/26.25  | | | | | | | 
% 160.01/26.25  | | | | | | | ALPHA: (33) implies:
% 160.01/26.25  | | | | | | |   (34)  op(e0, e2) = e0
% 160.01/26.25  | | | | | | | 
% 160.01/26.25  | | | | | | | REF_CLOSE: (4), (13), (14), (34) are inconsistent by sub-proof
% 160.01/26.25  | | | | | | |            #832.
% 160.01/26.25  | | | | | | | 
% 160.01/26.25  | | | | | | Case 2:
% 160.01/26.25  | | | | | | | 
% 160.01/26.25  | | | | | | |   (35)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 160.01/26.25  | | | | | | |         (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 160.01/26.25  | | | | | | |         e3 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)
% 160.01/26.25  | | | | | | | 
% 160.01/26.25  | | | | | | | ALPHA: (35) implies:
% 160.01/26.25  | | | | | | |   (36)  op(e2, e2) = e3
% 160.01/26.25  | | | | | | | 
% 160.01/26.25  | | | | | | | REF_CLOSE: (4), (10), (20), (36) are inconsistent by sub-proof
% 160.01/26.25  | | | | | | |            #945.
% 160.01/26.25  | | | | | | | 
% 160.01/26.25  | | | | | | End of split
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | Case 2:
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | |   (37)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3)
% 160.01/26.25  | | | | | |           = e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 &
% 160.01/26.25  | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) =
% 160.01/26.25  | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.01/26.25  | | | | | |           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 &
% 160.01/26.25  | | | | | |           all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 160.01/26.25  | | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 160.01/26.25  | | | | | |           & $i(all_57_12))
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | | REF_CLOSE: (4), (5), (10), (11), (15), (18), (19), (37) are
% 160.01/26.25  | | | | | |            inconsistent by sub-proof #824.
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | End of split
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | End of split
% 160.01/26.25  | | | | 
% 160.01/26.25  | | | Case 2:
% 160.01/26.25  | | | | 
% 160.01/26.25  | | | |   (38)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10
% 160.01/26.25  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 160.01/26.25  | | | |             e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 160.01/26.25  | | | |           & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2)
% 160.01/26.25  | | | |           = e3) | (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 160.01/26.25  | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2,
% 160.01/26.25  | | | |             e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_12)) |
% 160.01/26.25  | | | |         (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14
% 160.01/26.25  | | | |             = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1
% 160.01/26.25  | | | |           & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_2 = e1 &
% 160.01/26.25  | | | |           all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) & op(e3,
% 160.01/26.25  | | | |             e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 160.01/26.25  | | | |             e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 &
% 160.01/26.25  | | | |           all_57_12 = e1 &  ~ (all_57_14 = e3) & op(e2, e2) = e1 &
% 160.01/26.25  | | | |           op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 160.01/26.25  | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_8 = e0 & all_57_15 =
% 160.01/26.25  | | | |           e1 &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 160.01/26.25  | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 160.01/26.25  | | | |         | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~
% 160.01/26.25  | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 160.01/26.25  | | | |           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2
% 160.01/26.25  | | | |           = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 160.01/26.25  | | | |           op(e1, e1) = e1)
% 160.01/26.25  | | | | 
% 160.01/26.25  | | | | BETA: splitting (38) gives:
% 160.01/26.25  | | | | 
% 160.01/26.25  | | | | Case 1:
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | |   (39)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 160.01/26.25  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 160.01/26.25  | | | | |           & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 160.01/26.25  | | | | |         (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) =
% 160.01/26.25  | | | | |           e3 & op(e3, e2) = e3) | (all_57_1 = e3 & all_57_10 = e2 &
% 160.01/26.25  | | | | |           all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) = e2 &
% 160.01/26.25  | | | | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 160.01/26.25  | | | | |           $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10
% 160.01/26.25  | | | | |           = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 160.01/26.25  | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 160.01/26.25  | | | | |           $i(all_57_14))
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | | BETA: splitting (39) gives:
% 160.01/26.25  | | | | | 
% 160.01/26.25  | | | | | Case 1:
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | |   (40)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 160.01/26.25  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 160.01/26.25  | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 160.01/26.25  | | | | | |         (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3)
% 160.01/26.25  | | | | | |           = e3 & op(e3, e2) = e3)
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | | BETA: splitting (40) gives:
% 160.01/26.25  | | | | | | 
% 160.01/26.25  | | | | | | Case 1:
% 160.01/26.25  | | | | | | | 
% 160.01/26.26  | | | | | | |   (41)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 160.01/26.26  | | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 160.01/26.26  | | | | | | |         e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | | ALPHA: (41) implies:
% 160.01/26.26  | | | | | | |   (42)  op(e0, e0) = e3
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | | REF_CLOSE: (2), (3), (4), (42) are inconsistent by sub-proof #878.
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | Case 2:
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | |   (43)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3)
% 160.01/26.26  | | | | | | |         = e3 & op(e3, e2) = e3
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | | ALPHA: (43) implies:
% 160.01/26.26  | | | | | | |   (44)  op(e3, e3) = e3
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | | REF_CLOSE: (4), (11), (18), (44) are inconsistent by sub-proof
% 160.01/26.26  | | | | | | |            #995.
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | End of split
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | Case 2:
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | |   (45)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~
% 160.01/26.26  | | | | | |           (all_57_12 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 160.01/26.26  | | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_12))
% 160.01/26.26  | | | | | |         | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 160.01/26.26  | | | | | |           (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 160.01/26.26  | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | | REF_CLOSE: (4), (6), (7), (15), (21), (45) are inconsistent by
% 160.01/26.26  | | | | | |            sub-proof #812.
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | End of split
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | Case 2:
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | |   (46)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 160.01/26.26  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 160.01/26.26  | | | | |           & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 160.01/26.26  | | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 160.01/26.26  | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 160.01/26.26  | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 160.01/26.26  | | | | |         (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 160.01/26.26  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 160.01/26.26  | | | | |           & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) |
% 160.01/26.26  | | | | |         (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~
% 160.01/26.26  | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 160.01/26.26  | | | | |           & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 160.01/26.26  | | | | |         (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) =
% 160.01/26.26  | | | | |           e1 & op(e1, e1) = e1)
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | | BETA: splitting (46) gives:
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | | Case 1:
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | |   (47)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~
% 160.01/26.26  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 160.01/26.26  | | | | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 160.01/26.26  | | | | | |         (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 160.01/26.26  | | | | | |           (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 160.01/26.26  | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | | REF_CLOSE: (4), (5), (10), (13), (18), (47) are inconsistent by
% 160.01/26.26  | | | | | |            sub-proof #921.
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | Case 2:
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | |   (48)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 160.01/26.26  | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 160.01/26.26  | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 160.01/26.26  | | | | | |           $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 &
% 160.01/26.26  | | | | | |           all_57_14 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) =
% 160.01/26.26  | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.01/26.26  | | | | | |           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 & 
% 160.01/26.26  | | | | | |           ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (15), (18), (48) are
% 160.01/26.26  | | | | | |            inconsistent by sub-proof #874.
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | End of split
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | End of split
% 160.01/26.26  | | | | 
% 160.01/26.26  | | | End of split
% 160.01/26.26  | | | 
% 160.01/26.26  | | Case 2:
% 160.01/26.26  | | | 
% 160.01/26.26  | | |   (49)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 =
% 160.01/26.26  | | |             e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 &
% 160.01/26.26  | | |           op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 160.01/26.26  | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2,
% 160.01/26.26  | | |             e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 160.01/26.26  | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 160.01/26.26  | | |           all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 160.01/26.26  | | |           op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 160.01/26.26  | | |           $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 160.01/26.26  | | |           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 160.01/26.26  | | |           & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14)) | (all_57_3
% 160.01/26.26  | | |           = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 160.01/26.26  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 &
% 160.01/26.26  | | |           op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 =
% 160.01/26.26  | | |           e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1) |
% 160.01/26.26  | | |         (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 160.01/26.26  | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) =
% 160.01/26.26  | | |           e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 &
% 160.01/26.26  | | |           all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) =
% 160.01/26.26  | | |           e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 160.01/26.26  | | |           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 160.01/26.26  | | |             e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_5
% 160.01/26.26  | | |           = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 160.01/26.26  | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 &
% 160.01/26.26  | | |           op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 =
% 160.01/26.26  | | |           e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2) |
% 160.01/26.26  | | |         (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 160.01/26.26  | | |             e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) =
% 160.01/26.26  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 &
% 160.01/26.26  | | |           all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 160.01/26.26  | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 160.01/26.26  | | |             e0) = e3 & $i(all_57_10)) | (all_57_7 = e0 & all_57_11 = e2 &
% 160.01/26.26  | | |           all_57_15 = e2 &  ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 160.01/26.26  | | |           op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 160.01/26.26  | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 160.01/26.26  | | |           & op(e3, e3) = e3 & op(e3, e0) = e3) | (all_57_11 = e2 &
% 160.01/26.26  | | |           all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) =
% 160.01/26.26  | | |           e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 160.01/26.26  | | |             e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 160.01/26.26  | | |           $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0
% 160.01/26.26  | | |               &  ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 160.01/26.26  | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2 &
% 160.01/26.26  | | |               all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0 &
% 160.01/26.26  | | |               op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 160.01/26.26  | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.26  | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 160.01/26.26  | | |             (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) =
% 160.01/26.26  | | |               e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 160.01/26.26  | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 160.01/26.26  | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 160.01/26.26  | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 &
% 160.01/26.26  | | |               op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.01/26.26  | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 160.01/26.26  | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 160.01/26.26  | | |             (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 160.01/26.26  | | |               e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 160.01/26.26  | | |               (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 160.01/26.26  | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 160.01/26.26  | | |               all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 &
% 160.01/26.26  | | |               op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.26  | | |               all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.26  | | |               op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 160.01/26.26  | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 160.01/26.26  | | |               (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 160.01/26.26  | | |               & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 160.01/26.26  | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 160.01/26.26  | | | 
% 160.01/26.26  | | | BETA: splitting (49) gives:
% 160.01/26.26  | | | 
% 160.01/26.26  | | | Case 1:
% 160.01/26.26  | | | | 
% 160.01/26.26  | | | |   (50)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14
% 160.01/26.26  | | | |             = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1
% 160.01/26.26  | | | |           & op(e1, e1) = all_57_14 & $i(all_57_14)) | (all_57_3 = e1 &
% 160.01/26.26  | | | |           all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2) & op(e2,
% 160.01/26.26  | | | |             e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 160.01/26.26  | | | |           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 &
% 160.01/26.26  | | | |           all_57_14 = e2 &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12
% 160.01/26.26  | | | |           & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 160.01/26.26  | | | |           $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 =
% 160.01/26.26  | | | |           e1 &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 160.01/26.26  | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 160.01/26.26  | | | |         | (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 160.01/26.26  | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 160.01/26.26  | | | |           op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3
% 160.01/26.26  | | | |           = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 160.01/26.26  | | | |           op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 & all_57_15
% 160.01/26.26  | | | |           = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 160.01/26.26  | | | |             e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 160.01/26.26  | | | |           $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 =
% 160.01/26.26  | | | |             e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 160.01/26.26  | | | |           all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3,
% 160.01/26.26  | | | |             e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 160.01/26.26  | | | |             e0) = e1 & $i(all_57_14))
% 160.01/26.26  | | | | 
% 160.01/26.26  | | | | BETA: splitting (50) gives:
% 160.01/26.26  | | | | 
% 160.01/26.26  | | | | Case 1:
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | |   (51)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 160.01/26.26  | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 160.01/26.26  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 160.01/26.26  | | | | |         (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 160.01/26.26  | | | | |           (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 160.01/26.26  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14)) |
% 160.01/26.26  | | | | |         (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 160.01/26.26  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 160.01/26.26  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 160.01/26.26  | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 160.01/26.26  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 160.01/26.26  | | | | |           & op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | | BETA: splitting (51) gives:
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | | Case 1:
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | |   (52)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 160.01/26.26  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 160.01/26.26  | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.26  | | | | | |         | (all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~
% 160.01/26.26  | | | | | |           (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 160.01/26.26  | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | | REF_CLOSE: (1), (4), (8), (10), (13), (52) are inconsistent by
% 160.01/26.26  | | | | | |            sub-proof #822.
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | Case 2:
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | |   (53)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~
% 160.01/26.26  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 160.01/26.26  | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 160.01/26.26  | | | | | |         (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~
% 160.01/26.26  | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 160.01/26.26  | | | | | |           all_57_14 & op(e0, e1) = e0 & op(e0, e0) = e1 &
% 160.01/26.26  | | | | | |           $i(all_57_14))
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | | REF_CLOSE: (2), (4), (5), (15), (53) are inconsistent by sub-proof
% 160.01/26.26  | | | | | |            #873.
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | End of split
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | Case 2:
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | |   (54)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 160.01/26.26  | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 160.01/26.26  | | | | |           & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 160.01/26.26  | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) =
% 160.01/26.26  | | | | |           e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 160.01/26.26  | | | | |           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) =
% 160.01/26.26  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0) =
% 160.01/26.26  | | | | |           e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~
% 160.01/26.26  | | | | |           (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 =
% 160.01/26.26  | | | | |           e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 160.01/26.26  | | | | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 160.01/26.26  | | | | |           op(e1, e0) = e1 & $i(all_57_14))
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | | BETA: splitting (54) gives:
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | | Case 1:
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | |   (55)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~
% 160.01/26.26  | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 160.01/26.26  | | | | | |           e2 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) |
% 160.01/26.26  | | | | | |         (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2)
% 160.01/26.26  | | | | | |           = e1 & op(e1, e1) = e1)
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | | REF_CLOSE: (1), (4), (5), (8), (15), (55) are inconsistent by
% 160.01/26.26  | | | | | |            sub-proof #983.
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | Case 2:
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | |   (56)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 160.01/26.26  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 160.01/26.26  | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 160.01/26.26  | | | | | |         (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3)
% 160.01/26.26  | | | | | |           = e3 & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 160.01/26.26  | | | | | |           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 &
% 160.01/26.26  | | | | | |           op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 160.01/26.26  | | | | | |           & $i(all_57_14))
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | | BETA: splitting (56) gives:
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | | Case 1:
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | |   (57)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~
% 160.01/26.26  | | | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 160.01/26.26  | | | | | | |         e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | | ALPHA: (57) implies:
% 160.01/26.26  | | | | | | |   (58)  op(e0, e0) = e3
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | | REF_CLOSE: (2), (3), (4), (58) are inconsistent by sub-proof #878.
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | Case 2:
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | |   (59)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3,
% 160.01/26.26  | | | | | | |             e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 160.01/26.26  | | | | | | |           all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 160.01/26.26  | | | | | | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 160.01/26.26  | | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | | REF_CLOSE: (4), (9), (11), (16), (59) are inconsistent by
% 160.01/26.26  | | | | | | |            sub-proof #839.
% 160.01/26.26  | | | | | | | 
% 160.01/26.26  | | | | | | End of split
% 160.01/26.26  | | | | | | 
% 160.01/26.26  | | | | | End of split
% 160.01/26.26  | | | | | 
% 160.01/26.26  | | | | End of split
% 160.01/26.26  | | | | 
% 160.01/26.26  | | | Case 2:
% 160.01/26.26  | | | | 
% 160.01/26.26  | | | |   (60)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12
% 160.01/26.26  | | | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0,
% 160.01/26.26  | | | |             e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2
% 160.01/26.26  | | | |           & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1)
% 160.01/26.26  | | | |           = e2) | (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 160.01/26.26  | | | |           (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 160.01/26.26  | | | |             e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 160.01/26.26  | | | |         (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10
% 160.01/26.26  | | | |             = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0,
% 160.01/26.26  | | | |             e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_7 = e0
% 160.01/26.26  | | | |           & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 160.01/26.26  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 &
% 160.01/26.26  | | | |           op(e0, e0) = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10
% 160.01/26.27  | | | |           = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 & op(e3, e0) = e3) |
% 160.01/26.27  | | | |         (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2) =
% 160.01/26.27  | | | |           e2 & op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1 &  ~
% 160.01/26.27  | | | |           (e1 = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) =
% 160.01/26.27  | | | |           all_57_15 & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 160.01/26.27  | | | |               all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 &
% 160.01/26.27  | | | |               op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 160.01/26.27  | | | |               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.27  | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.01/26.27  | | | |             (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.01/26.27  | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 160.01/26.27  | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 160.01/26.27  | | | |               (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 =
% 160.01/26.27  | | | |               e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) =
% 160.01/26.27  | | | |               e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.01/26.27  | | | |               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) &
% 160.01/26.27  | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) |
% 160.01/26.27  | | | |             (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.01/26.27  | | | |               (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 160.01/26.27  | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~
% 160.01/26.27  | | | |               (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 =
% 160.01/26.27  | | | |               e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) =
% 160.01/26.27  | | | |               e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.27  | | | |               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.27  | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 160.01/26.27  | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.01/26.27  | | | |               (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 160.01/26.27  | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 160.01/26.27  | | | |               all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 160.01/26.27  | | | |               all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.01/26.27  | | | |               $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1
% 160.01/26.27  | | | |                 = e0) & op(e0, e1) = e0)))
% 160.01/26.27  | | | | 
% 160.01/26.27  | | | | BETA: splitting (60) gives:
% 160.01/26.27  | | | | 
% 160.01/26.27  | | | | Case 1:
% 160.01/26.27  | | | | | 
% 160.01/26.27  | | | | |   (61)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 160.01/26.27  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 160.01/26.27  | | | | |           & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 160.01/26.27  | | | | |         (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) =
% 160.01/26.27  | | | | |           e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1 &
% 160.01/26.27  | | | | |           all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 &
% 160.01/26.27  | | | | |           op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 160.01/26.27  | | | | |           $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15
% 160.01/26.27  | | | | |           = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3,
% 160.01/26.27  | | | | |             e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 160.01/26.27  | | | | |           $i(all_57_10))
% 160.01/26.27  | | | | | 
% 160.01/26.27  | | | | | BETA: splitting (61) gives:
% 160.01/26.27  | | | | | 
% 160.01/26.27  | | | | | Case 1:
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | |   (62)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 160.01/26.27  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 160.01/26.27  | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 160.01/26.27  | | | | | |         (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2)
% 160.01/26.27  | | | | | |           = e2 & op(e2, e1) = e2)
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | | BETA: splitting (62) gives:
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | | Case 1:
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | |   (63)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~
% 160.01/26.27  | | | | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 160.01/26.27  | | | | | | |         e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | ALPHA: (63) implies:
% 160.01/26.27  | | | | | | |   (64)  op(e0, e2) = e0
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | REF_CLOSE: (4), (13), (14), (64) are inconsistent by sub-proof
% 160.01/26.27  | | | | | | |            #832.
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | Case 2:
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | |   (65)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2)
% 160.01/26.27  | | | | | | |         = e2 & op(e2, e1) = e2
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | ALPHA: (65) implies:
% 160.01/26.27  | | | | | | |   (66)  op(e2, e2) = e2
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | REF_CLOSE: (4), (10), (19), (66) are inconsistent by sub-proof
% 160.01/26.27  | | | | | | |            #942.
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | End of split
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | Case 2:
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | |   (67)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~
% 160.01/26.27  | | | | | |           (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 160.01/26.27  | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.01/26.27  | | | | | |         | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~
% 160.01/26.27  | | | | | |           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 160.01/26.27  | | | | | |           e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | | REF_CLOSE: (2), (3), (4), (10), (13), (67) are inconsistent by
% 160.01/26.27  | | | | | |            sub-proof #854.
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | End of split
% 160.01/26.27  | | | | | 
% 160.01/26.27  | | | | Case 2:
% 160.01/26.27  | | | | | 
% 160.01/26.27  | | | | |   (68)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 160.01/26.27  | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 160.01/26.27  | | | | |           & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 160.01/26.27  | | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) =
% 160.01/26.27  | | | | |           e3 & op(e3, e0) = e3) | (all_57_11 = e2 & all_57_12 = e2 & 
% 160.01/26.27  | | | | |           ~ (e2 = e0) & op(e2, e2) = e2 & op(e2, e0) = e2) |
% 160.01/26.27  | | | | |         (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1, e1) =
% 160.01/26.27  | | | | |           e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15 &
% 160.01/26.27  | | | | |           $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 & all_57_10
% 160.01/26.27  | | | | |               = e0 &  ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3,
% 160.01/26.27  | | | | |                 e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 160.01/26.27  | | | | |               all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.27  | | | | |               op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.01/26.27  | | | | |             (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.01/26.27  | | | | |               (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 160.01/26.27  | | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 160.01/26.27  | | | | |               (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9
% 160.01/26.27  | | | | |               = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3)
% 160.01/26.27  | | | | |               = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 =
% 160.01/26.27  | | | | |               e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.27  | | | | |                 e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) =
% 160.01/26.27  | | | | |               e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &
% 160.01/26.27  | | | | |                ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1
% 160.01/26.27  | | | | |               & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 & 
% 160.01/26.27  | | | | |               ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 160.01/26.27  | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.27  | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 160.01/26.27  | | | | |             (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 160.01/26.27  | | | | |               (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 160.01/26.27  | | | | |               op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 160.01/26.27  | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 &
% 160.01/26.27  | | | | |               op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.27  | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 160.01/26.27  | | | | |               op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 160.01/26.27  | | | | |               e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 160.01/26.27  | | | | |               ~ (e1 = e0) & op(e0, e1) = e0)))
% 160.01/26.27  | | | | | 
% 160.01/26.27  | | | | | BETA: splitting (68) gives:
% 160.01/26.27  | | | | | 
% 160.01/26.27  | | | | | Case 1:
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | |   (69)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 160.01/26.27  | | | | | |           (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 160.01/26.27  | | | | | |           e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)) |
% 160.01/26.27  | | | | | |         (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3)
% 160.01/26.27  | | | | | |           = e3 & op(e3, e0) = e3)
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | | BETA: splitting (69) gives:
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | | Case 1:
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | |   (70)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~
% 160.01/26.27  | | | | | | |         (all_57_12 = e0) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 160.01/26.27  | | | | | | |         e2 & op(e0, e2) = e0 & op(e0, e0) = e2 & $i(all_57_12)
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | ALPHA: (70) implies:
% 160.01/26.27  | | | | | | |   (71)   ~ (all_57_12 = e0)
% 160.01/26.27  | | | | | | |   (72)  op(e2, e2) = all_57_12
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | REF_CLOSE: (4), (10), (71), (72) are inconsistent by sub-proof
% 160.01/26.27  | | | | | | |            #811.
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | Case 2:
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | |   (73)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3)
% 160.01/26.27  | | | | | | |         = e3 & op(e3, e0) = e3
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | ALPHA: (73) implies:
% 160.01/26.27  | | | | | | |   (74)  op(e3, e3) = e3
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | REF_CLOSE: (4), (11), (18), (74) are inconsistent by sub-proof
% 160.01/26.27  | | | | | | |            #995.
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | End of split
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | Case 2:
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | |   (75)  (all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2, e2)
% 160.01/26.27  | | | | | |           = e2 & op(e2, e0) = e2) | (all_57_13 = e1 & all_57_14 = e1
% 160.01/26.27  | | | | | |           &  ~ (e1 = e0) & op(e1, e1) = e1 & op(e1, e0) = e1) |
% 160.01/26.27  | | | | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 = e0 &
% 160.01/26.27  | | | | | |               all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.27  | | | | | |               op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 160.01/26.27  | | | | | |             (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 160.01/26.27  | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 160.01/26.27  | | | | | |               op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1 &
% 160.01/26.27  | | | | | |               all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 160.01/26.27  | | | | | |               & op(e1, e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0
% 160.01/26.27  | | | | | |               & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 160.01/26.27  | | | | | |             (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 160.01/26.27  | | | | | |               (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 160.01/26.27  | | | | | |               op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 &
% 160.01/26.27  | | | | | |               all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 160.01/26.27  | | | | | |               & op(e2, e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0
% 160.01/26.27  | | | | | |               & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.27  | | | | | |                 e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2)
% 160.01/26.27  | | | | | |               = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0)
% 160.01/26.27  | | | | | |               & op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 160.01/26.27  | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 160.01/26.27  | | | | | |               & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0
% 160.01/26.27  | | | | | |               & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.27  | | | | | |                 e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1)
% 160.01/26.27  | | | | | |               = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 160.01/26.27  | | | | | |               e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1,
% 160.01/26.27  | | | | | |                 e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.27  | | | | | |               all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 160.01/26.27  | | | | | |               & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 160.01/26.27  | | | | | |                 e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 160.01/26.27  | | | | | |               all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)))
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | | BETA: splitting (75) gives:
% 160.01/26.27  | | | | | | 
% 160.01/26.27  | | | | | | Case 1:
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | |   (76)  all_57_11 = e2 & all_57_12 = e2 &  ~ (e2 = e0) & op(e2,
% 160.01/26.27  | | | | | | |           e2) = e2 & op(e2, e0) = e2
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | ALPHA: (76) implies:
% 160.01/26.27  | | | | | | |   (77)  op(e2, e2) = e2
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | REF_CLOSE: (4), (10), (19), (77) are inconsistent by sub-proof
% 160.01/26.27  | | | | | | |            #942.
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | Case 2:
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | |   (78)  (all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 160.01/26.27  | | | | | | |             e1) = e1 & op(e1, e0) = e1) | (op(e0, e0) = all_57_15
% 160.01/26.27  | | | | | | |           & $i(all_57_15) & ((all_57_6 = e0 & all_57_9 = e3 &
% 160.01/26.27  | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e3) & op(e3, e3) =
% 160.01/26.27  | | | | | | |               e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6
% 160.01/26.27  | | | | | | |               = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 160.01/26.27  | | | | | | |               (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2
% 160.01/26.27  | | | | | | |               & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 160.01/26.27  | | | | | | |               & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1)
% 160.01/26.27  | | | | | | |               = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 160.01/26.27  | | | | | | |             (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 160.01/26.27  | | | | | | |               op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 160.01/26.27  | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) =
% 160.01/26.27  | | | | | | |               e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7
% 160.01/26.27  | | | | | | |               = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 160.01/26.27  | | | | | | |               (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2
% 160.01/26.27  | | | | | | |               & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_13 = e1
% 160.01/26.27  | | | | | | |               & all_57_14 = e0 &  ~ (all_57_15 = e2) & op(e1, e1)
% 160.01/26.27  | | | | | | |               = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 160.01/26.27  | | | | | | |             (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) &
% 160.01/26.27  | | | | | | |               op(e0, e2) = e0) | (all_57_8 = e0 & all_57_9 = e3 &
% 160.01/26.27  | | | | | | |               all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) =
% 160.01/26.27  | | | | | | |               e0 & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8
% 160.01/26.27  | | | | | | |               = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 160.01/26.27  | | | | | | |               (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) = e2
% 160.01/26.27  | | | | | | |               & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 160.01/26.27  | | | | | | |               & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1)
% 160.01/26.27  | | | | | | |               = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 160.01/26.27  | | | | | | |             (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 160.01/26.27  | | | | | | |               (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1,
% 160.01/26.27  | | | | | | |                 e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 160.01/26.27  | | | | | | |             (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 160.01/26.27  | | | | | | |               op(e0, e1) = e0)))
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | BETA: splitting (78) gives:
% 160.01/26.27  | | | | | | | 
% 160.01/26.27  | | | | | | | Case 1:
% 160.01/26.27  | | | | | | | | 
% 160.01/26.27  | | | | | | | |   (79)  all_57_13 = e1 & all_57_14 = e1 &  ~ (e1 = e0) & op(e1,
% 160.01/26.27  | | | | | | | |           e1) = e1 & op(e1, e0) = e1
% 160.01/26.27  | | | | | | | | 
% 160.01/26.27  | | | | | | | | ALPHA: (79) implies:
% 160.01/26.27  | | | | | | | |   (80)  op(e1, e0) = e1
% 160.01/26.27  | | | | | | | | 
% 160.01/26.27  | | | | | | | | REF_CLOSE: (4), (9), (16), (80) are inconsistent by sub-proof
% 160.01/26.27  | | | | | | | |            #974.
% 160.01/26.27  | | | | | | | | 
% 160.01/26.27  | | | | | | | Case 2:
% 160.01/26.27  | | | | | | | | 
% 160.01/26.27  | | | | | | | |   (81)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_6 = e0
% 160.01/26.27  | | | | | | | |             & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.01/26.27  | | | | | | | |               e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 160.01/26.27  | | | | | | | |               e3) = e0) | (all_57_6 = e0 & all_57_11 = e2 &
% 160.01/26.27  | | | | | | | |             all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 160.01/26.27  | | | | | | | |             e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6
% 160.01/26.27  | | | | | | | |             = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.01/26.27  | | | | | | | |             (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1
% 160.01/26.27  | | | | | | | |             & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0
% 160.01/26.27  | | | | | | | |             &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 160.01/26.27  | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 160.01/26.27  | | | | | | | |             & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 160.01/26.27  | | | | | | | |             e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 160.01/26.27  | | | | | | | |             e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 160.01/26.27  | | | | | | | |               e0) = e2 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.01/26.27  | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.27  | | | | | | | |               e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 160.01/26.27  | | | | | | | |               e2) = e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~
% 160.01/26.27  | | | | | | | |             (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 160.01/26.27  | | | | | | | |             all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 160.01/26.27  | | | | | | | |             & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 160.01/26.27  | | | | | | | |             e0) | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 160.01/26.27  | | | | | | | |             e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 160.01/26.27  | | | | | | | |               e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.27  | | | | | | | |             all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.27  | | | | | | | |               e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 160.01/26.27  | | | | | | | |               e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 160.01/26.27  | | | | | | | |             all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 160.01/26.27  | | | | | | | |             all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.01/26.27  | | | | | | | |             $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 160.01/26.27  | | | | | | | |             ~ (e1 = e0) & op(e0, e1) = e0))
% 160.01/26.27  | | | | | | | | 
% 160.01/26.27  | | | | | | | | ALPHA: (81) implies:
% 160.01/26.27  | | | | | | | |   (82)  op(e0, e0) = all_57_15
% 160.01/26.27  | | | | | | | |   (83)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 160.01/26.27  | | | | | | | |           (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 160.01/26.27  | | | | | | | |           op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2 &
% 160.01/26.27  | | | | | | | |           all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 160.01/26.27  | | | | | | | |           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0
% 160.01/26.27  | | | | | | | |           & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.27  | | | | | | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3)
% 160.01/26.27  | | | | | | | |           = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 160.01/26.27  | | | | | | | |           & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 160.01/26.27  | | | | | | | |           all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0
% 160.01/26.27  | | | | | | | |           & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0
% 160.01/26.27  | | | | | | | |           & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.27  | | | | | | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2)
% 160.01/26.27  | | | | | | | |           = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 =
% 160.01/26.27  | | | | | | | |           e0 &  ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1,
% 160.01/26.27  | | | | | | | |             e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.01/26.27  | | | | | | | |           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 160.01/26.27  | | | | | | | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 160.01/26.27  | | | | | | | |           (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 160.01/26.27  | | | | | | | |           op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 = e2 &
% 160.01/26.27  | | | | | | | |           all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0
% 160.01/26.27  | | | | | | | |           & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 160.01/26.27  | | | | | | | |           & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.27  | | | | | | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1)
% 160.01/26.27  | | | | | | | |           = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15 =
% 160.01/26.27  | | | | | | | |           e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 160.01/26.27  | | | | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) |
% 160.01/26.27  | | | | | | | |         (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0,
% 160.01/26.27  | | | | | | | |             e1) = e0)
% 160.01/26.27  | | | | | | | | 
% 160.01/26.27  | | | | | | | | BETA: splitting (83) gives:
% 160.01/26.27  | | | | | | | | 
% 160.01/26.27  | | | | | | | | Case 1:
% 160.01/26.27  | | | | | | | | | 
% 160.01/26.27  | | | | | | | | |   (84)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 160.01/26.27  | | | | | | | | |           (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) = e3
% 160.01/26.27  | | | | | | | | |           & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11 = e2
% 160.01/26.27  | | | | | | | | |           & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2)
% 160.01/26.27  | | | | | | | | |           = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.01/26.27  | | | | | | | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.01/26.27  | | | | | | | | |           (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1
% 160.01/26.27  | | | | | | | | |           & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0
% 160.01/26.27  | | | | | | | | |           &  ~ (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 &
% 160.01/26.27  | | | | | | | | |           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 160.01/26.27  | | | | | | | | |           & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 160.01/26.27  | | | | | | | | |           e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 160.01/26.27  | | | | | | | | |           e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2,
% 160.01/26.27  | | | | | | | | |             e0) = e2 & op(e0, e2) = e0)
% 160.01/26.27  | | | | | | | | | 
% 160.01/26.27  | | | | | | | | | BETA: splitting (84) gives:
% 160.01/26.27  | | | | | | | | | 
% 160.01/26.27  | | | | | | | | | Case 1:
% 160.01/26.27  | | | | | | | | | | 
% 160.01/26.27  | | | | | | | | | |   (85)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 160.01/26.27  | | | | | | | | | |           (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 160.01/26.27  | | | | | | | | | |           e3 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_11
% 160.01/26.27  | | | | | | | | | |           = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.27  | | | | | | | | | |           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 160.01/26.27  | | | | | | | | | |           e0) | (all_57_6 = e0 & all_57_13 = e1 & all_57_14
% 160.01/26.27  | | | | | | | | | |           = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 &
% 160.01/26.27  | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e3) = e0)
% 160.01/26.27  | | | | | | | | | | 
% 160.01/26.27  | | | | | | | | | | BETA: splitting (85) gives:
% 160.01/26.27  | | | | | | | | | | 
% 160.01/26.27  | | | | | | | | | | Case 1:
% 160.01/26.27  | | | | | | | | | | | 
% 160.01/26.27  | | | | | | | | | | |   (86)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 160.01/26.27  | | | | | | | | | | |         ~ (all_57_15 = e3) & op(e3, e3) = e0 & op(e3, e0)
% 160.01/26.27  | | | | | | | | | | |         = e3 & op(e0, e3) = e0
% 160.01/26.27  | | | | | | | | | | | 
% 160.01/26.27  | | | | | | | | | | | ALPHA: (86) implies:
% 160.01/26.27  | | | | | | | | | | |   (87)  op(e3, e3) = e0
% 160.01/26.27  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | | REF_CLOSE: (4), (11), (13), (87) are inconsistent by
% 160.01/26.28  | | | | | | | | | | |            sub-proof #834.
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | Case 2:
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | |   (88)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 160.01/26.28  | | | | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e2) = e0 & op(e2,
% 160.01/26.28  | | | | | | | | | | |             e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 160.01/26.28  | | | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 160.01/26.28  | | | | | | | | | | |             = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 160.01/26.28  | | | | | | | | | | |           op(e0, e3) = e0)
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | | REF_CLOSE: (4), (5), (13), (15), (21), (88) are inconsistent
% 160.01/26.28  | | | | | | | | | | |            by sub-proof #810.
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | End of split
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | Case 2:
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | |   (89)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 160.01/26.28  | | | | | | | | | |           op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3
% 160.01/26.28  | | | | | | | | | |           & all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3,
% 160.01/26.28  | | | | | | | | | |             e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 160.01/26.28  | | | | | | | | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 160.01/26.28  | | | | | | | | | |           ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 160.01/26.28  | | | | | | | | | |           = e2 & op(e0, e2) = e0)
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | BETA: splitting (89) gives:
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | Case 1:
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | |   (90)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) &
% 160.01/26.28  | | | | | | | | | | |         op(e0, e3) = e0
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | | ALPHA: (90) implies:
% 160.01/26.28  | | | | | | | | | | |   (91)  all_57_15 = e0
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | | REDUCE: (82), (91) imply:
% 160.01/26.28  | | | | | | | | | | |   (92)  op(e0, e0) = e0
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | | REF_CLOSE: (2), (4), (19), (92) are inconsistent by sub-proof
% 160.01/26.28  | | | | | | | | | | |            #979.
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | Case 2:
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | |   (93)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 160.01/26.28  | | | | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3,
% 160.01/26.28  | | | | | | | | | | |             e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.01/26.28  | | | | | | | | | | |           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 160.01/26.28  | | | | | | | | | | |             = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 160.01/26.28  | | | | | | | | | | |           op(e0, e2) = e0)
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | | REF_CLOSE: (4), (11), (13), (15), (21), (93) are inconsistent
% 160.01/26.28  | | | | | | | | | | |            by sub-proof #809.
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | End of split
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | End of split
% 160.01/26.28  | | | | | | | | | 
% 160.01/26.28  | | | | | | | | Case 2:
% 160.01/26.28  | | | | | | | | | 
% 160.01/26.28  | | | | | | | | |   (94)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.01/26.28  | | | | | | | | |           (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1
% 160.01/26.28  | | | | | | | | |           & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_15 = e0
% 160.01/26.28  | | | | | | | | |           &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 160.01/26.28  | | | | | | | | |           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 160.01/26.28  | | | | | | | | |           & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) =
% 160.01/26.28  | | | | | | | | |           e0) | (all_57_8 = e0 & all_57_11 = e2 & all_57_12 =
% 160.01/26.28  | | | | | | | | |           e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 160.01/26.28  | | | | | | | | |             e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.28  | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.28  | | | | | | | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 160.01/26.28  | | | | | | | | |             e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 160.01/26.28  | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) =
% 160.01/26.28  | | | | | | | | |           all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.01/26.28  | | | | | | | | |           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 & 
% 160.01/26.28  | | | | | | | | |           ~ (e1 = e0) & op(e0, e1) = e0)
% 160.01/26.28  | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | BETA: splitting (94) gives:
% 160.01/26.28  | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | Case 1:
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | |   (95)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 & 
% 160.01/26.28  | | | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0)
% 160.01/26.28  | | | | | | | | | |           = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.01/26.28  | | | | | | | | | |           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 160.01/26.28  | | | | | | | | | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 160.01/26.28  | | | | | | | | | |           (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) =
% 160.01/26.28  | | | | | | | | | |           e3 & op(e0, e1) = e0)
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | REF_CLOSE: (4), (5), (11), (13), (14), (95) are inconsistent
% 160.01/26.28  | | | | | | | | | |            by sub-proof #830.
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | Case 2:
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | |   (96)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 & 
% 160.01/26.28  | | | | | | | | | |           ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0)
% 160.01/26.28  | | | | | | | | | |           = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.28  | | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.28  | | | | | | | | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 160.01/26.28  | | | | | | | | | |             e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 &
% 160.01/26.28  | | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1)
% 160.01/26.28  | | | | | | | | | |           = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.01/26.28  | | | | | | | | | |           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &
% 160.01/26.28  | | | | | | | | | |            ~ (e1 = e0) & op(e0, e1) = e0)
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | BETA: splitting (96) gives:
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | Case 1:
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | |   (97)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &
% 160.01/26.28  | | | | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2,
% 160.01/26.28  | | | | | | | | | | |             e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.28  | | | | | | | | | | |           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 160.01/26.28  | | | | | | | | | | |             = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 160.01/26.28  | | | | | | | | | | |           op(e0, e1) = e0)
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | | REF_CLOSE: (4), (5), (13), (25), (97) are inconsistent by
% 160.01/26.28  | | | | | | | | | | |            sub-proof #808.
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | Case 2:
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | |   (98)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &
% 160.01/26.28  | | | | | | | | | | |            ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 160.01/26.28  | | | | | | | | | | |           op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.01/26.28  | | | | | | | | | | |           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 160.01/26.28  | | | | | | | | | | |           &  ~ (e1 = e0) & op(e0, e1) = e0)
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | | REF_CLOSE: (4), (9), (16), (25), (98) are inconsistent by
% 160.01/26.28  | | | | | | | | | | |            sub-proof #807.
% 160.01/26.28  | | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | | End of split
% 160.01/26.28  | | | | | | | | | | 
% 160.01/26.28  | | | | | | | | | End of split
% 160.01/26.28  | | | | | | | | | 
% 160.01/26.28  | | | | | | | | End of split
% 160.01/26.28  | | | | | | | | 
% 160.01/26.28  | | | | | | | End of split
% 160.01/26.28  | | | | | | | 
% 160.01/26.28  | | | | | | End of split
% 160.01/26.28  | | | | | | 
% 160.01/26.28  | | | | | End of split
% 160.01/26.28  | | | | | 
% 160.01/26.28  | | | | End of split
% 160.01/26.28  | | | | 
% 160.01/26.28  | | | End of split
% 160.01/26.28  | | | 
% 160.01/26.28  | | End of split
% 160.01/26.28  | | 
% 160.01/26.28  | End of split
% 160.01/26.28  | 
% 160.01/26.28  End of proof
% 160.01/26.28  
% 160.01/26.28  Sub-proof #807 shows that the following formulas are inconsistent:
% 160.01/26.28  ----------------------------------------------------------------
% 160.01/26.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.28    (2)  op(e1, e0) = all_52_14
% 160.01/26.28    (3)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 160.01/26.28           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.01/26.28           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 160.01/26.28           op(e0, e1) = e0)
% 160.01/26.28    (4)   ~ (all_57_8 = e0)
% 160.01/26.28    (5)   ~ (all_52_14 = e1)
% 160.01/26.28  
% 160.01/26.28  Begin of proof
% 160.01/26.28  | 
% 160.01/26.28  | BETA: splitting (3) gives:
% 160.01/26.28  | 
% 160.01/26.28  | Case 1:
% 160.01/26.28  | | 
% 160.01/26.28  | |   (6)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 160.01/26.28  | |        & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.01/26.28  | |        $i(all_57_14)
% 160.01/26.28  | | 
% 160.01/26.28  | | ALPHA: (6) implies:
% 160.01/26.28  | |   (7)  op(e1, e0) = e1
% 160.01/26.28  | | 
% 160.01/26.28  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #974.
% 160.01/26.28  | | 
% 160.01/26.28  | Case 2:
% 160.01/26.28  | | 
% 160.01/26.28  | |   (8)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | ALPHA: (8) implies:
% 160.01/26.28  | |   (9)  all_57_8 = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | REDUCE: (4), (9) imply:
% 160.01/26.28  | |   (10)  $false
% 160.01/26.28  | | 
% 160.01/26.28  | | CLOSE: (10) is inconsistent.
% 160.01/26.28  | | 
% 160.01/26.28  | End of split
% 160.01/26.28  | 
% 160.01/26.28  End of proof
% 160.01/26.28  
% 160.01/26.28  Sub-proof #808 shows that the following formulas are inconsistent:
% 160.01/26.28  ----------------------------------------------------------------
% 160.01/26.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.28    (2)  op(e1, e1) = e1
% 160.01/26.28    (3)   ~ (all_57_8 = e0)
% 160.01/26.28    (4)   ~ (e1 = e0)
% 160.01/26.28    (5)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.28           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.28           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 160.01/26.28           & op(e1, e0) = e1 & op(e0, e1) = e0)
% 160.01/26.28  
% 160.01/26.28  Begin of proof
% 160.01/26.28  | 
% 160.01/26.28  | BETA: splitting (5) gives:
% 160.01/26.28  | 
% 160.01/26.28  | Case 1:
% 160.01/26.28  | | 
% 160.01/26.28  | |   (6)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1)
% 160.01/26.28  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | ALPHA: (6) implies:
% 160.01/26.28  | |   (7)  all_57_8 = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | REDUCE: (3), (7) imply:
% 160.01/26.28  | |   (8)  $false
% 160.01/26.28  | | 
% 160.01/26.28  | | CLOSE: (8) is inconsistent.
% 160.01/26.28  | | 
% 160.01/26.28  | Case 2:
% 160.01/26.28  | | 
% 160.01/26.28  | |   (9)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1)
% 160.01/26.28  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | ALPHA: (9) implies:
% 160.01/26.28  | |   (10)  op(e1, e1) = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #903.
% 160.01/26.28  | | 
% 160.01/26.28  | End of split
% 160.01/26.28  | 
% 160.01/26.28  End of proof
% 160.01/26.28  
% 160.01/26.28  Sub-proof #809 shows that the following formulas are inconsistent:
% 160.01/26.28  ----------------------------------------------------------------
% 160.01/26.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.28    (2)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 160.01/26.28           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.01/26.28           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 160.01/26.28           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.01/26.28    (3)  op(e3, e3) = e1
% 160.01/26.28    (4)   ~ (e1 = e0)
% 160.01/26.28    (5)   ~ (e2 = e1)
% 160.01/26.28    (6)  op(e2, e0) = e1
% 160.01/26.28  
% 160.01/26.28  Begin of proof
% 160.01/26.28  | 
% 160.01/26.28  | BETA: splitting (2) gives:
% 160.01/26.28  | 
% 160.01/26.28  | Case 1:
% 160.01/26.28  | | 
% 160.01/26.28  | |   (7)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 160.01/26.28  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | ALPHA: (7) implies:
% 160.01/26.28  | |   (8)  op(e3, e3) = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #834.
% 160.01/26.28  | | 
% 160.01/26.28  | Case 2:
% 160.01/26.28  | | 
% 160.01/26.28  | |   (9)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2)
% 160.01/26.28  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | ALPHA: (9) implies:
% 160.01/26.28  | |   (10)  op(e2, e0) = e2
% 160.01/26.28  | | 
% 160.01/26.28  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #813.
% 160.01/26.28  | | 
% 160.01/26.28  | End of split
% 160.01/26.28  | 
% 160.01/26.28  End of proof
% 160.01/26.28  
% 160.01/26.28  Sub-proof #810 shows that the following formulas are inconsistent:
% 160.01/26.28  ----------------------------------------------------------------
% 160.01/26.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.28    (2)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.28           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 160.01/26.28           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 160.01/26.28           & op(e1, e0) = e1 & op(e0, e3) = e0)
% 160.01/26.28    (3)  op(e1, e1) = e1
% 160.01/26.28    (4)   ~ (e1 = e0)
% 160.01/26.28    (5)   ~ (e2 = e1)
% 160.01/26.28    (6)  op(e2, e0) = e1
% 160.01/26.28  
% 160.01/26.28  Begin of proof
% 160.01/26.28  | 
% 160.01/26.28  | BETA: splitting (2) gives:
% 160.01/26.28  | 
% 160.01/26.28  | Case 1:
% 160.01/26.28  | | 
% 160.01/26.28  | |   (7)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3)
% 160.01/26.28  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | ALPHA: (7) implies:
% 160.01/26.28  | |   (8)  op(e2, e0) = e2
% 160.01/26.28  | | 
% 160.01/26.28  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #813.
% 160.01/26.28  | | 
% 160.01/26.28  | Case 2:
% 160.01/26.28  | | 
% 160.01/26.28  | |   (9)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3)
% 160.01/26.28  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | ALPHA: (9) implies:
% 160.01/26.28  | |   (10)  op(e1, e1) = e0
% 160.01/26.28  | | 
% 160.01/26.28  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #903.
% 160.01/26.28  | | 
% 160.01/26.28  | End of split
% 160.01/26.28  | 
% 160.01/26.28  End of proof
% 160.01/26.28  
% 160.01/26.28  Sub-proof #811 shows that the following formulas are inconsistent:
% 160.01/26.28  ----------------------------------------------------------------
% 160.01/26.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.28    (2)  op(e2, e2) = all_57_12
% 160.01/26.28    (3)  op(e2, e2) = e0
% 160.01/26.28    (4)   ~ (all_57_12 = e0)
% 160.01/26.28  
% 160.01/26.28  Begin of proof
% 160.01/26.28  | 
% 160.01/26.28  | GROUND_INST: instantiating (1) with e0, all_57_12, e2, e2, simplifying with
% 160.01/26.28  |              (2), (3) gives:
% 160.01/26.28  |   (5)  all_57_12 = e0
% 160.01/26.28  | 
% 160.01/26.28  | REDUCE: (4), (5) imply:
% 160.01/26.28  |   (6)  $false
% 160.01/26.28  | 
% 160.01/26.28  | CLOSE: (6) is inconsistent.
% 160.01/26.28  | 
% 160.01/26.28  End of proof
% 160.01/26.28  
% 160.01/26.28  Sub-proof #812 shows that the following formulas are inconsistent:
% 160.01/26.28  ----------------------------------------------------------------
% 160.01/26.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.28    (2)  op(e1, e3) = all_52_2
% 160.01/26.28    (3)   ~ (all_52_2 = e1)
% 160.01/26.28    (4)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 160.01/26.28           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 160.01/26.28           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 160.01/26.28           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 160.01/26.28           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.28    (5)   ~ (e2 = e1)
% 160.01/26.28    (6)  op(e2, e0) = e1
% 160.01/26.28  
% 160.01/26.28  Begin of proof
% 160.01/26.28  | 
% 160.01/26.28  | BETA: splitting (4) gives:
% 160.01/26.28  | 
% 160.01/26.28  | Case 1:
% 160.01/26.28  | | 
% 160.01/26.28  | |   (7)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 160.01/26.28  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 160.01/26.28  | |          e0) = e2 & $i(all_57_12)
% 160.01/26.28  | | 
% 160.01/26.28  | | ALPHA: (7) implies:
% 160.01/26.28  | |   (8)  op(e2, e0) = e2
% 160.01/26.28  | | 
% 160.01/26.28  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #813.
% 160.01/26.28  | | 
% 160.01/26.28  | Case 2:
% 160.01/26.28  | | 
% 160.01/26.28  | |   (9)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 160.01/26.28  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 160.01/26.28  | |        all_57_14 & $i(all_57_14)
% 160.01/26.28  | | 
% 160.01/26.28  | | ALPHA: (9) implies:
% 160.01/26.28  | |   (10)  op(e1, e3) = e1
% 160.01/26.28  | | 
% 160.01/26.28  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #990.
% 160.01/26.28  | | 
% 160.01/26.28  | End of split
% 160.01/26.28  | 
% 160.01/26.28  End of proof
% 160.01/26.28  
% 160.01/26.28  Sub-proof #813 shows that the following formulas are inconsistent:
% 160.01/26.28  ----------------------------------------------------------------
% 160.01/26.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.28    (2)  op(e2, e0) = e2
% 160.01/26.28    (3)  op(e2, e0) = e1
% 160.01/26.28    (4)   ~ (e2 = e1)
% 160.01/26.28  
% 160.01/26.28  Begin of proof
% 160.01/26.28  | 
% 160.01/26.28  | GROUND_INST: instantiating (1) with e1, e2, e0, e2, simplifying with (2), (3)
% 160.01/26.28  |              gives:
% 160.01/26.28  |   (5)  e2 = e1
% 160.01/26.28  | 
% 160.01/26.28  | REDUCE: (4), (5) imply:
% 160.01/26.28  |   (6)  $false
% 160.01/26.28  | 
% 160.01/26.28  | CLOSE: (6) is inconsistent.
% 160.01/26.28  | 
% 160.01/26.28  End of proof
% 160.01/26.28  
% 160.01/26.28  Sub-proof #814 shows that the following formulas are inconsistent:
% 160.01/26.28  ----------------------------------------------------------------
% 160.01/26.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.28    (2)  op(e2, e2) = e0
% 160.01/26.28    (3)  op(e3, e3) = e1
% 160.01/26.28    (4)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) = e3) |
% 160.01/26.28             ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 & $i(all_57_0))) &
% 160.01/26.28           ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~ (all_57_2 = e1) & op(e1, e3)
% 160.01/26.28               = all_57_2 & $i(all_57_2))) & ((all_57_15 = e3 & op(e0, e0) = e3) |
% 160.01/26.28             ( ~ (all_57_6 = e0) & op(e0, e3) = all_57_6 & $i(all_57_6)))) |
% 160.01/26.28         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) = e2) |
% 160.01/26.28             ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 & $i(all_57_1))) &
% 160.01/26.28           ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~ (all_57_3 = e1) & op(e1, e2)
% 160.01/26.28               = all_57_3 & $i(all_57_3))) & ((all_57_15 = e2 & op(e0, e0) = e2) |
% 160.01/26.28             ( ~ (all_57_7 = e0) & op(e0, e2) = all_57_7 & $i(all_57_7))))
% 160.01/26.28    (5)   ~ (e3 = e1)
% 160.01/26.28    (6)   ~ (e2 = e0)
% 160.01/26.28  
% 160.01/26.28  Begin of proof
% 160.01/26.28  | 
% 160.01/26.28  | BETA: splitting (4) gives:
% 160.01/26.28  | 
% 160.01/26.28  | Case 1:
% 160.01/26.28  | | 
% 160.01/26.29  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_12 = e3 & op(e2, e2) =
% 160.01/26.29  | |            e3) | ( ~ (all_57_0 = e2) & op(e2, e3) = all_57_0 &
% 160.01/26.29  | |            $i(all_57_0))) & ((all_57_14 = e3 & op(e1, e1) = e3) | ( ~
% 160.01/26.29  | |            (all_57_2 = e1) & op(e1, e3) = all_57_2 & $i(all_57_2))) &
% 160.01/26.29  | |        ((all_57_15 = e3 & op(e0, e0) = e3) | ( ~ (all_57_6 = e0) & op(e0,
% 160.01/26.29  | |              e3) = all_57_6 & $i(all_57_6)))
% 160.01/26.29  | | 
% 160.01/26.29  | | ALPHA: (7) implies:
% 160.01/26.29  | |   (8)  op(e3, e3) = e3
% 160.01/26.29  | | 
% 160.01/26.29  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #995.
% 160.01/26.29  | | 
% 160.01/26.29  | Case 2:
% 160.01/26.29  | | 
% 160.01/26.29  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_10 = e2 & op(e3, e3) =
% 160.01/26.29  | |            e2) | ( ~ (all_57_1 = e3) & op(e3, e2) = all_57_1 &
% 160.01/26.29  | |            $i(all_57_1))) & ((all_57_14 = e2 & op(e1, e1) = e2) | ( ~
% 160.01/26.29  | |            (all_57_3 = e1) & op(e1, e2) = all_57_3 & $i(all_57_3))) &
% 160.01/26.29  | |        ((all_57_15 = e2 & op(e0, e0) = e2) | ( ~ (all_57_7 = e0) & op(e0,
% 160.01/26.29  | |              e2) = all_57_7 & $i(all_57_7)))
% 160.01/26.29  | | 
% 160.01/26.29  | | ALPHA: (9) implies:
% 160.01/26.29  | |   (10)  op(e2, e2) = e2
% 160.01/26.29  | | 
% 160.01/26.29  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #942.
% 160.01/26.29  | | 
% 160.01/26.29  | End of split
% 160.01/26.29  | 
% 160.01/26.29  End of proof
% 160.01/26.29  
% 160.01/26.29  Sub-proof #815 shows that the following formulas are inconsistent:
% 160.01/26.29  ----------------------------------------------------------------
% 160.01/26.29    (1)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 160.01/26.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.29    (3)  op(e1, e1) = e1
% 160.01/26.29    (4)  op(e1, e0) = all_52_14
% 160.01/26.29    (5)   ~ (all_52_14 = e2)
% 160.01/26.29    (6)   ~ (e2 = e1)
% 160.01/26.29  
% 160.01/26.29  Begin of proof
% 160.01/26.29  | 
% 160.01/26.29  | BETA: splitting (1) gives:
% 160.01/26.29  | 
% 160.01/26.29  | Case 1:
% 160.01/26.29  | | 
% 160.01/26.29  | |   (7)  all_56_8 = e2 & op(e1, e1) = e2
% 160.01/26.29  | | 
% 160.01/26.29  | | ALPHA: (7) implies:
% 160.01/26.29  | |   (8)  op(e1, e1) = e2
% 160.01/26.29  | | 
% 160.01/26.29  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #986.
% 160.01/26.29  | | 
% 160.01/26.29  | Case 2:
% 160.01/26.29  | | 
% 160.01/26.29  | |   (9)  all_56_11 = e2 & op(e1, e0) = e2
% 160.01/26.29  | | 
% 160.01/26.29  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #879.
% 160.01/26.29  | | 
% 160.01/26.29  | End of split
% 160.01/26.29  | 
% 160.01/26.29  End of proof
% 160.01/26.29  
% 160.01/26.29  Sub-proof #816 shows that the following formulas are inconsistent:
% 160.01/26.29  ----------------------------------------------------------------
% 160.01/26.29    (1)  all_56_7 = e2 & op(e1, e2) = e2
% 160.01/26.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.29    (3)  op(e1, e2) = all_52_6
% 160.01/26.29    (4)   ~ (all_52_6 = e2)
% 160.01/26.29  
% 160.01/26.29  Begin of proof
% 160.01/26.29  | 
% 160.01/26.29  | ALPHA: (1) implies:
% 160.01/26.29  |   (5)  op(e1, e2) = e2
% 160.01/26.29  | 
% 160.01/26.29  | GROUND_INST: instantiating (2) with all_52_6, e2, e2, e1, simplifying with
% 160.01/26.29  |              (3), (5) gives:
% 160.01/26.29  |   (6)  all_52_6 = e2
% 160.01/26.29  | 
% 160.01/26.29  | REDUCE: (4), (6) imply:
% 160.01/26.29  |   (7)  $false
% 160.01/26.29  | 
% 160.01/26.29  | CLOSE: (7) is inconsistent.
% 160.01/26.29  | 
% 160.01/26.29  End of proof
% 160.01/26.29  
% 160.01/26.29  Sub-proof #817 shows that the following formulas are inconsistent:
% 160.01/26.29  ----------------------------------------------------------------
% 160.01/26.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.29    (2)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 160.01/26.29           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 160.01/26.29           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 160.01/26.29           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 160.01/26.29    (3)  op(e2, e2) = e2
% 160.01/26.29    (4)   ~ (all_52_13 = all_4_2)
% 160.01/26.29    (5)  op(e2, e2) = all_4_2
% 160.01/26.29    (6)  op(e3, e3) = e1
% 160.01/26.29    (7)  op(e2, e0) = all_52_13
% 160.01/26.29    (8)   ~ (e3 = e1)
% 160.01/26.29  
% 160.01/26.29  Begin of proof
% 160.01/26.29  | 
% 160.01/26.29  | BETA: splitting (2) gives:
% 160.01/26.29  | 
% 160.01/26.29  | Case 1:
% 160.01/26.29  | | 
% 160.01/26.29  | |   (9)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 160.01/26.29  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 160.01/26.29  | |          e0) = e2 & $i(all_57_12)
% 160.01/26.29  | | 
% 160.01/26.29  | | ALPHA: (9) implies:
% 160.01/26.29  | |   (10)  op(e2, e0) = e2
% 160.01/26.29  | | 
% 160.01/26.29  | | REF_CLOSE: (1), (3), (4), (5), (7), (10) are inconsistent by sub-proof #972.
% 160.01/26.29  | | 
% 160.01/26.29  | Case 2:
% 160.01/26.29  | | 
% 160.01/26.29  | |   (11)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 160.01/26.29  | |         op(e3, e0) = e3
% 160.01/26.29  | | 
% 160.01/26.29  | | ALPHA: (11) implies:
% 160.01/26.29  | |   (12)  op(e3, e3) = e3
% 160.01/26.29  | | 
% 160.01/26.29  | | REF_CLOSE: (1), (6), (8), (12) are inconsistent by sub-proof #995.
% 160.01/26.29  | | 
% 160.01/26.29  | End of split
% 160.01/26.29  | 
% 160.01/26.29  End of proof
% 160.01/26.29  
% 160.01/26.29  Sub-proof #818 shows that the following formulas are inconsistent:
% 160.01/26.29  ----------------------------------------------------------------
% 160.01/26.29    (1)   ~ (all_52_12 = e2)
% 160.01/26.29    (2)   ~ (e3 = e2)
% 160.01/26.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.29    (4)  op(e2, e2) = e2
% 160.01/26.29    (5)  op(e1, e3) = all_52_2
% 160.01/26.29    (6)   ~ (all_52_13 = all_4_2)
% 160.01/26.29    (7)   ~ (all_52_2 = e1)
% 160.01/26.29    (8)  op(e1, e0) = all_52_14
% 160.01/26.29    (9)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 160.01/26.29         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 160.01/26.29    (10)  op(e2, e2) = all_4_2
% 160.01/26.29    (11)   ~ (all_52_14 = e2)
% 160.01/26.29    (12)  op(e3, e3) = e1
% 160.01/26.29    (13)  op(e2, e0) = all_52_13
% 160.01/26.29    (14)  op(e3, e0) = all_52_12
% 160.01/26.29    (15)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 160.01/26.29            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 160.01/26.29              e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3
% 160.01/26.29              = e2) & op(e3, e3) = e3 & op(e3, e2) = e3) | (all_57_1 = e3 &
% 160.01/26.29            all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) & op(e3, e3) =
% 160.01/26.29            e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 160.01/26.29            $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~
% 160.01/26.29            (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1
% 160.01/26.29            & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.29    (16)   ~ (e3 = e1)
% 160.01/26.29  
% 160.01/26.29  Begin of proof
% 160.01/26.29  | 
% 160.01/26.29  | BETA: splitting (15) gives:
% 160.01/26.29  | 
% 160.01/26.29  | Case 1:
% 160.01/26.29  | | 
% 160.01/26.29  | |   (17)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 160.01/26.29  | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0
% 160.01/26.29  | |           & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 =
% 160.01/26.29  | |           e3 &  ~ (e3 = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 160.01/26.29  | | 
% 160.01/26.29  | | BETA: splitting (17) gives:
% 160.01/26.29  | | 
% 160.01/26.29  | | Case 1:
% 160.01/26.29  | | | 
% 160.01/26.29  | | |   (18)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 160.01/26.29  | | |           e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0
% 160.01/26.29  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 160.01/26.29  | | | 
% 160.01/26.29  | | | ALPHA: (18) implies:
% 160.01/26.29  | | |   (19)  op(e0, e0) = e3
% 160.01/26.29  | | | 
% 160.01/26.29  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (13), (14), (19)
% 160.01/26.29  | | |            are inconsistent by sub-proof #877.
% 160.01/26.29  | | | 
% 160.01/26.29  | | Case 2:
% 160.01/26.29  | | | 
% 160.01/26.29  | | |   (20)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 160.01/26.29  | | |         op(e3, e2) = e3
% 160.01/26.29  | | | 
% 160.01/26.29  | | | ALPHA: (20) implies:
% 160.01/26.29  | | |   (21)  op(e3, e3) = e3
% 160.01/26.29  | | | 
% 160.01/26.29  | | | REF_CLOSE: (3), (12), (16), (21) are inconsistent by sub-proof #995.
% 160.01/26.29  | | | 
% 160.01/26.29  | | End of split
% 160.01/26.29  | | 
% 160.01/26.29  | Case 2:
% 160.01/26.29  | | 
% 160.01/26.29  | |   (22)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 =
% 160.01/26.29  | |             e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12
% 160.01/26.29  | |           & op(e2, e0) = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 =
% 160.01/26.29  | |           e3 & all_57_10 = e1 &  ~ (all_57_14 = e3) & op(e3, e3) = e1 &
% 160.01/26.29  | |           op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 160.01/26.29  | |           $i(all_57_14))
% 160.01/26.29  | | 
% 160.01/26.29  | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (13), (22) are inconsistent by
% 160.01/26.29  | |            sub-proof #849.
% 160.01/26.29  | | 
% 160.01/26.29  | End of split
% 160.01/26.29  | 
% 160.01/26.29  End of proof
% 160.01/26.29  
% 160.01/26.29  Sub-proof #819 shows that the following formulas are inconsistent:
% 160.01/26.29  ----------------------------------------------------------------
% 160.01/26.29    (1)  op(e0, e1) = all_52_11
% 160.01/26.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.29    (3)  op(e0, e3) = all_52_3
% 160.01/26.29    (4)  op(e1, e1) = e1
% 160.01/26.29    (5)   ~ (all_52_3 = e0)
% 160.01/26.29    (6)  op(e3, e3) = e1
% 160.01/26.29    (7)   ~ (e1 = e0)
% 160.01/26.29    (8)  op(e0, e2) = e1
% 160.01/26.29    (9)   ~ (all_52_11 = e0)
% 160.01/26.29    (10)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.29            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 160.01/26.29            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 160.01/26.29            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 160.01/26.29            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 160.01/26.29              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 160.01/26.29            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 160.01/26.29            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 160.01/26.29            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 160.01/26.29            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 160.01/26.29              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.01/26.29            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 160.01/26.29            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 160.01/26.29            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.01/26.29              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 160.01/26.29          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.29            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 160.01/26.29            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 160.01/26.29            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 160.01/26.29            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 160.01/26.29            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 160.01/26.29            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 160.01/26.29  
% 160.01/26.29  Begin of proof
% 160.01/26.29  | 
% 160.01/26.29  | BETA: splitting (10) gives:
% 160.01/26.29  | 
% 160.01/26.29  | Case 1:
% 160.01/26.29  | | 
% 160.01/26.29  | |   (11)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 160.01/26.29  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.01/26.29  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 160.01/26.29  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 160.01/26.29  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 160.01/26.29  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.01/26.29  | | 
% 160.01/26.29  | | BETA: splitting (11) gives:
% 160.01/26.29  | | 
% 160.01/26.29  | | Case 1:
% 160.01/26.29  | | | 
% 160.01/26.29  | | |   (12)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 160.01/26.29  | | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.01/26.29  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 160.01/26.29  | | | 
% 160.01/26.29  | | | REF_CLOSE: (2), (3), (4), (5), (7), (12) are inconsistent by sub-proof
% 160.01/26.29  | | |            #821.
% 160.01/26.29  | | | 
% 160.01/26.29  | | Case 2:
% 160.01/26.29  | | | 
% 160.01/26.29  | | |   (13)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0)
% 160.01/26.29  | | |         | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.01/26.29  | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 160.01/26.29  | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.01/26.29  | | | 
% 160.01/26.29  | | | BETA: splitting (13) gives:
% 160.01/26.29  | | | 
% 160.01/26.29  | | | Case 1:
% 160.01/26.29  | | | | 
% 160.01/26.29  | | | |   (14)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 160.01/26.29  | | | | 
% 160.01/26.29  | | | | ALPHA: (14) implies:
% 160.01/26.29  | | | |   (15)  op(e0, e3) = e0
% 160.01/26.29  | | | | 
% 160.01/26.29  | | | | REF_CLOSE: (2), (3), (5), (15) are inconsistent by sub-proof #973.
% 160.01/26.29  | | | | 
% 160.01/26.29  | | | Case 2:
% 160.01/26.29  | | | | 
% 160.01/26.29  | | | |   (16)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.01/26.29  | | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0)
% 160.01/26.29  | | | |         | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 160.01/26.29  | | | |           (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 160.01/26.29  | | | |             e2) = e0)
% 160.01/26.29  | | | | 
% 160.01/26.29  | | | | BETA: splitting (16) gives:
% 160.01/26.29  | | | | 
% 160.01/26.29  | | | | Case 1:
% 160.01/26.29  | | | | | 
% 160.01/26.29  | | | | |   (17)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.01/26.29  | | | | |           = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 160.01/26.29  | | | | | 
% 160.01/26.29  | | | | | ALPHA: (17) implies:
% 160.01/26.29  | | | | |   (18)  op(e3, e3) = e0
% 160.01/26.29  | | | | | 
% 160.01/26.29  | | | | | REF_CLOSE: (2), (6), (7), (18) are inconsistent by sub-proof #834.
% 160.01/26.29  | | | | | 
% 160.01/26.29  | | | | Case 2:
% 160.01/26.29  | | | | | 
% 160.01/26.29  | | | | |   (19)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 160.01/26.29  | | | | |         (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 160.01/26.29  | | | | |           e2) = e0
% 160.01/26.29  | | | | | 
% 160.01/26.29  | | | | | ALPHA: (19) implies:
% 160.01/26.29  | | | | |   (20)  op(e0, e2) = e0
% 160.01/26.29  | | | | | 
% 160.01/26.29  | | | | | REF_CLOSE: (2), (7), (8), (20) are inconsistent by sub-proof #832.
% 160.01/26.29  | | | | | 
% 160.01/26.29  | | | | End of split
% 160.01/26.29  | | | | 
% 160.01/26.29  | | | End of split
% 160.01/26.29  | | | 
% 160.01/26.29  | | End of split
% 160.01/26.29  | | 
% 160.01/26.29  | Case 2:
% 160.01/26.29  | | 
% 160.01/26.29  | |   (21)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 160.01/26.29  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 160.01/26.29  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 160.01/26.29  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 160.01/26.29  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.29  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 160.01/26.29  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 160.01/26.29  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 160.01/26.29  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 160.01/26.29  | |           & op(e0, e1) = e0)
% 160.01/26.29  | | 
% 160.01/26.29  | | BETA: splitting (21) gives:
% 160.01/26.29  | | 
% 160.01/26.29  | | Case 1:
% 160.01/26.29  | | | 
% 160.01/26.30  | | |   (22)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 160.01/26.30  | | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 160.01/26.30  | | |         | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.01/26.30  | | |             = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 160.01/26.30  | | | 
% 160.01/26.30  | | | REF_CLOSE: (2), (4), (6), (7), (8), (22) are inconsistent by sub-proof
% 160.01/26.30  | | |            #830.
% 160.01/26.30  | | | 
% 160.01/26.30  | | Case 2:
% 160.01/26.30  | | | 
% 160.01/26.30  | | |   (23)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 160.01/26.30  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 160.01/26.30  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 160.01/26.30  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 160.01/26.30  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 160.01/26.30  | | |             e0) & op(e0, e1) = e0)
% 160.01/26.30  | | | 
% 160.01/26.30  | | | REF_CLOSE: (1), (2), (4), (7), (9), (23) are inconsistent by sub-proof
% 160.01/26.30  | | |            #820.
% 160.01/26.30  | | | 
% 160.01/26.30  | | End of split
% 160.01/26.30  | | 
% 160.01/26.30  | End of split
% 160.01/26.30  | 
% 160.01/26.30  End of proof
% 160.01/26.30  
% 160.01/26.30  Sub-proof #820 shows that the following formulas are inconsistent:
% 160.01/26.30  ----------------------------------------------------------------
% 160.01/26.30    (1)  op(e0, e1) = all_52_11
% 160.01/26.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.30    (3)  op(e1, e1) = e1
% 160.01/26.30    (4)   ~ (e1 = e0)
% 160.01/26.30    (5)   ~ (all_52_11 = e0)
% 160.01/26.30    (6)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.30           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.30           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 160.01/26.30           & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 160.01/26.30           & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 160.01/26.30           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 160.01/26.30           all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 160.01/26.30  
% 160.01/26.30  Begin of proof
% 160.01/26.30  | 
% 160.01/26.30  | BETA: splitting (6) gives:
% 160.01/26.30  | 
% 160.01/26.30  | Case 1:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (7)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | |            e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 160.01/26.30  | |        (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | |            e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0)
% 160.01/26.30  | | 
% 160.01/26.30  | | BETA: splitting (7) gives:
% 160.01/26.30  | | 
% 160.01/26.30  | | Case 1:
% 160.01/26.30  | | | 
% 160.01/26.30  | | |   (8)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | | |          e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 160.01/26.30  | | | 
% 160.01/26.30  | | | ALPHA: (8) implies:
% 160.01/26.30  | | |   (9)  op(e0, e1) = e0
% 160.01/26.30  | | | 
% 160.01/26.30  | | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #966.
% 160.01/26.30  | | | 
% 160.01/26.30  | | Case 2:
% 160.01/26.30  | | | 
% 160.01/26.30  | | |   (10)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | | |           e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 160.01/26.30  | | | 
% 160.01/26.30  | | | ALPHA: (10) implies:
% 160.01/26.30  | | |   (11)  op(e1, e1) = e0
% 160.01/26.30  | | | 
% 160.01/26.30  | | | REF_CLOSE: (2), (3), (4), (11) are inconsistent by sub-proof #903.
% 160.01/26.30  | | | 
% 160.01/26.30  | | End of split
% 160.01/26.30  | | 
% 160.01/26.30  | Case 2:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (12)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 160.01/26.30  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 160.01/26.30  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 160.01/26.30  | |           & op(e0, e1) = e0)
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (2), (5), (12) are inconsistent by sub-proof #965.
% 160.01/26.30  | | 
% 160.01/26.30  | End of split
% 160.01/26.30  | 
% 160.01/26.30  End of proof
% 160.01/26.30  
% 160.01/26.30  Sub-proof #821 shows that the following formulas are inconsistent:
% 160.01/26.30  ----------------------------------------------------------------
% 160.01/26.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.30    (2)  op(e0, e3) = all_52_3
% 160.01/26.30    (3)  op(e1, e1) = e1
% 160.01/26.30    (4)   ~ (all_52_3 = e0)
% 160.01/26.30    (5)   ~ (e1 = e0)
% 160.01/26.30    (6)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.30           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 160.01/26.30           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 160.01/26.30           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 160.01/26.30           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 160.01/26.30           e1 & op(e0, e3) = e0)
% 160.01/26.30  
% 160.01/26.30  Begin of proof
% 160.01/26.30  | 
% 160.01/26.30  | BETA: splitting (6) gives:
% 160.01/26.30  | 
% 160.01/26.30  | Case 1:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (7)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 160.01/26.30  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (7) implies:
% 160.01/26.30  | |   (8)  op(e0, e3) = e0
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #973.
% 160.01/26.30  | | 
% 160.01/26.30  | Case 2:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (9)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | |            e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.01/26.30  | |        (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | |            e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 160.01/26.30  | | 
% 160.01/26.30  | | BETA: splitting (9) gives:
% 160.01/26.30  | | 
% 160.01/26.30  | | Case 1:
% 160.01/26.30  | | | 
% 160.01/26.30  | | |   (10)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | | |           e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 160.01/26.30  | | | 
% 160.01/26.30  | | | ALPHA: (10) implies:
% 160.01/26.30  | | |   (11)  op(e0, e3) = e0
% 160.01/26.30  | | | 
% 160.01/26.30  | | | REF_CLOSE: (1), (2), (4), (11) are inconsistent by sub-proof #973.
% 160.01/26.30  | | | 
% 160.01/26.30  | | Case 2:
% 160.01/26.30  | | | 
% 160.01/26.30  | | |   (12)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.30  | | |           e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 160.01/26.30  | | | 
% 160.01/26.30  | | | ALPHA: (12) implies:
% 160.01/26.30  | | |   (13)  op(e1, e1) = e0
% 160.01/26.30  | | | 
% 160.01/26.30  | | | REF_CLOSE: (1), (3), (5), (13) are inconsistent by sub-proof #903.
% 160.01/26.30  | | | 
% 160.01/26.30  | | End of split
% 160.01/26.30  | | 
% 160.01/26.30  | End of split
% 160.01/26.30  | 
% 160.01/26.30  End of proof
% 160.01/26.30  
% 160.01/26.30  Sub-proof #822 shows that the following formulas are inconsistent:
% 160.01/26.30  ----------------------------------------------------------------
% 160.01/26.30    (1)   ~ (all_52_6 = e1)
% 160.01/26.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.30    (3)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 160.01/26.30           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 160.01/26.30           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 160.01/26.30           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 160.01/26.30             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.30    (4)  op(e1, e2) = all_52_6
% 160.01/26.30    (5)  op(e2, e2) = e0
% 160.01/26.30    (6)   ~ (e1 = e0)
% 160.01/26.30  
% 160.01/26.30  Begin of proof
% 160.01/26.30  | 
% 160.01/26.30  | BETA: splitting (3) gives:
% 160.01/26.30  | 
% 160.01/26.30  | Case 1:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (7)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 160.01/26.30  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 160.01/26.30  | |        all_57_14 & $i(all_57_14)
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (7) implies:
% 160.01/26.30  | |   (8)  op(e1, e2) = e1
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #984.
% 160.01/26.30  | | 
% 160.01/26.30  | Case 2:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 160.01/26.30  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 160.01/26.30  | |        all_57_14 & $i(all_57_14)
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (9) implies:
% 160.01/26.30  | |   (10)  op(e2, e2) = e1
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #960.
% 160.01/26.30  | | 
% 160.01/26.30  | End of split
% 160.01/26.30  | 
% 160.01/26.30  End of proof
% 160.01/26.30  
% 160.01/26.30  Sub-proof #823 shows that the following formulas are inconsistent:
% 160.01/26.30  ----------------------------------------------------------------
% 160.01/26.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.30    (2)  op(e1, e3) = all_52_2
% 160.01/26.30    (3)   ~ (all_52_2 = e1)
% 160.01/26.30    (4)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 160.01/26.30           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 160.01/26.30           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 160.01/26.30           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 160.01/26.30           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.30    (5)  op(e3, e3) = e1
% 160.01/26.30    (6)   ~ (e2 = e1)
% 160.01/26.30  
% 160.01/26.30  Begin of proof
% 160.01/26.30  | 
% 160.01/26.30  | BETA: splitting (4) gives:
% 160.01/26.30  | 
% 160.01/26.30  | Case 1:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (7)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 160.01/26.30  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 160.01/26.30  | |          e0) = e2 & $i(all_57_12)
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (7) implies:
% 160.01/26.30  | |   (8)  op(e3, e3) = e2
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #828.
% 160.01/26.30  | | 
% 160.01/26.30  | Case 2:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (9)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 160.01/26.30  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 160.01/26.30  | |        all_57_14 & $i(all_57_14)
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (9) implies:
% 160.01/26.30  | |   (10)  op(e1, e3) = e1
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #990.
% 160.01/26.30  | | 
% 160.01/26.30  | End of split
% 160.01/26.30  | 
% 160.01/26.30  End of proof
% 160.01/26.30  
% 160.01/26.30  Sub-proof #824 shows that the following formulas are inconsistent:
% 160.01/26.30  ----------------------------------------------------------------
% 160.01/26.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.30    (2)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2,
% 160.01/26.30             e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 160.01/26.30           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 160.01/26.30             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 160.01/26.30           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 160.01/26.30           & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 160.01/26.30           $i(all_57_12))
% 160.01/26.30    (3)  op(e1, e1) = e1
% 160.01/26.30    (4)  op(e2, e2) = e0
% 160.01/26.30    (5)  op(e3, e3) = e1
% 160.01/26.30    (6)   ~ (e2 = e1)
% 160.01/26.30    (7)   ~ (e3 = e1)
% 160.01/26.30    (8)   ~ (e2 = e0)
% 160.01/26.30  
% 160.01/26.30  Begin of proof
% 160.01/26.30  | 
% 160.01/26.30  | BETA: splitting (2) gives:
% 160.01/26.30  | 
% 160.01/26.30  | Case 1:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (9)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 160.01/26.30  | |        op(e2, e2) = e2
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (9) implies:
% 160.01/26.30  | |   (10)  op(e2, e2) = e2
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (4), (8), (10) are inconsistent by sub-proof #942.
% 160.01/26.30  | | 
% 160.01/26.30  | Case 2:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (11)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 160.01/26.30  | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1
% 160.01/26.30  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 =
% 160.01/26.30  | |           e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 160.01/26.30  | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 160.01/26.30  | |           $i(all_57_12))
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (3), (5), (6), (7), (11) are inconsistent by sub-proof #825.
% 160.01/26.30  | | 
% 160.01/26.30  | End of split
% 160.01/26.30  | 
% 160.01/26.30  End of proof
% 160.01/26.30  
% 160.01/26.30  Sub-proof #825 shows that the following formulas are inconsistent:
% 160.01/26.30  ----------------------------------------------------------------
% 160.01/26.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.30    (2)  op(e1, e1) = e1
% 160.01/26.30    (3)  op(e3, e3) = e1
% 160.01/26.30    (4)   ~ (e2 = e1)
% 160.01/26.30    (5)   ~ (e3 = e1)
% 160.01/26.30    (6)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 160.01/26.30           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.01/26.30           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 160.01/26.30           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 160.01/26.30           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 160.01/26.30  
% 160.01/26.30  Begin of proof
% 160.01/26.30  | 
% 160.01/26.30  | BETA: splitting (6) gives:
% 160.01/26.30  | 
% 160.01/26.30  | Case 1:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (7)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 160.01/26.30  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 160.01/26.30  | |          e1) = e3 & $i(all_57_10)
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (7) implies:
% 160.01/26.30  | |   (8)  op(e1, e1) = e3
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1003.
% 160.01/26.30  | | 
% 160.01/26.30  | Case 2:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (9)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 160.01/26.30  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 160.01/26.30  | |          e1) = e2 & $i(all_57_12)
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (9) implies:
% 160.01/26.30  | |   (10)  op(e3, e3) = e2
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #828.
% 160.01/26.30  | | 
% 160.01/26.30  | End of split
% 160.01/26.30  | 
% 160.01/26.30  End of proof
% 160.01/26.30  
% 160.01/26.30  Sub-proof #826 shows that the following formulas are inconsistent:
% 160.01/26.30  ----------------------------------------------------------------
% 160.01/26.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.30    (2)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 160.01/26.30           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 160.01/26.30           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 160.01/26.30           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 160.01/26.30           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 160.01/26.30    (3)  op(e0, e0) = e0
% 160.01/26.30    (4)  op(e2, e2) = e0
% 160.01/26.30    (5)   ~ (e2 = e0)
% 160.01/26.30    (6)   ~ (e3 = e0)
% 160.01/26.30  
% 160.01/26.30  Begin of proof
% 160.01/26.30  | 
% 160.01/26.30  | BETA: splitting (2) gives:
% 160.01/26.30  | 
% 160.01/26.30  | Case 1:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (7)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 160.01/26.30  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 160.01/26.30  | |          e0) = e2 & $i(all_57_12)
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (7) implies:
% 160.01/26.30  | |   (8)  op(e0, e0) = e2
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #979.
% 160.01/26.30  | | 
% 160.01/26.30  | Case 2:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (9)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 160.01/26.30  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 160.01/26.30  | |          e2) = e3 & $i(all_57_10)
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (9) implies:
% 160.01/26.30  | |   (10)  op(e2, e2) = e3
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #945.
% 160.01/26.30  | | 
% 160.01/26.30  | End of split
% 160.01/26.30  | 
% 160.01/26.30  End of proof
% 160.01/26.30  
% 160.01/26.30  Sub-proof #827 shows that the following formulas are inconsistent:
% 160.01/26.30  ----------------------------------------------------------------
% 160.01/26.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.30    (2)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 160.01/26.30           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 160.01/26.30           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 160.01/26.30           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 160.01/26.30           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 160.01/26.30    (3)  op(e2, e2) = e0
% 160.01/26.30    (4)  op(e3, e3) = e1
% 160.01/26.30    (5)   ~ (e2 = e1)
% 160.01/26.30    (6)   ~ (e3 = e0)
% 160.01/26.30  
% 160.01/26.30  Begin of proof
% 160.01/26.30  | 
% 160.01/26.30  | BETA: splitting (2) gives:
% 160.01/26.30  | 
% 160.01/26.30  | Case 1:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (7)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 160.01/26.30  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 160.01/26.30  | |        all_57_12 & $i(all_57_12)
% 160.01/26.30  | | 
% 160.01/26.30  | | ALPHA: (7) implies:
% 160.01/26.30  | |   (8)  op(e3, e3) = e2
% 160.01/26.30  | | 
% 160.01/26.30  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #828.
% 160.01/26.30  | | 
% 160.01/26.30  | Case 2:
% 160.01/26.30  | | 
% 160.01/26.30  | |   (9)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2)
% 160.01/26.30  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 160.01/26.31  | |          e2) = e3 & $i(all_57_10)
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (9) implies:
% 160.01/26.31  | |   (10)  op(e2, e2) = e3
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #945.
% 160.01/26.31  | | 
% 160.01/26.31  | End of split
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #828 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (2)  op(e3, e3) = e2
% 160.01/26.31    (3)  op(e3, e3) = e1
% 160.01/26.31    (4)   ~ (e2 = e1)
% 160.01/26.31  
% 160.01/26.31  Begin of proof
% 160.01/26.31  | 
% 160.01/26.31  | GROUND_INST: instantiating (1) with e1, e2, e3, e3, simplifying with (2), (3)
% 160.01/26.31  |              gives:
% 160.01/26.31  |   (5)  e2 = e1
% 160.01/26.31  | 
% 160.01/26.31  | REDUCE: (4), (5) imply:
% 160.01/26.31  |   (6)  $false
% 160.01/26.31  | 
% 160.01/26.31  | CLOSE: (6) is inconsistent.
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #829 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (2)  op(e1, e1) = e1
% 160.01/26.31    (3)  op(e2, e2) = e2
% 160.01/26.31    (4)   ~ (all_52_13 = all_4_2)
% 160.01/26.31    (5)  op(e2, e2) = all_4_2
% 160.01/26.31    (6)   ~ (e1 = e0)
% 160.01/26.31    (7)  op(e2, e0) = all_52_13
% 160.01/26.31    (8)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.31           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.01/26.31           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 160.01/26.31           & op(e1, e0) = e1 & op(e0, e1) = e0)
% 160.01/26.31  
% 160.01/26.31  Begin of proof
% 160.01/26.31  | 
% 160.01/26.31  | BETA: splitting (8) gives:
% 160.01/26.31  | 
% 160.01/26.31  | Case 1:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (9)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1)
% 160.01/26.31  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (9) implies:
% 160.01/26.31  | |   (10)  op(e2, e0) = e2
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (3), (4), (5), (7), (10) are inconsistent by sub-proof #972.
% 160.01/26.31  | | 
% 160.01/26.31  | Case 2:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (11)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.31  | |           e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (11) implies:
% 160.01/26.31  | |   (12)  op(e1, e1) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (2), (6), (12) are inconsistent by sub-proof #903.
% 160.01/26.31  | | 
% 160.01/26.31  | End of split
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #830 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (2)  op(e1, e1) = e1
% 160.01/26.31    (3)  op(e3, e3) = e1
% 160.01/26.31    (4)   ~ (e1 = e0)
% 160.01/26.31    (5)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 160.01/26.31           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.01/26.31           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 160.01/26.31           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 160.01/26.31           & op(e3, e0) = e3 & op(e0, e1) = e0)
% 160.01/26.31    (6)  op(e0, e2) = e1
% 160.01/26.31  
% 160.01/26.31  Begin of proof
% 160.01/26.31  | 
% 160.01/26.31  | BETA: splitting (5) gives:
% 160.01/26.31  | 
% 160.01/26.31  | Case 1:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (7)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 160.01/26.31  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (7) implies:
% 160.01/26.31  | |   (8)  op(e1, e1) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #903.
% 160.01/26.31  | | 
% 160.01/26.31  | Case 2:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (9)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 160.01/26.31  | |        (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 160.01/26.31  | |          & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (3), (4), (6), (9) are inconsistent by sub-proof #831.
% 160.01/26.31  | | 
% 160.01/26.31  | End of split
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #831 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (2)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 160.01/26.31         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.31           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 160.01/26.31    (3)  op(e3, e3) = e1
% 160.01/26.31    (4)   ~ (e1 = e0)
% 160.01/26.31    (5)  op(e0, e2) = e1
% 160.01/26.31  
% 160.01/26.31  Begin of proof
% 160.01/26.31  | 
% 160.01/26.31  | BETA: splitting (2) gives:
% 160.01/26.31  | 
% 160.01/26.31  | Case 1:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (6)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (6) implies:
% 160.01/26.31  | |   (7)  op(e0, e2) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #832.
% 160.01/26.31  | | 
% 160.01/26.31  | Case 2:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (8)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 160.01/26.31  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (8) implies:
% 160.01/26.31  | |   (9)  op(e3, e3) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #834.
% 160.01/26.31  | | 
% 160.01/26.31  | End of split
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #832 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (2)  op(e0, e2) = e1
% 160.01/26.31    (3)  op(e0, e2) = e0
% 160.01/26.31    (4)   ~ (e1 = e0)
% 160.01/26.31  
% 160.01/26.31  Begin of proof
% 160.01/26.31  | 
% 160.01/26.31  | GROUND_INST: instantiating (1) with e1, e0, e2, e0, simplifying with (2), (3)
% 160.01/26.31  |              gives:
% 160.01/26.31  |   (5)  e1 = e0
% 160.01/26.31  | 
% 160.01/26.31  | REDUCE: (4), (5) imply:
% 160.01/26.31  |   (6)  $false
% 160.01/26.31  | 
% 160.01/26.31  | CLOSE: (6) is inconsistent.
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #833 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (2)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 160.01/26.31           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.01/26.31           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 160.01/26.31           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.01/26.31    (3)  op(e2, e2) = e2
% 160.01/26.31    (4)   ~ (all_52_13 = all_4_2)
% 160.01/26.31    (5)  op(e2, e2) = all_4_2
% 160.01/26.31    (6)  op(e3, e3) = e1
% 160.01/26.31    (7)   ~ (e1 = e0)
% 160.01/26.31    (8)  op(e2, e0) = all_52_13
% 160.01/26.31  
% 160.01/26.31  Begin of proof
% 160.01/26.31  | 
% 160.01/26.31  | BETA: splitting (2) gives:
% 160.01/26.31  | 
% 160.01/26.31  | Case 1:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (9)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 160.01/26.31  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (9) implies:
% 160.01/26.31  | |   (10)  op(e3, e3) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (6), (7), (10) are inconsistent by sub-proof #834.
% 160.01/26.31  | | 
% 160.01/26.31  | Case 2:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (11)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.31  | |           e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (11) implies:
% 160.01/26.31  | |   (12)  op(e2, e0) = e2
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (3), (4), (5), (8), (12) are inconsistent by sub-proof #972.
% 160.01/26.31  | | 
% 160.01/26.31  | End of split
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #834 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (2)  op(e3, e3) = e1
% 160.01/26.31    (3)  op(e3, e3) = e0
% 160.01/26.31    (4)   ~ (e1 = e0)
% 160.01/26.31  
% 160.01/26.31  Begin of proof
% 160.01/26.31  | 
% 160.01/26.31  | GROUND_INST: instantiating (1) with e0, e1, e3, e3, simplifying with (2), (3)
% 160.01/26.31  |              gives:
% 160.01/26.31  |   (5)  e1 = e0
% 160.01/26.31  | 
% 160.01/26.31  | REDUCE: (4), (5) imply:
% 160.01/26.31  |   (6)  $false
% 160.01/26.31  | 
% 160.01/26.31  | CLOSE: (6) is inconsistent.
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #835 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (2)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.31           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 160.01/26.31           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 160.01/26.31           & op(e1, e0) = e1 & op(e0, e3) = e0)
% 160.01/26.31    (3)  op(e1, e1) = e1
% 160.01/26.31    (4)  op(e2, e2) = e2
% 160.01/26.31    (5)   ~ (all_52_13 = all_4_2)
% 160.01/26.31    (6)  op(e2, e2) = all_4_2
% 160.01/26.31    (7)   ~ (e1 = e0)
% 160.01/26.31    (8)  op(e2, e0) = all_52_13
% 160.01/26.31  
% 160.01/26.31  Begin of proof
% 160.01/26.31  | 
% 160.01/26.31  | BETA: splitting (2) gives:
% 160.01/26.31  | 
% 160.01/26.31  | Case 1:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (9)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3)
% 160.01/26.31  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (9) implies:
% 160.01/26.31  | |   (10)  op(e2, e0) = e2
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (4), (5), (6), (8), (10) are inconsistent by sub-proof #972.
% 160.01/26.31  | | 
% 160.01/26.31  | Case 2:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (11)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.31  | |           e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (11) implies:
% 160.01/26.31  | |   (12)  op(e1, e1) = e0
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (3), (7), (12) are inconsistent by sub-proof #903.
% 160.01/26.31  | | 
% 160.01/26.31  | End of split
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #836 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (2)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 160.01/26.31           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 160.01/26.31           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 160.01/26.31           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 160.01/26.31    (3)  op(e0, e0) = e0
% 160.01/26.31    (4)  op(e3, e3) = e1
% 160.01/26.31    (5)   ~ (e3 = e1)
% 160.01/26.31    (6)   ~ (e2 = e0)
% 160.01/26.31  
% 160.01/26.31  Begin of proof
% 160.01/26.31  | 
% 160.01/26.31  | BETA: splitting (2) gives:
% 160.01/26.31  | 
% 160.01/26.31  | Case 1:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (7)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 160.01/26.31  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 160.01/26.31  | |          e0) = e2 & $i(all_57_12)
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (7) implies:
% 160.01/26.31  | |   (8)  op(e0, e0) = e2
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #979.
% 160.01/26.31  | | 
% 160.01/26.31  | Case 2:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (9)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 160.01/26.31  | |        op(e3, e0) = e3
% 160.01/26.31  | | 
% 160.01/26.31  | | ALPHA: (9) implies:
% 160.01/26.31  | |   (10)  op(e3, e3) = e3
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #995.
% 160.01/26.31  | | 
% 160.01/26.31  | End of split
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #837 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ~ (e3 = e2)
% 160.01/26.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (3)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 160.01/26.31           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 160.01/26.31           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 160.01/26.31           & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 160.01/26.31           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 160.01/26.31           e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 160.01/26.31         (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 160.01/26.31           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 160.01/26.31           = e3 & $i(all_57_10))
% 160.01/26.31    (4)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 160.01/26.31         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 160.01/26.31    (5)  op(e0, e0) = e0
% 160.01/26.31    (6)  all_56_10 = e1
% 160.01/26.31    (7)   ~ (e1 = e0)
% 160.01/26.31    (8)  op(e2, e1) = all_52_9
% 160.01/26.31    (9)   ~ (e2 = e1)
% 160.01/26.31    (10)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 160.01/26.31          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 160.01/26.31    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 160.01/26.31          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 160.01/26.31    (12)   ~ (all_52_9 = e2)
% 160.01/26.31    (13)   ~ (e3 = e1)
% 160.01/26.31    (14)   ~ (e2 = e0)
% 160.01/26.31    (15)   ~ (e3 = e0)
% 160.01/26.31  
% 160.01/26.31  Begin of proof
% 160.01/26.31  | 
% 160.01/26.31  | BETA: splitting (3) gives:
% 160.01/26.31  | 
% 160.01/26.31  | Case 1:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (16)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 160.01/26.31  | |             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0
% 160.01/26.31  | |           & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 =
% 160.01/26.31  | |           e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 160.01/26.31  | | 
% 160.01/26.31  | | REF_CLOSE: (2), (5), (8), (12), (14), (16) are inconsistent by sub-proof
% 160.01/26.31  | |            #978.
% 160.01/26.31  | | 
% 160.01/26.31  | Case 2:
% 160.01/26.31  | | 
% 160.01/26.31  | |   (17)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 160.01/26.31  | |             e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 160.01/26.31  | |           & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 160.01/26.31  | |           e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 160.01/26.31  | |           & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 160.01/26.31  | |           $i(all_57_10))
% 160.01/26.31  | | 
% 160.01/26.31  | | BETA: splitting (17) gives:
% 160.01/26.31  | | 
% 160.01/26.31  | | Case 1:
% 160.01/26.31  | | | 
% 160.01/26.31  | | |   (18)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 160.01/26.31  | | |           e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 160.01/26.31  | | |         & op(e1, e0) = e1 & $i(all_57_14)
% 160.01/26.31  | | | 
% 160.01/26.31  | | | ALPHA: (18) implies:
% 160.01/26.31  | | |   (19)  op(e2, e2) = e1
% 160.01/26.31  | | | 
% 160.01/26.31  | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 160.01/26.31  | | |            (14), (15), (19) are inconsistent by sub-proof #842.
% 160.01/26.31  | | | 
% 160.01/26.31  | | Case 2:
% 160.01/26.31  | | | 
% 160.01/26.31  | | |   (20)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 160.01/26.31  | | |           e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0
% 160.01/26.31  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 160.01/26.31  | | | 
% 160.01/26.31  | | | ALPHA: (20) implies:
% 160.01/26.31  | | |   (21)  op(e0, e0) = e3
% 160.01/26.31  | | | 
% 160.01/26.31  | | | REF_CLOSE: (2), (5), (15), (21) are inconsistent by sub-proof #999.
% 160.01/26.31  | | | 
% 160.01/26.31  | | End of split
% 160.01/26.31  | | 
% 160.01/26.31  | End of split
% 160.01/26.31  | 
% 160.01/26.31  End of proof
% 160.01/26.31  
% 160.01/26.31  Sub-proof #838 shows that the following formulas are inconsistent:
% 160.01/26.31  ----------------------------------------------------------------
% 160.01/26.31    (1)   ~ (all_52_6 = e1)
% 160.01/26.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.31    (3)  op(e1, e1) = e1
% 160.01/26.31    (4)  op(e0, e0) = e0
% 160.01/26.32    (5)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 160.01/26.32           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 160.01/26.32           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1)
% 160.01/26.32           & op(e1, e2) = e1 & op(e1, e1) = e1) | (all_57_4 = e3 & all_57_6 = e0 &
% 160.01/26.32           all_57_15 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 160.01/26.32             e1) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10)) |
% 160.01/26.32         (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 160.01/26.32             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 160.01/26.32           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 160.01/26.32           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.01/26.32    (6)  op(e1, e2) = all_52_6
% 160.01/26.32    (7)  op(e1, e0) = all_52_14
% 160.01/26.32    (8)  op(e3, e3) = e1
% 160.01/26.32    (9)   ~ (e2 = e1)
% 160.01/26.32    (10)   ~ (all_52_14 = e1)
% 160.01/26.32    (11)   ~ (e3 = e0)
% 160.01/26.32  
% 160.01/26.32  Begin of proof
% 160.01/26.32  | 
% 160.01/26.32  | BETA: splitting (5) gives:
% 160.01/26.32  | 
% 160.01/26.32  | Case 1:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (12)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 =
% 160.01/26.32  | |             e0) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1
% 160.01/26.32  | |           & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 =
% 160.01/26.32  | |           e1 &  ~ (e2 = e1) & op(e1, e2) = e1 & op(e1, e1) = e1)
% 160.01/26.32  | | 
% 160.01/26.32  | | REF_CLOSE: (1), (2), (3), (6), (9), (12) are inconsistent by sub-proof #983.
% 160.01/26.32  | | 
% 160.01/26.32  | Case 2:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (13)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 160.01/26.32  | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0
% 160.01/26.32  | |           & op(e0, e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 =
% 160.01/26.32  | |           e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4
% 160.01/26.32  | |           = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 160.01/26.32  | |           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 &
% 160.01/26.32  | |           op(e1, e0) = e1 & $i(all_57_14))
% 160.01/26.32  | | 
% 160.01/26.32  | | BETA: splitting (13) gives:
% 160.01/26.32  | | 
% 160.01/26.32  | | Case 1:
% 160.01/26.32  | | | 
% 160.01/26.32  | | |   (14)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 =
% 160.01/26.32  | | |           e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0
% 160.01/26.32  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 160.01/26.32  | | | 
% 160.01/26.32  | | | ALPHA: (14) implies:
% 160.01/26.32  | | |   (15)  op(e0, e0) = e3
% 160.01/26.32  | | | 
% 160.01/26.32  | | | REF_CLOSE: (2), (4), (11), (15) are inconsistent by sub-proof #999.
% 160.01/26.32  | | | 
% 160.01/26.32  | | Case 2:
% 160.01/26.32  | | | 
% 160.01/26.32  | | |   (16)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 160.01/26.32  | | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 =
% 160.01/26.32  | | |           e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 160.01/26.32  | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.01/26.32  | | | 
% 160.01/26.32  | | | REF_CLOSE: (2), (7), (8), (10), (16) are inconsistent by sub-proof #839.
% 160.01/26.32  | | | 
% 160.01/26.32  | | End of split
% 160.01/26.32  | | 
% 160.01/26.32  | End of split
% 160.01/26.32  | 
% 160.01/26.32  End of proof
% 160.01/26.32  
% 160.01/26.32  Sub-proof #839 shows that the following formulas are inconsistent:
% 160.01/26.32  ----------------------------------------------------------------
% 160.01/26.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.32    (2)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 160.01/26.32             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 160.01/26.32           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 160.01/26.32           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.01/26.32    (3)  op(e1, e0) = all_52_14
% 160.01/26.32    (4)  op(e3, e3) = e1
% 160.01/26.32    (5)   ~ (all_52_14 = e1)
% 160.01/26.32  
% 160.01/26.32  Begin of proof
% 160.01/26.32  | 
% 160.01/26.32  | BETA: splitting (2) gives:
% 160.01/26.32  | 
% 160.01/26.32  | Case 1:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (6)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 160.01/26.32  | |        op(e3, e1) = e3
% 160.01/26.32  | | 
% 160.01/26.32  | | ALPHA: (6) implies:
% 160.01/26.32  | |   (7)   ~ (e3 = e1)
% 160.01/26.32  | |   (8)  op(e3, e3) = e3
% 160.01/26.32  | | 
% 160.01/26.32  | | REF_CLOSE: (1), (4), (7), (8) are inconsistent by sub-proof #995.
% 160.01/26.32  | | 
% 160.01/26.32  | Case 2:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (9)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 160.01/26.32  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 160.01/26.32  | |          e0) = e1 & $i(all_57_14)
% 160.01/26.32  | | 
% 160.01/26.32  | | ALPHA: (9) implies:
% 160.01/26.32  | |   (10)  op(e1, e0) = e1
% 160.01/26.32  | | 
% 160.01/26.32  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #974.
% 160.01/26.32  | | 
% 160.01/26.32  | End of split
% 160.01/26.32  | 
% 160.01/26.32  End of proof
% 160.01/26.32  
% 160.01/26.32  Sub-proof #840 shows that the following formulas are inconsistent:
% 160.01/26.32  ----------------------------------------------------------------
% 160.01/26.32    (1)   ~ (all_52_6 = e1)
% 160.01/26.32    (2)   ~ (e3 = e2)
% 160.01/26.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.32    (4)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 160.01/26.32           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 160.01/26.32           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 160.01/26.32           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 160.01/26.32             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.32    (5)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 160.01/26.32         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 160.01/26.32    (6)  op(e1, e2) = all_52_6
% 160.01/26.32    (7)  all_56_10 = e1
% 160.01/26.32    (8)   ~ (e1 = e0)
% 160.01/26.32    (9)  op(e2, e1) = all_52_9
% 160.01/26.32    (10)   ~ (e2 = e1)
% 160.01/26.32    (11)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 160.01/26.32          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 160.01/26.32    (12)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 160.01/26.32          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 160.01/26.32    (13)   ~ (all_52_9 = e2)
% 160.01/26.32    (14)   ~ (e3 = e1)
% 160.01/26.32    (15)   ~ (e2 = e0)
% 160.01/26.32    (16)   ~ (e3 = e0)
% 160.01/26.32  
% 160.01/26.32  Begin of proof
% 160.01/26.32  | 
% 160.01/26.32  | BETA: splitting (4) gives:
% 160.01/26.32  | 
% 160.01/26.32  | Case 1:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (17)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 160.01/26.32  | |         & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 160.01/26.32  | |         all_57_14 & $i(all_57_14)
% 160.01/26.32  | | 
% 160.01/26.32  | | ALPHA: (17) implies:
% 160.01/26.32  | |   (18)  op(e1, e2) = e1
% 160.01/26.32  | | 
% 160.01/26.32  | | REF_CLOSE: (1), (3), (6), (18) are inconsistent by sub-proof #984.
% 160.01/26.32  | | 
% 160.01/26.32  | Case 2:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (19)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 160.01/26.32  | |         & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 160.01/26.32  | |         all_57_14 & $i(all_57_14)
% 160.01/26.32  | | 
% 160.01/26.32  | | ALPHA: (19) implies:
% 160.01/26.32  | |   (20)  op(e2, e2) = e1
% 160.01/26.32  | | 
% 160.01/26.32  | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 160.01/26.32  | |            (16), (20) are inconsistent by sub-proof #842.
% 160.01/26.32  | | 
% 160.01/26.32  | End of split
% 160.01/26.32  | 
% 160.01/26.32  End of proof
% 160.01/26.32  
% 160.01/26.32  Sub-proof #841 shows that the following formulas are inconsistent:
% 160.01/26.32  ----------------------------------------------------------------
% 160.01/26.32    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 160.01/26.32           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.01/26.32           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 160.01/26.32           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 160.01/26.32           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.32    (2)   ~ (e3 = e2)
% 160.01/26.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.32    (4)  op(e1, e1) = e1
% 160.01/26.32    (5)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 160.01/26.32         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 160.01/26.32    (6)  all_56_10 = e1
% 160.01/26.32    (7)   ~ (e1 = e0)
% 160.01/26.32    (8)  op(e2, e1) = all_52_9
% 160.01/26.32    (9)   ~ (e2 = e1)
% 160.01/26.32    (10)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 160.01/26.32          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 160.01/26.32    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 160.01/26.32          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 160.01/26.32    (12)   ~ (all_52_9 = e2)
% 160.01/26.32    (13)   ~ (e3 = e1)
% 160.01/26.32    (14)   ~ (e2 = e0)
% 160.01/26.32    (15)   ~ (e3 = e0)
% 160.01/26.32  
% 160.01/26.32  Begin of proof
% 160.01/26.32  | 
% 160.01/26.32  | BETA: splitting (1) gives:
% 160.01/26.32  | 
% 160.01/26.32  | Case 1:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (16)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 160.01/26.32  | |         & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 &
% 160.01/26.32  | |         op(e1, e1) = e3 & $i(all_57_10)
% 160.01/26.32  | | 
% 160.01/26.32  | | ALPHA: (16) implies:
% 160.01/26.32  | |   (17)  op(e1, e1) = e3
% 160.01/26.32  | | 
% 160.01/26.32  | | REF_CLOSE: (3), (4), (13), (17) are inconsistent by sub-proof #1003.
% 160.01/26.32  | | 
% 160.01/26.32  | Case 2:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (18)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 160.01/26.32  | |         & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 160.01/26.32  | |         all_57_14 & $i(all_57_14)
% 160.01/26.32  | | 
% 160.01/26.32  | | ALPHA: (18) implies:
% 160.01/26.32  | |   (19)  op(e2, e2) = e1
% 160.01/26.32  | | 
% 160.01/26.32  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 160.01/26.32  | |            (15), (19) are inconsistent by sub-proof #842.
% 160.01/26.32  | | 
% 160.01/26.32  | End of split
% 160.01/26.32  | 
% 160.01/26.32  End of proof
% 160.01/26.32  
% 160.01/26.32  Sub-proof #842 shows that the following formulas are inconsistent:
% 160.01/26.32  ----------------------------------------------------------------
% 160.01/26.32    (1)   ~ (e3 = e2)
% 160.01/26.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.32    (3)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 160.01/26.32         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 160.01/26.32    (4)  all_56_10 = e1
% 160.01/26.32    (5)  op(e2, e2) = e1
% 160.01/26.32    (6)   ~ (e1 = e0)
% 160.01/26.32    (7)  op(e2, e1) = all_52_9
% 160.01/26.32    (8)   ~ (e2 = e1)
% 160.01/26.32    (9)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 160.01/26.32         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 160.01/26.32    (10)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 160.01/26.32          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 160.01/26.32    (11)   ~ (all_52_9 = e2)
% 160.01/26.32    (12)   ~ (e3 = e1)
% 160.01/26.32    (13)   ~ (e2 = e0)
% 160.01/26.32    (14)   ~ (e3 = e0)
% 160.01/26.32  
% 160.01/26.32  Begin of proof
% 160.01/26.32  | 
% 160.01/26.32  | BETA: splitting (10) gives:
% 160.01/26.32  | 
% 160.01/26.32  | Case 1:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (15)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 160.01/26.32  | |           e2)
% 160.01/26.32  | | 
% 160.01/26.32  | | BETA: splitting (15) gives:
% 160.01/26.32  | | 
% 160.01/26.32  | | Case 1:
% 160.01/26.32  | | | 
% 160.01/26.32  | | |   (16)  all_56_2 = e2 & op(e2, e3) = e2
% 160.01/26.32  | | | 
% 160.01/26.32  | | | ALPHA: (16) implies:
% 160.01/26.32  | | |   (17)  all_56_2 = e2
% 160.01/26.32  | | | 
% 160.01/26.32  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (12), (13), (14), (17) are
% 160.01/26.32  | | |            inconsistent by sub-proof #843.
% 160.01/26.32  | | | 
% 160.01/26.32  | | Case 2:
% 160.01/26.32  | | | 
% 160.01/26.32  | | |   (18)  all_56_3 = e2 & op(e2, e2) = e2
% 160.01/26.32  | | | 
% 160.01/26.32  | | | ALPHA: (18) implies:
% 160.01/26.32  | | |   (19)  op(e2, e2) = e2
% 160.01/26.32  | | | 
% 160.01/26.32  | | | REF_CLOSE: (2), (5), (8), (19) are inconsistent by sub-proof #993.
% 160.01/26.32  | | | 
% 160.01/26.32  | | End of split
% 160.01/26.32  | | 
% 160.01/26.32  | Case 2:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (20)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 160.01/26.32  | |           e2)
% 160.01/26.32  | | 
% 160.01/26.32  | | BETA: splitting (20) gives:
% 160.01/26.32  | | 
% 160.01/26.32  | | Case 1:
% 160.01/26.32  | | | 
% 160.01/26.32  | | |   (21)  all_56_5 = e2 & op(e2, e1) = e2
% 160.01/26.32  | | | 
% 160.01/26.32  | | | ALPHA: (21) implies:
% 160.01/26.32  | | |   (22)  op(e2, e1) = e2
% 160.01/26.32  | | | 
% 160.01/26.32  | | | REF_CLOSE: (2), (7), (11), (22) are inconsistent by sub-proof #1002.
% 160.01/26.32  | | | 
% 160.01/26.32  | | Case 2:
% 160.01/26.32  | | | 
% 160.01/26.32  | | |   (23)  all_56_10 = e2 & op(e2, e0) = e2
% 160.01/26.32  | | | 
% 160.01/26.32  | | | ALPHA: (23) implies:
% 160.01/26.32  | | |   (24)  all_56_10 = e2
% 160.01/26.32  | | | 
% 160.01/26.32  | | | REF_CLOSE: (4), (8), (24) are inconsistent by sub-proof #886.
% 160.01/26.32  | | | 
% 160.01/26.32  | | End of split
% 160.01/26.32  | | 
% 160.01/26.32  | End of split
% 160.01/26.32  | 
% 160.01/26.32  End of proof
% 160.01/26.32  
% 160.01/26.32  Sub-proof #843 shows that the following formulas are inconsistent:
% 160.01/26.32  ----------------------------------------------------------------
% 160.01/26.32    (1)   ~ (e3 = e2)
% 160.01/26.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.32    (3)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 160.01/26.32         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 160.01/26.32    (4)  all_56_2 = e2
% 160.01/26.32    (5)  all_56_10 = e1
% 160.01/26.32    (6)  op(e2, e2) = e1
% 160.01/26.32    (7)   ~ (e1 = e0)
% 160.01/26.32    (8)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 160.01/26.32         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 160.01/26.32    (9)   ~ (e3 = e1)
% 160.01/26.32    (10)   ~ (e2 = e0)
% 160.01/26.32    (11)   ~ (e3 = e0)
% 160.01/26.32  
% 160.01/26.32  Begin of proof
% 160.01/26.32  | 
% 160.01/26.32  | BETA: splitting (3) gives:
% 160.01/26.32  | 
% 160.01/26.32  | Case 1:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (12)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 160.01/26.32  | |           e3)
% 160.01/26.32  | | 
% 160.01/26.32  | | BETA: splitting (12) gives:
% 160.01/26.32  | | 
% 160.01/26.32  | | Case 1:
% 160.01/26.32  | | | 
% 160.01/26.32  | | |   (13)  all_56_2 = e3 & op(e2, e3) = e3
% 160.01/26.32  | | | 
% 160.01/26.32  | | | ALPHA: (13) implies:
% 160.01/26.32  | | |   (14)  all_56_2 = e3
% 160.01/26.32  | | | 
% 160.01/26.32  | | | REF_CLOSE: (1), (4), (14) are inconsistent by sub-proof #848.
% 160.01/26.32  | | | 
% 160.01/26.32  | | Case 2:
% 160.01/26.32  | | | 
% 160.01/26.32  | | |   (15)  all_56_3 = e3 & op(e2, e2) = e3
% 160.01/26.32  | | | 
% 160.01/26.32  | | | ALPHA: (15) implies:
% 160.01/26.32  | | |   (16)  op(e2, e2) = e3
% 160.01/26.32  | | | 
% 160.01/26.32  | | | REF_CLOSE: (2), (6), (9), (16) are inconsistent by sub-proof #847.
% 160.01/26.32  | | | 
% 160.01/26.32  | | End of split
% 160.01/26.32  | | 
% 160.01/26.32  | Case 2:
% 160.01/26.32  | | 
% 160.01/26.32  | |   (17)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 160.01/26.32  | |           e3)
% 160.01/26.32  | | 
% 160.01/26.32  | | BETA: splitting (17) gives:
% 160.01/26.32  | | 
% 160.01/26.32  | | Case 1:
% 160.01/26.32  | | | 
% 160.01/26.32  | | |   (18)  all_56_5 = e3 & op(e2, e1) = e3
% 160.01/26.32  | | | 
% 160.01/26.32  | | | ALPHA: (18) implies:
% 160.01/26.32  | | |   (19)  all_56_5 = e3
% 160.01/26.32  | | | 
% 160.01/26.32  | | | BETA: splitting (8) gives:
% 160.01/26.32  | | | 
% 160.01/26.32  | | | Case 1:
% 160.01/26.32  | | | | 
% 160.01/26.32  | | | |   (20)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2)
% 160.01/26.32  | | | |           = e0)
% 160.01/26.32  | | | | 
% 160.01/26.32  | | | | BETA: splitting (20) gives:
% 160.01/26.32  | | | | 
% 160.01/26.32  | | | | Case 1:
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | |   (21)  all_56_2 = e0 & op(e2, e3) = e0
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | | REF_CLOSE: (4), (10), (21) are inconsistent by sub-proof #846.
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | Case 2:
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | |   (22)  all_56_3 = e0 & op(e2, e2) = e0
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | | ALPHA: (22) implies:
% 160.01/26.32  | | | | |   (23)  op(e2, e2) = e0
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | | REF_CLOSE: (2), (6), (7), (23) are inconsistent by sub-proof #960.
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | End of split
% 160.01/26.32  | | | | 
% 160.01/26.32  | | | Case 2:
% 160.01/26.32  | | | | 
% 160.01/26.32  | | | |   (24)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0)
% 160.01/26.32  | | | |           = e0)
% 160.01/26.32  | | | | 
% 160.01/26.32  | | | | BETA: splitting (24) gives:
% 160.01/26.32  | | | | 
% 160.01/26.32  | | | | Case 1:
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | |   (25)  all_56_5 = e0 & op(e2, e1) = e0
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | | REF_CLOSE: (11), (19), (25) are inconsistent by sub-proof #845.
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | Case 2:
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | |   (26)  all_56_10 = e0 & op(e2, e0) = e0
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | | REF_CLOSE: (5), (7), (26) are inconsistent by sub-proof #844.
% 160.01/26.32  | | | | | 
% 160.01/26.32  | | | | End of split
% 160.01/26.32  | | | | 
% 160.01/26.32  | | | End of split
% 160.01/26.32  | | | 
% 160.01/26.32  | | Case 2:
% 160.01/26.32  | | | 
% 160.01/26.32  | | |   (27)  all_56_10 = e3 & op(e2, e0) = e3
% 160.01/26.32  | | | 
% 160.01/26.32  | | | ALPHA: (27) implies:
% 160.01/26.32  | | |   (28)  all_56_10 = e3
% 160.01/26.32  | | | 
% 160.01/26.32  | | | REF_CLOSE: (5), (9), (28) are inconsistent by sub-proof #887.
% 160.01/26.32  | | | 
% 160.01/26.32  | | End of split
% 160.01/26.32  | | 
% 160.01/26.32  | End of split
% 160.01/26.32  | 
% 160.01/26.32  End of proof
% 160.01/26.32  
% 160.01/26.32  Sub-proof #844 shows that the following formulas are inconsistent:
% 160.01/26.32  ----------------------------------------------------------------
% 160.01/26.32    (1)  all_56_10 = e0 & op(e2, e0) = e0
% 160.01/26.32    (2)  all_56_10 = e1
% 160.01/26.32    (3)   ~ (e1 = e0)
% 160.01/26.32  
% 160.01/26.32  Begin of proof
% 160.01/26.32  | 
% 160.01/26.32  | ALPHA: (1) implies:
% 160.01/26.32  |   (4)  all_56_10 = e0
% 160.01/26.32  | 
% 160.01/26.32  | COMBINE_EQS: (2), (4) imply:
% 160.01/26.32  |   (5)  e1 = e0
% 160.01/26.32  | 
% 160.01/26.32  | REDUCE: (3), (5) imply:
% 160.01/26.32  |   (6)  $false
% 160.01/26.32  | 
% 160.01/26.32  | CLOSE: (6) is inconsistent.
% 160.01/26.32  | 
% 160.01/26.32  End of proof
% 160.01/26.32  
% 160.01/26.32  Sub-proof #845 shows that the following formulas are inconsistent:
% 160.01/26.32  ----------------------------------------------------------------
% 160.01/26.32    (1)  all_56_5 = e0 & op(e2, e1) = e0
% 160.01/26.32    (2)  all_56_5 = e3
% 160.01/26.32    (3)   ~ (e3 = e0)
% 160.01/26.32  
% 160.01/26.32  Begin of proof
% 160.01/26.32  | 
% 160.01/26.32  | ALPHA: (1) implies:
% 160.01/26.32  |   (4)  all_56_5 = e0
% 160.01/26.32  | 
% 160.01/26.32  | COMBINE_EQS: (2), (4) imply:
% 160.01/26.32  |   (5)  e3 = e0
% 160.01/26.32  | 
% 160.01/26.32  | REDUCE: (3), (5) imply:
% 160.01/26.32  |   (6)  $false
% 160.01/26.32  | 
% 160.01/26.32  | CLOSE: (6) is inconsistent.
% 160.01/26.32  | 
% 160.01/26.32  End of proof
% 160.01/26.32  
% 160.01/26.32  Sub-proof #846 shows that the following formulas are inconsistent:
% 160.01/26.32  ----------------------------------------------------------------
% 160.01/26.32    (1)  all_56_2 = e0 & op(e2, e3) = e0
% 160.01/26.32    (2)  all_56_2 = e2
% 160.01/26.32    (3)   ~ (e2 = e0)
% 160.01/26.32  
% 160.01/26.32  Begin of proof
% 160.01/26.32  | 
% 160.01/26.32  | ALPHA: (1) implies:
% 160.01/26.32  |   (4)  all_56_2 = e0
% 160.01/26.32  | 
% 160.01/26.32  | COMBINE_EQS: (2), (4) imply:
% 160.01/26.32  |   (5)  e2 = e0
% 160.01/26.32  | 
% 160.01/26.32  | REDUCE: (3), (5) imply:
% 160.01/26.32  |   (6)  $false
% 160.01/26.32  | 
% 160.01/26.32  | CLOSE: (6) is inconsistent.
% 160.01/26.32  | 
% 160.01/26.32  End of proof
% 160.01/26.32  
% 160.01/26.32  Sub-proof #847 shows that the following formulas are inconsistent:
% 160.01/26.32  ----------------------------------------------------------------
% 160.01/26.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.33    (2)  op(e2, e2) = e3
% 160.01/26.33    (3)  op(e2, e2) = e1
% 160.01/26.33    (4)   ~ (e3 = e1)
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | GROUND_INST: instantiating (1) with e1, e3, e2, e2, simplifying with (2), (3)
% 160.01/26.33  |              gives:
% 160.01/26.33  |   (5)  e3 = e1
% 160.01/26.33  | 
% 160.01/26.33  | REDUCE: (4), (5) imply:
% 160.01/26.33  |   (6)  $false
% 160.01/26.33  | 
% 160.01/26.33  | CLOSE: (6) is inconsistent.
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #848 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)  all_56_2 = e3
% 160.01/26.33    (2)  all_56_2 = e2
% 160.01/26.33    (3)   ~ (e3 = e2)
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | COMBINE_EQS: (1), (2) imply:
% 160.01/26.33  |   (4)  e3 = e2
% 160.01/26.33  | 
% 160.01/26.33  | SIMP: (4) implies:
% 160.01/26.33  |   (5)  e3 = e2
% 160.01/26.33  | 
% 160.01/26.33  | REDUCE: (3), (5) imply:
% 160.01/26.33  |   (6)  $false
% 160.01/26.33  | 
% 160.01/26.33  | CLOSE: (6) is inconsistent.
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #849 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.33    (2)  op(e2, e2) = e2
% 160.01/26.33    (3)  op(e1, e3) = all_52_2
% 160.01/26.33    (4)   ~ (all_52_13 = all_4_2)
% 160.01/26.33    (5)   ~ (all_52_2 = e1)
% 160.01/26.33    (6)  op(e2, e2) = all_4_2
% 160.01/26.33    (7)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 160.01/26.33           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 160.01/26.33           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 160.01/26.33           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 160.01/26.33           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.01/26.33    (8)  op(e2, e0) = all_52_13
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | BETA: splitting (7) gives:
% 160.01/26.33  | 
% 160.01/26.33  | Case 1:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (9)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 160.01/26.33  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 160.01/26.33  | |          e0) = e2 & $i(all_57_12)
% 160.01/26.33  | | 
% 160.01/26.33  | | ALPHA: (9) implies:
% 160.01/26.33  | |   (10)  op(e2, e0) = e2
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (1), (2), (4), (6), (8), (10) are inconsistent by sub-proof #972.
% 160.01/26.33  | | 
% 160.01/26.33  | Case 2:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (11)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 160.01/26.33  | |         & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 160.01/26.33  | |         all_57_14 & $i(all_57_14)
% 160.01/26.33  | | 
% 160.01/26.33  | | ALPHA: (11) implies:
% 160.01/26.33  | |   (12)  op(e1, e3) = e1
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (1), (3), (5), (12) are inconsistent by sub-proof #990.
% 160.01/26.33  | | 
% 160.01/26.33  | End of split
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #850 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.33    (2)  op(e0, e0) = e0
% 160.01/26.33    (3)  op(e3, e3) = e1
% 160.01/26.33    (4)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 160.01/26.33           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 160.01/26.33           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 160.01/26.33           & op(e3, e3) = e3 & op(e3, e2) = e3)
% 160.01/26.33    (5)   ~ (e3 = e1)
% 160.01/26.33    (6)   ~ (e3 = e0)
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | BETA: splitting (4) gives:
% 160.01/26.33  | 
% 160.01/26.33  | Case 1:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (7)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 160.01/26.33  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 160.01/26.33  | |          e0) = e3 & $i(all_57_10)
% 160.01/26.33  | | 
% 160.01/26.33  | | ALPHA: (7) implies:
% 160.01/26.33  | |   (8)  op(e0, e0) = e3
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #999.
% 160.01/26.33  | | 
% 160.01/26.33  | Case 2:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (9)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 160.01/26.33  | |        op(e3, e2) = e3
% 160.01/26.33  | | 
% 160.01/26.33  | | ALPHA: (9) implies:
% 160.01/26.33  | |   (10)  op(e3, e3) = e3
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #995.
% 160.01/26.33  | | 
% 160.01/26.33  | End of split
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #851 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)  all_56_9 = e1 & op(e3, e0) = e1
% 160.01/26.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.33    (3)  op(e3, e0) = all_52_12
% 160.01/26.33    (4)   ~ (all_52_12 = e1)
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | ALPHA: (1) implies:
% 160.01/26.33  |   (5)  op(e3, e0) = e1
% 160.01/26.33  | 
% 160.01/26.33  | GROUND_INST: instantiating (2) with all_52_12, e1, e0, e3, simplifying with
% 160.01/26.33  |              (3), (5) gives:
% 160.01/26.33  |   (6)  all_52_12 = e1
% 160.01/26.33  | 
% 160.01/26.33  | REDUCE: (4), (6) imply:
% 160.01/26.33  |   (7)  $false
% 160.01/26.33  | 
% 160.01/26.33  | CLOSE: (7) is inconsistent.
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #852 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)  all_56_12 = e1 & op(e0, e3) = e1
% 160.01/26.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.33    (3)  op(e0, e3) = all_52_3
% 160.01/26.33    (4)   ~ (all_52_3 = e1)
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | ALPHA: (1) implies:
% 160.01/26.33  |   (5)  op(e0, e3) = e1
% 160.01/26.33  | 
% 160.01/26.33  | GROUND_INST: instantiating (2) with all_52_3, e1, e3, e0, simplifying with
% 160.01/26.33  |              (3), (5) gives:
% 160.01/26.33  |   (6)  all_52_3 = e1
% 160.01/26.33  | 
% 160.01/26.33  | REDUCE: (4), (6) imply:
% 160.01/26.33  |   (7)  $false
% 160.01/26.33  | 
% 160.01/26.33  | CLOSE: (7) is inconsistent.
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #853 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)   ~ (all_6_2 = e0)
% 160.01/26.33    (2)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 160.01/26.33    (3)   ~ (all_6_2 = e1)
% 160.01/26.33    (4)  all_54_0 = all_6_2
% 160.01/26.33    (5)   ~ (all_6_2 = e2)
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | BETA: splitting (2) gives:
% 160.01/26.33  | 
% 160.01/26.33  | Case 1:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (6)  all_54_0 = e2
% 160.01/26.33  | | 
% 160.01/26.33  | | COMBINE_EQS: (4), (6) imply:
% 160.01/26.33  | |   (7)  all_6_2 = e2
% 160.01/26.33  | | 
% 160.01/26.33  | | REDUCE: (5), (7) imply:
% 160.01/26.33  | |   (8)  $false
% 160.01/26.33  | | 
% 160.01/26.33  | | CLOSE: (8) is inconsistent.
% 160.01/26.33  | | 
% 160.01/26.33  | Case 2:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (9)  all_54_0 = e1 | all_54_0 = e0
% 160.01/26.33  | | 
% 160.01/26.33  | | BETA: splitting (9) gives:
% 160.01/26.33  | | 
% 160.01/26.33  | | Case 1:
% 160.01/26.33  | | | 
% 160.01/26.33  | | |   (10)  all_54_0 = e1
% 160.01/26.33  | | | 
% 160.01/26.33  | | | COMBINE_EQS: (4), (10) imply:
% 160.01/26.33  | | |   (11)  all_6_2 = e1
% 160.01/26.33  | | | 
% 160.01/26.33  | | | REDUCE: (3), (11) imply:
% 160.01/26.33  | | |   (12)  $false
% 160.01/26.33  | | | 
% 160.01/26.33  | | | CLOSE: (12) is inconsistent.
% 160.01/26.33  | | | 
% 160.01/26.33  | | Case 2:
% 160.01/26.33  | | | 
% 160.01/26.33  | | |   (13)  all_54_0 = e0
% 160.01/26.33  | | | 
% 160.01/26.33  | | | COMBINE_EQS: (4), (13) imply:
% 160.01/26.33  | | |   (14)  all_6_2 = e0
% 160.01/26.33  | | | 
% 160.01/26.33  | | | REDUCE: (1), (14) imply:
% 160.01/26.33  | | |   (15)  $false
% 160.01/26.33  | | | 
% 160.01/26.33  | | | CLOSE: (15) is inconsistent.
% 160.01/26.33  | | | 
% 160.01/26.33  | | End of split
% 160.01/26.33  | | 
% 160.01/26.33  | End of split
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #854 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)  op(e0, e0) = e2
% 160.01/26.33    (2)   ~ (e3 = e2)
% 160.01/26.33    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.33    (4)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 160.01/26.33           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 160.01/26.33           = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3
% 160.01/26.33           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 160.01/26.33           op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 160.01/26.33    (5)  op(e2, e2) = e0
% 160.01/26.33    (6)   ~ (e1 = e0)
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | BETA: splitting (4) gives:
% 160.01/26.33  | 
% 160.01/26.33  | Case 1:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (7)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 160.01/26.33  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 160.01/26.33  | |          e0) = e1 & $i(all_57_14)
% 160.01/26.33  | | 
% 160.01/26.33  | | ALPHA: (7) implies:
% 160.01/26.33  | |   (8)  op(e2, e2) = e1
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #960.
% 160.01/26.33  | | 
% 160.01/26.33  | Case 2:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0)
% 160.01/26.33  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 160.01/26.33  | |          e0) = e3 & $i(all_57_10)
% 160.01/26.33  | | 
% 160.01/26.33  | | ALPHA: (9) implies:
% 160.01/26.33  | |   (10)  op(e0, e0) = e3
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #878.
% 160.01/26.33  | | 
% 160.01/26.33  | End of split
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #855 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)  op(e0, e0) = e2
% 160.01/26.33    (2)   ~ (e3 = e2)
% 160.01/26.33    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.33    (4)  op(e3, e1) = all_52_8
% 160.01/26.33    (5)  op(e3, e3) = e3
% 160.01/26.33    (6)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 160.01/26.33           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 160.01/26.33           = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1)
% 160.01/26.33           & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 160.01/26.33           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 160.01/26.33           e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.01/26.33    (7)   ~ (e3 = e1)
% 160.01/26.33    (8)   ~ (all_52_8 = e3)
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | BETA: splitting (6) gives:
% 160.01/26.33  | 
% 160.01/26.33  | Case 1:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (9)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1)
% 160.01/26.33  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 160.01/26.33  | |          e0) = e3 & $i(all_57_10)
% 160.01/26.33  | | 
% 160.01/26.33  | | ALPHA: (9) implies:
% 160.01/26.33  | |   (10)  op(e0, e0) = e3
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #878.
% 160.01/26.33  | | 
% 160.01/26.33  | Case 2:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (11)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 160.01/26.33  | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 =
% 160.01/26.33  | |           e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 160.01/26.33  | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (3), (4), (5), (7), (8), (11) are inconsistent by sub-proof #981.
% 160.01/26.33  | | 
% 160.01/26.33  | End of split
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #856 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)   ~ (all_52_4 = e3)
% 160.01/26.33    (2)  op(e0, e0) = e2
% 160.01/26.33    (3)   ~ (e3 = e2)
% 160.01/26.33    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.33    (5)  op(e3, e2) = all_52_4
% 160.01/26.33    (6)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 160.01/26.33           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 160.01/26.33           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 160.01/26.33           & op(e3, e3) = e3 & op(e3, e2) = e3)
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | BETA: splitting (6) gives:
% 160.01/26.33  | 
% 160.01/26.33  | Case 1:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (7)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 160.01/26.33  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 160.01/26.33  | |          e0) = e3 & $i(all_57_10)
% 160.01/26.33  | | 
% 160.01/26.33  | | ALPHA: (7) implies:
% 160.01/26.33  | |   (8)  op(e0, e0) = e3
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #878.
% 160.01/26.33  | | 
% 160.01/26.33  | Case 2:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (9)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 160.01/26.33  | |        op(e3, e2) = e3
% 160.01/26.33  | | 
% 160.01/26.33  | | ALPHA: (9) implies:
% 160.01/26.33  | |   (10)  op(e3, e2) = e3
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #998.
% 160.01/26.33  | | 
% 160.01/26.33  | End of split
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #857 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 160.01/26.33         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 160.01/26.33    (2)   ~ (all_52_1 = e2)
% 160.01/26.33    (3)  op(e0, e0) = e2
% 160.01/26.33    (4)   ~ (e3 = e2)
% 160.01/26.33    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.33    (6)  op(e0, e3) = all_52_3
% 160.01/26.33    (7)  op(e1, e1) = e1
% 160.01/26.33    (8)  op(e1, e0) = all_52_14
% 160.01/26.33    (9)  op(e0, e0) = all_57_15
% 160.01/26.33    (10)   ~ (all_52_3 = e2)
% 160.01/26.33    (11)  op(e3, e3) = e3
% 160.01/26.33    (12)  op(e2, e3) = all_52_1
% 160.01/26.33    (13)   ~ (e1 = e0)
% 160.01/26.33    (14)  op(e2, e0) = all_52_13
% 160.01/26.33    (15)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.33            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 160.01/26.33            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 160.01/26.33            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 160.01/26.33            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 160.01/26.33              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 160.01/26.33            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 160.01/26.33            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 160.01/26.33            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 160.01/26.33            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 160.01/26.33              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.01/26.33            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 160.01/26.33            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 160.01/26.33            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.01/26.33              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 160.01/26.33          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 160.01/26.33            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 160.01/26.33            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 160.01/26.33            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 160.01/26.33            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 160.01/26.33            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 160.01/26.33            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 160.01/26.33    (16)   ~ (all_52_14 = e1)
% 160.01/26.33    (17)   ~ (e2 = e0)
% 160.01/26.33    (18)   ~ (e3 = e0)
% 160.01/26.33    (19)   ~ (all_52_13 = e2)
% 160.01/26.33  
% 160.01/26.33  Begin of proof
% 160.01/26.33  | 
% 160.01/26.33  | BETA: splitting (1) gives:
% 160.01/26.33  | 
% 160.01/26.33  | Case 1:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (20)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 160.01/26.33  | |           e2)
% 160.01/26.33  | | 
% 160.01/26.33  | | REF_CLOSE: (2), (4), (5), (11), (12), (20) are inconsistent by sub-proof
% 160.01/26.33  | |            #868.
% 160.01/26.33  | | 
% 160.01/26.33  | Case 2:
% 160.01/26.33  | | 
% 160.01/26.33  | |   (21)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 160.01/26.33  | |           e2)
% 160.01/26.33  | | 
% 160.01/26.33  | | BETA: splitting (21) gives:
% 160.01/26.33  | | 
% 160.01/26.33  | | Case 1:
% 160.01/26.33  | | | 
% 160.01/26.33  | | | 
% 160.01/26.33  | | | GROUND_INST: instantiating (5) with e2, all_57_15, e0, e0, simplifying
% 160.01/26.33  | | |              with (3), (9) gives:
% 160.01/26.33  | | |   (22)  all_57_15 = e2
% 160.01/26.33  | | | 
% 160.01/26.33  | | | REF_CLOSE: (5), (7), (8), (11), (13), (14), (15), (16), (17), (18), (19),
% 160.01/26.33  | | |            (22) are inconsistent by sub-proof #859.
% 160.01/26.33  | | | 
% 160.01/26.33  | | Case 2:
% 160.01/26.33  | | | 
% 160.01/26.33  | | |   (23)  all_56_12 = e2 & op(e0, e3) = e2
% 160.01/26.33  | | | 
% 160.01/26.33  | | | REF_CLOSE: (5), (6), (10), (23) are inconsistent by sub-proof #858.
% 160.01/26.33  | | | 
% 160.01/26.33  | | End of split
% 160.01/26.33  | | 
% 160.01/26.33  | End of split
% 160.01/26.33  | 
% 160.01/26.33  End of proof
% 160.01/26.33  
% 160.01/26.33  Sub-proof #858 shows that the following formulas are inconsistent:
% 160.01/26.33  ----------------------------------------------------------------
% 160.01/26.33    (1)  all_56_12 = e2 & op(e0, e3) = e2
% 160.01/26.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.34    (3)  op(e0, e3) = all_52_3
% 160.01/26.34    (4)   ~ (all_52_3 = e2)
% 160.01/26.34  
% 160.01/26.34  Begin of proof
% 160.01/26.34  | 
% 160.01/26.34  | ALPHA: (1) implies:
% 160.01/26.34  |   (5)  op(e0, e3) = e2
% 160.01/26.34  | 
% 160.01/26.34  | GROUND_INST: instantiating (2) with all_52_3, e2, e3, e0, simplifying with
% 160.01/26.34  |              (3), (5) gives:
% 160.01/26.34  |   (6)  all_52_3 = e2
% 160.01/26.34  | 
% 160.01/26.34  | REDUCE: (4), (6) imply:
% 160.01/26.34  |   (7)  $false
% 160.01/26.34  | 
% 160.01/26.34  | CLOSE: (7) is inconsistent.
% 160.01/26.34  | 
% 160.01/26.34  End of proof
% 160.01/26.34  
% 160.01/26.34  Sub-proof #859 shows that the following formulas are inconsistent:
% 160.01/26.34  ----------------------------------------------------------------
% 160.01/26.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.34    (2)  op(e1, e1) = e1
% 160.01/26.34    (3)  op(e1, e0) = all_52_14
% 160.01/26.34    (4)  op(e3, e3) = e3
% 160.01/26.34    (5)   ~ (e1 = e0)
% 160.01/26.34    (6)  op(e2, e0) = all_52_13
% 160.01/26.34    (7)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 160.01/26.34           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 160.01/26.34           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 160.01/26.34           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 160.01/26.34           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 160.01/26.34           e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0)
% 160.01/26.34           & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 & 
% 160.01/26.34           ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) =
% 160.01/26.34           e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 160.01/26.34             = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0) |
% 160.01/26.34         (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 160.01/26.34           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.01/26.34           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 160.01/26.34           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 160.01/26.34           & op(e3, e0) = e3 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_11 = e2
% 160.01/26.34           & all_57_12 = e0 &  ~ (all_57_15 = e1) & op(e2, e2) = e0 & op(e2, e0) =
% 160.01/26.34           e2 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 =
% 160.01/26.34           e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 160.01/26.34             e1) = e0) | (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~
% 160.01/26.34           (all_57_14 = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 160.01/26.34             e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1
% 160.01/26.34             = e0) & op(e0, e1) = e0)
% 160.01/26.34    (8)   ~ (all_52_14 = e1)
% 160.01/26.34    (9)  all_57_15 = e2
% 160.01/26.34    (10)   ~ (e2 = e0)
% 160.01/26.34    (11)   ~ (e3 = e0)
% 160.01/26.34    (12)   ~ (all_52_13 = e2)
% 160.01/26.34  
% 160.01/26.34  Begin of proof
% 160.01/26.34  | 
% 160.01/26.34  | BETA: splitting (7) gives:
% 160.01/26.34  | 
% 160.01/26.34  | Case 1:
% 160.01/26.34  | | 
% 160.01/26.34  | |   (13)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 160.01/26.34  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.01/26.34  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 160.01/26.34  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 160.01/26.34  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 160.01/26.34  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.01/26.34  | | 
% 160.01/26.34  | | BETA: splitting (13) gives:
% 160.01/26.34  | | 
% 160.01/26.34  | | Case 1:
% 160.01/26.34  | | | 
% 160.01/26.34  | | |   (14)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 160.01/26.34  | | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.01/26.34  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 160.01/26.34  | | | 
% 160.01/26.34  | | | REF_CLOSE: (1), (2), (4), (5), (6), (11), (12), (14) are inconsistent by
% 160.01/26.34  | | |            sub-proof #866.
% 160.01/26.34  | | | 
% 160.01/26.34  | | Case 2:
% 160.01/26.34  | | | 
% 160.01/26.34  | | |   (15)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0)
% 160.01/26.34  | | |         | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.01/26.34  | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 160.01/26.34  | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.01/26.34  | | | 
% 160.01/26.34  | | | BETA: splitting (15) gives:
% 160.01/26.34  | | | 
% 160.01/26.34  | | | Case 1:
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | |   (16)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | | REF_CLOSE: (9), (10), (16) are inconsistent by sub-proof #865.
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | Case 2:
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | |   (17)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.01/26.34  | | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0)
% 160.01/26.34  | | | |         | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 160.01/26.34  | | | |           (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 160.01/26.34  | | | |             e2) = e0)
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | | REF_CLOSE: (1), (4), (6), (11), (12), (17) are inconsistent by sub-proof
% 160.01/26.34  | | | |            #864.
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | End of split
% 160.01/26.34  | | | 
% 160.01/26.34  | | End of split
% 160.01/26.34  | | 
% 160.01/26.34  | Case 2:
% 160.01/26.34  | | 
% 160.01/26.34  | |   (18)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 160.01/26.34  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 160.01/26.34  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 160.01/26.34  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 160.01/26.34  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 160.01/26.34  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 160.01/26.34  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 160.01/26.34  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 160.01/26.34  | |           & op(e0, e1) = e0)
% 160.01/26.34  | | 
% 160.01/26.34  | | BETA: splitting (18) gives:
% 160.01/26.34  | | 
% 160.01/26.34  | | Case 1:
% 160.01/26.34  | | | 
% 160.01/26.34  | | |   (19)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 160.01/26.34  | | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 160.01/26.34  | | |         | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.01/26.34  | | |             = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 160.01/26.34  | | | 
% 160.01/26.34  | | | BETA: splitting (19) gives:
% 160.01/26.34  | | | 
% 160.01/26.34  | | | Case 1:
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | |   (20)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15
% 160.01/26.34  | | | |           = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | | ALPHA: (20) implies:
% 160.01/26.34  | | | |   (21)  op(e1, e1) = e0
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | | REF_CLOSE: (1), (2), (5), (21) are inconsistent by sub-proof #903.
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | Case 2:
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | |   (22)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 160.01/26.34  | | | |           e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~
% 160.01/26.34  | | | |           (all_57_15 = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0,
% 160.01/26.34  | | | |             e1) = e0)
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | | BETA: splitting (22) gives:
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | | Case 1:
% 160.01/26.34  | | | | | 
% 160.01/26.34  | | | | |   (23)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 160.01/26.34  | | | | |         e0
% 160.01/26.34  | | | | | 
% 160.01/26.34  | | | | | REF_CLOSE: (9), (23) are inconsistent by sub-proof #863.
% 160.01/26.34  | | | | | 
% 160.01/26.34  | | | | Case 2:
% 160.01/26.34  | | | | | 
% 160.01/26.34  | | | | |   (24)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.01/26.34  | | | | |           = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 160.01/26.34  | | | | | 
% 160.01/26.34  | | | | | ALPHA: (24) implies:
% 160.01/26.34  | | | | |   (25)  op(e3, e3) = e0
% 160.01/26.34  | | | | | 
% 160.01/26.34  | | | | | REF_CLOSE: (1), (4), (11), (25) are inconsistent by sub-proof #971.
% 160.01/26.34  | | | | | 
% 160.01/26.34  | | | | End of split
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | End of split
% 160.01/26.34  | | | 
% 160.01/26.34  | | Case 2:
% 160.01/26.34  | | | 
% 160.01/26.34  | | |   (26)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 160.01/26.34  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.01/26.34  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 160.01/26.34  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 160.01/26.34  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 160.01/26.34  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 160.01/26.34  | | |             e0) & op(e0, e1) = e0)
% 160.01/26.34  | | | 
% 160.01/26.34  | | | BETA: splitting (26) gives:
% 160.01/26.34  | | | 
% 160.01/26.34  | | | Case 1:
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | |   (27)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 160.01/26.34  | | | |             = e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0)
% 160.01/26.34  | | | |         | (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.01/26.34  | | | |           (all_57_15 = e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 160.01/26.34  | | | |             e1) = e0)
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | | REF_CLOSE: (1), (2), (5), (6), (12), (27) are inconsistent by sub-proof
% 160.01/26.34  | | | |            #862.
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | Case 2:
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | |   (28)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14
% 160.01/26.34  | | | |             = e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0,
% 160.01/26.34  | | | |             e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0
% 160.01/26.34  | | | |           &  ~ (e1 = e0) & op(e0, e1) = e0)
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | | REF_CLOSE: (1), (3), (8), (9), (10), (28) are inconsistent by sub-proof
% 160.01/26.34  | | | |            #860.
% 160.01/26.34  | | | | 
% 160.01/26.34  | | | End of split
% 160.01/26.34  | | | 
% 160.01/26.34  | | End of split
% 160.01/26.34  | | 
% 160.01/26.34  | End of split
% 160.01/26.34  | 
% 160.01/26.34  End of proof
% 160.01/26.34  
% 160.01/26.34  Sub-proof #860 shows that the following formulas are inconsistent:
% 160.01/26.34  ----------------------------------------------------------------
% 160.01/26.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.34    (2)  op(e1, e0) = all_52_14
% 160.01/26.34    (3)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 160.01/26.34           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.01/26.34           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 160.01/26.34           op(e0, e1) = e0)
% 160.01/26.34    (4)   ~ (all_52_14 = e1)
% 160.01/26.34    (5)  all_57_15 = e2
% 160.01/26.34    (6)   ~ (e2 = e0)
% 160.01/26.34  
% 160.01/26.34  Begin of proof
% 160.01/26.34  | 
% 160.01/26.34  | BETA: splitting (3) gives:
% 160.01/26.34  | 
% 160.01/26.34  | Case 1:
% 160.01/26.34  | | 
% 160.01/26.34  | |   (7)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 160.01/26.34  | |        & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.01/26.34  | |        $i(all_57_14)
% 160.01/26.34  | | 
% 160.01/26.34  | | ALPHA: (7) implies:
% 160.01/26.34  | |   (8)  op(e1, e0) = e1
% 160.01/26.34  | | 
% 160.01/26.34  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #974.
% 160.01/26.34  | | 
% 160.01/26.34  | Case 2:
% 160.01/26.34  | | 
% 160.01/26.34  | |   (9)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0
% 160.01/26.34  | | 
% 160.01/26.34  | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #861.
% 160.01/26.34  | | 
% 160.01/26.34  | End of split
% 160.01/26.34  | 
% 160.01/26.34  End of proof
% 160.01/26.34  
% 160.01/26.34  Sub-proof #861 shows that the following formulas are inconsistent:
% 160.01/26.34  ----------------------------------------------------------------
% 160.01/26.34    (1)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0
% 160.01/26.34    (2)  all_57_15 = e2
% 160.01/26.34    (3)   ~ (e2 = e0)
% 160.01/26.34  
% 160.01/26.34  Begin of proof
% 160.01/26.34  | 
% 160.01/26.34  | ALPHA: (1) implies:
% 160.01/26.34  |   (4)  all_57_15 = e0
% 160.01/26.34  | 
% 160.01/26.34  | COMBINE_EQS: (2), (4) imply:
% 160.01/26.34  |   (5)  e2 = e0
% 160.01/26.34  | 
% 160.01/26.34  | REDUCE: (3), (5) imply:
% 160.01/26.34  |   (6)  $false
% 160.01/26.34  | 
% 160.01/26.34  | CLOSE: (6) is inconsistent.
% 160.01/26.34  | 
% 160.01/26.34  End of proof
% 160.01/26.34  
% 160.01/26.34  Sub-proof #862 shows that the following formulas are inconsistent:
% 160.01/26.34  ----------------------------------------------------------------
% 160.01/26.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.01/26.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.01/26.34    (2)  op(e1, e1) = e1
% 160.01/26.34    (3)   ~ (e1 = e0)
% 160.01/26.34    (4)  op(e2, e0) = all_52_13
% 160.10/26.34    (5)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 160.10/26.34           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.10/26.34           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 160.10/26.34           & op(e1, e0) = e1 & op(e0, e1) = e0)
% 160.10/26.34    (6)   ~ (all_52_13 = e2)
% 160.10/26.34  
% 160.10/26.34  Begin of proof
% 160.10/26.34  | 
% 160.10/26.34  | BETA: splitting (5) gives:
% 160.10/26.34  | 
% 160.10/26.34  | Case 1:
% 160.10/26.34  | | 
% 160.10/26.34  | |   (7)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1)
% 160.10/26.34  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 160.10/26.34  | | 
% 160.10/26.34  | | ALPHA: (7) implies:
% 160.10/26.34  | |   (8)  op(e2, e0) = e2
% 160.10/26.34  | | 
% 160.10/26.34  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #996.
% 160.10/26.34  | | 
% 160.10/26.34  | Case 2:
% 160.10/26.34  | | 
% 160.10/26.34  | |   (9)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1)
% 160.10/26.34  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 160.10/26.34  | | 
% 160.10/26.34  | | ALPHA: (9) implies:
% 160.10/26.34  | |   (10)  op(e1, e1) = e0
% 160.10/26.34  | | 
% 160.10/26.34  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #903.
% 160.10/26.34  | | 
% 160.10/26.34  | End of split
% 160.10/26.34  | 
% 160.10/26.34  End of proof
% 160.10/26.34  
% 160.10/26.34  Sub-proof #863 shows that the following formulas are inconsistent:
% 160.10/26.34  ----------------------------------------------------------------
% 160.10/26.34    (1)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 160.10/26.34    (2)  all_57_15 = e2
% 160.10/26.34  
% 160.10/26.34  Begin of proof
% 160.10/26.34  | 
% 160.10/26.34  | ALPHA: (1) implies:
% 160.10/26.34  |   (3)  all_57_15 = e0
% 160.10/26.34  |   (4)   ~ (e2 = e0)
% 160.10/26.34  | 
% 160.10/26.34  | COMBINE_EQS: (2), (3) imply:
% 160.10/26.34  |   (5)  e2 = e0
% 160.10/26.34  | 
% 160.10/26.34  | REDUCE: (4), (5) imply:
% 160.10/26.34  |   (6)  $false
% 160.10/26.34  | 
% 160.10/26.34  | CLOSE: (6) is inconsistent.
% 160.10/26.34  | 
% 160.10/26.34  End of proof
% 160.10/26.34  
% 160.10/26.34  Sub-proof #864 shows that the following formulas are inconsistent:
% 160.10/26.34  ----------------------------------------------------------------
% 160.10/26.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.34    (2)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 160.10/26.34           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.10/26.34           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 160.10/26.34           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.10/26.34    (3)  op(e3, e3) = e3
% 160.10/26.34    (4)  op(e2, e0) = all_52_13
% 160.10/26.34    (5)   ~ (e3 = e0)
% 160.10/26.34    (6)   ~ (all_52_13 = e2)
% 160.10/26.34  
% 160.10/26.34  Begin of proof
% 160.10/26.34  | 
% 160.10/26.34  | BETA: splitting (2) gives:
% 160.10/26.34  | 
% 160.10/26.34  | Case 1:
% 160.10/26.34  | | 
% 160.10/26.34  | |   (7)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 160.10/26.34  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 160.10/26.34  | | 
% 160.10/26.34  | | ALPHA: (7) implies:
% 160.10/26.34  | |   (8)  op(e3, e3) = e0
% 160.10/26.34  | | 
% 160.10/26.34  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #971.
% 160.10/26.34  | | 
% 160.10/26.34  | Case 2:
% 160.10/26.34  | | 
% 160.10/26.34  | |   (9)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2)
% 160.10/26.34  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 160.10/26.34  | | 
% 160.10/26.34  | | ALPHA: (9) implies:
% 160.10/26.34  | |   (10)  op(e2, e0) = e2
% 160.10/26.34  | | 
% 160.10/26.34  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #996.
% 160.10/26.34  | | 
% 160.10/26.34  | End of split
% 160.10/26.34  | 
% 160.10/26.34  End of proof
% 160.10/26.34  
% 160.10/26.34  Sub-proof #865 shows that the following formulas are inconsistent:
% 160.10/26.34  ----------------------------------------------------------------
% 160.10/26.34    (1)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 160.10/26.34    (2)  all_57_15 = e2
% 160.10/26.34    (3)   ~ (e2 = e0)
% 160.10/26.34  
% 160.10/26.34  Begin of proof
% 160.10/26.34  | 
% 160.10/26.34  | ALPHA: (1) implies:
% 160.10/26.34  |   (4)  all_57_15 = e0
% 160.10/26.34  | 
% 160.10/26.34  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.34  |   (5)  e2 = e0
% 160.10/26.34  | 
% 160.10/26.35  | REDUCE: (3), (5) imply:
% 160.10/26.35  |   (6)  $false
% 160.10/26.35  | 
% 160.10/26.35  | CLOSE: (6) is inconsistent.
% 160.10/26.35  | 
% 160.10/26.35  End of proof
% 160.10/26.35  
% 160.10/26.35  Sub-proof #866 shows that the following formulas are inconsistent:
% 160.10/26.35  ----------------------------------------------------------------
% 160.10/26.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.35    (2)  op(e1, e1) = e1
% 160.10/26.35    (3)  op(e3, e3) = e3
% 160.10/26.35    (4)   ~ (e1 = e0)
% 160.10/26.35    (5)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 160.10/26.35           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 160.10/26.35           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) = e0
% 160.10/26.35           & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 = e1
% 160.10/26.35           & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) =
% 160.10/26.35           e1 & op(e0, e3) = e0)
% 160.10/26.35    (6)  op(e2, e0) = all_52_13
% 160.10/26.35    (7)   ~ (e3 = e0)
% 160.10/26.35    (8)   ~ (all_52_13 = e2)
% 160.10/26.35  
% 160.10/26.35  Begin of proof
% 160.10/26.35  | 
% 160.10/26.35  | BETA: splitting (5) gives:
% 160.10/26.35  | 
% 160.10/26.35  | Case 1:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3)
% 160.10/26.35  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (9) implies:
% 160.10/26.35  | |   (10)  op(e3, e3) = e0
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (1), (3), (7), (10) are inconsistent by sub-proof #971.
% 160.10/26.35  | | 
% 160.10/26.35  | Case 2:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (11)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.10/26.35  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.10/26.35  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.10/26.35  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (1), (2), (4), (6), (8), (11) are inconsistent by sub-proof #867.
% 160.10/26.35  | | 
% 160.10/26.35  | End of split
% 160.10/26.35  | 
% 160.10/26.35  End of proof
% 160.10/26.35  
% 160.10/26.35  Sub-proof #867 shows that the following formulas are inconsistent:
% 160.10/26.35  ----------------------------------------------------------------
% 160.10/26.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.35    (2)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) &
% 160.10/26.35           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 &
% 160.10/26.35           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0
% 160.10/26.35           & op(e1, e0) = e1 & op(e0, e3) = e0)
% 160.10/26.35    (3)  op(e1, e1) = e1
% 160.10/26.35    (4)   ~ (e1 = e0)
% 160.10/26.35    (5)  op(e2, e0) = all_52_13
% 160.10/26.35    (6)   ~ (all_52_13 = e2)
% 160.10/26.35  
% 160.10/26.35  Begin of proof
% 160.10/26.35  | 
% 160.10/26.35  | BETA: splitting (2) gives:
% 160.10/26.35  | 
% 160.10/26.35  | Case 1:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (7)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3)
% 160.10/26.35  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (7) implies:
% 160.10/26.35  | |   (8)  op(e2, e0) = e2
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #996.
% 160.10/26.35  | | 
% 160.10/26.35  | Case 2:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (9)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e3)
% 160.10/26.35  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (9) implies:
% 160.10/26.35  | |   (10)  op(e1, e1) = e0
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #903.
% 160.10/26.35  | | 
% 160.10/26.35  | End of split
% 160.10/26.35  | 
% 160.10/26.35  End of proof
% 160.10/26.35  
% 160.10/26.35  Sub-proof #868 shows that the following formulas are inconsistent:
% 160.10/26.35  ----------------------------------------------------------------
% 160.10/26.35    (1)   ~ (all_52_1 = e2)
% 160.10/26.35    (2)   ~ (e3 = e2)
% 160.10/26.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.35    (4)  op(e3, e3) = e3
% 160.10/26.35    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 160.10/26.35    (6)  op(e2, e3) = all_52_1
% 160.10/26.35  
% 160.10/26.35  Begin of proof
% 160.10/26.35  | 
% 160.10/26.35  | BETA: splitting (5) gives:
% 160.10/26.35  | 
% 160.10/26.35  | Case 1:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (7) implies:
% 160.10/26.35  | |   (8)  op(e3, e3) = e2
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #958.
% 160.10/26.35  | | 
% 160.10/26.35  | Case 2:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (9) implies:
% 160.10/26.35  | |   (10)  op(e2, e3) = e2
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #1007.
% 160.10/26.35  | | 
% 160.10/26.35  | End of split
% 160.10/26.35  | 
% 160.10/26.35  End of proof
% 160.10/26.35  
% 160.10/26.35  Sub-proof #869 shows that the following formulas are inconsistent:
% 160.10/26.35  ----------------------------------------------------------------
% 160.10/26.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.35    (2)   ~ (all_52_12 = e3)
% 160.10/26.35    (3)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 160.10/26.35           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 160.10/26.35           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 160.10/26.35           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 160.10/26.35    (4)  op(e2, e0) = all_52_13
% 160.10/26.35    (5)  op(e3, e0) = all_52_12
% 160.10/26.35    (6)   ~ (all_52_13 = e2)
% 160.10/26.35  
% 160.10/26.35  Begin of proof
% 160.10/26.35  | 
% 160.10/26.35  | BETA: splitting (3) gives:
% 160.10/26.35  | 
% 160.10/26.35  | Case 1:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (7)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 160.10/26.35  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 160.10/26.35  | |          e0) = e2 & $i(all_57_12)
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (7) implies:
% 160.10/26.35  | |   (8)  op(e2, e0) = e2
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #996.
% 160.10/26.35  | | 
% 160.10/26.35  | Case 2:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (9)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 160.10/26.35  | |        op(e3, e0) = e3
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (9) implies:
% 160.10/26.35  | |   (10)  op(e3, e0) = e3
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #976.
% 160.10/26.35  | | 
% 160.10/26.35  | End of split
% 160.10/26.35  | 
% 160.10/26.35  End of proof
% 160.10/26.35  
% 160.10/26.35  Sub-proof #870 shows that the following formulas are inconsistent:
% 160.10/26.35  ----------------------------------------------------------------
% 160.10/26.35    (1)   ~ (all_52_12 = e2)
% 160.10/26.35    (2)   ~ (e3 = e2)
% 160.10/26.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.35    (4)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 160.10/26.35           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 160.10/26.35           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 160.10/26.35           & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 160.10/26.35           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 160.10/26.35           e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 160.10/26.35         (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 160.10/26.35           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 160.10/26.35           = e3 & $i(all_57_10))
% 160.10/26.35    (5)  op(e2, e2) = e2
% 160.10/26.35    (6)   ~ (all_52_13 = all_4_2)
% 160.10/26.35    (7)  op(e1, e0) = all_52_14
% 160.10/26.35    (8)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 160.10/26.35         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 160.10/26.35    (9)  op(e2, e2) = all_4_2
% 160.10/26.35    (10)   ~ (all_52_14 = e2)
% 160.10/26.35    (11)  op(e2, e1) = all_52_9
% 160.10/26.35    (12)  op(e2, e0) = all_52_13
% 160.10/26.35    (13)   ~ (e2 = e1)
% 160.10/26.35    (14)  op(e3, e0) = all_52_12
% 160.10/26.35    (15)   ~ (all_52_9 = e2)
% 160.10/26.35  
% 160.10/26.35  Begin of proof
% 160.10/26.35  | 
% 160.10/26.35  | BETA: splitting (4) gives:
% 160.10/26.35  | 
% 160.10/26.35  | Case 1:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (16)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 160.10/26.35  | |             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0
% 160.10/26.35  | |           & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 =
% 160.10/26.35  | |           e2 &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (3), (11), (15), (16) are inconsistent by sub-proof #871.
% 160.10/26.35  | | 
% 160.10/26.35  | Case 2:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (17)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 160.10/26.35  | |             e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 160.10/26.35  | |           & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 =
% 160.10/26.35  | |           e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 160.10/26.35  | |           & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 160.10/26.35  | |           $i(all_57_10))
% 160.10/26.35  | | 
% 160.10/26.35  | | BETA: splitting (17) gives:
% 160.10/26.35  | | 
% 160.10/26.35  | | Case 1:
% 160.10/26.35  | | | 
% 160.10/26.35  | | |   (18)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 160.10/26.35  | | |           e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 160.10/26.35  | | |         & op(e1, e0) = e1 & $i(all_57_14)
% 160.10/26.35  | | | 
% 160.10/26.35  | | | ALPHA: (18) implies:
% 160.10/26.35  | | |   (19)  op(e2, e2) = e1
% 160.10/26.35  | | | 
% 160.10/26.35  | | | REF_CLOSE: (3), (5), (13), (19) are inconsistent by sub-proof #993.
% 160.10/26.35  | | | 
% 160.10/26.35  | | Case 2:
% 160.10/26.35  | | | 
% 160.10/26.35  | | |   (20)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 160.10/26.35  | | |           e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0
% 160.10/26.35  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 160.10/26.35  | | | 
% 160.10/26.35  | | | ALPHA: (20) implies:
% 160.10/26.35  | | |   (21)  op(e0, e0) = e3
% 160.10/26.35  | | | 
% 160.10/26.35  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (14), (21)
% 160.10/26.35  | | |            are inconsistent by sub-proof #877.
% 160.10/26.35  | | | 
% 160.10/26.35  | | End of split
% 160.10/26.35  | | 
% 160.10/26.35  | End of split
% 160.10/26.35  | 
% 160.10/26.35  End of proof
% 160.10/26.35  
% 160.10/26.35  Sub-proof #871 shows that the following formulas are inconsistent:
% 160.10/26.35  ----------------------------------------------------------------
% 160.10/26.35    (1)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 160.10/26.35           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 160.10/26.35           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 160.10/26.35           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 160.10/26.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.35    (3)  op(e2, e1) = all_52_9
% 160.10/26.35    (4)   ~ (all_52_9 = e2)
% 160.10/26.35  
% 160.10/26.35  Begin of proof
% 160.10/26.35  | 
% 160.10/26.35  | BETA: splitting (1) gives:
% 160.10/26.35  | 
% 160.10/26.35  | Case 1:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (5)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 160.10/26.35  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 160.10/26.35  | |          e0) = e2 & $i(all_57_12)
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (5) implies:
% 160.10/26.35  | |   (6)  op(e2, e1) = e2
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #1002.
% 160.10/26.35  | | 
% 160.10/26.35  | Case 2:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (7)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 160.10/26.35  | |        op(e2, e1) = e2
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (7) implies:
% 160.10/26.35  | |   (8)  op(e2, e1) = e2
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1002.
% 160.10/26.35  | | 
% 160.10/26.35  | End of split
% 160.10/26.35  | 
% 160.10/26.35  End of proof
% 160.10/26.35  
% 160.10/26.35  Sub-proof #872 shows that the following formulas are inconsistent:
% 160.10/26.35  ----------------------------------------------------------------
% 160.10/26.35    (1)   ~ (all_52_12 = e2)
% 160.10/26.35    (2)   ~ (e3 = e2)
% 160.10/26.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.35    (4)  op(e3, e1) = all_52_8
% 160.10/26.35    (5)  op(e2, e2) = e2
% 160.10/26.35    (6)   ~ (all_52_13 = all_4_2)
% 160.10/26.35    (7)  op(e1, e0) = all_52_14
% 160.10/26.35    (8)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 160.10/26.35         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 160.10/26.35    (9)  op(e2, e2) = all_4_2
% 160.10/26.35    (10)   ~ (all_52_14 = e2)
% 160.10/26.35    (11)  op(e3, e3) = e3
% 160.10/26.35    (12)  op(e2, e0) = all_52_13
% 160.10/26.35    (13)  op(e3, e0) = all_52_12
% 160.10/26.35    (14)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 160.10/26.35            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 160.10/26.35              e0) = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3
% 160.10/26.35              = e1) & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 &
% 160.10/26.35            all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) =
% 160.10/26.35            e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 160.10/26.35            $i(all_57_14))
% 160.10/26.35    (15)   ~ (e3 = e1)
% 160.10/26.35    (16)   ~ (all_52_8 = e3)
% 160.10/26.35  
% 160.10/26.35  Begin of proof
% 160.10/26.35  | 
% 160.10/26.35  | BETA: splitting (14) gives:
% 160.10/26.35  | 
% 160.10/26.35  | Case 1:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (17)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1)
% 160.10/26.35  | |         & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 &
% 160.10/26.35  | |         op(e0, e0) = e3 & $i(all_57_10)
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (17) implies:
% 160.10/26.35  | |   (18)  op(e0, e0) = e3
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (13), (18)
% 160.10/26.35  | |            are inconsistent by sub-proof #877.
% 160.10/26.35  | | 
% 160.10/26.35  | Case 2:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (19)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 160.10/26.35  | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 =
% 160.10/26.35  | |           e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 160.10/26.35  | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.10/26.35  | | 
% 160.10/26.35  | | REF_CLOSE: (3), (4), (11), (15), (16), (19) are inconsistent by sub-proof
% 160.10/26.35  | |            #981.
% 160.10/26.35  | | 
% 160.10/26.35  | End of split
% 160.10/26.35  | 
% 160.10/26.35  End of proof
% 160.10/26.35  
% 160.10/26.35  Sub-proof #873 shows that the following formulas are inconsistent:
% 160.10/26.35  ----------------------------------------------------------------
% 160.10/26.35    (1)  op(e0, e0) = e2
% 160.10/26.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.35    (3)  op(e1, e1) = e1
% 160.10/26.35    (4)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 160.10/26.35           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 160.10/26.35           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 160.10/26.35           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 160.10/26.35           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 160.10/26.35    (5)   ~ (e2 = e1)
% 160.10/26.35  
% 160.10/26.35  Begin of proof
% 160.10/26.35  | 
% 160.10/26.35  | BETA: splitting (4) gives:
% 160.10/26.35  | 
% 160.10/26.35  | Case 1:
% 160.10/26.35  | | 
% 160.10/26.35  | |   (6)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 160.10/26.35  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 160.10/26.35  | |          e1) = e2 & $i(all_57_12)
% 160.10/26.35  | | 
% 160.10/26.35  | | ALPHA: (6) implies:
% 160.10/26.35  | |   (7)  op(e1, e1) = e2
% 160.10/26.35  | | 
% 160.10/26.36  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #986.
% 160.10/26.36  | | 
% 160.10/26.36  | Case 2:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (8)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 160.10/26.36  | |        & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 160.10/26.36  | |          e0) = e1 & $i(all_57_14)
% 160.10/26.36  | | 
% 160.10/26.36  | | ALPHA: (8) implies:
% 160.10/26.36  | |   (9)  op(e0, e0) = e1
% 160.10/26.36  | | 
% 160.10/26.36  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #875.
% 160.10/26.36  | | 
% 160.10/26.36  | End of split
% 160.10/26.36  | 
% 160.10/26.36  End of proof
% 160.10/26.36  
% 160.10/26.36  Sub-proof #874 shows that the following formulas are inconsistent:
% 160.10/26.36  ----------------------------------------------------------------
% 160.10/26.36    (1)  op(e0, e0) = e2
% 160.10/26.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.36    (3)  op(e1, e1) = e1
% 160.10/26.36    (4)  op(e1, e3) = all_52_2
% 160.10/26.36    (5)   ~ (all_52_2 = e1)
% 160.10/26.36    (6)   ~ (e2 = e1)
% 160.10/26.36    (7)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 160.10/26.36           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 160.10/26.36           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 160.10/26.36           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 160.10/26.36           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 160.10/26.36           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 160.10/26.36    (8)   ~ (e3 = e1)
% 160.10/26.36  
% 160.10/26.36  Begin of proof
% 160.10/26.36  | 
% 160.10/26.36  | BETA: splitting (7) gives:
% 160.10/26.36  | 
% 160.10/26.36  | Case 1:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (9)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 160.10/26.36  | |        & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0,
% 160.10/26.36  | |          e0) = e1 & $i(all_57_14)
% 160.10/26.36  | | 
% 160.10/26.36  | | ALPHA: (9) implies:
% 160.10/26.36  | |   (10)  op(e0, e0) = e1
% 160.10/26.36  | | 
% 160.10/26.36  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #875.
% 160.10/26.36  | | 
% 160.10/26.36  | Case 2:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (11)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 160.10/26.36  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 160.10/26.36  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 160.10/26.36  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 160.10/26.36  | | 
% 160.10/26.36  | | REF_CLOSE: (2), (3), (4), (5), (8), (11) are inconsistent by sub-proof #989.
% 160.10/26.36  | | 
% 160.10/26.36  | End of split
% 160.10/26.36  | 
% 160.10/26.36  End of proof
% 160.10/26.36  
% 160.10/26.36  Sub-proof #875 shows that the following formulas are inconsistent:
% 160.10/26.36  ----------------------------------------------------------------
% 160.10/26.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.36    (2)  op(e0, e0) = e2
% 160.10/26.36    (3)  op(e0, e0) = e1
% 160.10/26.36    (4)   ~ (e2 = e1)
% 160.10/26.36  
% 160.10/26.36  Begin of proof
% 160.10/26.36  | 
% 160.10/26.36  | GROUND_INST: instantiating (1) with e1, e2, e0, e0, simplifying with (2), (3)
% 160.10/26.36  |              gives:
% 160.10/26.36  |   (5)  e2 = e1
% 160.10/26.36  | 
% 160.10/26.36  | REDUCE: (4), (5) imply:
% 160.10/26.36  |   (6)  $false
% 160.10/26.36  | 
% 160.10/26.36  | CLOSE: (6) is inconsistent.
% 160.10/26.36  | 
% 160.10/26.36  End of proof
% 160.10/26.36  
% 160.10/26.36  Sub-proof #876 shows that the following formulas are inconsistent:
% 160.10/26.36  ----------------------------------------------------------------
% 160.10/26.36    (1)   ~ (all_52_4 = e3)
% 160.10/26.36    (2)   ~ (all_52_12 = e2)
% 160.10/26.36    (3)   ~ (e3 = e2)
% 160.10/26.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.36    (5)  op(e2, e2) = e2
% 160.10/26.36    (6)   ~ (all_52_13 = all_4_2)
% 160.10/26.36    (7)  op(e1, e0) = all_52_14
% 160.10/26.36    (8)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 160.10/26.36         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 160.10/26.36    (9)  op(e2, e2) = all_4_2
% 160.10/26.36    (10)   ~ (all_52_14 = e2)
% 160.10/26.36    (11)  op(e3, e2) = all_52_4
% 160.10/26.36    (12)  op(e2, e0) = all_52_13
% 160.10/26.36    (13)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 160.10/26.36            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 160.10/26.36              e0) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3
% 160.10/26.36              = e2) & op(e3, e3) = e3 & op(e3, e2) = e3)
% 160.10/26.36    (14)  op(e3, e0) = all_52_12
% 160.10/26.36  
% 160.10/26.36  Begin of proof
% 160.10/26.36  | 
% 160.10/26.36  | BETA: splitting (13) gives:
% 160.10/26.36  | 
% 160.10/26.36  | Case 1:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (15)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 160.10/26.36  | |         & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 &
% 160.10/26.36  | |         op(e0, e0) = e3 & $i(all_57_10)
% 160.10/26.36  | | 
% 160.10/26.36  | | ALPHA: (15) implies:
% 160.10/26.36  | |   (16)  op(e0, e0) = e3
% 160.10/26.36  | | 
% 160.10/26.36  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14), (16)
% 160.10/26.36  | |            are inconsistent by sub-proof #877.
% 160.10/26.36  | | 
% 160.10/26.36  | Case 2:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (17)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 160.10/26.36  | |         op(e3, e2) = e3
% 160.10/26.36  | | 
% 160.10/26.36  | | ALPHA: (17) implies:
% 160.10/26.36  | |   (18)  op(e3, e2) = e3
% 160.10/26.36  | | 
% 160.10/26.36  | | REF_CLOSE: (1), (4), (11), (18) are inconsistent by sub-proof #998.
% 160.10/26.36  | | 
% 160.10/26.36  | End of split
% 160.10/26.36  | 
% 160.10/26.36  End of proof
% 160.10/26.36  
% 160.10/26.36  Sub-proof #877 shows that the following formulas are inconsistent:
% 160.10/26.36  ----------------------------------------------------------------
% 160.10/26.36    (1)   ~ (all_52_12 = e2)
% 160.10/26.36    (2)   ~ (e3 = e2)
% 160.10/26.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.36    (4)  op(e2, e2) = e2
% 160.10/26.36    (5)  op(e0, e0) = e3
% 160.10/26.36    (6)   ~ (all_52_13 = all_4_2)
% 160.10/26.36    (7)  op(e1, e0) = all_52_14
% 160.10/26.36    (8)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 160.10/26.36         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 160.10/26.36    (9)  op(e2, e2) = all_4_2
% 160.10/26.36    (10)   ~ (all_52_14 = e2)
% 160.10/26.36    (11)  op(e2, e0) = all_52_13
% 160.10/26.36    (12)  op(e3, e0) = all_52_12
% 160.10/26.36  
% 160.10/26.36  Begin of proof
% 160.10/26.36  | 
% 160.10/26.36  | BETA: splitting (8) gives:
% 160.10/26.36  | 
% 160.10/26.36  | Case 1:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (13)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 160.10/26.36  | |           e2)
% 160.10/26.36  | | 
% 160.10/26.36  | | BETA: splitting (13) gives:
% 160.10/26.36  | | 
% 160.10/26.36  | | Case 1:
% 160.10/26.36  | | | 
% 160.10/26.36  | | |   (14)  all_56_9 = e2 & op(e3, e0) = e2
% 160.10/26.36  | | | 
% 160.10/26.36  | | | REF_CLOSE: (1), (3), (12), (14) are inconsistent by sub-proof #880.
% 160.10/26.36  | | | 
% 160.10/26.36  | | Case 2:
% 160.10/26.36  | | | 
% 160.10/26.36  | | |   (15)  all_56_10 = e2 & op(e2, e0) = e2
% 160.10/26.36  | | | 
% 160.10/26.36  | | | ALPHA: (15) implies:
% 160.10/26.36  | | |   (16)  op(e2, e0) = e2
% 160.10/26.36  | | | 
% 160.10/26.36  | | | REF_CLOSE: (3), (4), (6), (9), (11), (16) are inconsistent by sub-proof
% 160.10/26.36  | | |            #972.
% 160.10/26.36  | | | 
% 160.10/26.36  | | End of split
% 160.10/26.36  | | 
% 160.10/26.36  | Case 2:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (17)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 160.10/26.36  | |           e2)
% 160.10/26.36  | | 
% 160.10/26.36  | | BETA: splitting (17) gives:
% 160.10/26.36  | | 
% 160.10/26.36  | | Case 1:
% 160.10/26.36  | | | 
% 160.10/26.36  | | |   (18)  all_56_11 = e2 & op(e1, e0) = e2
% 160.10/26.36  | | | 
% 160.10/26.36  | | | REF_CLOSE: (3), (7), (10), (18) are inconsistent by sub-proof #879.
% 160.10/26.36  | | | 
% 160.10/26.36  | | Case 2:
% 160.10/26.36  | | | 
% 160.10/26.36  | | |   (19)  all_56_15 = e2 & op(e0, e0) = e2
% 160.10/26.36  | | | 
% 160.10/26.36  | | | ALPHA: (19) implies:
% 160.10/26.36  | | |   (20)  op(e0, e0) = e2
% 160.10/26.36  | | | 
% 160.10/26.36  | | | REF_CLOSE: (2), (3), (5), (20) are inconsistent by sub-proof #878.
% 160.10/26.36  | | | 
% 160.10/26.36  | | End of split
% 160.10/26.36  | | 
% 160.10/26.36  | End of split
% 160.10/26.36  | 
% 160.10/26.36  End of proof
% 160.10/26.36  
% 160.10/26.36  Sub-proof #878 shows that the following formulas are inconsistent:
% 160.10/26.36  ----------------------------------------------------------------
% 160.10/26.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.36    (2)  op(e0, e0) = e3
% 160.10/26.36    (3)  op(e0, e0) = e2
% 160.10/26.36    (4)   ~ (e3 = e2)
% 160.10/26.36  
% 160.10/26.36  Begin of proof
% 160.10/26.36  | 
% 160.10/26.36  | GROUND_INST: instantiating (1) with e2, e3, e0, e0, simplifying with (2), (3)
% 160.10/26.36  |              gives:
% 160.10/26.36  |   (5)  e3 = e2
% 160.10/26.36  | 
% 160.10/26.36  | REDUCE: (4), (5) imply:
% 160.10/26.36  |   (6)  $false
% 160.10/26.36  | 
% 160.10/26.36  | CLOSE: (6) is inconsistent.
% 160.10/26.36  | 
% 160.10/26.36  End of proof
% 160.10/26.36  
% 160.10/26.36  Sub-proof #879 shows that the following formulas are inconsistent:
% 160.10/26.36  ----------------------------------------------------------------
% 160.10/26.36    (1)  all_56_11 = e2 & op(e1, e0) = e2
% 160.10/26.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.36    (3)  op(e1, e0) = all_52_14
% 160.10/26.36    (4)   ~ (all_52_14 = e2)
% 160.10/26.36  
% 160.10/26.36  Begin of proof
% 160.10/26.36  | 
% 160.10/26.36  | ALPHA: (1) implies:
% 160.10/26.36  |   (5)  op(e1, e0) = e2
% 160.10/26.36  | 
% 160.10/26.36  | GROUND_INST: instantiating (2) with all_52_14, e2, e0, e1, simplifying with
% 160.10/26.36  |              (3), (5) gives:
% 160.10/26.36  |   (6)  all_52_14 = e2
% 160.10/26.36  | 
% 160.10/26.36  | REDUCE: (4), (6) imply:
% 160.10/26.36  |   (7)  $false
% 160.10/26.36  | 
% 160.10/26.36  | CLOSE: (7) is inconsistent.
% 160.10/26.36  | 
% 160.10/26.36  End of proof
% 160.10/26.36  
% 160.10/26.36  Sub-proof #880 shows that the following formulas are inconsistent:
% 160.10/26.36  ----------------------------------------------------------------
% 160.10/26.36    (1)  all_56_9 = e2 & op(e3, e0) = e2
% 160.10/26.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.36    (3)  op(e3, e0) = all_52_12
% 160.10/26.36    (4)   ~ (all_52_12 = e2)
% 160.10/26.36  
% 160.10/26.36  Begin of proof
% 160.10/26.36  | 
% 160.10/26.36  | ALPHA: (1) implies:
% 160.10/26.36  |   (5)  op(e3, e0) = e2
% 160.10/26.36  | 
% 160.10/26.36  | GROUND_INST: instantiating (2) with all_52_12, e2, e0, e3, simplifying with
% 160.10/26.36  |              (3), (5) gives:
% 160.10/26.36  |   (6)  all_52_12 = e2
% 160.10/26.36  | 
% 160.10/26.36  | REDUCE: (4), (6) imply:
% 160.10/26.36  |   (7)  $false
% 160.10/26.36  | 
% 160.10/26.36  | CLOSE: (7) is inconsistent.
% 160.10/26.36  | 
% 160.10/26.36  End of proof
% 160.10/26.36  
% 160.10/26.36  Sub-proof #881 shows that the following formulas are inconsistent:
% 160.10/26.36  ----------------------------------------------------------------
% 160.10/26.36    (1)   ~ (all_52_7 = e0)
% 160.10/26.36    (2)  op(e0, e1) = all_52_11
% 160.10/26.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.36    (4)  op(e0, e3) = all_52_3
% 160.10/26.36    (5)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 160.10/26.36         (all_56_14 = e0 & op(e0, e1) = e0)
% 160.10/26.36    (6)   ~ (all_52_3 = e0)
% 160.10/26.36    (7)  op(e0, e2) = all_52_7
% 160.10/26.36    (8)   ~ (all_52_11 = e0)
% 160.10/26.36  
% 160.10/26.36  Begin of proof
% 160.10/26.36  | 
% 160.10/26.36  | BETA: splitting (5) gives:
% 160.10/26.36  | 
% 160.10/26.36  | Case 1:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (9)  all_56_12 = e0 & op(e0, e3) = e0
% 160.10/26.36  | | 
% 160.10/26.36  | | ALPHA: (9) implies:
% 160.10/26.36  | |   (10)  op(e0, e3) = e0
% 160.10/26.36  | | 
% 160.10/26.36  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #973.
% 160.10/26.36  | | 
% 160.10/26.36  | Case 2:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (11)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 160.10/26.36  | |           e0)
% 160.10/26.36  | | 
% 160.10/26.36  | | REF_CLOSE: (1), (2), (3), (7), (8), (11) are inconsistent by sub-proof #882.
% 160.10/26.36  | | 
% 160.10/26.36  | End of split
% 160.10/26.36  | 
% 160.10/26.36  End of proof
% 160.10/26.36  
% 160.10/26.36  Sub-proof #882 shows that the following formulas are inconsistent:
% 160.10/26.36  ----------------------------------------------------------------
% 160.10/26.36    (1)   ~ (all_52_7 = e0)
% 160.10/26.36    (2)  op(e0, e1) = all_52_11
% 160.10/26.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.36    (4)  op(e0, e2) = all_52_7
% 160.10/26.36    (5)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 160.10/26.36    (6)   ~ (all_52_11 = e0)
% 160.10/26.36  
% 160.10/26.36  Begin of proof
% 160.10/26.36  | 
% 160.10/26.36  | BETA: splitting (5) gives:
% 160.10/26.36  | 
% 160.10/26.36  | Case 1:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (7)  all_56_13 = e0 & op(e0, e2) = e0
% 160.10/26.36  | | 
% 160.10/26.36  | | ALPHA: (7) implies:
% 160.10/26.36  | |   (8)  op(e0, e2) = e0
% 160.10/26.36  | | 
% 160.10/26.36  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #969.
% 160.10/26.36  | | 
% 160.10/26.36  | Case 2:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (9)  all_56_14 = e0 & op(e0, e1) = e0
% 160.10/26.36  | | 
% 160.10/26.36  | | ALPHA: (9) implies:
% 160.10/26.36  | |   (10)  op(e0, e1) = e0
% 160.10/26.36  | | 
% 160.10/26.36  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #966.
% 160.10/26.36  | | 
% 160.10/26.36  | End of split
% 160.10/26.36  | 
% 160.10/26.36  End of proof
% 160.10/26.36  
% 160.10/26.36  Sub-proof #883 shows that the following formulas are inconsistent:
% 160.10/26.36  ----------------------------------------------------------------
% 160.10/26.36    (1)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 160.10/26.36         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 160.10/26.36    (2)   ~ (e3 = e2)
% 160.10/26.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.36    (4)  all_56_11 = e0
% 160.10/26.36    (5)  op(e0, e0) = e0
% 160.10/26.36    (6)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 160.10/26.36         (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 160.10/26.36    (7)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 160.10/26.36         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 160.10/26.36    (8)   ~ (e1 = e0)
% 160.10/26.36    (9)   ~ (e2 = e1)
% 160.10/26.36    (10)  all_56_15 = e0
% 160.10/26.36    (11)   ~ (e3 = e1)
% 160.10/26.36    (12)   ~ (e2 = e0)
% 160.10/26.36    (13)   ~ (e3 = e0)
% 160.10/26.36  
% 160.10/26.36  Begin of proof
% 160.10/26.36  | 
% 160.10/26.36  | BETA: splitting (1) gives:
% 160.10/26.36  | 
% 160.10/26.36  | Case 1:
% 160.10/26.36  | | 
% 160.10/26.36  | |   (14)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 160.10/26.36  | |           e1)
% 160.10/26.36  | | 
% 160.10/26.36  | | BETA: splitting (14) gives:
% 160.10/26.36  | | 
% 160.10/26.36  | | Case 1:
% 160.10/26.36  | | | 
% 160.10/26.36  | | |   (15)  all_56_9 = e1 & op(e3, e0) = e1
% 160.10/26.36  | | | 
% 160.10/26.36  | | | ALPHA: (15) implies:
% 160.10/26.36  | | |   (16)  all_56_9 = e1
% 160.10/26.36  | | | 
% 160.10/26.36  | | | BETA: splitting (7) gives:
% 160.10/26.36  | | | 
% 160.10/26.36  | | | Case 1:
% 160.10/26.36  | | | | 
% 160.10/26.36  | | | |   (17)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0)
% 160.10/26.36  | | | |           = e2)
% 160.10/26.36  | | | | 
% 160.10/26.36  | | | | BETA: splitting (17) gives:
% 160.10/26.36  | | | | 
% 160.10/26.36  | | | | Case 1:
% 160.10/26.36  | | | | | 
% 160.10/26.36  | | | | |   (18)  all_56_9 = e2 & op(e3, e0) = e2
% 160.10/26.36  | | | | | 
% 160.10/26.36  | | | | | ALPHA: (18) implies:
% 160.10/26.36  | | | | |   (19)  all_56_9 = e2
% 160.10/26.36  | | | | | 
% 160.10/26.36  | | | | | REF_CLOSE: (9), (16), (19) are inconsistent by sub-proof #896.
% 160.10/26.36  | | | | | 
% 160.10/26.36  | | | | Case 2:
% 160.10/26.36  | | | | | 
% 160.10/26.36  | | | | |   (20)  all_56_10 = e2 & op(e2, e0) = e2
% 160.10/26.36  | | | | | 
% 160.10/26.36  | | | | | ALPHA: (20) implies:
% 160.10/26.36  | | | | |   (21)  all_56_10 = e2
% 160.10/26.36  | | | | | 
% 160.10/26.36  | | | | | BETA: splitting (6) gives:
% 160.10/26.36  | | | | | 
% 160.10/26.36  | | | | | Case 1:
% 160.10/26.36  | | | | | | 
% 160.10/26.36  | | | | | |   (22)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2,
% 160.10/26.36  | | | | | |             e0) = e3)
% 160.10/26.36  | | | | | | 
% 160.10/26.36  | | | | | | BETA: splitting (22) gives:
% 160.10/26.36  | | | | | | 
% 160.10/26.36  | | | | | | Case 1:
% 160.10/26.36  | | | | | | | 
% 160.10/26.36  | | | | | | |   (23)  all_56_9 = e3 & op(e3, e0) = e3
% 160.10/26.36  | | | | | | | 
% 160.10/26.36  | | | | | | | REF_CLOSE: (11), (16), (23) are inconsistent by sub-proof #895.
% 160.10/26.36  | | | | | | | 
% 160.10/26.36  | | | | | | Case 2:
% 160.10/26.36  | | | | | | | 
% 160.10/26.36  | | | | | | |   (24)  all_56_10 = e3 & op(e2, e0) = e3
% 160.10/26.36  | | | | | | | 
% 160.10/26.36  | | | | | | | REF_CLOSE: (2), (21), (24) are inconsistent by sub-proof #894.
% 160.10/26.36  | | | | | | | 
% 160.10/26.36  | | | | | | End of split
% 160.10/26.36  | | | | | | 
% 160.10/26.36  | | | | | Case 2:
% 160.10/26.36  | | | | | | 
% 160.10/26.37  | | | | | |   (25)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 &
% 160.10/26.37  | | | | | |           op(e0, e0) = e3)
% 160.10/26.37  | | | | | | 
% 160.10/26.37  | | | | | | REF_CLOSE: (4), (10), (13), (25) are inconsistent by sub-proof #891.
% 160.10/26.37  | | | | | | 
% 160.10/26.37  | | | | | End of split
% 160.10/26.37  | | | | | 
% 160.10/26.37  | | | | End of split
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | Case 2:
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | |   (26)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0,
% 160.10/26.37  | | | |             e0) = e2)
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | | REF_CLOSE: (3), (4), (5), (12), (26) are inconsistent by sub-proof #889.
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | End of split
% 160.10/26.37  | | | 
% 160.10/26.37  | | Case 2:
% 160.10/26.37  | | | 
% 160.10/26.37  | | |   (27)  all_56_10 = e1 & op(e2, e0) = e1
% 160.10/26.37  | | | 
% 160.10/26.37  | | | ALPHA: (27) implies:
% 160.10/26.37  | | |   (28)  all_56_10 = e1
% 160.10/26.37  | | | 
% 160.10/26.37  | | | BETA: splitting (7) gives:
% 160.10/26.37  | | | 
% 160.10/26.37  | | | Case 1:
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | |   (29)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0)
% 160.10/26.37  | | | |           = e2)
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | | BETA: splitting (29) gives:
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | | Case 1:
% 160.10/26.37  | | | | | 
% 160.10/26.37  | | | | |   (30)  all_56_9 = e2 & op(e3, e0) = e2
% 160.10/26.37  | | | | | 
% 160.10/26.37  | | | | | ALPHA: (30) implies:
% 160.10/26.37  | | | | |   (31)  all_56_9 = e2
% 160.10/26.37  | | | | | 
% 160.10/26.37  | | | | | BETA: splitting (6) gives:
% 160.10/26.37  | | | | | 
% 160.10/26.37  | | | | | Case 1:
% 160.10/26.37  | | | | | | 
% 160.10/26.37  | | | | | |   (32)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2,
% 160.10/26.37  | | | | | |             e0) = e3)
% 160.10/26.37  | | | | | | 
% 160.10/26.37  | | | | | | BETA: splitting (32) gives:
% 160.10/26.37  | | | | | | 
% 160.10/26.37  | | | | | | Case 1:
% 160.10/26.37  | | | | | | | 
% 160.10/26.37  | | | | | | |   (33)  all_56_9 = e3 & op(e3, e0) = e3
% 160.10/26.37  | | | | | | | 
% 160.10/26.37  | | | | | | | ALPHA: (33) implies:
% 160.10/26.37  | | | | | | |   (34)  all_56_9 = e3
% 160.10/26.37  | | | | | | | 
% 160.10/26.37  | | | | | | | REF_CLOSE: (2), (31), (34) are inconsistent by sub-proof #888.
% 160.10/26.37  | | | | | | | 
% 160.10/26.37  | | | | | | Case 2:
% 160.10/26.37  | | | | | | | 
% 160.10/26.37  | | | | | | |   (35)  all_56_10 = e3 & op(e2, e0) = e3
% 160.10/26.37  | | | | | | | 
% 160.10/26.37  | | | | | | | ALPHA: (35) implies:
% 160.10/26.37  | | | | | | |   (36)  all_56_10 = e3
% 160.10/26.37  | | | | | | | 
% 160.10/26.37  | | | | | | | REF_CLOSE: (11), (28), (36) are inconsistent by sub-proof #887.
% 160.10/26.37  | | | | | | | 
% 160.10/26.37  | | | | | | End of split
% 160.10/26.37  | | | | | | 
% 160.10/26.37  | | | | | Case 2:
% 160.10/26.37  | | | | | | 
% 160.10/26.37  | | | | | |   (37)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 &
% 160.10/26.37  | | | | | |           op(e0, e0) = e3)
% 160.10/26.37  | | | | | | 
% 160.10/26.37  | | | | | | REF_CLOSE: (4), (10), (13), (37) are inconsistent by sub-proof #891.
% 160.10/26.37  | | | | | | 
% 160.10/26.37  | | | | | End of split
% 160.10/26.37  | | | | | 
% 160.10/26.37  | | | | Case 2:
% 160.10/26.37  | | | | | 
% 160.10/26.37  | | | | |   (38)  all_56_10 = e2 & op(e2, e0) = e2
% 160.10/26.37  | | | | | 
% 160.10/26.37  | | | | | ALPHA: (38) implies:
% 160.10/26.37  | | | | |   (39)  all_56_10 = e2
% 160.10/26.37  | | | | | 
% 160.10/26.37  | | | | | REF_CLOSE: (9), (28), (39) are inconsistent by sub-proof #886.
% 160.10/26.37  | | | | | 
% 160.10/26.37  | | | | End of split
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | Case 2:
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | |   (40)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0,
% 160.10/26.37  | | | |             e0) = e2)
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | | REF_CLOSE: (3), (4), (5), (12), (40) are inconsistent by sub-proof #889.
% 160.10/26.37  | | | | 
% 160.10/26.37  | | | End of split
% 160.10/26.37  | | | 
% 160.10/26.37  | | End of split
% 160.10/26.37  | | 
% 160.10/26.37  | Case 2:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (41)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 160.10/26.37  | |           e1)
% 160.10/26.37  | | 
% 160.10/26.37  | | BETA: splitting (41) gives:
% 160.10/26.37  | | 
% 160.10/26.37  | | Case 1:
% 160.10/26.37  | | | 
% 160.10/26.37  | | |   (42)  all_56_11 = e1 & op(e1, e0) = e1
% 160.10/26.37  | | | 
% 160.10/26.37  | | | REF_CLOSE: (4), (8), (42) are inconsistent by sub-proof #885.
% 160.10/26.37  | | | 
% 160.10/26.37  | | Case 2:
% 160.10/26.37  | | | 
% 160.10/26.37  | | |   (43)  all_56_15 = e1 & op(e0, e0) = e1
% 160.10/26.37  | | | 
% 160.10/26.37  | | | REF_CLOSE: (8), (10), (43) are inconsistent by sub-proof #884.
% 160.10/26.37  | | | 
% 160.10/26.37  | | End of split
% 160.10/26.37  | | 
% 160.10/26.37  | End of split
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #884 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_15 = e1 & op(e0, e0) = e1
% 160.10/26.37    (2)  all_56_15 = e0
% 160.10/26.37    (3)   ~ (e1 = e0)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | ALPHA: (1) implies:
% 160.10/26.37  |   (4)  all_56_15 = e1
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.37  |   (5)  e1 = e0
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (5) implies:
% 160.10/26.37  |   (6)  e1 = e0
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (6) imply:
% 160.10/26.37  |   (7)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (7) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #885 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_11 = e1 & op(e1, e0) = e1
% 160.10/26.37    (2)  all_56_11 = e0
% 160.10/26.37    (3)   ~ (e1 = e0)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | ALPHA: (1) implies:
% 160.10/26.37  |   (4)  all_56_11 = e1
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.37  |   (5)  e1 = e0
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (5) implies:
% 160.10/26.37  |   (6)  e1 = e0
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (6) imply:
% 160.10/26.37  |   (7)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (7) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #886 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_10 = e2
% 160.10/26.37    (2)  all_56_10 = e1
% 160.10/26.37    (3)   ~ (e2 = e1)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (1), (2) imply:
% 160.10/26.37  |   (4)  e2 = e1
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (4) implies:
% 160.10/26.37  |   (5)  e2 = e1
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (5) imply:
% 160.10/26.37  |   (6)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (6) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #887 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_10 = e3
% 160.10/26.37    (2)  all_56_10 = e1
% 160.10/26.37    (3)   ~ (e3 = e1)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (1), (2) imply:
% 160.10/26.37  |   (4)  e3 = e1
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (4) implies:
% 160.10/26.37  |   (5)  e3 = e1
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (5) imply:
% 160.10/26.37  |   (6)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (6) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #888 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_9 = e3
% 160.10/26.37    (2)  all_56_9 = e2
% 160.10/26.37    (3)   ~ (e3 = e2)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (1), (2) imply:
% 160.10/26.37  |   (4)  e3 = e2
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (4) implies:
% 160.10/26.37  |   (5)  e3 = e2
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (5) imply:
% 160.10/26.37  |   (6)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (6) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #889 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.37    (2)  all_56_11 = e0
% 160.10/26.37    (3)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 160.10/26.37    (4)  op(e0, e0) = e0
% 160.10/26.37    (5)   ~ (e2 = e0)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | BETA: splitting (3) gives:
% 160.10/26.37  | 
% 160.10/26.37  | Case 1:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (6)  all_56_11 = e2 & op(e1, e0) = e2
% 160.10/26.37  | | 
% 160.10/26.37  | | ALPHA: (6) implies:
% 160.10/26.37  | |   (7)  all_56_11 = e2
% 160.10/26.37  | | 
% 160.10/26.37  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #890.
% 160.10/26.37  | | 
% 160.10/26.37  | Case 2:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (8)  all_56_15 = e2 & op(e0, e0) = e2
% 160.10/26.37  | | 
% 160.10/26.37  | | ALPHA: (8) implies:
% 160.10/26.37  | |   (9)  op(e0, e0) = e2
% 160.10/26.37  | | 
% 160.10/26.37  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #979.
% 160.10/26.37  | | 
% 160.10/26.37  | End of split
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #890 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_11 = e2
% 160.10/26.37    (2)  all_56_11 = e0
% 160.10/26.37    (3)   ~ (e2 = e0)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (1), (2) imply:
% 160.10/26.37  |   (4)  e2 = e0
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (4) implies:
% 160.10/26.37  |   (5)  e2 = e0
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (5) imply:
% 160.10/26.37  |   (6)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (6) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #891 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 160.10/26.37    (2)  all_56_11 = e0
% 160.10/26.37    (3)   ~ (e3 = e0)
% 160.10/26.37    (4)  all_56_15 = e0
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | BETA: splitting (1) gives:
% 160.10/26.37  | 
% 160.10/26.37  | Case 1:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (5)  all_56_11 = e3 & op(e1, e0) = e3
% 160.10/26.37  | | 
% 160.10/26.37  | | ALPHA: (5) implies:
% 160.10/26.37  | |   (6)  all_56_11 = e3
% 160.10/26.37  | | 
% 160.10/26.37  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #893.
% 160.10/26.37  | | 
% 160.10/26.37  | Case 2:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (7)  all_56_15 = e3 & op(e0, e0) = e3
% 160.10/26.37  | | 
% 160.10/26.37  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #892.
% 160.10/26.37  | | 
% 160.10/26.37  | End of split
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #892 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_15 = e3 & op(e0, e0) = e3
% 160.10/26.37    (2)  all_56_15 = e0
% 160.10/26.37    (3)   ~ (e3 = e0)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | ALPHA: (1) implies:
% 160.10/26.37  |   (4)  all_56_15 = e3
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.37  |   (5)  e3 = e0
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (5) implies:
% 160.10/26.37  |   (6)  e3 = e0
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (6) imply:
% 160.10/26.37  |   (7)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (7) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #893 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_11 = e3
% 160.10/26.37    (2)  all_56_11 = e0
% 160.10/26.37    (3)   ~ (e3 = e0)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (1), (2) imply:
% 160.10/26.37  |   (4)  e3 = e0
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (4) implies:
% 160.10/26.37  |   (5)  e3 = e0
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (5) imply:
% 160.10/26.37  |   (6)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (6) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #894 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_10 = e3 & op(e2, e0) = e3
% 160.10/26.37    (2)  all_56_10 = e2
% 160.10/26.37    (3)   ~ (e3 = e2)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | ALPHA: (1) implies:
% 160.10/26.37  |   (4)  all_56_10 = e3
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.37  |   (5)  e3 = e2
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (5) implies:
% 160.10/26.37  |   (6)  e3 = e2
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (6) imply:
% 160.10/26.37  |   (7)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (7) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #895 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_9 = e3 & op(e3, e0) = e3
% 160.10/26.37    (2)  all_56_9 = e1
% 160.10/26.37    (3)   ~ (e3 = e1)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | ALPHA: (1) implies:
% 160.10/26.37  |   (4)  all_56_9 = e3
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.37  |   (5)  e3 = e1
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (5) implies:
% 160.10/26.37  |   (6)  e3 = e1
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (6) imply:
% 160.10/26.37  |   (7)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (7) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #896 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_9 = e2
% 160.10/26.37    (2)  all_56_9 = e1
% 160.10/26.37    (3)   ~ (e2 = e1)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | COMBINE_EQS: (1), (2) imply:
% 160.10/26.37  |   (4)  e2 = e1
% 160.10/26.37  | 
% 160.10/26.37  | SIMP: (4) implies:
% 160.10/26.37  |   (5)  e2 = e1
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (3), (5) imply:
% 160.10/26.37  |   (6)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (6) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #897 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)   ~ (all_52_7 = e0)
% 160.10/26.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.37    (3)   ~ (all_52_6 = e0)
% 160.10/26.37    (4)  op(e0, e2) = all_52_7
% 160.10/26.37    (5)  op(e1, e2) = all_52_6
% 160.10/26.37    (6)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | BETA: splitting (6) gives:
% 160.10/26.37  | 
% 160.10/26.37  | Case 1:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (7)  all_56_7 = e0 & op(e1, e2) = e0
% 160.10/26.37  | | 
% 160.10/26.37  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #898.
% 160.10/26.37  | | 
% 160.10/26.37  | Case 2:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (8)  all_56_13 = e0 & op(e0, e2) = e0
% 160.10/26.37  | | 
% 160.10/26.37  | | ALPHA: (8) implies:
% 160.10/26.37  | |   (9)  op(e0, e2) = e0
% 160.10/26.37  | | 
% 160.10/26.37  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #969.
% 160.10/26.37  | | 
% 160.10/26.37  | End of split
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #898 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  all_56_7 = e0 & op(e1, e2) = e0
% 160.10/26.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.37    (3)  op(e1, e2) = all_52_6
% 160.10/26.37    (4)   ~ (all_52_6 = e0)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | ALPHA: (1) implies:
% 160.10/26.37  |   (5)  op(e1, e2) = e0
% 160.10/26.37  | 
% 160.10/26.37  | GROUND_INST: instantiating (2) with all_52_6, e0, e2, e1, simplifying with
% 160.10/26.37  |              (3), (5) gives:
% 160.10/26.37  |   (6)  all_52_6 = e0
% 160.10/26.37  | 
% 160.10/26.37  | REDUCE: (4), (6) imply:
% 160.10/26.37  |   (7)  $false
% 160.10/26.37  | 
% 160.10/26.37  | CLOSE: (7) is inconsistent.
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #899 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)   ~ (all_52_7 = e0)
% 160.10/26.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.37    (3)  op(e0, e3) = all_52_3
% 160.10/26.37    (4)   ~ (all_52_3 = e0)
% 160.10/26.37    (5)  op(e0, e2) = all_52_7
% 160.10/26.37    (6)  op(e3, e3) = e3
% 160.10/26.37    (7)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 160.10/26.37         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 160.10/26.37           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.10/26.37           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 160.10/26.37           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.10/26.37    (8)   ~ (e3 = e0)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | BETA: splitting (7) gives:
% 160.10/26.37  | 
% 160.10/26.37  | Case 1:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (9)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 160.10/26.37  | | 
% 160.10/26.37  | | ALPHA: (9) implies:
% 160.10/26.37  | |   (10)  op(e0, e3) = e0
% 160.10/26.37  | | 
% 160.10/26.37  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #973.
% 160.10/26.37  | | 
% 160.10/26.37  | Case 2:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (11)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.10/26.37  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 160.10/26.37  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.10/26.37  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.10/26.37  | | 
% 160.10/26.37  | | REF_CLOSE: (1), (2), (5), (6), (8), (11) are inconsistent by sub-proof #900.
% 160.10/26.37  | | 
% 160.10/26.37  | End of split
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #900 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)   ~ (all_52_7 = e0)
% 160.10/26.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.37    (3)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 160.10/26.37           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.10/26.37           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 160.10/26.37           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.10/26.37    (4)  op(e0, e2) = all_52_7
% 160.10/26.37    (5)  op(e3, e3) = e3
% 160.10/26.37    (6)   ~ (e3 = e0)
% 160.10/26.37  
% 160.10/26.37  Begin of proof
% 160.10/26.37  | 
% 160.10/26.37  | BETA: splitting (3) gives:
% 160.10/26.37  | 
% 160.10/26.37  | Case 1:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (7)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 160.10/26.37  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 160.10/26.37  | | 
% 160.10/26.37  | | ALPHA: (7) implies:
% 160.10/26.37  | |   (8)  op(e3, e3) = e0
% 160.10/26.37  | | 
% 160.10/26.37  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #971.
% 160.10/26.37  | | 
% 160.10/26.37  | Case 2:
% 160.10/26.37  | | 
% 160.10/26.37  | |   (9)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2)
% 160.10/26.37  | |        & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 160.10/26.37  | | 
% 160.10/26.37  | | ALPHA: (9) implies:
% 160.10/26.37  | |   (10)  op(e0, e2) = e0
% 160.10/26.37  | | 
% 160.10/26.37  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #969.
% 160.10/26.37  | | 
% 160.10/26.37  | End of split
% 160.10/26.37  | 
% 160.10/26.37  End of proof
% 160.10/26.37  
% 160.10/26.37  Sub-proof #901 shows that the following formulas are inconsistent:
% 160.10/26.37  ----------------------------------------------------------------
% 160.10/26.37    (1)  op(e1, e3) = e0
% 160.10/26.37    (2)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 160.10/26.37         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 160.10/26.37    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 160.10/26.37         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 160.10/26.38    (4)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 160.10/26.38         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 160.10/26.38    (5)  op(e1, e1) = e0
% 160.10/26.38    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 160.10/26.38         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 160.10/26.38    (7)   ~ (e3 = e2)
% 160.10/26.38    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.38    (9)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 160.10/26.38         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 160.10/26.38    (10)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 160.10/26.38          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 160.10/26.38    (11)  op(e1, e0) = all_52_14
% 160.10/26.38    (12)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 160.10/26.38          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 160.10/26.38    (13)  op(e3, e3) = e3
% 160.10/26.38    (14)  op(e2, e2) = e0
% 160.10/26.38    (15)  all_56_3 = e0
% 160.10/26.38    (16)  all_56_6 = e0
% 160.10/26.38    (17)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 160.10/26.38          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 160.10/26.38    (18)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 160.10/26.38          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 160.10/26.38    (19)   ~ (e1 = e0)
% 160.10/26.38    (20)   ~ (e2 = e1)
% 160.10/26.38    (21)   ~ (all_52_14 = e1)
% 160.10/26.38    (22)   ~ (e3 = e1)
% 160.10/26.38    (23)   ~ (e2 = e0)
% 160.10/26.38    (24)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 160.10/26.38          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 160.10/26.38    (25)   ~ (e3 = e0)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | BETA: splitting (9) gives:
% 160.10/26.38  | 
% 160.10/26.38  | Case 1:
% 160.10/26.38  | | 
% 160.10/26.38  | |   (26)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 160.10/26.38  | |           e1)
% 160.10/26.38  | | 
% 160.10/26.38  | | BETA: splitting (26) gives:
% 160.10/26.38  | | 
% 160.10/26.38  | | Case 1:
% 160.10/26.38  | | | 
% 160.10/26.38  | | |   (27)  all_56_6 = e1 & op(e1, e3) = e1
% 160.10/26.38  | | | 
% 160.10/26.38  | | | REF_CLOSE: (16), (19), (27) are inconsistent by sub-proof #917.
% 160.10/26.38  | | | 
% 160.10/26.38  | | Case 2:
% 160.10/26.38  | | | 
% 160.10/26.38  | | |   (28)  all_56_7 = e1 & op(e1, e2) = e1
% 160.10/26.38  | | | 
% 160.10/26.38  | | | ALPHA: (28) implies:
% 160.10/26.38  | | |   (29)  all_56_7 = e1
% 160.10/26.38  | | |   (30)  op(e1, e2) = e1
% 160.10/26.38  | | | 
% 160.10/26.38  | | | BETA: splitting (24) gives:
% 160.10/26.38  | | | 
% 160.10/26.38  | | | Case 1:
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | |   (31)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2)
% 160.10/26.38  | | | |           = e2)
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | | BETA: splitting (31) gives:
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | | Case 1:
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | |   (32)  all_56_6 = e2 & op(e1, e3) = e2
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | ALPHA: (32) implies:
% 160.10/26.38  | | | | |   (33)  all_56_6 = e2
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | REF_CLOSE: (16), (23), (33) are inconsistent by sub-proof #916.
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | Case 2:
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | |   (34)  all_56_7 = e2 & op(e1, e2) = e2
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | REF_CLOSE: (20), (29), (34) are inconsistent by sub-proof #915.
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | End of split
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | Case 2:
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | |   (35)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0)
% 160.10/26.38  | | | |           = e2)
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | | BETA: splitting (35) gives:
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | | Case 1:
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | |   (36)  all_56_8 = e2 & op(e1, e1) = e2
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | ALPHA: (36) implies:
% 160.10/26.38  | | | | |   (37)  op(e1, e1) = e2
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | REF_CLOSE: (5), (8), (23), (37) are inconsistent by sub-proof #914.
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | Case 2:
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | |   (38)  all_56_11 = e2 & op(e1, e0) = e2
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | ALPHA: (38) implies:
% 160.10/26.38  | | | | |   (39)  all_56_11 = e2
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | BETA: splitting (12) gives:
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | Case 1:
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | |   (40)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2,
% 160.10/26.38  | | | | | |             e2) = e3)
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | | REF_CLOSE: (3), (6), (7), (8), (13), (14), (18), (19), (20), (22),
% 160.10/26.38  | | | | | |            (23), (25), (40) are inconsistent by sub-proof #944.
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | Case 2:
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | |   (41)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0,
% 160.10/26.38  | | | | | |             e2) = e3)
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | | BETA: splitting (41) gives:
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | | Case 1:
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | |   (42)  all_56_7 = e3 & op(e1, e2) = e3
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | ALPHA: (42) implies:
% 160.10/26.38  | | | | | | |   (43)  op(e1, e2) = e3
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | REF_CLOSE: (8), (22), (30), (43) are inconsistent by sub-proof
% 160.10/26.38  | | | | | | |            #939.
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | Case 2:
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | |   (44)  all_56_13 = e3 & op(e0, e2) = e3
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | ALPHA: (44) implies:
% 160.10/26.38  | | | | | | |   (45)  all_56_13 = e3
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | BETA: splitting (10) gives:
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | Case 1:
% 160.10/26.38  | | | | | | | | 
% 160.10/26.38  | | | | | | | |   (46)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 &
% 160.10/26.38  | | | | | | | |           op(e2, e2) = e2)
% 160.10/26.38  | | | | | | | | 
% 160.10/26.38  | | | | | | | | BETA: splitting (46) gives:
% 160.10/26.38  | | | | | | | | 
% 160.10/26.38  | | | | | | | | Case 1:
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | |   (47)  all_56_1 = e2 & op(e3, e2) = e2
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | ALPHA: (47) implies:
% 160.10/26.38  | | | | | | | | |   (48)  all_56_1 = e2
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | BETA: splitting (17) gives:
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | Case 1:
% 160.10/26.38  | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | |   (49)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 &
% 160.10/26.38  | | | | | | | | | |           op(e1, e2) = e3)
% 160.10/26.38  | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | BETA: splitting (49) gives:
% 160.10/26.38  | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | Case 1:
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | |   (50)  all_56_6 = e3 & op(e1, e3) = e3
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | ALPHA: (50) implies:
% 160.10/26.38  | | | | | | | | | | |   (51)  op(e1, e3) = e3
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | REF_CLOSE: (1), (8), (25), (51) are inconsistent by sub-proof
% 160.10/26.38  | | | | | | | | | | |            #913.
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | Case 2:
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | |   (52)  all_56_7 = e3 & op(e1, e2) = e3
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | ALPHA: (52) implies:
% 160.10/26.38  | | | | | | | | | | |   (53)  op(e1, e2) = e3
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | REF_CLOSE: (8), (22), (30), (53) are inconsistent by
% 160.10/26.38  | | | | | | | | | | |            sub-proof #939.
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | End of split
% 160.10/26.38  | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | Case 2:
% 160.10/26.38  | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | |   (54)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3
% 160.10/26.38  | | | | | | | | | |           & op(e1, e0) = e3)
% 160.10/26.38  | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | BETA: splitting (54) gives:
% 160.10/26.38  | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | Case 1:
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | |   (55)  all_56_8 = e3 & op(e1, e1) = e3
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | ALPHA: (55) implies:
% 160.10/26.38  | | | | | | | | | | |   (56)  op(e1, e1) = e3
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | REF_CLOSE: (5), (8), (25), (56) are inconsistent by sub-proof
% 160.10/26.38  | | | | | | | | | | |            #912.
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | Case 2:
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | |   (57)  all_56_11 = e3 & op(e1, e0) = e3
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | ALPHA: (57) implies:
% 160.10/26.38  | | | | | | | | | | |   (58)  all_56_11 = e3
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | COMBINE_EQS: (39), (58) imply:
% 160.10/26.38  | | | | | | | | | | |   (59)  e3 = e2
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | SIMP: (59) implies:
% 160.10/26.38  | | | | | | | | | | |   (60)  e3 = e2
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | COMBINE_EQS: (45), (60) imply:
% 160.10/26.38  | | | | | | | | | | |   (61)  all_56_13 = e2
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (12), (13), (15),
% 160.10/26.38  | | | | | | | | | | |            (18), (19), (20), (22), (23), (25), (48), (61) are
% 160.10/26.38  | | | | | | | | | | |            inconsistent by sub-proof #905.
% 160.10/26.38  | | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | | End of split
% 160.10/26.38  | | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | End of split
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | Case 2:
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | |   (62)  all_56_3 = e2 & op(e2, e2) = e2
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | ALPHA: (62) implies:
% 160.10/26.38  | | | | | | | | |   (63)  op(e2, e2) = e2
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | REF_CLOSE: (8), (14), (23), (63) are inconsistent by sub-proof
% 160.10/26.38  | | | | | | | | |            #942.
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | End of split
% 160.10/26.38  | | | | | | | | 
% 160.10/26.38  | | | | | | | Case 2:
% 160.10/26.38  | | | | | | | | 
% 160.10/26.38  | | | | | | | |   (64)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 &
% 160.10/26.38  | | | | | | | |           op(e0, e2) = e2)
% 160.10/26.38  | | | | | | | | 
% 160.10/26.38  | | | | | | | | BETA: splitting (64) gives:
% 160.10/26.38  | | | | | | | | 
% 160.10/26.38  | | | | | | | | Case 1:
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | |   (65)  all_56_7 = e2 & op(e1, e2) = e2
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | REF_CLOSE: (20), (29), (65) are inconsistent by sub-proof
% 160.10/26.38  | | | | | | | | |            #915.
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | Case 2:
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | |   (66)  all_56_13 = e2 & op(e0, e2) = e2
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | | REF_CLOSE: (7), (45), (66) are inconsistent by sub-proof #904.
% 160.10/26.38  | | | | | | | | | 
% 160.10/26.38  | | | | | | | | End of split
% 160.10/26.38  | | | | | | | | 
% 160.10/26.38  | | | | | | | End of split
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | End of split
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | End of split
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | End of split
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | End of split
% 160.10/26.38  | | | 
% 160.10/26.38  | | End of split
% 160.10/26.38  | | 
% 160.10/26.38  | Case 2:
% 160.10/26.38  | | 
% 160.10/26.38  | |   (67)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 160.10/26.38  | |           e1)
% 160.10/26.38  | | 
% 160.10/26.38  | | REF_CLOSE: (5), (8), (11), (19), (21), (67) are inconsistent by sub-proof
% 160.10/26.38  | |            #902.
% 160.10/26.38  | | 
% 160.10/26.38  | End of split
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #902 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.38    (1)  op(e1, e1) = e0
% 160.10/26.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.38    (3)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 160.10/26.38    (4)  op(e1, e0) = all_52_14
% 160.10/26.38    (5)   ~ (e1 = e0)
% 160.10/26.38    (6)   ~ (all_52_14 = e1)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | BETA: splitting (3) gives:
% 160.10/26.38  | 
% 160.10/26.38  | Case 1:
% 160.10/26.38  | | 
% 160.10/26.38  | |   (7)  all_56_8 = e1 & op(e1, e1) = e1
% 160.10/26.38  | | 
% 160.10/26.38  | | ALPHA: (7) implies:
% 160.10/26.38  | |   (8)  op(e1, e1) = e1
% 160.10/26.38  | | 
% 160.10/26.38  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #903.
% 160.10/26.38  | | 
% 160.10/26.38  | Case 2:
% 160.10/26.38  | | 
% 160.10/26.38  | |   (9)  all_56_11 = e1 & op(e1, e0) = e1
% 160.10/26.38  | | 
% 160.10/26.38  | | ALPHA: (9) implies:
% 160.10/26.38  | |   (10)  op(e1, e0) = e1
% 160.10/26.38  | | 
% 160.10/26.38  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #974.
% 160.10/26.38  | | 
% 160.10/26.38  | End of split
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #903 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.38    (2)  op(e1, e1) = e1
% 160.10/26.38    (3)  op(e1, e1) = e0
% 160.10/26.38    (4)   ~ (e1 = e0)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | GROUND_INST: instantiating (1) with e0, e1, e1, e1, simplifying with (2), (3)
% 160.10/26.38  |              gives:
% 160.10/26.38  |   (5)  e1 = e0
% 160.10/26.38  | 
% 160.10/26.38  | REDUCE: (4), (5) imply:
% 160.10/26.38  |   (6)  $false
% 160.10/26.38  | 
% 160.10/26.38  | CLOSE: (6) is inconsistent.
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #904 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.38    (1)  all_56_13 = e2 & op(e0, e2) = e2
% 160.10/26.38    (2)  all_56_13 = e3
% 160.10/26.38    (3)   ~ (e3 = e2)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | ALPHA: (1) implies:
% 160.10/26.38  |   (4)  all_56_13 = e2
% 160.10/26.38  | 
% 160.10/26.38  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.38  |   (5)  e3 = e2
% 160.10/26.38  | 
% 160.10/26.38  | REDUCE: (3), (5) imply:
% 160.10/26.38  |   (6)  $false
% 160.10/26.38  | 
% 160.10/26.38  | CLOSE: (6) is inconsistent.
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #905 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.38    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 160.10/26.38         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 160.10/26.38    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 160.10/26.38         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 160.10/26.38    (3)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 160.10/26.38         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 160.10/26.38    (4)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 160.10/26.38         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 160.10/26.38    (5)   ~ (e3 = e2)
% 160.10/26.38    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.38    (7)  all_56_13 = e2
% 160.10/26.38    (8)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 160.10/26.38         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 160.10/26.38    (9)  all_56_1 = e2
% 160.10/26.38    (10)  op(e3, e3) = e3
% 160.10/26.38    (11)  all_56_3 = e0
% 160.10/26.38    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 160.10/26.38          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 160.10/26.38    (13)   ~ (e1 = e0)
% 160.10/26.38    (14)   ~ (e2 = e1)
% 160.10/26.38    (15)   ~ (e3 = e1)
% 160.10/26.38    (16)   ~ (e2 = e0)
% 160.10/26.38    (17)   ~ (e3 = e0)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | BETA: splitting (8) gives:
% 160.10/26.38  | 
% 160.10/26.38  | Case 1:
% 160.10/26.38  | | 
% 160.10/26.38  | |   (18)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 160.10/26.38  | |           e3)
% 160.10/26.38  | | 
% 160.10/26.38  | | BETA: splitting (18) gives:
% 160.10/26.38  | | 
% 160.10/26.38  | | Case 1:
% 160.10/26.38  | | | 
% 160.10/26.38  | | |   (19)  all_56_1 = e3 & op(e3, e2) = e3
% 160.10/26.38  | | | 
% 160.10/26.38  | | | ALPHA: (19) implies:
% 160.10/26.38  | | |   (20)  all_56_1 = e3
% 160.10/26.38  | | | 
% 160.10/26.38  | | | REF_CLOSE: (2), (4), (5), (6), (10), (12), (13), (14), (15), (16), (17),
% 160.10/26.38  | | |            (20) are inconsistent by sub-proof #946.
% 160.10/26.38  | | | 
% 160.10/26.38  | | Case 2:
% 160.10/26.38  | | | 
% 160.10/26.38  | | |   (21)  all_56_3 = e3 & op(e2, e2) = e3
% 160.10/26.38  | | | 
% 160.10/26.38  | | | ALPHA: (21) implies:
% 160.10/26.38  | | |   (22)  all_56_3 = e3
% 160.10/26.38  | | | 
% 160.10/26.38  | | | COMBINE_EQS: (11), (22) imply:
% 160.10/26.38  | | |   (23)  e3 = e0
% 160.10/26.38  | | | 
% 160.10/26.38  | | | SIMP: (23) implies:
% 160.10/26.38  | | |   (24)  e3 = e0
% 160.10/26.38  | | | 
% 160.10/26.38  | | | REDUCE: (17), (24) imply:
% 160.10/26.38  | | |   (25)  $false
% 160.10/26.38  | | | 
% 160.10/26.38  | | | CLOSE: (25) is inconsistent.
% 160.10/26.38  | | | 
% 160.10/26.38  | | End of split
% 160.10/26.38  | | 
% 160.10/26.38  | Case 2:
% 160.10/26.38  | | 
% 160.10/26.38  | |   (26)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 160.10/26.38  | |           e3)
% 160.10/26.38  | | 
% 160.10/26.38  | | BETA: splitting (26) gives:
% 160.10/26.38  | | 
% 160.10/26.38  | | Case 1:
% 160.10/26.38  | | | 
% 160.10/26.38  | | |   (27)  all_56_7 = e3 & op(e1, e2) = e3
% 160.10/26.38  | | | 
% 160.10/26.38  | | | ALPHA: (27) implies:
% 160.10/26.38  | | |   (28)  all_56_7 = e3
% 160.10/26.38  | | | 
% 160.10/26.38  | | | BETA: splitting (1) gives:
% 160.10/26.38  | | | 
% 160.10/26.38  | | | Case 1:
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | |   (29)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2)
% 160.10/26.38  | | | |           = e1)
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | | BETA: splitting (29) gives:
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | | Case 1:
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | |   (30)  all_56_1 = e1 & op(e3, e2) = e1
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | REF_CLOSE: (9), (14), (30) are inconsistent by sub-proof #911.
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | Case 2:
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | |   (31)  all_56_3 = e1 & op(e2, e2) = e1
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | ALPHA: (31) implies:
% 160.10/26.38  | | | | |   (32)  all_56_3 = e1
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | BETA: splitting (3) gives:
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | Case 1:
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | |   (33)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2,
% 160.10/26.38  | | | | | |             e2) = e0)
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | | BETA: splitting (33) gives:
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | | Case 1:
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | |   (34)  all_56_1 = e0 & op(e3, e2) = e0
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | REF_CLOSE: (9), (16), (34) are inconsistent by sub-proof #910.
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | Case 2:
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | |   (35)  all_56_3 = e0 & op(e2, e2) = e0
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | COMBINE_EQS: (11), (32) imply:
% 160.10/26.38  | | | | | | |   (36)  e1 = e0
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | REDUCE: (13), (36) imply:
% 160.10/26.38  | | | | | | |   (37)  $false
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | CLOSE: (37) is inconsistent.
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | End of split
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | Case 2:
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | |   (38)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0,
% 160.10/26.38  | | | | | |             e2) = e0)
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | | BETA: splitting (38) gives:
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | | Case 1:
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | |   (39)  all_56_7 = e0 & op(e1, e2) = e0
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | REF_CLOSE: (17), (28), (39) are inconsistent by sub-proof #909.
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | Case 2:
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | |   (40)  all_56_13 = e0 & op(e0, e2) = e0
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | | REF_CLOSE: (7), (16), (40) are inconsistent by sub-proof #908.
% 160.10/26.38  | | | | | | | 
% 160.10/26.38  | | | | | | End of split
% 160.10/26.38  | | | | | | 
% 160.10/26.38  | | | | | End of split
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | End of split
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | Case 2:
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | |   (41)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2)
% 160.10/26.38  | | | |           = e1)
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | | BETA: splitting (41) gives:
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | | Case 1:
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | |   (42)  all_56_7 = e1 & op(e1, e2) = e1
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | ALPHA: (42) implies:
% 160.10/26.38  | | | | |   (43)  all_56_7 = e1
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | COMBINE_EQS: (28), (43) imply:
% 160.10/26.38  | | | | |   (44)  e3 = e1
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | SIMP: (44) implies:
% 160.10/26.38  | | | | |   (45)  e3 = e1
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | REDUCE: (15), (45) imply:
% 160.10/26.38  | | | | |   (46)  $false
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | CLOSE: (46) is inconsistent.
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | Case 2:
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | |   (47)  all_56_13 = e1 & op(e0, e2) = e1
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | ALPHA: (47) implies:
% 160.10/26.38  | | | | |   (48)  all_56_13 = e1
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | | REF_CLOSE: (7), (14), (48) are inconsistent by sub-proof #907.
% 160.10/26.38  | | | | | 
% 160.10/26.38  | | | | End of split
% 160.10/26.38  | | | | 
% 160.10/26.38  | | | End of split
% 160.10/26.38  | | | 
% 160.10/26.38  | | Case 2:
% 160.10/26.38  | | | 
% 160.10/26.38  | | |   (49)  all_56_13 = e3 & op(e0, e2) = e3
% 160.10/26.38  | | | 
% 160.10/26.38  | | | REF_CLOSE: (5), (7), (49) are inconsistent by sub-proof #906.
% 160.10/26.38  | | | 
% 160.10/26.38  | | End of split
% 160.10/26.38  | | 
% 160.10/26.38  | End of split
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #906 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.38    (1)  all_56_13 = e3 & op(e0, e2) = e3
% 160.10/26.38    (2)  all_56_13 = e2
% 160.10/26.38    (3)   ~ (e3 = e2)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | ALPHA: (1) implies:
% 160.10/26.38  |   (4)  all_56_13 = e3
% 160.10/26.38  | 
% 160.10/26.38  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.38  |   (5)  e3 = e2
% 160.10/26.38  | 
% 160.10/26.38  | REDUCE: (3), (5) imply:
% 160.10/26.38  |   (6)  $false
% 160.10/26.38  | 
% 160.10/26.38  | CLOSE: (6) is inconsistent.
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #907 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.38    (1)  all_56_13 = e2
% 160.10/26.38    (2)  all_56_13 = e1
% 160.10/26.38    (3)   ~ (e2 = e1)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | COMBINE_EQS: (1), (2) imply:
% 160.10/26.38  |   (4)  e2 = e1
% 160.10/26.38  | 
% 160.10/26.38  | SIMP: (4) implies:
% 160.10/26.38  |   (5)  e2 = e1
% 160.10/26.38  | 
% 160.10/26.38  | REDUCE: (3), (5) imply:
% 160.10/26.38  |   (6)  $false
% 160.10/26.38  | 
% 160.10/26.38  | CLOSE: (6) is inconsistent.
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #908 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.38    (1)  all_56_13 = e0 & op(e0, e2) = e0
% 160.10/26.38    (2)  all_56_13 = e2
% 160.10/26.38    (3)   ~ (e2 = e0)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | ALPHA: (1) implies:
% 160.10/26.38  |   (4)  all_56_13 = e0
% 160.10/26.38  | 
% 160.10/26.38  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.38  |   (5)  e2 = e0
% 160.10/26.38  | 
% 160.10/26.38  | REDUCE: (3), (5) imply:
% 160.10/26.38  |   (6)  $false
% 160.10/26.38  | 
% 160.10/26.38  | CLOSE: (6) is inconsistent.
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #909 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.38    (1)  all_56_7 = e0 & op(e1, e2) = e0
% 160.10/26.38    (2)  all_56_7 = e3
% 160.10/26.38    (3)   ~ (e3 = e0)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | ALPHA: (1) implies:
% 160.10/26.38  |   (4)  all_56_7 = e0
% 160.10/26.38  | 
% 160.10/26.38  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.38  |   (5)  e3 = e0
% 160.10/26.38  | 
% 160.10/26.38  | REDUCE: (3), (5) imply:
% 160.10/26.38  |   (6)  $false
% 160.10/26.38  | 
% 160.10/26.38  | CLOSE: (6) is inconsistent.
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #910 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.38    (1)  all_56_1 = e0 & op(e3, e2) = e0
% 160.10/26.38    (2)  all_56_1 = e2
% 160.10/26.38    (3)   ~ (e2 = e0)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | ALPHA: (1) implies:
% 160.10/26.38  |   (4)  all_56_1 = e0
% 160.10/26.38  | 
% 160.10/26.38  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.38  |   (5)  e2 = e0
% 160.10/26.38  | 
% 160.10/26.38  | REDUCE: (3), (5) imply:
% 160.10/26.38  |   (6)  $false
% 160.10/26.38  | 
% 160.10/26.38  | CLOSE: (6) is inconsistent.
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #911 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.38    (1)  all_56_1 = e1 & op(e3, e2) = e1
% 160.10/26.38    (2)  all_56_1 = e2
% 160.10/26.38    (3)   ~ (e2 = e1)
% 160.10/26.38  
% 160.10/26.38  Begin of proof
% 160.10/26.38  | 
% 160.10/26.38  | ALPHA: (1) implies:
% 160.10/26.38  |   (4)  all_56_1 = e1
% 160.10/26.38  | 
% 160.10/26.38  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.38  |   (5)  e2 = e1
% 160.10/26.38  | 
% 160.10/26.38  | REDUCE: (3), (5) imply:
% 160.10/26.38  |   (6)  $false
% 160.10/26.38  | 
% 160.10/26.38  | CLOSE: (6) is inconsistent.
% 160.10/26.38  | 
% 160.10/26.38  End of proof
% 160.10/26.38  
% 160.10/26.38  Sub-proof #912 shows that the following formulas are inconsistent:
% 160.10/26.38  ----------------------------------------------------------------
% 160.10/26.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (2)  op(e1, e1) = e3
% 160.10/26.39    (3)  op(e1, e1) = e0
% 160.10/26.39    (4)   ~ (e3 = e0)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | GROUND_INST: instantiating (1) with e0, e3, e1, e1, simplifying with (2), (3)
% 160.10/26.39  |              gives:
% 160.10/26.39  |   (5)  e3 = e0
% 160.10/26.39  | 
% 160.10/26.39  | REDUCE: (4), (5) imply:
% 160.10/26.39  |   (6)  $false
% 160.10/26.39  | 
% 160.10/26.39  | CLOSE: (6) is inconsistent.
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #913 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (2)  op(e1, e3) = e3
% 160.10/26.39    (3)  op(e1, e3) = e0
% 160.10/26.39    (4)   ~ (e3 = e0)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | GROUND_INST: instantiating (1) with e0, e3, e3, e1, simplifying with (2), (3)
% 160.10/26.39  |              gives:
% 160.10/26.39  |   (5)  e3 = e0
% 160.10/26.39  | 
% 160.10/26.39  | REDUCE: (4), (5) imply:
% 160.10/26.39  |   (6)  $false
% 160.10/26.39  | 
% 160.10/26.39  | CLOSE: (6) is inconsistent.
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #914 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (2)  op(e1, e1) = e2
% 160.10/26.39    (3)  op(e1, e1) = e0
% 160.10/26.39    (4)   ~ (e2 = e0)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | GROUND_INST: instantiating (1) with e2, e0, e1, e1, simplifying with (2), (3)
% 160.10/26.39  |              gives:
% 160.10/26.39  |   (5)  e2 = e0
% 160.10/26.39  | 
% 160.10/26.39  | REDUCE: (4), (5) imply:
% 160.10/26.39  |   (6)  $false
% 160.10/26.39  | 
% 160.10/26.39  | CLOSE: (6) is inconsistent.
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #915 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  all_56_7 = e2 & op(e1, e2) = e2
% 160.10/26.39    (2)  all_56_7 = e1
% 160.10/26.39    (3)   ~ (e2 = e1)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | ALPHA: (1) implies:
% 160.10/26.39  |   (4)  all_56_7 = e2
% 160.10/26.39  | 
% 160.10/26.39  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.39  |   (5)  e2 = e1
% 160.10/26.39  | 
% 160.10/26.39  | SIMP: (5) implies:
% 160.10/26.39  |   (6)  e2 = e1
% 160.10/26.39  | 
% 160.10/26.39  | REDUCE: (3), (6) imply:
% 160.10/26.39  |   (7)  $false
% 160.10/26.39  | 
% 160.10/26.39  | CLOSE: (7) is inconsistent.
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #916 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  all_56_6 = e2
% 160.10/26.39    (2)  all_56_6 = e0
% 160.10/26.39    (3)   ~ (e2 = e0)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | COMBINE_EQS: (1), (2) imply:
% 160.10/26.39  |   (4)  e2 = e0
% 160.10/26.39  | 
% 160.10/26.39  | SIMP: (4) implies:
% 160.10/26.39  |   (5)  e2 = e0
% 160.10/26.39  | 
% 160.10/26.39  | REDUCE: (3), (5) imply:
% 160.10/26.39  |   (6)  $false
% 160.10/26.39  | 
% 160.10/26.39  | CLOSE: (6) is inconsistent.
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #917 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  all_56_6 = e1 & op(e1, e3) = e1
% 160.10/26.39    (2)  all_56_6 = e0
% 160.10/26.39    (3)   ~ (e1 = e0)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | ALPHA: (1) implies:
% 160.10/26.39  |   (4)  all_56_6 = e1
% 160.10/26.39  | 
% 160.10/26.39  | COMBINE_EQS: (2), (4) imply:
% 160.10/26.39  |   (5)  e1 = e0
% 160.10/26.39  | 
% 160.10/26.39  | SIMP: (5) implies:
% 160.10/26.39  |   (6)  e1 = e0
% 160.10/26.39  | 
% 160.10/26.39  | REDUCE: (3), (6) imply:
% 160.10/26.39  |   (7)  $false
% 160.10/26.39  | 
% 160.10/26.39  | CLOSE: (7) is inconsistent.
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #918 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (2)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 160.10/26.39           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 160.10/26.39           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 160.10/26.39           & op(e2, e2) = e2 & op(e2, e1) = e2) | (all_57_5 = e2 & all_57_12 = e1
% 160.10/26.39           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e2, e2) = e1 & op(e2, e1) =
% 160.10/26.39           e2 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14)) |
% 160.10/26.39         (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0) &
% 160.10/26.39           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 160.10/26.39           = e3 & $i(all_57_10))
% 160.10/26.39    (3)  op(e0, e0) = e0
% 160.10/26.39    (4)  op(e2, e2) = e0
% 160.10/26.39    (5)   ~ (e1 = e0)
% 160.10/26.39    (6)   ~ (e2 = e0)
% 160.10/26.39    (7)   ~ (e3 = e0)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (2) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (8)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 160.10/26.39  | |          & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 &
% 160.10/26.39  | |          op(e0, e0) = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2
% 160.10/26.39  | |          &  ~ (e2 = e1) & op(e2, e2) = e2 & op(e2, e1) = e2)
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (3), (4), (6), (8) are inconsistent by sub-proof #919.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (9)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 160.10/26.39  | |            e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 160.10/26.39  | |          & op(e1, e0) = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3
% 160.10/26.39  | |          & all_57_15 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 160.10/26.39  | |          op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0, e0) = e3 &
% 160.10/26.39  | |          $i(all_57_10))
% 160.10/26.39  | | 
% 160.10/26.39  | | BETA: splitting (9) gives:
% 160.10/26.39  | | 
% 160.10/26.39  | | Case 1:
% 160.10/26.39  | | | 
% 160.10/26.39  | | |   (10)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 =
% 160.10/26.39  | | |           e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14
% 160.10/26.39  | | |         & op(e1, e0) = e1 & $i(all_57_14)
% 160.10/26.39  | | | 
% 160.10/26.39  | | | ALPHA: (10) implies:
% 160.10/26.39  | | |   (11)  op(e2, e2) = e1
% 160.10/26.39  | | | 
% 160.10/26.39  | | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #960.
% 160.10/26.39  | | | 
% 160.10/26.39  | | Case 2:
% 160.10/26.39  | | | 
% 160.10/26.39  | | |   (12)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 =
% 160.10/26.39  | | |           e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0
% 160.10/26.39  | | |         & op(e0, e0) = e3 & $i(all_57_10)
% 160.10/26.39  | | | 
% 160.10/26.39  | | | ALPHA: (12) implies:
% 160.10/26.39  | | |   (13)  op(e0, e0) = e3
% 160.10/26.39  | | | 
% 160.10/26.39  | | | REF_CLOSE: (1), (3), (7), (13) are inconsistent by sub-proof #999.
% 160.10/26.39  | | | 
% 160.10/26.39  | | End of split
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #919 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (2)  op(e0, e0) = e0
% 160.10/26.39    (3)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 160.10/26.39           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 160.10/26.39           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 160.10/26.39           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 160.10/26.39    (4)  op(e2, e2) = e0
% 160.10/26.39    (5)   ~ (e2 = e0)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (3) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (6)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 160.10/26.39  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 160.10/26.39  | |          e0) = e2 & $i(all_57_12)
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (6) implies:
% 160.10/26.39  | |   (7)  op(e0, e0) = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #979.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (8)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 160.10/26.39  | |        op(e2, e1) = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (8) implies:
% 160.10/26.39  | |   (9)  op(e2, e2) = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #942.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #920 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (2)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 160.10/26.39           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 160.10/26.39           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 160.10/26.39           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 160.10/26.39             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.10/26.39    (3)  op(e3, e3) = e3
% 160.10/26.39    (4)  op(e2, e2) = e0
% 160.10/26.39    (5)   ~ (e1 = e0)
% 160.10/26.39    (6)   ~ (e3 = e1)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (2) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (7)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 160.10/26.39  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 160.10/26.39  | |        all_57_14 & $i(all_57_14)
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (7) implies:
% 160.10/26.39  | |   (8)  op(e3, e3) = e1
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #995.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 160.10/26.39  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 160.10/26.39  | |        all_57_14 & $i(all_57_14)
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (9) implies:
% 160.10/26.39  | |   (10)  op(e2, e2) = e1
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #960.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #921 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 160.10/26.39           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.10/26.39           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 160.10/26.39           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 160.10/26.39           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.10/26.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (3)  op(e1, e1) = e1
% 160.10/26.39    (4)  op(e2, e2) = e0
% 160.10/26.39    (5)   ~ (e1 = e0)
% 160.10/26.39    (6)   ~ (e3 = e1)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (1) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 160.10/26.39  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 160.10/26.39  | |          e1) = e3 & $i(all_57_10)
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (7) implies:
% 160.10/26.39  | |   (8)  op(e1, e1) = e3
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1003.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 160.10/26.39  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 160.10/26.39  | |        all_57_14 & $i(all_57_14)
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (9) implies:
% 160.10/26.39  | |   (10)  op(e2, e2) = e1
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #960.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #922 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)   ~ (e3 = e2)
% 160.10/26.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (3)  op(e3, e3) = e3
% 160.10/26.39    (4)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 160.10/26.39           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 160.10/26.39           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 160.10/26.39           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 160.10/26.39           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.10/26.39    (5)   ~ (e3 = e1)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (4) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (6)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 160.10/26.39  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 160.10/26.39  | |          e0) = e2 & $i(all_57_12)
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (6) implies:
% 160.10/26.39  | |   (7)  op(e3, e3) = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #958.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (8)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 160.10/26.39  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 160.10/26.39  | |        all_57_14 & $i(all_57_14)
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (8) implies:
% 160.10/26.39  | |   (9)  op(e3, e3) = e1
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #995.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #923 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  all_54_5 = all_4_2
% 160.10/26.39    (2)   ~ (all_52_1 = e3)
% 160.10/26.39    (3)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 160.10/26.39    (4)   ~ (e3 = e2)
% 160.10/26.39    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (6)   ~ (all_4_2 = e3)
% 160.10/26.39    (7)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2,
% 160.10/26.39             e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~
% 160.10/26.39           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 160.10/26.39             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 &
% 160.10/26.39           all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2
% 160.10/26.39           & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 160.10/26.39           $i(all_57_12))
% 160.10/26.39    (8)  op(e1, e1) = e1
% 160.10/26.39    (9)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 160.10/26.39    (10)  op(e2, e2) = all_4_2
% 160.10/26.39    (11)  op(e3, e3) = e3
% 160.10/26.39    (12)  op(e2, e3) = all_52_1
% 160.10/26.39    (13)   ~ (all_4_2 = e1)
% 160.10/26.39    (14)  all_54_4 = all_52_1
% 160.10/26.39    (15)   ~ (e3 = e1)
% 160.10/26.39    (16)   ~ (all_52_1 = all_4_2)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (7) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (17)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 160.10/26.39  | |         op(e2, e2) = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (17) implies:
% 160.10/26.39  | |   (18)  op(e2, e2) = e2
% 160.10/26.39  | |   (19)  op(e2, e3) = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (12), (13), (14), (16), (18),
% 160.10/26.39  | |            (19) are inconsistent by sub-proof #925.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (20)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 =
% 160.10/26.39  | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1
% 160.10/26.39  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 =
% 160.10/26.39  | |           e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) & op(e3, e3) = e2 &
% 160.10/26.39  | |           op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 160.10/26.39  | |           $i(all_57_12))
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (4), (5), (8), (11), (15), (20) are inconsistent by sub-proof
% 160.10/26.39  | |            #924.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #924 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)   ~ (e3 = e2)
% 160.10/26.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (3)  op(e1, e1) = e1
% 160.10/26.39    (4)  op(e3, e3) = e3
% 160.10/26.39    (5)   ~ (e3 = e1)
% 160.10/26.39    (6)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 160.10/26.39           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.10/26.39           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 160.10/26.39           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 160.10/26.39           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (6) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (7)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 160.10/26.39  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 160.10/26.39  | |          e1) = e3 & $i(all_57_10)
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (7) implies:
% 160.10/26.39  | |   (8)  op(e1, e1) = e3
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1003.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (9)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 160.10/26.39  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 160.10/26.39  | |          e1) = e2 & $i(all_57_12)
% 160.10/26.39  | | 
% 160.10/26.39  | | ALPHA: (9) implies:
% 160.10/26.39  | |   (10)  op(e3, e3) = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #958.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #925 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  op(e2, e3) = e2
% 160.10/26.39    (2)  all_54_5 = all_4_2
% 160.10/26.39    (3)   ~ (all_52_1 = e3)
% 160.10/26.39    (4)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 160.10/26.39    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (6)   ~ (all_4_2 = e3)
% 160.10/26.39    (7)  op(e2, e2) = e2
% 160.10/26.39    (8)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 160.10/26.39    (9)  op(e2, e2) = all_4_2
% 160.10/26.39    (10)  op(e2, e3) = all_52_1
% 160.10/26.39    (11)   ~ (all_4_2 = e1)
% 160.10/26.39    (12)  all_54_4 = all_52_1
% 160.10/26.39    (13)   ~ (all_52_1 = all_4_2)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (8) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (14)  all_54_4 = e3
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (3), (12), (14) are inconsistent by sub-proof #931.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (15)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (15)
% 160.10/26.39  | |            are inconsistent by sub-proof #926.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #926 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  op(e2, e3) = e2
% 160.10/26.39    (2)  all_54_5 = all_4_2
% 160.10/26.39    (3)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 160.10/26.39    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (5)   ~ (all_4_2 = e3)
% 160.10/26.39    (6)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 160.10/26.39    (7)  op(e2, e2) = e2
% 160.10/26.39    (8)  op(e2, e2) = all_4_2
% 160.10/26.39    (9)  op(e2, e3) = all_52_1
% 160.10/26.39    (10)   ~ (all_4_2 = e1)
% 160.10/26.39    (11)  all_54_4 = all_52_1
% 160.10/26.39    (12)   ~ (all_52_1 = all_4_2)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (6) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (13)  all_54_4 = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | COMBINE_EQS: (11), (13) imply:
% 160.10/26.39  | |   (14)  all_52_1 = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | SIMP: (14) implies:
% 160.10/26.39  | |   (15)  all_52_1 = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | REDUCE: (12), (15) imply:
% 160.10/26.39  | |   (16)   ~ (all_4_2 = e2)
% 160.10/26.39  | | 
% 160.10/26.39  | | SIMP: (16) implies:
% 160.10/26.39  | |   (17)   ~ (all_4_2 = e2)
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (17) are inconsistent by
% 160.10/26.39  | |            sub-proof #927.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (18)   ~ (all_54_4 = e2)
% 160.10/26.39  | | 
% 160.10/26.39  | | REDUCE: (11), (18) imply:
% 160.10/26.39  | |   (19)   ~ (all_52_1 = e2)
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (4), (9), (19) are inconsistent by sub-proof #1007.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #927 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  all_54_5 = all_4_2
% 160.10/26.39    (2)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 160.10/26.39    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (4)   ~ (all_4_2 = e3)
% 160.10/26.39    (5)  op(e2, e2) = e2
% 160.10/26.39    (6)  op(e2, e2) = all_4_2
% 160.10/26.39    (7)   ~ (all_4_2 = e2)
% 160.10/26.39    (8)   ~ (all_4_2 = e1)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (2) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (9)  all_54_5 = e3
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #930.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (10)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (10) are inconsistent by sub-proof
% 160.10/26.39  | |            #928.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #928 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  all_54_5 = all_4_2
% 160.10/26.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (3)  op(e2, e2) = e2
% 160.10/26.39    (4)  op(e2, e2) = all_4_2
% 160.10/26.39    (5)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 160.10/26.39    (6)   ~ (all_4_2 = e2)
% 160.10/26.39    (7)   ~ (all_4_2 = e1)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (5) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (8)  all_54_5 = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | COMBINE_EQS: (1), (8) imply:
% 160.10/26.39  | |   (9)  all_4_2 = e2
% 160.10/26.39  | | 
% 160.10/26.39  | | REDUCE: (6), (9) imply:
% 160.10/26.39  | |   (10)  $false
% 160.10/26.39  | | 
% 160.10/26.39  | | CLOSE: (10) is inconsistent.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (11)   ~ (all_54_5 = e2)
% 160.10/26.39  | |   (12)  all_54_5 = e1 | all_54_5 = e0
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (12) are inconsistent by sub-proof
% 160.10/26.39  | |            #929.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #929 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  all_54_5 = all_4_2
% 160.10/26.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (3)  op(e2, e2) = e2
% 160.10/26.39    (4)  op(e2, e2) = all_4_2
% 160.10/26.39    (5)   ~ (all_4_2 = e2)
% 160.10/26.39    (6)   ~ (all_4_2 = e1)
% 160.10/26.39    (7)  all_54_5 = e1 | all_54_5 = e0
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | BETA: splitting (7) gives:
% 160.10/26.39  | 
% 160.10/26.39  | Case 1:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (8)  all_54_5 = e1
% 160.10/26.39  | | 
% 160.10/26.39  | | COMBINE_EQS: (1), (8) imply:
% 160.10/26.39  | |   (9)  all_4_2 = e1
% 160.10/26.39  | | 
% 160.10/26.39  | | REDUCE: (6), (9) imply:
% 160.10/26.39  | |   (10)  $false
% 160.10/26.39  | | 
% 160.10/26.39  | | CLOSE: (10) is inconsistent.
% 160.10/26.39  | | 
% 160.10/26.39  | Case 2:
% 160.10/26.39  | | 
% 160.10/26.39  | |   (11)  all_54_5 = e0
% 160.10/26.39  | | 
% 160.10/26.39  | | COMBINE_EQS: (1), (11) imply:
% 160.10/26.39  | |   (12)  all_4_2 = e0
% 160.10/26.39  | | 
% 160.10/26.39  | | REDUCE: (5), (12) imply:
% 160.10/26.39  | |   (13)   ~ (e2 = e0)
% 160.10/26.39  | | 
% 160.10/26.39  | | SIMP: (13) implies:
% 160.10/26.39  | |   (14)   ~ (e2 = e0)
% 160.10/26.39  | | 
% 160.10/26.39  | | REDUCE: (4), (12) imply:
% 160.10/26.39  | |   (15)  op(e2, e2) = e0
% 160.10/26.39  | | 
% 160.10/26.39  | | REF_CLOSE: (2), (3), (14), (15) are inconsistent by sub-proof #942.
% 160.10/26.39  | | 
% 160.10/26.39  | End of split
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #930 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  all_54_5 = all_4_2
% 160.10/26.39    (2)  all_54_5 = e3
% 160.10/26.39    (3)   ~ (all_4_2 = e3)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | COMBINE_EQS: (1), (2) imply:
% 160.10/26.39  |   (4)  all_4_2 = e3
% 160.10/26.39  | 
% 160.10/26.39  | SIMP: (4) implies:
% 160.10/26.39  |   (5)  all_4_2 = e3
% 160.10/26.39  | 
% 160.10/26.39  | REDUCE: (3), (5) imply:
% 160.10/26.39  |   (6)  $false
% 160.10/26.39  | 
% 160.10/26.39  | CLOSE: (6) is inconsistent.
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #931 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)  all_54_4 = all_52_1
% 160.10/26.39    (2)  all_54_4 = e3
% 160.10/26.39    (3)   ~ (all_52_1 = e3)
% 160.10/26.39  
% 160.10/26.39  Begin of proof
% 160.10/26.39  | 
% 160.10/26.39  | COMBINE_EQS: (1), (2) imply:
% 160.10/26.39  |   (4)  all_52_1 = e3
% 160.10/26.39  | 
% 160.10/26.39  | SIMP: (4) implies:
% 160.10/26.39  |   (5)  all_52_1 = e3
% 160.10/26.39  | 
% 160.10/26.39  | REDUCE: (3), (5) imply:
% 160.10/26.39  |   (6)  $false
% 160.10/26.39  | 
% 160.10/26.39  | CLOSE: (6) is inconsistent.
% 160.10/26.39  | 
% 160.10/26.39  End of proof
% 160.10/26.39  
% 160.10/26.39  Sub-proof #932 shows that the following formulas are inconsistent:
% 160.10/26.39  ----------------------------------------------------------------
% 160.10/26.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.39    (2)   ~ (all_52_12 = e3)
% 160.10/26.39    (3)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 160.10/26.39           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 160.10/26.39           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 160.10/26.39           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 160.10/26.39           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 160.10/26.39    (4)  op(e0, e0) = e0
% 160.10/26.39    (5)  op(e3, e0) = all_52_12
% 160.10/26.40    (6)   ~ (e2 = e0)
% 160.10/26.40  
% 160.10/26.40  Begin of proof
% 160.10/26.40  | 
% 160.10/26.40  | BETA: splitting (3) gives:
% 160.10/26.40  | 
% 160.10/26.40  | Case 1:
% 160.10/26.40  | | 
% 160.10/26.40  | |   (7)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 160.10/26.40  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 160.10/26.40  | |          e0) = e2 & $i(all_57_12)
% 160.10/26.40  | | 
% 160.10/26.40  | | ALPHA: (7) implies:
% 160.10/26.40  | |   (8)  op(e0, e0) = e2
% 160.10/26.40  | | 
% 160.10/26.40  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #979.
% 160.10/26.40  | | 
% 160.10/26.40  | Case 2:
% 160.10/26.40  | | 
% 160.10/26.40  | |   (9)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 160.10/26.40  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 160.10/26.40  | |          e2) = e3 & $i(all_57_10)
% 160.10/26.40  | | 
% 160.10/26.40  | | ALPHA: (9) implies:
% 160.10/26.40  | |   (10)  op(e3, e0) = e3
% 160.10/26.40  | | 
% 160.10/26.40  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #976.
% 160.10/26.40  | | 
% 160.10/26.40  | End of split
% 160.10/26.40  | 
% 160.10/26.40  End of proof
% 160.10/26.40  
% 160.10/26.40  Sub-proof #933 shows that the following formulas are inconsistent:
% 160.10/26.40  ----------------------------------------------------------------
% 160.10/26.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.10/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.10/26.40    (2)  op(e1, e1) = e1
% 160.10/26.40    (3)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) &
% 160.10/26.40           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1)
% 160.10/26.40           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3
% 160.10/26.40           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 160.10/26.40           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 160.10/26.40    (4)  op(e2, e2) = e0
% 160.10/26.40    (5)   ~ (e2 = e1)
% 160.10/26.40    (6)   ~ (e3 = e0)
% 160.10/26.40  
% 160.10/26.40  Begin of proof
% 160.10/26.40  | 
% 160.10/26.40  | BETA: splitting (3) gives:
% 160.10/26.40  | 
% 160.10/26.40  | Case 1:
% 160.10/26.40  | | 
% 160.10/26.40  | |   (7)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 160.10/26.40  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1,
% 160.10/26.40  | |          e1) = e2 & $i(all_57_12)
% 160.10/26.40  | | 
% 160.10/26.40  | | ALPHA: (7) implies:
% 160.18/26.40  | |   (8)  op(e1, e1) = e2
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #986.
% 160.18/26.40  | | 
% 160.18/26.40  | Case 2:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (9)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1)
% 160.18/26.40  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2,
% 160.18/26.40  | |          e2) = e3 & $i(all_57_10)
% 160.18/26.40  | | 
% 160.18/26.40  | | ALPHA: (9) implies:
% 160.18/26.40  | |   (10)  op(e2, e2) = e3
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #945.
% 160.18/26.40  | | 
% 160.18/26.40  | End of split
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #934 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)   ~ (e3 = e2)
% 160.18/26.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (3)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 160.18/26.40           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 160.18/26.40           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 160.18/26.40           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 160.18/26.40           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 160.18/26.40    (4)  op(e3, e3) = e3
% 160.18/26.40    (5)  op(e2, e2) = e0
% 160.18/26.40    (6)   ~ (e3 = e0)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | BETA: splitting (3) gives:
% 160.18/26.40  | 
% 160.18/26.40  | Case 1:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (7)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 160.18/26.40  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 160.18/26.40  | |        all_57_12 & $i(all_57_12)
% 160.18/26.40  | | 
% 160.18/26.40  | | ALPHA: (7) implies:
% 160.18/26.40  | |   (8)  op(e3, e3) = e2
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #958.
% 160.18/26.40  | | 
% 160.18/26.40  | Case 2:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (9)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2)
% 160.18/26.40  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 160.18/26.40  | |          e2) = e3 & $i(all_57_10)
% 160.18/26.40  | | 
% 160.18/26.40  | | ALPHA: (9) implies:
% 160.18/26.40  | |   (10)  op(e2, e2) = e3
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #945.
% 160.18/26.40  | | 
% 160.18/26.40  | End of split
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #935 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 160.18/26.40         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 160.18/26.40    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 160.18/26.40         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 160.18/26.40    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 160.18/26.40         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 160.18/26.40    (4)   ~ (e3 = e2)
% 160.18/26.40    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (6)  all_56_13 = e1
% 160.18/26.40    (7)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 160.18/26.40         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 160.18/26.40    (8)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 160.18/26.40         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 160.18/26.40    (9)  op(e3, e3) = e3
% 160.18/26.40    (10)  op(e2, e2) = e0
% 160.18/26.40    (11)  all_56_1 = e0
% 160.18/26.40    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 160.18/26.40          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 160.18/26.40    (13)   ~ (e1 = e0)
% 160.18/26.40    (14)   ~ (e2 = e1)
% 160.18/26.40    (15)   ~ (e3 = e1)
% 160.18/26.40    (16)   ~ (e2 = e0)
% 160.18/26.40    (17)   ~ (e3 = e0)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | BETA: splitting (8) gives:
% 160.18/26.40  | 
% 160.18/26.40  | Case 1:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (18)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 160.18/26.40  | |           e3)
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (2), (3), (4), (5), (9), (10), (12), (13), (14), (15), (16),
% 160.18/26.40  | |            (17), (18) are inconsistent by sub-proof #944.
% 160.18/26.40  | | 
% 160.18/26.40  | Case 2:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (19)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 160.18/26.40  | |           e3)
% 160.18/26.40  | | 
% 160.18/26.40  | | BETA: splitting (19) gives:
% 160.18/26.40  | | 
% 160.18/26.40  | | Case 1:
% 160.18/26.40  | | | 
% 160.18/26.40  | | |   (20)  all_56_7 = e3 & op(e1, e2) = e3
% 160.18/26.40  | | | 
% 160.18/26.40  | | | ALPHA: (20) implies:
% 160.18/26.40  | | |   (21)  all_56_7 = e3
% 160.18/26.40  | | |   (22)  op(e1, e2) = e3
% 160.18/26.40  | | | 
% 160.18/26.40  | | | REF_CLOSE: (1), (4), (5), (7), (10), (11), (13), (14), (15), (16), (21),
% 160.18/26.40  | | |            (22) are inconsistent by sub-proof #937.
% 160.18/26.40  | | | 
% 160.18/26.40  | | Case 2:
% 160.18/26.40  | | | 
% 160.18/26.40  | | |   (23)  all_56_13 = e3 & op(e0, e2) = e3
% 160.18/26.40  | | | 
% 160.18/26.40  | | | ALPHA: (23) implies:
% 160.18/26.40  | | |   (24)  all_56_13 = e3
% 160.18/26.40  | | | 
% 160.18/26.40  | | | REF_CLOSE: (6), (15), (24) are inconsistent by sub-proof #936.
% 160.18/26.40  | | | 
% 160.18/26.40  | | End of split
% 160.18/26.40  | | 
% 160.18/26.40  | End of split
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #936 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  all_56_13 = e3
% 160.18/26.40    (2)  all_56_13 = e1
% 160.18/26.40    (3)   ~ (e3 = e1)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | COMBINE_EQS: (1), (2) imply:
% 160.18/26.40  |   (4)  e3 = e1
% 160.18/26.40  | 
% 160.18/26.40  | SIMP: (4) implies:
% 160.18/26.40  |   (5)  e3 = e1
% 160.18/26.40  | 
% 160.18/26.40  | REDUCE: (3), (5) imply:
% 160.18/26.40  |   (6)  $false
% 160.18/26.40  | 
% 160.18/26.40  | CLOSE: (6) is inconsistent.
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #937 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 160.18/26.40         (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 160.18/26.40    (2)   ~ (e3 = e2)
% 160.18/26.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (4)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 160.18/26.40         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 160.18/26.40    (5)  op(e2, e2) = e0
% 160.18/26.40    (6)  all_56_1 = e0
% 160.18/26.40    (7)  op(e1, e2) = e3
% 160.18/26.40    (8)  all_56_7 = e3
% 160.18/26.40    (9)   ~ (e1 = e0)
% 160.18/26.40    (10)   ~ (e2 = e1)
% 160.18/26.40    (11)   ~ (e3 = e1)
% 160.18/26.40    (12)   ~ (e2 = e0)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | BETA: splitting (4) gives:
% 160.18/26.40  | 
% 160.18/26.40  | Case 1:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (13)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 160.18/26.40  | |           e2)
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (3), (5), (6), (12), (13) are inconsistent by sub-proof #941.
% 160.18/26.40  | | 
% 160.18/26.40  | Case 2:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (14)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 160.18/26.40  | |           e2)
% 160.18/26.40  | | 
% 160.18/26.40  | | BETA: splitting (14) gives:
% 160.18/26.40  | | 
% 160.18/26.40  | | Case 1:
% 160.18/26.40  | | | 
% 160.18/26.40  | | |   (15)  all_56_7 = e2 & op(e1, e2) = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | REF_CLOSE: (2), (8), (15) are inconsistent by sub-proof #940.
% 160.18/26.40  | | | 
% 160.18/26.40  | | Case 2:
% 160.18/26.40  | | | 
% 160.18/26.40  | | |   (16)  all_56_13 = e2 & op(e0, e2) = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | ALPHA: (16) implies:
% 160.18/26.40  | | |   (17)  all_56_13 = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | BETA: splitting (1) gives:
% 160.18/26.40  | | | 
% 160.18/26.40  | | | Case 1:
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | |   (18)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2)
% 160.18/26.40  | | | |           = e1)
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | | REF_CLOSE: (3), (5), (6), (9), (18) are inconsistent by sub-proof #959.
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | Case 2:
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | |   (19)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2)
% 160.18/26.40  | | | |           = e1)
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | | BETA: splitting (19) gives:
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | | Case 1:
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | |   (20)  all_56_7 = e1 & op(e1, e2) = e1
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | | ALPHA: (20) implies:
% 160.18/26.40  | | | | |   (21)  op(e1, e2) = e1
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | | REF_CLOSE: (3), (7), (11), (21) are inconsistent by sub-proof #939.
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | Case 2:
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | |   (22)  all_56_13 = e1 & op(e0, e2) = e1
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | | REF_CLOSE: (10), (17), (22) are inconsistent by sub-proof #938.
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | End of split
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | End of split
% 160.18/26.40  | | | 
% 160.18/26.40  | | End of split
% 160.18/26.40  | | 
% 160.18/26.40  | End of split
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #938 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  all_56_13 = e1 & op(e0, e2) = e1
% 160.18/26.40    (2)  all_56_13 = e2
% 160.18/26.40    (3)   ~ (e2 = e1)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | ALPHA: (1) implies:
% 160.18/26.40  |   (4)  all_56_13 = e1
% 160.18/26.40  | 
% 160.18/26.40  | COMBINE_EQS: (2), (4) imply:
% 160.18/26.40  |   (5)  e2 = e1
% 160.18/26.40  | 
% 160.18/26.40  | REDUCE: (3), (5) imply:
% 160.18/26.40  |   (6)  $false
% 160.18/26.40  | 
% 160.18/26.40  | CLOSE: (6) is inconsistent.
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #939 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (2)  op(e1, e2) = e3
% 160.18/26.40    (3)  op(e1, e2) = e1
% 160.18/26.40    (4)   ~ (e3 = e1)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | GROUND_INST: instantiating (1) with e3, e1, e2, e1, simplifying with (2), (3)
% 160.18/26.40  |              gives:
% 160.18/26.40  |   (5)  e3 = e1
% 160.18/26.40  | 
% 160.18/26.40  | REDUCE: (4), (5) imply:
% 160.18/26.40  |   (6)  $false
% 160.18/26.40  | 
% 160.18/26.40  | CLOSE: (6) is inconsistent.
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #940 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  all_56_7 = e2 & op(e1, e2) = e2
% 160.18/26.40    (2)  all_56_7 = e3
% 160.18/26.40    (3)   ~ (e3 = e2)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | ALPHA: (1) implies:
% 160.18/26.40  |   (4)  all_56_7 = e2
% 160.18/26.40  | 
% 160.18/26.40  | COMBINE_EQS: (2), (4) imply:
% 160.18/26.40  |   (5)  e3 = e2
% 160.18/26.40  | 
% 160.18/26.40  | REDUCE: (3), (5) imply:
% 160.18/26.40  |   (6)  $false
% 160.18/26.40  | 
% 160.18/26.40  | CLOSE: (6) is inconsistent.
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #941 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 160.18/26.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (3)  op(e2, e2) = e0
% 160.18/26.40    (4)  all_56_1 = e0
% 160.18/26.40    (5)   ~ (e2 = e0)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | BETA: splitting (1) gives:
% 160.18/26.40  | 
% 160.18/26.40  | Case 1:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (6)  all_56_1 = e2 & op(e3, e2) = e2
% 160.18/26.40  | | 
% 160.18/26.40  | | ALPHA: (6) implies:
% 160.18/26.40  | |   (7)  all_56_1 = e2
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #943.
% 160.18/26.40  | | 
% 160.18/26.40  | Case 2:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (8)  all_56_3 = e2 & op(e2, e2) = e2
% 160.18/26.40  | | 
% 160.18/26.40  | | ALPHA: (8) implies:
% 160.18/26.40  | |   (9)  op(e2, e2) = e2
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #942.
% 160.18/26.40  | | 
% 160.18/26.40  | End of split
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #942 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (2)  op(e2, e2) = e2
% 160.18/26.40    (3)  op(e2, e2) = e0
% 160.18/26.40    (4)   ~ (e2 = e0)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | GROUND_INST: instantiating (1) with e0, e2, e2, e2, simplifying with (2), (3)
% 160.18/26.40  |              gives:
% 160.18/26.40  |   (5)  e2 = e0
% 160.18/26.40  | 
% 160.18/26.40  | REDUCE: (4), (5) imply:
% 160.18/26.40  |   (6)  $false
% 160.18/26.40  | 
% 160.18/26.40  | CLOSE: (6) is inconsistent.
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #943 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  all_56_1 = e2
% 160.18/26.40    (2)  all_56_1 = e0
% 160.18/26.40    (3)   ~ (e2 = e0)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | COMBINE_EQS: (1), (2) imply:
% 160.18/26.40  |   (4)  e2 = e0
% 160.18/26.40  | 
% 160.18/26.40  | SIMP: (4) implies:
% 160.18/26.40  |   (5)  e2 = e0
% 160.18/26.40  | 
% 160.18/26.40  | REDUCE: (3), (5) imply:
% 160.18/26.40  |   (6)  $false
% 160.18/26.40  | 
% 160.18/26.40  | CLOSE: (6) is inconsistent.
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #944 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 160.18/26.40         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 160.18/26.40    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 160.18/26.40         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 160.18/26.40    (3)   ~ (e3 = e2)
% 160.18/26.40    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (5)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 160.18/26.40    (6)  op(e3, e3) = e3
% 160.18/26.40    (7)  op(e2, e2) = e0
% 160.18/26.40    (8)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 160.18/26.40         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 160.18/26.40    (9)   ~ (e1 = e0)
% 160.18/26.40    (10)   ~ (e2 = e1)
% 160.18/26.40    (11)   ~ (e3 = e1)
% 160.18/26.40    (12)   ~ (e2 = e0)
% 160.18/26.40    (13)   ~ (e3 = e0)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | BETA: splitting (5) gives:
% 160.18/26.40  | 
% 160.18/26.40  | Case 1:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (14)  all_56_1 = e3 & op(e3, e2) = e3
% 160.18/26.40  | | 
% 160.18/26.40  | | ALPHA: (14) implies:
% 160.18/26.40  | |   (15)  all_56_1 = e3
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (15)
% 160.18/26.40  | |            are inconsistent by sub-proof #946.
% 160.18/26.40  | | 
% 160.18/26.40  | Case 2:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (16)  all_56_3 = e3 & op(e2, e2) = e3
% 160.18/26.40  | | 
% 160.18/26.40  | | ALPHA: (16) implies:
% 160.18/26.40  | |   (17)  op(e2, e2) = e3
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (4), (7), (13), (17) are inconsistent by sub-proof #945.
% 160.18/26.40  | | 
% 160.18/26.40  | End of split
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #945 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (2)  op(e2, e2) = e3
% 160.18/26.40    (3)  op(e2, e2) = e0
% 160.18/26.40    (4)   ~ (e3 = e0)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | GROUND_INST: instantiating (1) with e0, e3, e2, e2, simplifying with (2), (3)
% 160.18/26.40  |              gives:
% 160.18/26.40  |   (5)  e3 = e0
% 160.18/26.40  | 
% 160.18/26.40  | REDUCE: (4), (5) imply:
% 160.18/26.40  |   (6)  $false
% 160.18/26.40  | 
% 160.18/26.40  | CLOSE: (6) is inconsistent.
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #946 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 160.18/26.40         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 160.18/26.40    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 160.18/26.40         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 160.18/26.40    (3)   ~ (e3 = e2)
% 160.18/26.40    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (5)  op(e3, e3) = e3
% 160.18/26.40    (6)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 160.18/26.40         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 160.18/26.40    (7)   ~ (e1 = e0)
% 160.18/26.40    (8)   ~ (e2 = e1)
% 160.18/26.40    (9)   ~ (e3 = e1)
% 160.18/26.40    (10)   ~ (e2 = e0)
% 160.18/26.40    (11)   ~ (e3 = e0)
% 160.18/26.40    (12)  all_56_1 = e3
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | BETA: splitting (1) gives:
% 160.18/26.40  | 
% 160.18/26.40  | Case 1:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (13)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) =
% 160.18/26.40  | |           e2)
% 160.18/26.40  | | 
% 160.18/26.40  | | BETA: splitting (13) gives:
% 160.18/26.40  | | 
% 160.18/26.40  | | Case 1:
% 160.18/26.40  | | | 
% 160.18/26.40  | | |   (14)  all_56_0 = e2 & op(e3, e3) = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | ALPHA: (14) implies:
% 160.18/26.40  | | |   (15)  op(e3, e3) = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | REF_CLOSE: (3), (4), (5), (15) are inconsistent by sub-proof #958.
% 160.18/26.40  | | | 
% 160.18/26.40  | | Case 2:
% 160.18/26.40  | | | 
% 160.18/26.40  | | |   (16)  all_56_1 = e2 & op(e3, e2) = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | ALPHA: (16) implies:
% 160.18/26.40  | | |   (17)  all_56_1 = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | COMBINE_EQS: (12), (17) imply:
% 160.18/26.40  | | |   (18)  e3 = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | REDUCE: (3), (18) imply:
% 160.18/26.40  | | |   (19)  $false
% 160.18/26.40  | | | 
% 160.18/26.40  | | | CLOSE: (19) is inconsistent.
% 160.18/26.40  | | | 
% 160.18/26.40  | | End of split
% 160.18/26.40  | | 
% 160.18/26.40  | Case 2:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (20)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 160.18/26.40  | |           e2)
% 160.18/26.40  | | 
% 160.18/26.40  | | BETA: splitting (20) gives:
% 160.18/26.40  | | 
% 160.18/26.40  | | Case 1:
% 160.18/26.40  | | | 
% 160.18/26.40  | | |   (21)  all_56_4 = e2 & op(e3, e1) = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | ALPHA: (21) implies:
% 160.18/26.40  | | |   (22)  all_56_4 = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | BETA: splitting (6) gives:
% 160.18/26.40  | | | 
% 160.18/26.40  | | | Case 1:
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | |   (23)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2)
% 160.18/26.40  | | | |           = e1)
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | | REF_CLOSE: (4), (5), (9), (12), (23) are inconsistent by sub-proof #957.
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | Case 2:
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | |   (24)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0)
% 160.18/26.40  | | | |           = e1)
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | | BETA: splitting (24) gives:
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | | Case 1:
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | |   (25)  all_56_4 = e1 & op(e3, e1) = e1
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | | REF_CLOSE: (8), (22), (25) are inconsistent by sub-proof #956.
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | Case 2:
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | |   (26)  all_56_9 = e1 & op(e3, e0) = e1
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | | ALPHA: (26) implies:
% 160.18/26.40  | | | | |   (27)  all_56_9 = e1
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | | BETA: splitting (2) gives:
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | | Case 1:
% 160.18/26.40  | | | | | | 
% 160.18/26.40  | | | | | |   (28)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3,
% 160.18/26.40  | | | | | |             e2) = e0)
% 160.18/26.40  | | | | | | 
% 160.18/26.40  | | | | | | REF_CLOSE: (4), (5), (11), (12), (28) are inconsistent by sub-proof
% 160.18/26.40  | | | | | |            #954.
% 160.18/26.40  | | | | | | 
% 160.18/26.40  | | | | | Case 2:
% 160.18/26.40  | | | | | | 
% 160.18/26.40  | | | | | |   (29)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3,
% 160.18/26.40  | | | | | |             e0) = e0)
% 160.18/26.40  | | | | | | 
% 160.18/26.40  | | | | | | BETA: splitting (29) gives:
% 160.18/26.40  | | | | | | 
% 160.18/26.40  | | | | | | Case 1:
% 160.18/26.40  | | | | | | | 
% 160.18/26.40  | | | | | | |   (30)  all_56_4 = e0 & op(e3, e1) = e0
% 160.18/26.40  | | | | | | | 
% 160.18/26.40  | | | | | | | REF_CLOSE: (10), (22), (30) are inconsistent by sub-proof #953.
% 160.18/26.40  | | | | | | | 
% 160.18/26.40  | | | | | | Case 2:
% 160.18/26.40  | | | | | | | 
% 160.18/26.40  | | | | | | |   (31)  all_56_9 = e0 & op(e3, e0) = e0
% 160.18/26.40  | | | | | | | 
% 160.18/26.40  | | | | | | | REF_CLOSE: (7), (27), (31) are inconsistent by sub-proof #952.
% 160.18/26.40  | | | | | | | 
% 160.18/26.40  | | | | | | End of split
% 160.18/26.40  | | | | | | 
% 160.18/26.40  | | | | | End of split
% 160.18/26.40  | | | | | 
% 160.18/26.40  | | | | End of split
% 160.18/26.40  | | | | 
% 160.18/26.40  | | | End of split
% 160.18/26.40  | | | 
% 160.18/26.40  | | Case 2:
% 160.18/26.40  | | | 
% 160.18/26.40  | | |   (32)  all_56_9 = e2 & op(e3, e0) = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | ALPHA: (32) implies:
% 160.18/26.40  | | |   (33)  all_56_9 = e2
% 160.18/26.40  | | | 
% 160.18/26.40  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (33) are
% 160.18/26.40  | | |            inconsistent by sub-proof #947.
% 160.18/26.40  | | | 
% 160.18/26.40  | | End of split
% 160.18/26.40  | | 
% 160.18/26.40  | End of split
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #947 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  all_56_9 = e2
% 160.18/26.40    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 160.18/26.40         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 160.18/26.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (4)  op(e3, e3) = e3
% 160.18/26.40    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 160.18/26.40         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 160.18/26.40    (6)   ~ (e1 = e0)
% 160.18/26.40    (7)   ~ (e2 = e1)
% 160.18/26.40    (8)   ~ (e3 = e1)
% 160.18/26.40    (9)   ~ (e2 = e0)
% 160.18/26.40    (10)   ~ (e3 = e0)
% 160.18/26.40    (11)  all_56_1 = e3
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | BETA: splitting (5) gives:
% 160.18/26.40  | 
% 160.18/26.40  | Case 1:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 160.18/26.40  | |           e1)
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (3), (4), (8), (11), (12) are inconsistent by sub-proof #957.
% 160.18/26.40  | | 
% 160.18/26.40  | Case 2:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (13)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 160.18/26.40  | |           e1)
% 160.18/26.40  | | 
% 160.18/26.40  | | BETA: splitting (13) gives:
% 160.18/26.40  | | 
% 160.18/26.40  | | Case 1:
% 160.18/26.40  | | | 
% 160.18/26.40  | | |   (14)  all_56_4 = e1 & op(e3, e1) = e1
% 160.18/26.40  | | | 
% 160.18/26.40  | | | ALPHA: (14) implies:
% 160.18/26.40  | | |   (15)  all_56_4 = e1
% 160.18/26.40  | | | 
% 160.18/26.40  | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (15) are inconsistent
% 160.18/26.40  | | |            by sub-proof #949.
% 160.18/26.40  | | | 
% 160.18/26.40  | | Case 2:
% 160.18/26.40  | | | 
% 160.18/26.40  | | |   (16)  all_56_9 = e1 & op(e3, e0) = e1
% 160.18/26.40  | | | 
% 160.18/26.40  | | | REF_CLOSE: (1), (7), (16) are inconsistent by sub-proof #948.
% 160.18/26.40  | | | 
% 160.18/26.40  | | End of split
% 160.18/26.40  | | 
% 160.18/26.40  | End of split
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #948 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  all_56_9 = e1 & op(e3, e0) = e1
% 160.18/26.40    (2)  all_56_9 = e2
% 160.18/26.40    (3)   ~ (e2 = e1)
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | ALPHA: (1) implies:
% 160.18/26.40  |   (4)  all_56_9 = e1
% 160.18/26.40  | 
% 160.18/26.40  | COMBINE_EQS: (2), (4) imply:
% 160.18/26.40  |   (5)  e2 = e1
% 160.18/26.40  | 
% 160.18/26.40  | REDUCE: (3), (5) imply:
% 160.18/26.40  |   (6)  $false
% 160.18/26.40  | 
% 160.18/26.40  | CLOSE: (6) is inconsistent.
% 160.18/26.40  | 
% 160.18/26.40  End of proof
% 160.18/26.40  
% 160.18/26.40  Sub-proof #949 shows that the following formulas are inconsistent:
% 160.18/26.40  ----------------------------------------------------------------
% 160.18/26.40    (1)  all_56_9 = e2
% 160.18/26.40    (2)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 160.18/26.40         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 160.18/26.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.40    (4)  op(e3, e3) = e3
% 160.18/26.40    (5)   ~ (e1 = e0)
% 160.18/26.40    (6)  all_56_4 = e1
% 160.18/26.40    (7)   ~ (e2 = e0)
% 160.18/26.40    (8)   ~ (e3 = e0)
% 160.18/26.40    (9)  all_56_1 = e3
% 160.18/26.40  
% 160.18/26.40  Begin of proof
% 160.18/26.40  | 
% 160.18/26.40  | BETA: splitting (2) gives:
% 160.18/26.40  | 
% 160.18/26.40  | Case 1:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 160.18/26.40  | |           e0)
% 160.18/26.40  | | 
% 160.18/26.40  | | REF_CLOSE: (3), (4), (8), (9), (10) are inconsistent by sub-proof #954.
% 160.18/26.40  | | 
% 160.18/26.40  | Case 2:
% 160.18/26.40  | | 
% 160.18/26.40  | |   (11)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 160.18/26.40  | |           e0)
% 160.18/26.40  | | 
% 160.18/26.40  | | BETA: splitting (11) gives:
% 160.18/26.40  | | 
% 160.18/26.41  | | Case 1:
% 160.18/26.41  | | | 
% 160.18/26.41  | | |   (12)  all_56_4 = e0 & op(e3, e1) = e0
% 160.18/26.41  | | | 
% 160.18/26.41  | | | REF_CLOSE: (5), (6), (12) are inconsistent by sub-proof #951.
% 160.18/26.41  | | | 
% 160.18/26.41  | | Case 2:
% 160.18/26.41  | | | 
% 160.18/26.41  | | |   (13)  all_56_9 = e0 & op(e3, e0) = e0
% 160.18/26.41  | | | 
% 160.18/26.41  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #950.
% 160.18/26.41  | | | 
% 160.18/26.41  | | End of split
% 160.18/26.41  | | 
% 160.18/26.41  | End of split
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #950 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)  all_56_9 = e0 & op(e3, e0) = e0
% 160.18/26.41    (2)  all_56_9 = e2
% 160.18/26.41    (3)   ~ (e2 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | ALPHA: (1) implies:
% 160.18/26.41  |   (4)  all_56_9 = e0
% 160.18/26.41  | 
% 160.18/26.41  | COMBINE_EQS: (2), (4) imply:
% 160.18/26.41  |   (5)  e2 = e0
% 160.18/26.41  | 
% 160.18/26.41  | REDUCE: (3), (5) imply:
% 160.18/26.41  |   (6)  $false
% 160.18/26.41  | 
% 160.18/26.41  | CLOSE: (6) is inconsistent.
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #951 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)  all_56_4 = e0 & op(e3, e1) = e0
% 160.18/26.41    (2)  all_56_4 = e1
% 160.18/26.41    (3)   ~ (e1 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | ALPHA: (1) implies:
% 160.18/26.41  |   (4)  all_56_4 = e0
% 160.18/26.41  | 
% 160.18/26.41  | COMBINE_EQS: (2), (4) imply:
% 160.18/26.41  |   (5)  e1 = e0
% 160.18/26.41  | 
% 160.18/26.41  | REDUCE: (3), (5) imply:
% 160.18/26.41  |   (6)  $false
% 160.18/26.41  | 
% 160.18/26.41  | CLOSE: (6) is inconsistent.
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #952 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)  all_56_9 = e0 & op(e3, e0) = e0
% 160.18/26.41    (2)  all_56_9 = e1
% 160.18/26.41    (3)   ~ (e1 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | ALPHA: (1) implies:
% 160.18/26.41  |   (4)  all_56_9 = e0
% 160.18/26.41  | 
% 160.18/26.41  | COMBINE_EQS: (2), (4) imply:
% 160.18/26.41  |   (5)  e1 = e0
% 160.18/26.41  | 
% 160.18/26.41  | REDUCE: (3), (5) imply:
% 160.18/26.41  |   (6)  $false
% 160.18/26.41  | 
% 160.18/26.41  | CLOSE: (6) is inconsistent.
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #953 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)  all_56_4 = e0 & op(e3, e1) = e0
% 160.18/26.41    (2)  all_56_4 = e2
% 160.18/26.41    (3)   ~ (e2 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | ALPHA: (1) implies:
% 160.18/26.41  |   (4)  all_56_4 = e0
% 160.18/26.41  | 
% 160.18/26.41  | COMBINE_EQS: (2), (4) imply:
% 160.18/26.41  |   (5)  e2 = e0
% 160.18/26.41  | 
% 160.18/26.41  | REDUCE: (3), (5) imply:
% 160.18/26.41  |   (6)  $false
% 160.18/26.41  | 
% 160.18/26.41  | CLOSE: (6) is inconsistent.
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #954 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (2)  op(e3, e3) = e3
% 160.18/26.41    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 160.18/26.41    (4)   ~ (e3 = e0)
% 160.18/26.41    (5)  all_56_1 = e3
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | BETA: splitting (3) gives:
% 160.18/26.41  | 
% 160.18/26.41  | Case 1:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (6)  all_56_0 = e0 & op(e3, e3) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | ALPHA: (6) implies:
% 160.18/26.41  | |   (7)  op(e3, e3) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #971.
% 160.18/26.41  | | 
% 160.18/26.41  | Case 2:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (8)  all_56_1 = e0 & op(e3, e2) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #955.
% 160.18/26.41  | | 
% 160.18/26.41  | End of split
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #955 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)  all_56_1 = e0 & op(e3, e2) = e0
% 160.18/26.41    (2)  all_56_1 = e3
% 160.18/26.41    (3)   ~ (e3 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | ALPHA: (1) implies:
% 160.18/26.41  |   (4)  all_56_1 = e0
% 160.18/26.41  | 
% 160.18/26.41  | COMBINE_EQS: (2), (4) imply:
% 160.18/26.41  |   (5)  e3 = e0
% 160.18/26.41  | 
% 160.18/26.41  | REDUCE: (3), (5) imply:
% 160.18/26.41  |   (6)  $false
% 160.18/26.41  | 
% 160.18/26.41  | CLOSE: (6) is inconsistent.
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #956 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)  all_56_4 = e1 & op(e3, e1) = e1
% 160.18/26.41    (2)  all_56_4 = e2
% 160.18/26.41    (3)   ~ (e2 = e1)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | ALPHA: (1) implies:
% 160.18/26.41  |   (4)  all_56_4 = e1
% 160.18/26.41  | 
% 160.18/26.41  | COMBINE_EQS: (2), (4) imply:
% 160.18/26.41  |   (5)  e2 = e1
% 160.18/26.41  | 
% 160.18/26.41  | REDUCE: (3), (5) imply:
% 160.18/26.41  |   (6)  $false
% 160.18/26.41  | 
% 160.18/26.41  | CLOSE: (6) is inconsistent.
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #957 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1)
% 160.18/26.41    (3)  op(e3, e3) = e3
% 160.18/26.41    (4)   ~ (e3 = e1)
% 160.18/26.41    (5)  all_56_1 = e3
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | BETA: splitting (2) gives:
% 160.18/26.41  | 
% 160.18/26.41  | Case 1:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (6)  all_56_0 = e1 & op(e3, e3) = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | ALPHA: (6) implies:
% 160.18/26.41  | |   (7)  op(e3, e3) = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #995.
% 160.18/26.41  | | 
% 160.18/26.41  | Case 2:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (8)  all_56_1 = e1 & op(e3, e2) = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | ALPHA: (8) implies:
% 160.18/26.41  | |   (9)  all_56_1 = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | COMBINE_EQS: (5), (9) imply:
% 160.18/26.41  | |   (10)  e3 = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | REDUCE: (4), (10) imply:
% 160.18/26.41  | |   (11)  $false
% 160.18/26.41  | | 
% 160.18/26.41  | | CLOSE: (11) is inconsistent.
% 160.18/26.41  | | 
% 160.18/26.41  | End of split
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #958 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (2)  op(e3, e3) = e3
% 160.18/26.41    (3)  op(e3, e3) = e2
% 160.18/26.41    (4)   ~ (e3 = e2)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | GROUND_INST: instantiating (1) with e2, e3, e3, e3, simplifying with (2), (3)
% 160.18/26.41  |              gives:
% 160.18/26.41  |   (5)  e3 = e2
% 160.18/26.41  | 
% 160.18/26.41  | REDUCE: (4), (5) imply:
% 160.18/26.41  |   (6)  $false
% 160.18/26.41  | 
% 160.18/26.41  | CLOSE: (6) is inconsistent.
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #959 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (2)  op(e2, e2) = e0
% 160.18/26.41    (3)  all_56_1 = e0
% 160.18/26.41    (4)   ~ (e1 = e0)
% 160.18/26.41    (5)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | BETA: splitting (5) gives:
% 160.18/26.41  | 
% 160.18/26.41  | Case 1:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (6)  all_56_1 = e1 & op(e3, e2) = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | ALPHA: (6) implies:
% 160.18/26.41  | |   (7)  all_56_1 = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #961.
% 160.18/26.41  | | 
% 160.18/26.41  | Case 2:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (8)  all_56_3 = e1 & op(e2, e2) = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | ALPHA: (8) implies:
% 160.18/26.41  | |   (9)  op(e2, e2) = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #960.
% 160.18/26.41  | | 
% 160.18/26.41  | End of split
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #960 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (2)  op(e2, e2) = e1
% 160.18/26.41    (3)  op(e2, e2) = e0
% 160.18/26.41    (4)   ~ (e1 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | GROUND_INST: instantiating (1) with e0, e1, e2, e2, simplifying with (2), (3)
% 160.18/26.41  |              gives:
% 160.18/26.41  |   (5)  e1 = e0
% 160.18/26.41  | 
% 160.18/26.41  | REDUCE: (4), (5) imply:
% 160.18/26.41  |   (6)  $false
% 160.18/26.41  | 
% 160.18/26.41  | CLOSE: (6) is inconsistent.
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #961 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)  all_56_1 = e1
% 160.18/26.41    (2)  all_56_1 = e0
% 160.18/26.41    (3)   ~ (e1 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | COMBINE_EQS: (1), (2) imply:
% 160.18/26.41  |   (4)  e1 = e0
% 160.18/26.41  | 
% 160.18/26.41  | SIMP: (4) implies:
% 160.18/26.41  |   (5)  e1 = e0
% 160.18/26.41  | 
% 160.18/26.41  | REDUCE: (3), (5) imply:
% 160.18/26.41  |   (6)  $false
% 160.18/26.41  | 
% 160.18/26.41  | CLOSE: (6) is inconsistent.
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #962 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)  all_54_5 = e1 | all_54_5 = e0
% 160.18/26.41    (2)  all_54_5 = all_4_2
% 160.18/26.41    (3)   ~ (all_4_2 = e1)
% 160.18/26.41    (4)   ~ (all_4_2 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | BETA: splitting (1) gives:
% 160.18/26.41  | 
% 160.18/26.41  | Case 1:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (5)  all_54_5 = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | COMBINE_EQS: (2), (5) imply:
% 160.18/26.41  | |   (6)  all_4_2 = e1
% 160.18/26.41  | | 
% 160.18/26.41  | | REDUCE: (3), (6) imply:
% 160.18/26.41  | |   (7)  $false
% 160.18/26.41  | | 
% 160.18/26.41  | | CLOSE: (7) is inconsistent.
% 160.18/26.41  | | 
% 160.18/26.41  | Case 2:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (8)  all_54_5 = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | COMBINE_EQS: (2), (8) imply:
% 160.18/26.41  | |   (9)  all_4_2 = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | REDUCE: (4), (9) imply:
% 160.18/26.41  | |   (10)  $false
% 160.18/26.41  | | 
% 160.18/26.41  | | CLOSE: (10) is inconsistent.
% 160.18/26.41  | | 
% 160.18/26.41  | End of split
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #963 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)   ~ (all_52_7 = e0)
% 160.18/26.41    (2)  op(e0, e1) = all_52_11
% 160.18/26.41    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (4)  op(e0, e3) = all_52_3
% 160.18/26.41    (5)  op(e2, e2) = e2
% 160.18/26.41    (6)   ~ (all_52_3 = e0)
% 160.18/26.41    (7)  op(e0, e2) = all_52_7
% 160.18/26.41    (8)   ~ (all_52_13 = all_4_2)
% 160.18/26.41    (9)  op(e2, e2) = all_4_2
% 160.18/26.41    (10)  op(e3, e3) = e3
% 160.18/26.41    (11)  op(e2, e0) = all_52_13
% 160.18/26.41    (12)   ~ (all_52_11 = e0)
% 160.18/26.41    (13)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e3) &
% 160.18/26.41            op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) | (all_57_6 = e0
% 160.18/26.41            & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e3) & op(e2, e2) =
% 160.18/26.41            e0 & op(e2, e0) = e2 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_13 =
% 160.18/26.41            e1 & all_57_14 = e0 &  ~ (all_57_15 = e3) & op(e1, e1) = e0 & op(e1,
% 160.18/26.41              e0) = e1 & op(e0, e3) = e0) | (all_57_6 = e0 & all_57_15 = e0 &  ~
% 160.18/26.41            (e3 = e0) & op(e0, e3) = e0) | (all_57_7 = e0 & all_57_9 = e3 &
% 160.18/26.41            all_57_10 = e0 &  ~ (all_57_15 = e2) & op(e3, e3) = e0 & op(e3, e0) =
% 160.18/26.41            e3 & op(e0, e2) = e0) | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 =
% 160.18/26.41            e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 160.18/26.41              e2) = e0) | (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.18/26.41            (all_57_15 = e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) =
% 160.18/26.41            e0) | (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) =
% 160.18/26.41            e0) | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.18/26.41              = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 160.18/26.41          (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 160.18/26.41            op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0
% 160.18/26.41            & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) =
% 160.18/26.41            e0 & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 =
% 160.18/26.41            e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 160.18/26.41            op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 160.18/26.41            all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 160.18/26.41    (14)   ~ (e3 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | BETA: splitting (13) gives:
% 160.18/26.41  | 
% 160.18/26.41  | Case 1:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (15)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 160.18/26.41  | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.18/26.41  | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0) |
% 160.18/26.41  | |         (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0) |
% 160.18/26.41  | |         (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |             e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 160.18/26.41  | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.18/26.41  | | 
% 160.18/26.41  | | BETA: splitting (15) gives:
% 160.18/26.41  | | 
% 160.18/26.41  | | Case 1:
% 160.18/26.41  | | | 
% 160.18/26.41  | | |   (16)  (all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | | |             e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0) |
% 160.18/26.41  | | |         (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | | |             e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0) |
% 160.18/26.41  | | |         (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | | |             e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = e0)
% 160.18/26.41  | | | 
% 160.18/26.41  | | | BETA: splitting (16) gives:
% 160.18/26.41  | | | 
% 160.18/26.41  | | | Case 1:
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | |   (17)  all_57_6 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | | | |           e3) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = e0
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | | ALPHA: (17) implies:
% 160.18/26.41  | | | |   (18)  op(e0, e3) = e0
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | | REF_CLOSE: (3), (4), (6), (18) are inconsistent by sub-proof #973.
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | Case 2:
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | |   (19)  (all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15
% 160.18/26.41  | | | |             = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = e0)
% 160.18/26.41  | | | |         | (all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.18/26.41  | | | |           (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 160.18/26.41  | | | |             e3) = e0)
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | | BETA: splitting (19) gives:
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | | Case 1:
% 160.18/26.41  | | | | | 
% 160.18/26.41  | | | | |   (20)  all_57_6 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 160.18/26.41  | | | | |         (all_57_15 = e3) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 160.18/26.41  | | | | |           e3) = e0
% 160.18/26.41  | | | | | 
% 160.18/26.41  | | | | | ALPHA: (20) implies:
% 160.18/26.41  | | | | |   (21)  op(e2, e0) = e2
% 160.18/26.41  | | | | | 
% 160.18/26.41  | | | | | REF_CLOSE: (3), (5), (8), (9), (11), (21) are inconsistent by
% 160.18/26.41  | | | | |            sub-proof #972.
% 160.18/26.41  | | | | | 
% 160.18/26.41  | | | | Case 2:
% 160.18/26.41  | | | | | 
% 160.18/26.41  | | | | |   (22)  all_57_6 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~
% 160.18/26.41  | | | | |         (all_57_15 = e3) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 160.18/26.41  | | | | |           e3) = e0
% 160.18/26.41  | | | | | 
% 160.18/26.41  | | | | | ALPHA: (22) implies:
% 160.18/26.41  | | | | |   (23)  op(e0, e3) = e0
% 160.18/26.41  | | | | | 
% 160.18/26.41  | | | | | REF_CLOSE: (3), (4), (6), (23) are inconsistent by sub-proof #973.
% 160.18/26.41  | | | | | 
% 160.18/26.41  | | | | End of split
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | End of split
% 160.18/26.41  | | | 
% 160.18/26.41  | | Case 2:
% 160.18/26.41  | | | 
% 160.18/26.41  | | |   (24)  (all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0)
% 160.18/26.41  | | |         | (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.18/26.41  | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) |
% 160.18/26.41  | | |         (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | | |             e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.18/26.41  | | | 
% 160.18/26.41  | | | BETA: splitting (24) gives:
% 160.18/26.41  | | | 
% 160.18/26.41  | | | Case 1:
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | |   (25)  all_57_6 = e0 & all_57_15 = e0 &  ~ (e3 = e0) & op(e0, e3) = e0
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | | ALPHA: (25) implies:
% 160.18/26.41  | | | |   (26)  op(e0, e3) = e0
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | | REF_CLOSE: (3), (4), (6), (26) are inconsistent by sub-proof #973.
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | Case 2:
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | |   (27)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.18/26.41  | | | |             = e2) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0)
% 160.18/26.41  | | | |         | (all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~
% 160.18/26.41  | | | |           (all_57_15 = e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0,
% 160.18/26.41  | | | |             e2) = e0)
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | | REF_CLOSE: (3), (5), (8), (9), (10), (11), (14), (27) are inconsistent
% 160.18/26.41  | | | |            by sub-proof #970.
% 160.18/26.41  | | | | 
% 160.18/26.41  | | | End of split
% 160.18/26.41  | | | 
% 160.18/26.41  | | End of split
% 160.18/26.41  | | 
% 160.18/26.41  | Case 2:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (28)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 160.18/26.41  | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 160.18/26.41  | |         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |             e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0) |
% 160.18/26.41  | |         (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 160.18/26.41  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 160.18/26.41  | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 160.18/26.41  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 160.18/26.41  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 160.18/26.41  | |           & op(e0, e1) = e0)
% 160.18/26.41  | | 
% 160.18/26.41  | | BETA: splitting (28) gives:
% 160.18/26.41  | | 
% 160.18/26.41  | | Case 1:
% 160.18/26.41  | | | 
% 160.18/26.41  | | |   (29)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | | |             e2) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) |
% 160.18/26.41  | | |         (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0)
% 160.18/26.41  | | |         | (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15
% 160.18/26.41  | | |             = e1) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 160.18/26.41  | | | 
% 160.18/26.41  | | | REF_CLOSE: (1), (3), (7), (10), (14), (29) are inconsistent by sub-proof
% 160.18/26.41  | | |            #967.
% 160.18/26.41  | | | 
% 160.18/26.41  | | Case 2:
% 160.18/26.41  | | | 
% 160.18/26.41  | | |   (30)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | | |             e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 160.18/26.41  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | | |             e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0) |
% 160.18/26.41  | | |         (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 160.18/26.41  | | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) =
% 160.18/26.41  | | |           e0 & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 =
% 160.18/26.41  | | |             e0) & op(e0, e1) = e0)
% 160.18/26.41  | | | 
% 160.18/26.41  | | | REF_CLOSE: (2), (3), (5), (8), (9), (11), (12), (30) are inconsistent by
% 160.18/26.41  | | |            sub-proof #964.
% 160.18/26.41  | | | 
% 160.18/26.41  | | End of split
% 160.18/26.41  | | 
% 160.18/26.41  | End of split
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #964 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)  op(e0, e1) = all_52_11
% 160.18/26.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (3)  op(e2, e2) = e2
% 160.18/26.41    (4)   ~ (all_52_13 = all_4_2)
% 160.18/26.41    (5)  op(e2, e2) = all_4_2
% 160.18/26.41    (6)  op(e2, e0) = all_52_13
% 160.18/26.41    (7)   ~ (all_52_11 = e0)
% 160.18/26.41    (8)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e1) &
% 160.18/26.41           op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) | (all_57_8 = e0 &
% 160.18/26.41           all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e1) & op(e1, e1) = e0
% 160.18/26.41           & op(e1, e0) = e1 & op(e0, e1) = e0) | (all_57_8 = e0 & all_57_13 = e1
% 160.18/26.41           & all_57_15 = e1 &  ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 160.18/26.41           op(e1, e0) = e1 & op(e0, e1) = e0 & $i(all_57_14)) | (all_57_8 = e0 &
% 160.18/26.41           all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | BETA: splitting (8) gives:
% 160.18/26.41  | 
% 160.18/26.41  | Case 1:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (9)  (all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |            e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0) |
% 160.18/26.41  | |        (all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | |            e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0)
% 160.18/26.41  | | 
% 160.18/26.41  | | BETA: splitting (9) gives:
% 160.18/26.41  | | 
% 160.18/26.41  | | Case 1:
% 160.18/26.41  | | | 
% 160.18/26.41  | | |   (10)  all_57_8 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | | |           e1) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e1) = e0
% 160.18/26.41  | | | 
% 160.18/26.41  | | | ALPHA: (10) implies:
% 160.18/26.41  | | |   (11)  op(e2, e0) = e2
% 160.18/26.41  | | | 
% 160.18/26.41  | | | REF_CLOSE: (2), (3), (4), (5), (6), (11) are inconsistent by sub-proof
% 160.18/26.41  | | |            #972.
% 160.18/26.41  | | | 
% 160.18/26.41  | | Case 2:
% 160.18/26.41  | | | 
% 160.18/26.41  | | |   (12)  all_57_8 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 =
% 160.18/26.41  | | |           e1) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e1) = e0
% 160.18/26.41  | | | 
% 160.18/26.41  | | | ALPHA: (12) implies:
% 160.18/26.41  | | |   (13)  op(e0, e1) = e0
% 160.18/26.41  | | | 
% 160.18/26.41  | | | REF_CLOSE: (1), (2), (7), (13) are inconsistent by sub-proof #966.
% 160.18/26.41  | | | 
% 160.18/26.41  | | End of split
% 160.18/26.41  | | 
% 160.18/26.41  | Case 2:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (14)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 =
% 160.18/26.41  | |             e0) & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0
% 160.18/26.41  | |           & $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0)
% 160.18/26.41  | |           & op(e0, e1) = e0)
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (1), (2), (7), (14) are inconsistent by sub-proof #965.
% 160.18/26.41  | | 
% 160.18/26.41  | End of split
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #965 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)  (all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0) &
% 160.18/26.41           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.18/26.41           $i(all_57_14)) | (all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) &
% 160.18/26.41           op(e0, e1) = e0)
% 160.18/26.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (3)  op(e0, e1) = all_52_11
% 160.18/26.41    (4)   ~ (all_52_11 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | BETA: splitting (1) gives:
% 160.18/26.41  | 
% 160.18/26.41  | Case 1:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (5)  all_57_8 = e0 & all_57_13 = e1 & all_57_15 = e1 &  ~ (all_57_14 = e0)
% 160.18/26.41  | |        & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & op(e0, e1) = e0 &
% 160.18/26.41  | |        $i(all_57_14)
% 160.18/26.41  | | 
% 160.18/26.41  | | ALPHA: (5) implies:
% 160.18/26.41  | |   (6)  op(e0, e1) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #966.
% 160.18/26.41  | | 
% 160.18/26.41  | Case 2:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (7)  all_57_8 = e0 & all_57_15 = e0 &  ~ (e1 = e0) & op(e0, e1) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | ALPHA: (7) implies:
% 160.18/26.41  | |   (8)  op(e0, e1) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #966.
% 160.18/26.41  | | 
% 160.18/26.41  | End of split
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #966 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (2)  op(e0, e1) = all_52_11
% 160.18/26.41    (3)  op(e0, e1) = e0
% 160.18/26.41    (4)   ~ (all_52_11 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | GROUND_INST: instantiating (1) with all_52_11, e0, e1, e0, simplifying with
% 160.18/26.41  |              (2), (3) gives:
% 160.18/26.41  |   (5)  all_52_11 = e0
% 160.18/26.41  | 
% 160.18/26.41  | REDUCE: (4), (5) imply:
% 160.18/26.41  |   (6)  $false
% 160.18/26.41  | 
% 160.18/26.41  | CLOSE: (6) is inconsistent.
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #967 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)   ~ (all_52_7 = e0)
% 160.18/26.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (3)  op(e0, e2) = all_52_7
% 160.18/26.41    (4)  op(e3, e3) = e3
% 160.18/26.41    (5)  (all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2) &
% 160.18/26.41           op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.18/26.41           all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) | (all_57_8 = e0 &
% 160.18/26.41           all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) & op(e3, e3) = e0
% 160.18/26.41           & op(e3, e0) = e3 & op(e0, e1) = e0)
% 160.18/26.41    (6)   ~ (e3 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | BETA: splitting (5) gives:
% 160.18/26.41  | 
% 160.18/26.41  | Case 1:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (7)  all_57_7 = e0 & all_57_13 = e1 & all_57_14 = e0 &  ~ (all_57_15 = e2)
% 160.18/26.41  | |        & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e2) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | ALPHA: (7) implies:
% 160.18/26.41  | |   (8)  op(e0, e2) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #969.
% 160.18/26.41  | | 
% 160.18/26.41  | Case 2:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (9)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 160.18/26.41  | |        (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 160.18/26.41  | |          & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (1), (2), (3), (4), (6), (9) are inconsistent by sub-proof #968.
% 160.18/26.41  | | 
% 160.18/26.41  | End of split
% 160.18/26.41  | 
% 160.18/26.41  End of proof
% 160.18/26.41  
% 160.18/26.41  Sub-proof #968 shows that the following formulas are inconsistent:
% 160.18/26.41  ----------------------------------------------------------------
% 160.18/26.41    (1)   ~ (all_52_7 = e0)
% 160.18/26.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.41    (3)  (all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0) |
% 160.18/26.41         (all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1) &
% 160.18/26.41           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0)
% 160.18/26.41    (4)  op(e0, e2) = all_52_7
% 160.18/26.41    (5)  op(e3, e3) = e3
% 160.18/26.41    (6)   ~ (e3 = e0)
% 160.18/26.41  
% 160.18/26.41  Begin of proof
% 160.18/26.41  | 
% 160.18/26.41  | BETA: splitting (3) gives:
% 160.18/26.41  | 
% 160.18/26.41  | Case 1:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (7)  all_57_7 = e0 & all_57_15 = e0 &  ~ (e2 = e0) & op(e0, e2) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | ALPHA: (7) implies:
% 160.18/26.41  | |   (8)  op(e0, e2) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #969.
% 160.18/26.41  | | 
% 160.18/26.41  | Case 2:
% 160.18/26.41  | | 
% 160.18/26.41  | |   (9)  all_57_8 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e1)
% 160.18/26.41  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e1) = e0
% 160.18/26.41  | | 
% 160.18/26.41  | | ALPHA: (9) implies:
% 160.18/26.42  | |   (10)  op(e3, e3) = e0
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #971.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #969 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e0, e2) = all_52_7
% 160.18/26.42    (3)  op(e0, e2) = e0
% 160.18/26.42    (4)   ~ (all_52_7 = e0)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with all_52_7, e0, e2, e0, simplifying with
% 160.18/26.42  |              (2), (3) gives:
% 160.18/26.42  |   (5)  all_52_7 = e0
% 160.18/26.42  | 
% 160.18/26.42  | REDUCE: (4), (5) imply:
% 160.18/26.42  |   (6)  $false
% 160.18/26.42  | 
% 160.18/26.42  | CLOSE: (6) is inconsistent.
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #970 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  (all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2) &
% 160.18/26.42           op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0) | (all_57_7 = e0 &
% 160.18/26.42           all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 = e2) & op(e2, e2) = e0
% 160.18/26.42           & op(e2, e0) = e2 & op(e0, e2) = e0)
% 160.18/26.42    (3)  op(e2, e2) = e2
% 160.18/26.42    (4)   ~ (all_52_13 = all_4_2)
% 160.18/26.42    (5)  op(e2, e2) = all_4_2
% 160.18/26.42    (6)  op(e3, e3) = e3
% 160.18/26.42    (7)  op(e2, e0) = all_52_13
% 160.18/26.42    (8)   ~ (e3 = e0)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | BETA: splitting (2) gives:
% 160.18/26.42  | 
% 160.18/26.42  | Case 1:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (9)  all_57_7 = e0 & all_57_9 = e3 & all_57_10 = e0 &  ~ (all_57_15 = e2)
% 160.18/26.42  | |        & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e2) = e0
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (9) implies:
% 160.18/26.42  | |   (10)  op(e3, e3) = e0
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (6), (8), (10) are inconsistent by sub-proof #971.
% 160.18/26.42  | | 
% 160.18/26.42  | Case 2:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (11)  all_57_7 = e0 & all_57_11 = e2 & all_57_12 = e0 &  ~ (all_57_15 =
% 160.18/26.42  | |           e2) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e2) = e0
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (11) implies:
% 160.18/26.42  | |   (12)  op(e2, e0) = e2
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (3), (4), (5), (7), (12) are inconsistent by sub-proof #972.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #971 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e3, e3) = e3
% 160.18/26.42    (3)  op(e3, e3) = e0
% 160.18/26.42    (4)   ~ (e3 = e0)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with e0, e3, e3, e3, simplifying with (2), (3)
% 160.18/26.42  |              gives:
% 160.18/26.42  |   (5)  e3 = e0
% 160.18/26.42  | 
% 160.18/26.42  | REDUCE: (4), (5) imply:
% 160.18/26.42  |   (6)  $false
% 160.18/26.42  | 
% 160.18/26.42  | CLOSE: (6) is inconsistent.
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #972 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e2, e2) = e2
% 160.18/26.42    (3)  op(e2, e0) = e2
% 160.18/26.42    (4)   ~ (all_52_13 = all_4_2)
% 160.18/26.42    (5)  op(e2, e2) = all_4_2
% 160.18/26.42    (6)  op(e2, e0) = all_52_13
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with all_52_13, e2, e0, e2, simplifying with
% 160.18/26.42  |              (3), (6) gives:
% 160.18/26.42  |   (7)  all_52_13 = e2
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with all_4_2, e2, e2, e2, simplifying with (2),
% 160.18/26.42  |              (5) gives:
% 160.18/26.42  |   (8)  all_4_2 = e2
% 160.18/26.42  | 
% 160.18/26.42  | REDUCE: (4), (7), (8) imply:
% 160.18/26.42  |   (9)  $false
% 160.18/26.42  | 
% 160.18/26.42  | CLOSE: (9) is inconsistent.
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #973 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e0, e3) = all_52_3
% 160.18/26.42    (3)  op(e0, e3) = e0
% 160.18/26.42    (4)   ~ (all_52_3 = e0)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with all_52_3, e0, e3, e0, simplifying with
% 160.18/26.42  |              (2), (3) gives:
% 160.18/26.42  |   (5)  all_52_3 = e0
% 160.18/26.42  | 
% 160.18/26.42  | REDUCE: (4), (5) imply:
% 160.18/26.42  |   (6)  $false
% 160.18/26.42  | 
% 160.18/26.42  | CLOSE: (6) is inconsistent.
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #974 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e1, e0) = all_52_14
% 160.18/26.42    (3)  op(e1, e0) = e1
% 160.18/26.42    (4)   ~ (all_52_14 = e1)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with all_52_14, e1, e0, e1, simplifying with
% 160.18/26.42  |              (2), (3) gives:
% 160.18/26.42  |   (5)  all_52_14 = e1
% 160.18/26.42  | 
% 160.18/26.42  | REDUCE: (4), (5) imply:
% 160.18/26.42  |   (6)  $false
% 160.18/26.42  | 
% 160.18/26.42  | CLOSE: (6) is inconsistent.
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #975 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)   ~ (all_52_12 = e3)
% 160.18/26.42    (3)  (all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0) &
% 160.18/26.42           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 160.18/26.42           = e2 & $i(all_57_12)) | (all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0)
% 160.18/26.42           & op(e3, e3) = e3 & op(e3, e0) = e3)
% 160.18/26.42    (4)  op(e0, e0) = e0
% 160.18/26.42    (5)  op(e3, e0) = all_52_12
% 160.18/26.42    (6)   ~ (e2 = e0)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | BETA: splitting (3) gives:
% 160.18/26.42  | 
% 160.18/26.42  | Case 1:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (7)  all_57_7 = e0 & all_57_11 = e2 & all_57_15 = e2 &  ~ (all_57_12 = e0)
% 160.18/26.42  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e0, e2) = e0 & op(e0,
% 160.18/26.42  | |          e0) = e2 & $i(all_57_12)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (7) implies:
% 160.18/26.42  | |   (8)  op(e0, e0) = e2
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #979.
% 160.18/26.42  | | 
% 160.18/26.42  | Case 2:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (9)  all_57_9 = e3 & all_57_10 = e3 &  ~ (e3 = e0) & op(e3, e3) = e3 &
% 160.18/26.42  | |        op(e3, e0) = e3
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (9) implies:
% 160.18/26.42  | |   (10)  op(e3, e0) = e3
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #976.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #976 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e3, e0) = all_52_12
% 160.18/26.42    (3)  op(e3, e0) = e3
% 160.18/26.42    (4)   ~ (all_52_12 = e3)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with all_52_12, e3, e0, e3, simplifying with
% 160.18/26.42  |              (2), (3) gives:
% 160.18/26.42  |   (5)  all_52_12 = e3
% 160.18/26.42  | 
% 160.18/26.42  | REDUCE: (4), (5) imply:
% 160.18/26.42  |   (6)  $false
% 160.18/26.42  | 
% 160.18/26.42  | CLOSE: (6) is inconsistent.
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #977 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e2, e2) = e2
% 160.18/26.42    (3)  (all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0) &
% 160.18/26.42           op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1, e0)
% 160.18/26.42           = e1 & $i(all_57_14)) | (all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3
% 160.18/26.42           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 160.18/26.42           op(e0, e3) = e0 & op(e0, e0) = e3 & $i(all_57_10))
% 160.18/26.42    (4)  op(e0, e0) = e0
% 160.18/26.42    (5)   ~ (e2 = e1)
% 160.18/26.42    (6)   ~ (e3 = e0)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | BETA: splitting (3) gives:
% 160.18/26.42  | 
% 160.18/26.42  | Case 1:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (7)  all_57_5 = e2 & all_57_12 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 160.18/26.42  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e1) = all_57_14 & op(e1,
% 160.18/26.42  | |          e0) = e1 & $i(all_57_14)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (7) implies:
% 160.18/26.42  | |   (8)  op(e2, e2) = e1
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #993.
% 160.18/26.42  | | 
% 160.18/26.42  | Case 2:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (9)  all_57_6 = e0 & all_57_9 = e3 & all_57_15 = e3 &  ~ (all_57_10 = e0)
% 160.18/26.42  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e0, e3) = e0 & op(e0,
% 160.18/26.42  | |          e0) = e3 & $i(all_57_10)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (9) implies:
% 160.18/26.42  | |   (10)  op(e0, e0) = e3
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #999.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #978 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e0, e0) = e0
% 160.18/26.42    (3)  (all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1) &
% 160.18/26.42           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0, e0)
% 160.18/26.42           = e2 & $i(all_57_12)) | (all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1)
% 160.18/26.42           & op(e2, e2) = e2 & op(e2, e1) = e2)
% 160.18/26.42    (4)  op(e2, e1) = all_52_9
% 160.18/26.42    (5)   ~ (all_52_9 = e2)
% 160.18/26.42    (6)   ~ (e2 = e0)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | BETA: splitting (3) gives:
% 160.18/26.42  | 
% 160.18/26.42  | Case 1:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (7)  all_57_5 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e1)
% 160.18/26.42  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e2) = e0 & op(e0,
% 160.18/26.42  | |          e0) = e2 & $i(all_57_12)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (7) implies:
% 160.18/26.42  | |   (8)  op(e0, e0) = e2
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #979.
% 160.18/26.42  | | 
% 160.18/26.42  | Case 2:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (9)  all_57_5 = e2 & all_57_12 = e2 &  ~ (e2 = e1) & op(e2, e2) = e2 &
% 160.18/26.42  | |        op(e2, e1) = e2
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (9) implies:
% 160.18/26.42  | |   (10)  op(e2, e1) = e2
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #1002.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #979 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e0, e0) = e2
% 160.18/26.42    (3)  op(e0, e0) = e0
% 160.18/26.42    (4)   ~ (e2 = e0)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with e0, e2, e0, e0, simplifying with (2), (3)
% 160.18/26.42  |              gives:
% 160.18/26.42  |   (5)  e2 = e0
% 160.18/26.42  | 
% 160.18/26.42  | REDUCE: (4), (5) imply:
% 160.18/26.42  |   (6)  $false
% 160.18/26.42  | 
% 160.18/26.42  | CLOSE: (6) is inconsistent.
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #980 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e3, e1) = all_52_8
% 160.18/26.42    (3)  op(e0, e0) = e0
% 160.18/26.42    (4)  op(e3, e3) = e3
% 160.18/26.42    (5)  (all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1) &
% 160.18/26.42           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 160.18/26.42           = e3 & $i(all_57_10)) | (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1)
% 160.18/26.42           & op(e3, e3) = e3 & op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1
% 160.18/26.42           & all_57_13 = e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 160.18/26.42           e3 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.18/26.42    (6)   ~ (e3 = e1)
% 160.18/26.42    (7)   ~ (all_52_8 = e3)
% 160.18/26.42    (8)   ~ (e3 = e0)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | BETA: splitting (5) gives:
% 160.18/26.42  | 
% 160.18/26.42  | Case 1:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (9)  all_57_4 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e1)
% 160.18/26.42  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e3) = e0 & op(e0,
% 160.18/26.42  | |          e0) = e3 & $i(all_57_10)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (9) implies:
% 160.18/26.42  | |   (10)  op(e0, e0) = e3
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (3), (8), (10) are inconsistent by sub-proof #999.
% 160.18/26.42  | | 
% 160.18/26.42  | Case 2:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (11)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 160.18/26.42  | |           op(e3, e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 =
% 160.18/26.42  | |           e1 &  ~ (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 160.18/26.42  | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (2), (4), (6), (7), (11) are inconsistent by sub-proof #981.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #981 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e3, e1) = all_52_8
% 160.18/26.42    (3)  (all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 & op(e3,
% 160.18/26.42             e1) = e3) | (all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~
% 160.18/26.42           (all_57_14 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) =
% 160.18/26.42           all_57_14 & op(e1, e0) = e1 & $i(all_57_14))
% 160.18/26.42    (4)  op(e3, e3) = e3
% 160.18/26.42    (5)   ~ (e3 = e1)
% 160.18/26.42    (6)   ~ (all_52_8 = e3)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | BETA: splitting (3) gives:
% 160.18/26.42  | 
% 160.18/26.42  | Case 1:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (7)  all_57_4 = e3 & all_57_10 = e3 &  ~ (e3 = e1) & op(e3, e3) = e3 &
% 160.18/26.42  | |        op(e3, e1) = e3
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (7) implies:
% 160.18/26.42  | |   (8)  op(e3, e1) = e3
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #982.
% 160.18/26.42  | | 
% 160.18/26.42  | Case 2:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (9)  all_57_4 = e3 & all_57_10 = e1 & all_57_13 = e1 &  ~ (all_57_14 = e0)
% 160.18/26.42  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e1) = all_57_14 & op(e1,
% 160.18/26.42  | |          e0) = e1 & $i(all_57_14)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (9) implies:
% 160.18/26.42  | |   (10)  op(e3, e3) = e1
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #995.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #982 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e3, e1) = all_52_8
% 160.18/26.42    (3)  op(e3, e1) = e3
% 160.18/26.42    (4)   ~ (all_52_8 = e3)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with all_52_8, e3, e1, e3, simplifying with
% 160.18/26.42  |              (2), (3) gives:
% 160.18/26.42  |   (5)  all_52_8 = e3
% 160.18/26.42  | 
% 160.18/26.42  | REDUCE: (4), (5) imply:
% 160.18/26.42  |   (6)  $false
% 160.18/26.42  | 
% 160.18/26.42  | CLOSE: (6) is inconsistent.
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #983 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ~ (all_52_6 = e1)
% 160.18/26.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (3)  op(e1, e1) = e1
% 160.18/26.42    (4)  (all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0) &
% 160.18/26.42           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 160.18/26.42           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1)
% 160.18/26.42           & op(e1, e2) = e1 & op(e1, e1) = e1)
% 160.18/26.42    (5)  op(e1, e2) = all_52_6
% 160.18/26.42    (6)   ~ (e2 = e1)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | BETA: splitting (4) gives:
% 160.18/26.42  | 
% 160.18/26.42  | Case 1:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (7)  all_57_3 = e1 & all_57_11 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e0)
% 160.18/26.42  | |        & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e2) = e1 & op(e1,
% 160.18/26.42  | |          e1) = e2 & $i(all_57_12)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (7) implies:
% 160.18/26.42  | |   (8)  op(e1, e1) = e2
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #986.
% 160.18/26.42  | | 
% 160.18/26.42  | Case 2:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (9)  all_57_3 = e1 & all_57_14 = e1 &  ~ (e2 = e1) & op(e1, e2) = e1 &
% 160.18/26.42  | |        op(e1, e1) = e1
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (9) implies:
% 160.18/26.42  | |   (10)  op(e1, e2) = e1
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #984.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #984 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e1, e2) = all_52_6
% 160.18/26.42    (3)  op(e1, e2) = e1
% 160.18/26.42    (4)   ~ (all_52_6 = e1)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with all_52_6, e1, e2, e1, simplifying with
% 160.18/26.42  |              (2), (3) gives:
% 160.18/26.42  |   (5)  all_52_6 = e1
% 160.18/26.42  | 
% 160.18/26.42  | REDUCE: (4), (5) imply:
% 160.18/26.42  |   (6)  $false
% 160.18/26.42  | 
% 160.18/26.42  | CLOSE: (6) is inconsistent.
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #985 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e1, e1) = e1
% 160.18/26.42    (3)  op(e0, e0) = e0
% 160.18/26.42    (4)  op(e0, e0) = all_14_2
% 160.18/26.42    (5)  (all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1) &
% 160.18/26.42           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1)
% 160.18/26.42           = e2 & $i(all_57_12)) | (all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1
% 160.18/26.42           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 160.18/26.42           op(e0, e1) = e0 & op(e0, e0) = e1 & $i(all_57_14))
% 160.18/26.42    (6)   ~ (e1 = e0)
% 160.18/26.42    (7)   ~ (e2 = e1)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | BETA: splitting (5) gives:
% 160.18/26.42  | 
% 160.18/26.42  | Case 1:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (8)  all_57_3 = e1 & all_57_5 = e2 & all_57_14 = e2 &  ~ (all_57_12 = e1)
% 160.18/26.42  | |        & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1,
% 160.18/26.42  | |          e1) = e2 & $i(all_57_12)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (8) implies:
% 160.18/26.42  | |   (9)  op(e1, e1) = e2
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (2), (7), (9) are inconsistent by sub-proof #986.
% 160.18/26.42  | | 
% 160.18/26.42  | Case 2:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (10)  all_57_3 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e2)
% 160.18/26.42  | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 160.18/26.42  | |         op(e0, e0) = e1 & $i(all_57_14)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (10) implies:
% 160.18/26.42  | |   (11)  op(e0, e0) = e1
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (3), (4), (6), (11) are inconsistent by sub-proof #991.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #986 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e1, e1) = e2
% 160.18/26.42    (3)  op(e1, e1) = e1
% 160.18/26.42    (4)   ~ (e2 = e1)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | GROUND_INST: instantiating (1) with e2, e1, e1, e1, simplifying with (2), (3)
% 160.18/26.42  |              gives:
% 160.18/26.42  |   (5)  e2 = e1
% 160.18/26.42  | 
% 160.18/26.42  | REDUCE: (4), (5) imply:
% 160.18/26.42  |   (6)  $false
% 160.18/26.42  | 
% 160.18/26.42  | CLOSE: (6) is inconsistent.
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #987 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e2, e2) = e2
% 160.18/26.42    (3)  (all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2) &
% 160.18/26.42           op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 160.18/26.42           all_57_14 & $i(all_57_14)) | (all_57_3 = e1 & all_57_5 = e2 & all_57_12
% 160.18/26.42           = e1 &  ~ (all_57_14 = e2) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 160.18/26.42             e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.18/26.42    (4)  op(e3, e3) = e3
% 160.18/26.42    (5)   ~ (e2 = e1)
% 160.18/26.42    (6)   ~ (e3 = e1)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | BETA: splitting (3) gives:
% 160.18/26.42  | 
% 160.18/26.42  | Case 1:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (7)  all_57_3 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e2)
% 160.18/26.42  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e2) = e1 & op(e1, e1) =
% 160.18/26.42  | |        all_57_14 & $i(all_57_14)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (7) implies:
% 160.18/26.42  | |   (8)  op(e3, e3) = e1
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #995.
% 160.18/26.42  | | 
% 160.18/26.42  | Case 2:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (9)  all_57_3 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e2)
% 160.18/26.42  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e2) = e1 & op(e1, e1) =
% 160.18/26.42  | |        all_57_14 & $i(all_57_14)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (9) implies:
% 160.18/26.42  | |   (10)  op(e2, e2) = e1
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #993.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #988 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e1, e1) = e1
% 160.18/26.42    (3)  op(e1, e3) = all_52_2
% 160.18/26.42    (4)   ~ (all_52_2 = e1)
% 160.18/26.42    (5)  op(e0, e0) = e0
% 160.18/26.42    (6)  op(e0, e0) = all_14_2
% 160.18/26.42    (7)   ~ (e1 = e0)
% 160.18/26.42    (8)  (all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3) &
% 160.18/26.42           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 & op(e0, e0)
% 160.18/26.42           = e1 & $i(all_57_14)) | (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3
% 160.18/26.42           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 160.18/26.42           op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 &
% 160.18/26.42           all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 160.18/26.42    (9)   ~ (e3 = e1)
% 160.18/26.42  
% 160.18/26.42  Begin of proof
% 160.18/26.42  | 
% 160.18/26.42  | BETA: splitting (8) gives:
% 160.18/26.42  | 
% 160.18/26.42  | Case 1:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (10)  all_57_2 = e1 & all_57_8 = e0 & all_57_15 = e1 &  ~ (all_57_14 = e3)
% 160.18/26.42  | |         & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e1) = e0 &
% 160.18/26.42  | |         op(e0, e0) = e1 & $i(all_57_14)
% 160.18/26.42  | | 
% 160.18/26.42  | | ALPHA: (10) implies:
% 160.18/26.42  | |   (11)  op(e0, e0) = e1
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (5), (6), (7), (11) are inconsistent by sub-proof #991.
% 160.18/26.42  | | 
% 160.18/26.42  | Case 2:
% 160.18/26.42  | | 
% 160.18/26.42  | |   (12)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 =
% 160.18/26.42  | |             e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1
% 160.18/26.42  | |           & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 =
% 160.18/26.42  | |           e1 &  ~ (e3 = e1) & op(e1, e3) = e1 & op(e1, e1) = e1)
% 160.18/26.42  | | 
% 160.18/26.42  | | REF_CLOSE: (1), (2), (3), (4), (9), (12) are inconsistent by sub-proof #989.
% 160.18/26.42  | | 
% 160.18/26.42  | End of split
% 160.18/26.42  | 
% 160.18/26.42  End of proof
% 160.18/26.42  
% 160.18/26.42  Sub-proof #989 shows that the following formulas are inconsistent:
% 160.18/26.42  ----------------------------------------------------------------
% 160.18/26.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.42    (2)  op(e1, e1) = e1
% 160.18/26.42    (3)  op(e1, e3) = all_52_2
% 160.18/26.42    (4)   ~ (all_52_2 = e1)
% 160.18/26.43    (5)  (all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0) &
% 160.18/26.43           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.18/26.43           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1)
% 160.18/26.43           & op(e1, e3) = e1 & op(e1, e1) = e1)
% 160.18/26.43    (6)   ~ (e3 = e1)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | BETA: splitting (5) gives:
% 160.18/26.43  | 
% 160.18/26.43  | Case 1:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (7)  all_57_2 = e1 & all_57_9 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e0)
% 160.18/26.43  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e3) = e1 & op(e1,
% 160.18/26.43  | |          e1) = e3 & $i(all_57_10)
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (7) implies:
% 160.18/26.43  | |   (8)  op(e1, e1) = e3
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #1003.
% 160.18/26.43  | | 
% 160.18/26.43  | Case 2:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (9)  all_57_2 = e1 & all_57_14 = e1 &  ~ (e3 = e1) & op(e1, e3) = e1 &
% 160.18/26.43  | |        op(e1, e1) = e1
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (9) implies:
% 160.18/26.43  | |   (10)  op(e1, e3) = e1
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #990.
% 160.18/26.43  | | 
% 160.18/26.43  | End of split
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #990 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (2)  op(e1, e3) = all_52_2
% 160.18/26.43    (3)  op(e1, e3) = e1
% 160.18/26.43    (4)   ~ (all_52_2 = e1)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | GROUND_INST: instantiating (1) with all_52_2, e1, e3, e1, simplifying with
% 160.18/26.43  |              (2), (3) gives:
% 160.18/26.43  |   (5)  all_52_2 = e1
% 160.18/26.43  | 
% 160.18/26.43  | REDUCE: (4), (5) imply:
% 160.18/26.43  |   (6)  $false
% 160.18/26.43  | 
% 160.18/26.43  | CLOSE: (6) is inconsistent.
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #991 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)  op(e0, e0) = e1
% 160.18/26.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (3)  op(e0, e0) = e0
% 160.18/26.43    (4)  op(e0, e0) = all_14_2
% 160.18/26.43    (5)   ~ (e1 = e0)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | GROUND_INST: instantiating (2) with all_14_2, e0, e0, e0, simplifying with
% 160.18/26.43  |              (3), (4) gives:
% 160.18/26.43  |   (6)  all_14_2 = e0
% 160.18/26.43  | 
% 160.18/26.43  | GROUND_INST: instantiating (2) with all_14_2, e1, e0, e0, simplifying with
% 160.18/26.43  |              (1), (4) gives:
% 160.18/26.43  |   (7)  all_14_2 = e1
% 160.18/26.43  | 
% 160.18/26.43  | COMBINE_EQS: (6), (7) imply:
% 160.18/26.43  |   (8)  e1 = e0
% 160.18/26.43  | 
% 160.18/26.43  | SIMP: (8) implies:
% 160.18/26.43  |   (9)  e1 = e0
% 160.18/26.43  | 
% 160.18/26.43  | REDUCE: (5), (9) imply:
% 160.18/26.43  |   (10)  $false
% 160.18/26.43  | 
% 160.18/26.43  | CLOSE: (10) is inconsistent.
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #992 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)  (all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1) &
% 160.18/26.43           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.18/26.43           = e3 & $i(all_57_10)) | (all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1
% 160.18/26.43           &  ~ (all_57_14 = e3) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 160.18/26.43           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.18/26.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (3)  op(e1, e1) = e1
% 160.18/26.43    (4)  op(e2, e2) = e2
% 160.18/26.43    (5)   ~ (e2 = e1)
% 160.18/26.43    (6)   ~ (e3 = e1)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | BETA: splitting (1) gives:
% 160.18/26.43  | 
% 160.18/26.43  | Case 1:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (7)  all_57_2 = e1 & all_57_4 = e3 & all_57_14 = e3 &  ~ (all_57_10 = e1)
% 160.18/26.43  | |        & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1,
% 160.18/26.43  | |          e1) = e3 & $i(all_57_10)
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (7) implies:
% 160.18/26.43  | |   (8)  op(e1, e1) = e3
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1003.
% 160.18/26.43  | | 
% 160.18/26.43  | Case 2:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (9)  all_57_2 = e1 & all_57_5 = e2 & all_57_12 = e1 &  ~ (all_57_14 = e3)
% 160.18/26.43  | |        & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = e1 & op(e1, e1) =
% 160.18/26.43  | |        all_57_14 & $i(all_57_14)
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (9) implies:
% 160.18/26.43  | |   (10)  op(e2, e2) = e1
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #993.
% 160.18/26.43  | | 
% 160.18/26.43  | End of split
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #993 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (2)  op(e2, e2) = e2
% 160.18/26.43    (3)  op(e2, e2) = e1
% 160.18/26.43    (4)   ~ (e2 = e1)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | GROUND_INST: instantiating (1) with e1, e2, e2, e2, simplifying with (2), (3)
% 160.18/26.43  |              gives:
% 160.18/26.43  |   (5)  e2 = e1
% 160.18/26.43  | 
% 160.18/26.43  | REDUCE: (4), (5) imply:
% 160.18/26.43  |   (6)  $false
% 160.18/26.43  | 
% 160.18/26.43  | CLOSE: (6) is inconsistent.
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #994 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (2)  op(e3, e3) = e3
% 160.18/26.43    (3)  (all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0) &
% 160.18/26.43           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2, e0)
% 160.18/26.43           = e2 & $i(all_57_12)) | (all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1
% 160.18/26.43           &  ~ (all_57_14 = e3) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3)
% 160.18/26.43           = e1 & op(e1, e1) = all_57_14 & $i(all_57_14))
% 160.18/26.43    (4)  op(e2, e0) = all_52_13
% 160.18/26.43    (5)   ~ (e3 = e1)
% 160.18/26.43    (6)   ~ (all_52_13 = e2)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | BETA: splitting (3) gives:
% 160.18/26.43  | 
% 160.18/26.43  | Case 1:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (7)  all_57_1 = e3 & all_57_10 = e2 & all_57_11 = e2 &  ~ (all_57_12 = e0)
% 160.18/26.43  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 160.18/26.43  | |          e0) = e2 & $i(all_57_12)
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (7) implies:
% 160.18/26.43  | |   (8)  op(e2, e0) = e2
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #996.
% 160.18/26.43  | | 
% 160.18/26.43  | Case 2:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (9)  all_57_2 = e1 & all_57_4 = e3 & all_57_10 = e1 &  ~ (all_57_14 = e3)
% 160.18/26.43  | |        & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 160.18/26.43  | |        all_57_14 & $i(all_57_14)
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (9) implies:
% 160.18/26.43  | |   (10)  op(e3, e3) = e1
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #995.
% 160.18/26.43  | | 
% 160.18/26.43  | End of split
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #995 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (2)  op(e3, e3) = e3
% 160.18/26.43    (3)  op(e3, e3) = e1
% 160.18/26.43    (4)   ~ (e3 = e1)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | GROUND_INST: instantiating (1) with e1, e3, e3, e3, simplifying with (2), (3)
% 160.18/26.43  |              gives:
% 160.18/26.43  |   (5)  e3 = e1
% 160.18/26.43  | 
% 160.18/26.43  | REDUCE: (4), (5) imply:
% 160.18/26.43  |   (6)  $false
% 160.18/26.43  | 
% 160.18/26.43  | CLOSE: (6) is inconsistent.
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #996 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (2)  op(e2, e0) = all_52_13
% 160.18/26.43    (3)  op(e2, e0) = e2
% 160.18/26.43    (4)   ~ (all_52_13 = e2)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | GROUND_INST: instantiating (1) with all_52_13, e2, e0, e2, simplifying with
% 160.18/26.43  |              (2), (3) gives:
% 160.18/26.43  |   (5)  all_52_13 = e2
% 160.18/26.43  | 
% 160.18/26.43  | REDUCE: (4), (5) imply:
% 160.18/26.43  |   (6)  $false
% 160.18/26.43  | 
% 160.18/26.43  | CLOSE: (6) is inconsistent.
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #997 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ~ (all_52_4 = e3)
% 160.18/26.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (3)  op(e0, e0) = e0
% 160.18/26.43    (4)  op(e3, e2) = all_52_4
% 160.18/26.43    (5)  (all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2) &
% 160.18/26.43           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0, e0)
% 160.18/26.43           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2)
% 160.18/26.43           & op(e3, e3) = e3 & op(e3, e2) = e3)
% 160.18/26.43    (6)   ~ (e3 = e0)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | BETA: splitting (5) gives:
% 160.18/26.43  | 
% 160.18/26.43  | Case 1:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (7)  all_57_1 = e3 & all_57_6 = e0 & all_57_15 = e3 &  ~ (all_57_10 = e2)
% 160.18/26.43  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e3) = e0 & op(e0,
% 160.18/26.43  | |          e0) = e3 & $i(all_57_10)
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (7) implies:
% 160.18/26.43  | |   (8)  op(e0, e0) = e3
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #999.
% 160.18/26.43  | | 
% 160.18/26.43  | Case 2:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (9)  all_57_1 = e3 & all_57_10 = e3 &  ~ (e3 = e2) & op(e3, e3) = e3 &
% 160.18/26.43  | |        op(e3, e2) = e3
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (9) implies:
% 160.18/26.43  | |   (10)  op(e3, e2) = e3
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #998.
% 160.18/26.43  | | 
% 160.18/26.43  | End of split
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #998 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (2)  op(e3, e2) = all_52_4
% 160.18/26.43    (3)  op(e3, e2) = e3
% 160.18/26.43    (4)   ~ (all_52_4 = e3)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | GROUND_INST: instantiating (1) with all_52_4, e3, e2, e3, simplifying with
% 160.18/26.43  |              (2), (3) gives:
% 160.18/26.43  |   (5)  all_52_4 = e3
% 160.18/26.43  | 
% 160.18/26.43  | REDUCE: (4), (5) imply:
% 160.18/26.43  |   (6)  $false
% 160.18/26.43  | 
% 160.18/26.43  | CLOSE: (6) is inconsistent.
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #999 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (2)  op(e0, e0) = e3
% 160.18/26.43    (3)  op(e0, e0) = e0
% 160.18/26.43    (4)   ~ (e3 = e0)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | GROUND_INST: instantiating (1) with e0, e3, e0, e0, simplifying with (2), (3)
% 160.18/26.43  |              gives:
% 160.18/26.43  |   (5)  e3 = e0
% 160.18/26.43  | 
% 160.18/26.43  | REDUCE: (4), (5) imply:
% 160.18/26.43  |   (6)  $false
% 160.18/26.43  | 
% 160.18/26.43  | CLOSE: (6) is inconsistent.
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #1000 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ~ (all_52_1 = e2)
% 160.18/26.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (3)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 160.18/26.43           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 160.18/26.43           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 160.18/26.43           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 160.18/26.43           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 160.18/26.43           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 160.18/26.43           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 160.18/26.43           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 160.18/26.43           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 160.18/26.43             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 160.18/26.43           all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 160.18/26.43           & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0) = e2 &
% 160.18/26.43           $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~
% 160.18/26.43           (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 160.18/26.43             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 160.18/26.43           all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 & op(e2, e2) = e2) |
% 160.18/26.43         (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 160.18/26.43           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.18/26.43           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 160.18/26.43           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 160.18/26.43           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 160.18/26.43    (4)  op(e1, e1) = e1
% 160.18/26.43    (5)  op(e2, e3) = all_52_1
% 160.18/26.43    (6)  op(e2, e1) = all_52_9
% 160.18/26.43    (7)   ~ (all_52_9 = e2)
% 160.18/26.43    (8)   ~ (e3 = e1)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | BETA: splitting (3) gives:
% 160.18/26.43  | 
% 160.18/26.43  | Case 1:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (9)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 160.18/26.43  | |          & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 160.18/26.43  | |          = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 160.18/26.43  | |          all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 160.18/26.43  | |          op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 160.18/26.43  | |          $i(all_57_10)) | (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 & 
% 160.18/26.43  | |          ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 160.18/26.43  | |          op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2
% 160.18/26.43  | |          & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3)
% 160.18/26.43  | |          = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 160.18/26.43  | |          $i(all_57_10))
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #1005.
% 160.18/26.43  | | 
% 160.18/26.43  | Case 2:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (10)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 160.18/26.43  | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0
% 160.18/26.43  | |           & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 =
% 160.18/26.43  | |           e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10
% 160.18/26.43  | |           & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 160.18/26.43  | |           $i(all_57_10)) | (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) &
% 160.18/26.43  | |           op(e2, e3) = e2 & op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 =
% 160.18/26.43  | |           e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 160.18/26.43  | |           & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 160.18/26.43  | |           $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &
% 160.18/26.43  | |            ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2,
% 160.18/26.43  | |             e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 160.18/26.43  | | 
% 160.18/26.43  | | BETA: splitting (10) gives:
% 160.18/26.43  | | 
% 160.18/26.43  | | Case 1:
% 160.18/26.43  | | | 
% 160.18/26.43  | | |   (11)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 =
% 160.18/26.43  | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) =
% 160.18/26.43  | | |           e0 & op(e0, e0) = e2 & $i(all_57_12)) | (all_57_0 = e2 &
% 160.18/26.43  | | |           all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0) & op(e3,
% 160.18/26.43  | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 160.18/26.43  | | |             e2) = e3 & $i(all_57_10))
% 160.18/26.43  | | | 
% 160.18/26.43  | | | REF_CLOSE: (1), (2), (5), (11) are inconsistent by sub-proof #1004.
% 160.18/26.43  | | | 
% 160.18/26.43  | | Case 2:
% 160.18/26.43  | | | 
% 160.18/26.43  | | |   (12)  (all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2 &
% 160.18/26.43  | | |           op(e2, e2) = e2) | (all_57_1 = e3 & all_57_2 = e1 & all_57_14 =
% 160.18/26.43  | | |           e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 160.18/26.43  | | |           e3 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) |
% 160.18/26.43  | | |         (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 =
% 160.18/26.43  | | |             e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) =
% 160.18/26.43  | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 160.18/26.43  | | | 
% 160.18/26.43  | | | BETA: splitting (12) gives:
% 160.18/26.43  | | | 
% 160.18/26.43  | | | Case 1:
% 160.18/26.43  | | | | 
% 160.18/26.43  | | | |   (13)  all_57_0 = e2 & all_57_12 = e2 &  ~ (e3 = e2) & op(e2, e3) = e2
% 160.18/26.43  | | | |         & op(e2, e2) = e2
% 160.18/26.43  | | | | 
% 160.18/26.43  | | | | ALPHA: (13) implies:
% 160.18/26.43  | | | |   (14)  op(e2, e3) = e2
% 160.18/26.43  | | | | 
% 160.18/26.43  | | | | REF_CLOSE: (1), (2), (5), (14) are inconsistent by sub-proof #1007.
% 160.18/26.43  | | | | 
% 160.18/26.43  | | | Case 2:
% 160.18/26.43  | | | | 
% 160.18/26.43  | | | |   (15)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10
% 160.18/26.43  | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 160.18/26.43  | | | |             e3) = e1 & op(e1, e1) = e3 & $i(all_57_10)) | (all_57_1 = e3
% 160.18/26.43  | | | |           & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1) &
% 160.18/26.43  | | | |           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 &
% 160.18/26.43  | | | |           op(e2, e1) = e2 & $i(all_57_12))
% 160.18/26.43  | | | | 
% 160.18/26.43  | | | | REF_CLOSE: (2), (4), (6), (7), (8), (15) are inconsistent by sub-proof
% 160.18/26.43  | | | |            #1001.
% 160.18/26.43  | | | | 
% 160.18/26.43  | | | End of split
% 160.18/26.43  | | | 
% 160.18/26.43  | | End of split
% 160.18/26.43  | | 
% 160.18/26.43  | End of split
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #1001 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (2)  op(e1, e1) = e1
% 160.18/26.43    (3)  op(e2, e1) = all_52_9
% 160.18/26.43    (4)   ~ (all_52_9 = e2)
% 160.18/26.43    (5)   ~ (e3 = e1)
% 160.18/26.43    (6)  (all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2) &
% 160.18/26.43           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1, e1)
% 160.18/26.43           = e3 & $i(all_57_10)) | (all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2
% 160.18/26.43           &  ~ (all_57_12 = e1) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2)
% 160.18/26.43           = all_57_12 & op(e2, e1) = e2 & $i(all_57_12))
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | BETA: splitting (6) gives:
% 160.18/26.43  | 
% 160.18/26.43  | Case 1:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (7)  all_57_1 = e3 & all_57_2 = e1 & all_57_14 = e3 &  ~ (all_57_10 = e2)
% 160.18/26.43  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 160.18/26.43  | |          e1) = e3 & $i(all_57_10)
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (7) implies:
% 160.18/26.43  | |   (8)  op(e1, e1) = e3
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1003.
% 160.18/26.43  | | 
% 160.18/26.43  | Case 2:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (9)  all_57_1 = e3 & all_57_5 = e2 & all_57_10 = e2 &  ~ (all_57_12 = e1)
% 160.18/26.43  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e2) = all_57_12 & op(e2,
% 160.18/26.43  | |          e1) = e2 & $i(all_57_12)
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (9) implies:
% 160.18/26.43  | |   (10)  op(e2, e1) = e2
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1002.
% 160.18/26.43  | | 
% 160.18/26.43  | End of split
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #1002 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (2)  op(e2, e1) = all_52_9
% 160.18/26.43    (3)  op(e2, e1) = e2
% 160.18/26.43    (4)   ~ (all_52_9 = e2)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | GROUND_INST: instantiating (1) with all_52_9, e2, e1, e2, simplifying with
% 160.18/26.43  |              (2), (3) gives:
% 160.18/26.43  |   (5)  all_52_9 = e2
% 160.18/26.43  | 
% 160.18/26.43  | REDUCE: (4), (5) imply:
% 160.18/26.43  |   (6)  $false
% 160.18/26.43  | 
% 160.18/26.43  | CLOSE: (6) is inconsistent.
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #1003 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (2)  op(e1, e1) = e3
% 160.18/26.43    (3)  op(e1, e1) = e1
% 160.18/26.43    (4)   ~ (e3 = e1)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | GROUND_INST: instantiating (1) with e1, e3, e1, e1, simplifying with (2), (3)
% 160.18/26.43  |              gives:
% 160.18/26.43  |   (5)  e3 = e1
% 160.18/26.43  | 
% 160.18/26.43  | REDUCE: (4), (5) imply:
% 160.18/26.43  |   (6)  $false
% 160.18/26.43  | 
% 160.18/26.43  | CLOSE: (6) is inconsistent.
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #1004 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)  (all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3) &
% 160.18/26.43           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0, e0)
% 160.18/26.43           = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3
% 160.18/26.43           &  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 160.18/26.43           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 160.18/26.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (3)  op(e2, e3) = all_52_1
% 160.18/26.43    (4)   ~ (all_52_1 = e2)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | BETA: splitting (1) gives:
% 160.18/26.43  | 
% 160.18/26.43  | Case 1:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (5)  all_57_0 = e2 & all_57_7 = e0 & all_57_15 = e2 &  ~ (all_57_12 = e3)
% 160.18/26.43  | |        & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e2) = e0 & op(e0,
% 160.18/26.43  | |          e0) = e2 & $i(all_57_12)
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (5) implies:
% 160.18/26.43  | |   (6)  op(e2, e3) = e2
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #1007.
% 160.18/26.43  | | 
% 160.18/26.43  | Case 2:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (7)  all_57_0 = e2 & all_57_9 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e0)
% 160.18/26.43  | |        & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e3) = e2 & op(e2,
% 160.18/26.43  | |          e2) = e3 & $i(all_57_10)
% 160.18/26.43  | | 
% 160.18/26.43  | | ALPHA: (7) implies:
% 160.18/26.43  | |   (8)  op(e2, e3) = e2
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1007.
% 160.18/26.43  | | 
% 160.18/26.43  | End of split
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #1005 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.43    (1)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 160.18/26.43           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 160.18/26.43           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 160.18/26.43           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 160.18/26.43           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10)) | (all_57_0 = e2 &
% 160.18/26.43           all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3) & op(e2, e3) = e2
% 160.18/26.43           & op(e2, e2) = all_57_12 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 160.18/26.43           $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~
% 160.18/26.43           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 160.18/26.43             e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 160.18/26.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.43    (3)  op(e2, e3) = all_52_1
% 160.18/26.43    (4)   ~ (all_52_1 = e2)
% 160.18/26.43  
% 160.18/26.43  Begin of proof
% 160.18/26.43  | 
% 160.18/26.43  | BETA: splitting (1) gives:
% 160.18/26.43  | 
% 160.18/26.43  | Case 1:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (5)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 160.18/26.43  | |          & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2)
% 160.18/26.43  | |          = all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 &
% 160.18/26.43  | |          all_57_12 = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 160.18/26.43  | |          op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 160.18/26.43  | |          $i(all_57_10))
% 160.18/26.43  | | 
% 160.18/26.43  | | REF_CLOSE: (2), (3), (4), (5) are inconsistent by sub-proof #1006.
% 160.18/26.43  | | 
% 160.18/26.43  | Case 2:
% 160.18/26.43  | | 
% 160.18/26.43  | |   (6)  (all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 = e3)
% 160.18/26.43  | |          & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1 &
% 160.18/26.43  | |          op(e1, e1) = e2 & $i(all_57_12)) | (all_57_0 = e2 & all_57_4 = e3 &
% 160.18/26.43  | |          all_57_12 = e3 &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 160.18/26.43  | |          op(e3, e1) = e3 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 160.18/26.43  | |          $i(all_57_10))
% 160.18/26.43  | | 
% 160.18/26.43  | | BETA: splitting (6) gives:
% 160.18/26.43  | | 
% 160.18/26.43  | | Case 1:
% 160.18/26.43  | | | 
% 160.18/26.43  | | |   (7)  all_57_0 = e2 & all_57_3 = e1 & all_57_14 = e2 &  ~ (all_57_12 =
% 160.18/26.43  | | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e2) = e1
% 160.18/26.43  | | |        & op(e1, e1) = e2 & $i(all_57_12)
% 160.18/26.43  | | | 
% 160.18/26.43  | | | ALPHA: (7) implies:
% 160.18/26.43  | | |   (8)  op(e2, e3) = e2
% 160.18/26.43  | | | 
% 160.18/26.43  | | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1007.
% 160.18/26.43  | | | 
% 160.18/26.43  | | Case 2:
% 160.18/26.43  | | | 
% 160.18/26.43  | | |   (9)  all_57_0 = e2 & all_57_4 = e3 & all_57_12 = e3 &  ~ (all_57_10 =
% 160.18/26.43  | | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e3) = e2
% 160.18/26.43  | | |        & op(e2, e2) = e3 & $i(all_57_10)
% 160.18/26.43  | | | 
% 160.18/26.43  | | | ALPHA: (9) implies:
% 160.18/26.43  | | |   (10)  op(e2, e3) = e2
% 160.18/26.43  | | | 
% 160.18/26.43  | | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #1007.
% 160.18/26.43  | | | 
% 160.18/26.43  | | End of split
% 160.18/26.43  | | 
% 160.18/26.43  | End of split
% 160.18/26.43  | 
% 160.18/26.43  End of proof
% 160.18/26.43  
% 160.18/26.43  Sub-proof #1006 shows that the following formulas are inconsistent:
% 160.18/26.43  ----------------------------------------------------------------
% 160.18/26.44    (1)  (all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3) &
% 160.18/26.44           op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 160.18/26.44           all_57_12 & $i(all_57_12)) | (all_57_0 = e2 & all_57_1 = e3 & all_57_12
% 160.18/26.44           = e3 &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 160.18/26.44           op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_57_10))
% 160.18/26.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.44    (3)  op(e2, e3) = all_52_1
% 160.18/26.44    (4)   ~ (all_52_1 = e2)
% 160.18/26.44  
% 160.18/26.44  Begin of proof
% 160.18/26.44  | 
% 160.18/26.44  | BETA: splitting (1) gives:
% 160.18/26.44  | 
% 160.18/26.44  | Case 1:
% 160.18/26.44  | | 
% 160.18/26.44  | |   (5)  all_57_0 = e2 & all_57_1 = e3 & all_57_10 = e2 &  ~ (all_57_12 = e3)
% 160.18/26.44  | |        & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2, e2) =
% 160.18/26.44  | |        all_57_12 & $i(all_57_12)
% 160.18/26.44  | | 
% 160.18/26.44  | | ALPHA: (5) implies:
% 160.18/26.44  | |   (6)  op(e2, e3) = e2
% 160.18/26.44  | | 
% 160.18/26.44  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #1007.
% 160.18/26.44  | | 
% 160.18/26.44  | Case 2:
% 160.18/26.44  | | 
% 160.18/26.44  | |   (7)  all_57_0 = e2 & all_57_1 = e3 & all_57_12 = e3 &  ~ (all_57_10 = e2)
% 160.18/26.44  | |        & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e2, e3) = e2 & op(e2,
% 160.18/26.44  | |          e2) = e3 & $i(all_57_10)
% 160.18/26.44  | | 
% 160.18/26.44  | | ALPHA: (7) implies:
% 160.18/26.44  | |   (8)  op(e2, e3) = e2
% 160.18/26.44  | | 
% 160.18/26.44  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1007.
% 160.18/26.44  | | 
% 160.18/26.44  | End of split
% 160.18/26.44  | 
% 160.18/26.44  End of proof
% 160.18/26.44  
% 160.18/26.44  Sub-proof #1007 shows that the following formulas are inconsistent:
% 160.18/26.44  ----------------------------------------------------------------
% 160.18/26.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 160.18/26.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 160.18/26.44    (2)  op(e2, e3) = all_52_1
% 160.18/26.44    (3)  op(e2, e3) = e2
% 160.18/26.44    (4)   ~ (all_52_1 = e2)
% 160.18/26.44  
% 160.18/26.44  Begin of proof
% 160.18/26.44  | 
% 160.18/26.44  | GROUND_INST: instantiating (1) with all_52_1, e2, e3, e2, simplifying with
% 160.18/26.44  |              (2), (3) gives:
% 160.18/26.44  |   (5)  all_52_1 = e2
% 160.18/26.44  | 
% 160.18/26.44  | REDUCE: (4), (5) imply:
% 160.18/26.44  |   (6)  $false
% 160.18/26.44  | 
% 160.18/26.44  | CLOSE: (6) is inconsistent.
% 160.18/26.44  | 
% 160.18/26.44  End of proof
% 160.18/26.44  
% 160.18/26.44  Sub-proof #1008 shows that the following formulas are inconsistent:
% 160.18/26.44  ----------------------------------------------------------------
% 160.18/26.44    (1)  all_54_15 = all_14_2
% 160.18/26.44    (2)  all_54_15 = e1
% 160.18/26.44    (3)   ~ (all_14_2 = e1)
% 160.18/26.44  
% 160.18/26.44  Begin of proof
% 160.18/26.44  | 
% 160.18/26.44  | COMBINE_EQS: (1), (2) imply:
% 160.18/26.44  |   (4)  all_14_2 = e1
% 160.18/26.44  | 
% 160.18/26.44  | SIMP: (4) implies:
% 160.18/26.44  |   (5)  all_14_2 = e1
% 160.18/26.44  | 
% 160.18/26.44  | REDUCE: (3), (5) imply:
% 160.18/26.44  |   (6)  $false
% 160.18/26.44  | 
% 160.18/26.44  | CLOSE: (6) is inconsistent.
% 160.18/26.44  | 
% 160.18/26.44  End of proof
% 160.18/26.44  
% 160.18/26.44  Sub-proof #1009 shows that the following formulas are inconsistent:
% 160.18/26.44  ----------------------------------------------------------------
% 160.18/26.44    (1)  all_54_15 = all_14_2
% 160.18/26.44    (2)  all_54_15 = e2
% 160.18/26.44    (3)   ~ (all_14_2 = e2)
% 160.18/26.44  
% 160.18/26.44  Begin of proof
% 160.18/26.44  | 
% 160.18/26.44  | COMBINE_EQS: (1), (2) imply:
% 160.18/26.44  |   (4)  all_14_2 = e2
% 160.18/26.44  | 
% 160.18/26.44  | SIMP: (4) implies:
% 160.18/26.44  |   (5)  all_14_2 = e2
% 160.18/26.44  | 
% 160.18/26.44  | REDUCE: (3), (5) imply:
% 160.18/26.44  |   (6)  $false
% 160.18/26.44  | 
% 160.18/26.44  | CLOSE: (6) is inconsistent.
% 160.18/26.44  | 
% 160.18/26.44  End of proof
% 160.18/26.44  
% 160.18/26.44  Sub-proof #1010 shows that the following formulas are inconsistent:
% 160.18/26.44  ----------------------------------------------------------------
% 160.18/26.44    (1)  all_54_15 = all_14_2
% 160.18/26.44    (2)  all_54_15 = e3
% 160.18/26.44    (3)   ~ (all_14_2 = e3)
% 160.18/26.44  
% 160.18/26.44  Begin of proof
% 160.18/26.44  | 
% 160.18/26.44  | COMBINE_EQS: (1), (2) imply:
% 160.18/26.44  |   (4)  all_14_2 = e3
% 160.18/26.44  | 
% 160.18/26.44  | SIMP: (4) implies:
% 160.18/26.44  |   (5)  all_14_2 = e3
% 160.18/26.44  | 
% 160.18/26.44  | REDUCE: (3), (5) imply:
% 160.18/26.44  |   (6)  $false
% 160.18/26.44  | 
% 160.18/26.44  | CLOSE: (6) is inconsistent.
% 160.18/26.44  | 
% 160.18/26.44  End of proof
% 160.18/26.44  % SZS output end Proof for theBenchmark
% 160.18/26.44  
% 160.18/26.44  25819ms
%------------------------------------------------------------------------------